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ELEMENTS
PHILOSOPHY OF THE HUMAN MIND.
BY DUGALD STEWART.
IN TWO VOLUMES.
VOL. II.
CAMBRIDGE :
PUBLISHED BY HILLIARD AND BROWN.
1829.
ELEMENTS
PHILOSOPHY OF THE HUMAN MIND.
VOL. II.
\
ADVERTISEMENT.
After an interval of more than twenty years, I ven- ture to present to the pubhc a Second Volume on the Philosophy of the Human Mind.
When the Preceding Part was sent to the press, I ex- pected that a few short chapters would comprehend all that I had further to offer concerning the Intellectual Powers ; and that I should be able to employ the great- er part of this Volume in examining those principles of our constitution, which are immediately connected with the Theory of Morals. On proceeding, however, to at- tempt an analysis of Reason, in the more strict accepta- tion of that term, I found so many doubts crowding on me with respect to the logical doctrines then generally received, that I was forced to abandon the comparatively limited plan according to which I had originally intended to treat of the Understanding, and, in the mean time, to suspend the continuation of my work, till a more unbro- ken leisure should allow me to resume it with a less di- vided attention.
Of the accidents which have since occurred to retard my progress, it is unnecessary to take any notice here. I allude to them, merely as an apology for those defects of method, which are the natural, and perhaps the una- voidable, consequences of the frequent interruptions by which the train of my thoughts has been diverted to other pursuits. Such of my readers as are able to judge bQw very large a proportion of my materials has been
VI ADVERTISEMENT.
the fruit of my own meditations ; and who are aware of the fugitive nature of our reasonings concerning pheno- mena so far removed from the perceptions of Sense, will easily conceive the difficulty I must occasionally have experienced, in deciphering the short and slight hints on these topics, which I had committed to writing at remote periods of my life ; and still more, in recover- ing the thread which had at first connected them togeth- er in the order of my researches,
I have repeatedly had occasion to regret the tendency of this intermitted and irregular mode of composition, to deprive my speculations of those advantages, in point of continuity, which, to the utmost of my power, I have endeavoured to give them. But I would willingly in- dulge the hope, that this is a blemish more likely to meet the eye of the author than of the reader ; and I am confident, that the critic who shall honor me with a sufficient degree of attention, to detect it where it may occur, will not be inclined to treat it with an undue se- verity.
A Third Volume (of which the chief materials are already prepared) will comprehend all that I mean to pubhsh under the title of the Philosophy of the Hu- man Mind. The principal subjects allotted for it are Language ; Imitation ; the Varieties of Intellectual Character ; and the Faculties by which Man is distin- guished from the lower animals. The two first of these articles belong, in strict propriety, to this second part of my work ; but the size of the Volume has prevent- ed me from entering on the consideration of them at present.
The circumstances which have so long delayed the publication of these volumes on the Intellectual Powers, have not operated, in an equal degree, to prevent the prosecution of my inquiries into those principles of Hu-
ADVERTISEMENT. Vll
man Nature, to which my attention was, for many years, statedly and forcibly called by my official duty. Much, indeed, still remains to be done in maturing, digesting, and arranging many of the doctrines which I was accus- tomed to introduce into my lectures ; but if I shall be blessed, for a few years longer, with a moderate share of health and of mental vigor, I do not altogether despair of yet contributing something, in the form of Essaijs, to fill up the outline which the sanguine imagination of youth encouraged me to conceive, before I had duly measured the magnitude of my undertaking with the time or with the abilities which I could devote to the execution.
The volume which I now publish is more particularly intended for the use of Academical Students ; and is offered to them as a guide or assistant, at that important stage of their progress when, the usual course of dis- cipline being completed, an inquisitive mind is naturally led to review its past attainments, and to form plans for its future improvement. In the prosecution of this de- sign, I have not aimed at the estabhshment of new the- ories ; far less have I aspired to the invention of any new organ for the discovery of truth. My principal ob- ject is to aid my readers in unlearning the scholastic errors which, in a greater or less degree, still maintain their ground in our most celebrated seats of learning ; and by subjecting to free^ but I trust, not sceptical dis- cussion, the more enlightened though discordant sys- tems of modern Logicians, to accustom the understand- ing to the unfettered exercise of its native capacities. That several of the views opened in the following pa- ges appear to myself original, and of some importance, I will not deny ; but the reception these may meet with, I shall regard as a matter of comparative indifference, if my labors be found useful in training the mind to those
Vlll ADVERTISEMENT.
habits of reflection on its own operations, which may enable it to superadd to the instructions of the schools, that higher education which no schools can bestow.
Kinneil-Uouse, 22d JYovember, 1813.
CONTENTS.
PART SECOND.
OF REASON, OR THE UNDERSTANDING, PROPERLY SO CALLED ; AND THE VARIOUS FACULTIES AND OPERATIONS MORE IMMEDI- ATELY CONNECTED WITH IT _ _ - Page 1
Preliminary Observations on the Vagueness and Ambiguity of the common Philosophical Language relative to this part of or Constitution, — Reason and Reasoning, — Understanding, — Intellect, — Judgment, &lc. _ _ - - j.
CHAPTER I.
Of the Fundamental Laws of Human Belief; or the Primary Ele- ments of Human Reason.
Sect. I. — Of Mathematical Axioms - - - 18
1. ----- - 19
2. Continuation of the same Subject - - 31 II. — Of certain Laws of Belief, inseparably connected
with the Exercise of Consciousness, Memory, Per- ception, and Reasoning _ _ _ 35 III. — Continuation of the Subject. — Critical Remarks on some late Controversies to which it has given rise. — Of the Appeals which Dr. Reid and some other Modern Writers have made, in their Philosophical Discussions, to Common Sense, as a Criterion of Truth - - - - - - 40
CHAPTER II.
Of Reasoning and of Deductive Evidence.
Sect. I. ----- - 04
1. Doubts with respect to Locke's Distinction be- tween tlie Powers of Intuition and of Reasoning (34
2. Conclusions obtained by a process of Deduction
often mistaken for Intuitive Judgments - - 70
h
CONTENTS.
II. — Of General Reasoning - - - 75
1., Illustrations of some Remarks formerly stated in treating of Abstraction - - - - 75
2. ContinuatiOTi of the Subject. — Of Language con- sidered as an Instrument of Thought - 91
3. Continuation of the Subject. — Visionary Theories of some Logicians, occasioned by their inattention to the Essential Distinction between Mathematics
and other Sciences - - - - 97
4. Continuation of the Subject. — Peculiar and super- eminent Advantages possessed by Mathematicians,
in consequence of their definite Phraseology 104
III. — Of Mathematical Demonstration - - 106
1. Of the circumstance on which Demonstrative Evi- dence essentially depends _ . _ 106
2. Continuation of the Subject. — How far it is true that all Mathematical Evidence is resolvable into Identical Propositions - - - 117
3. Continuation of the Subject. — Evidence of the Mechanical Philosophy, not to be confounded with that which is properly called Demonstrative or Mathematical. — Opposite Error of some late Wri- ters _.--.- 127
IV. — Of our Reasoning concerning Probable or Contin- gent Truths ----- 144
1. Narrow Field of Demonstrative Evidence. — Of Demonstrative Evidence, when combined with that of Sense, as in Practical Geometry ; and with those of Sense and of Induction, as in the Mechanical Philosophy. — Remarks on a Fundamental Law of Belief, involved in all our Reasonings concerning Contingent Truths _ . - - 144
2. Continuation of the Subject. — Of that Permanence or Stability in the Order of Nature, which is pre- supposed in our Reasonings concerning Contingent Truths _. - - - 149
3. Continuation of the Subject. — General Remarks on the Diiference between the Evidence of Experi- ence, and that of Analogy _ - - 162
4. Continuation of the Subject. — Evidence of Testi- mony tacitly recognised as a ground of Belief, in our most certain Conclusions concerning Contin- gent Truths. — Difference between the logical and
the popular meaning of the Avord Probability 171
i'--
CONTENTS. xi
CHAPTER III.
Of the Aristotelian Logic.
Sect. I. — Of the Demonstrations of the Syllogistic Rules given
by Aristotle and his Commentators - - 175
II. — General Reflections on the Aim of the Aristotelian Logic, and on the Intellectual Habits which the Study of it has a tendency to form. — That the im- provement of the power of Reasoning ought to be regarded as only a Secondary Object in the Culture of the Understanding - _ _ - 193
III. — In what respects the Study of the Aristotelian Logic may be useful to Disputants. — A general acquaint- ance with it justly regarded as an essential accom- plishment to those Avho are liberally educated. — Doubts suggested by some late Writers, concerning Aristotle's claims to the invention of the Syllogistic Theory 207
CHAPTER IV.
Of the Method of Inquiry pointed out in the Experimental or Induc- tive Logic.
Sect. I. — Mistakes of the Ancients concerning the proper ob- ject of Philosophy. — Ideas of Bacon on the same Subject. — Inductive Reasoning. — Analysis and Syn- thesis.— Essential difference between Legitimate and Hypothetical Theories _ _ _ 220
II. — Continuation of the Subject. — The Induction of
Aristotle compared with that of Bacon - 242
HI. — Of the Import of the words Analysis and Synthesis
in the Language of Modern Philosophy - - 252
1. Preliminary Observations on the Analysis and Syn- thesis of the Greek Geometricians - - 252
2. Critical Remarks on the vague Use, among Mod- ern Writers, of the Terms Analysis and Synthesis 261
IV. — The Consideration of the Inductive Logic resumed 273
1. Additional Remarks on the distinction between Experience and Analogy. — Of the grounds afforded
by the latter for Scientific Inference and Conjecture 273
2. Use and Abuse of Hypotheses in Philosophical Inquiries. — Difference between Gratuitous Hypoth- eses, and those which are supported by presump- tions suggested by Analogy. — Indirect Evidence which a Hypothesis may derive from its agreement with the Phenomena. — Cautions against extending some of these Conclusions to the Philosophy of the Human Mind 287
xii CONTENTS.
3. Supplemental Observations on the words Induc- tion and Analogy, as used in Mathematics - 304
V. — Of certain misapplications of the words Experience and Induction in the Phraseology of Modern Sci- ence.— Illustrations from Medicine and from Politi- cal Economy . _ _ _ _ 310
VI. — Of the Speculation concerning Final Causes 323
1. Opinion of Lord Bacon on the Subject.— Final Causes rejected by Descartes, and by the majority of French Philosophers. — Recognised as legitimate Objects of research by Newton. — Tacitly acknowl- edged by all as a useful Logical Guide, even in Sciences which have no immediate relation to The- ology _ _ - - . 323
2. Danger of confounding Final with Physical Causes
in the Philosophy of the Human Mind - 337
Conclusion of Part Second _ _ _ _ 346
Notes and Illustrations - - - - 355
Appendix ------- 385
ELEMENTS
PHILOSOPHY OF THE HUMAN MIND.
PART SECOND.
OP REASON, OR THE UNDERSTANDING PROPERLY SO CALLED ; AND THE VARIOUS FACULTIES AND OPERATIONS MORE IMMEDIATELY CONNECT- ED WITH IT.
PRELIMINARY OBSERVATIONS ON THE VAGUENESS AND AMBIGUITY OF THE COMMON PHILOSOPHICAL LANGUAGE RELATIVE TO THIS PART OP
OUR CONSTITUTION, REASON AND REASONING, UNDERSTANDING, — ■
INTELLECT, JUDGMENT, vStC.
The power of Reason, of which I am now to treat, is unquestionably the most important by far, of those which are comprehended under the general title of Intellectual. It is on the right use of this power, that our success in the pursuit both of knowledge and of happiness depends; and it is by the exclusive possession of it that Man is distinguished, in the most essential respects, from the lower animals. It is, indeed, from their subserviency to its operations, that the other faculties, which have been hitherto under our consideration, derive their chief value.
In proportion to thepecuhar importance of this subject are its extent and its difficulty ; — both of them such as to lay me under a necessity, now that I am to enter on the discussion, to contract, in various instances, those de- signs in which I was accustomed to indulge myself, when I looked forward to it from a distance. The exe- cution of them at present, even if I were more compe- tent to the task, appears to me, on a closer examination,
VOL. II. 1
is ELEMENTS OF THE PHILOSOPHY
to be altogether incompatible with the comprehensive- ness of the general plan which was sketched out in the advertisement prefixed to the former volume ; and to the accomplishment of which I am anxious, in the first instance, to direct my efi'orts. If that undertaking should ever be completed, I may perhaps be able afterwards to offer additional illustrations of certain articles, which the limits of this part of my work prevent me from consid- ering with the attention which the}' deserve. I should wish in particular, to contribute something more than I can here introduce, towards a rational and practical system of Logic, adapted to the present state of human knowledge, and to the real business of human life.
"What subject," says Burke, "does not branch out to infinity ! It is the nature of our particular scheme, and the single point of view in which we consider it, which ought to put" a stop to our researches." * How forcibly does the remark apply to all those specula- tions which relate to the principles of the Human Mind !
I have frequently had occasion, in the course of the foregoing disquisitions, to regret the obscurity in which this department of philosophy is involved, by the vague- ness and ambiguity of words ; and I have mentioned, at the same time, my unwillingness to attempt verbal innovations, wherever I could possibly avoid them, with- out essential injury to my argument. The rule which I have adopted in my own practice is, to give to every faculty and operation of the mind its own appropriate name ; following, in the selection of this name, the prevalent use of our best writers ; and endeavouring afterwards, as far as I have been able, to employ each word exclusively, in that acceptation in which it has hith- erto been used most generally. In the judgments which I have formed on points of this sort, it is more than prob- able that I may sometimes have been mistaken : but the mistake is of little consequence, if I myself have invari- ably annexed the same meaning to the same phrase ; — an accuracy which I am not so presumptuous as to im-
* Conclusion of the Inquiry into the Sublime and the Beautiful.
OF THE HUMAN MIND. S
agine that I have uniformly attained, but which I am conscious of having, at least, uniformly attempted. How far I have succeeded, they alone who have follow- ed my reasonings with a very critical attention are qualified to determine ; for it is not by the statement of formal definitions, but by the habitual use of precise and appropriate language, that I have endeavoured to fix in my reader's mind the exact import of my ex- pressions.
In appropriating, however, particular words to par- ticular ideas, I do not mean to censure the practice of those who may have understood them in a sense diff"er- ent from that which .1 annex to them ; but I found that, without such an appropriation, I could not explain my notions respecting the human mind, with any tolerable degree of distinctness. This scrupulous appropriation of terms, if it can be called an innovation, is the only one which I have attempted to introduce ; for in no in- stance have I presumed to annex a philosophical mean- ing to a technical word belonging to this branch of sci- ence, without having previously shown, that it has been used in the same sense by good writers, in some passa- ges of their works. After doing this, I hope I shall not be accused of afi"ectation, when I decline to use it in any of the other acceptations in which, from carelessness or from want of precision, they may have been led occa- sionally to employ it.
Some remarkable instances of vagueness and ambi- guity in the employment of words, occur in that branch of my subject of which I am now to treat. The word reason itself is far from being precise in its meaning. In common and popular discourse, it denotes that pow- er by which we distinguish truth from falsehood, and right from wrong ; and by which we are enabled to com- bine means for the attainment of particular ends. Whether these dilferent capacities are, with strict logic- al propriety, referred to the same power, is a question which I shall examine in another part of my work ; but that they are all included in the idea which is generally annexed to the word reason, there can be no doubt ; and the case, so far as I know, is the same with the cor-
4 ELEMENTS OF THE PHILOSOPHY
responding term in all languages whatever. The fact probably is, that this word was first employed to com- prehend the principles, whatever they are, by which man is distinguished from the brutes ; and afterwards came to be somewhat limited in its meaning, by the more obvious conclusions concerning the nature of that distinction, which present themselves to the common sense of mankind. It is in this e-nlarged meaning that it is opposed to instinct hj Pope :
" And Reason raise o'er Instinct as you can : In this 't is God directs, in that 'tis Man."
It was thus, too, that Milton plainly understood the term, when he remarked, that smiles imply the exercise of reason :
" Smiles from Reason flow,
To brutes denied : "
And still more explicitly in these noble lines :
" There wanted yet the master-work, the end Of all yet done ; a creature who, not prone And brute as other creatures, but endued With sanctity of Reason, might erect His stature, and upright with front serene Govern the rest, self-knowing ; and from thence. Magnanimous, to correspond with Heaven ; But, grateful to acknowledge whence his good Descends, thither with heart, and voice, and eyes Directed in devotion, to adore And worship God Supreme, who made him chief Of all his works."
Among the various characteristics of humanity, the powder of devising means to accomplish ends, together with the power of distinguishing truth from fslsehood, and right from wrong, are obviously the most conspicu- ous and important ; and accordingly it is to these that the word reason, even in its most comprehensive accep- tation, is now exclusively restricted.*
*This, I think, is the meaning which most naturally presents itself to common readers, when the word reason occurs in authors not affecting to aim at any nice logical distinctions; and it is certainly the meaning which must be annexed to it, in some of the most serious and important arguments in which it has ever been em- ployed. In the following passage, for example, where Mr. Locke contrasts the light of Reason with that of Revelation, he plainly proceeds on the supposition, that it is
OF THE HUMAN MIND. 6
By some philosophers, the meaning of the word has been, of late, restricted still farther ; to the power by which we distinguish truth from falsehood, and combine means for the accomplishment of our purposes ; — the capacity of distinguishing right from wrong, being re- ferred to a separate principle or faculty, to which differ- ent names have been assigned in different ethical the- ories. The following passage from Mr. Hume contains one of the most explicit statements of this limitation which I can recollect : " Thus, the distinct boundaries and offices of reason and of taste are easily ascertained. The former conveys the knowledge of truth and false- hood ; the latter gives the sentiment of beauty and de- formity,— vice and virtue. Reason, being cool and disengaged, is no motive to action, and directs only the impulse received from appetite or inclination, by show- ing us the means of attaining happiness or avoiding misery. Taste, as it gives pleasure or pain, and thereby constitutes happiness or misery, becomes a motive to action, and is the first spring or impulse to desire and voUtion." *
On the justness of this statement of Mr. Hume, I have no remarks to offer here ; as my sole object in quoting it was to illustrate the different meanings annex- ed to the word reason by different writers. It will
competent to appeal to the former, as affording a standard of right and wrong, not less than of speculative truth and falsehood ; nor can there be a doubt that, when he speaks oi truth as the object of natural reason, it was principallj', if not wholly, moral truth, which he had in his view : — " Reason is natural revelation, whereby the eternal Father of Light, and fountain of all knowledge, communicates to mankind that por- tion of truth which he has laid within the reach of their natural faculties. Revela- tion is natural reason, enlarged by a new set of discoveries, communicated by God immediately, which reason vouches the truth of, by the testimony and proofs it gives that they come from God. So that he who takes away reason to make way for revela- tion, puts out the light of both, and does much the same, as if he would persuade a man to put out his eyes, the better to receive the remote light of an invisible star by a telescope." — Locke's Essay, B.iv. c. 19.
A passage still more explicit for my present purpose, occurs in the pleasing and philosophical conjectures of Huygens, conceining the planetary worlds. " Positis vero ejusmodi planetarum incolis rationc utentibus, quarri adhuc potest, anne idem illic, atquc apud nos, sit hoc quod rationem vocamus. Quod quidcm ita esse omnino dicendum videtur, neque aliter fieri posse ; sive usum rationis in his considercmu3 qua2 ad mores et anpiitatem pertinent, sive in lis qufc si)cctant ad principia ct Ainda- menta scientiarum. Etenim ratio apud nos est, qua^scnsum justitia-, honesti,laudis, clementioe, gratitudinis ingenerat, mala acbona in universum discernere docet : quaj- que ad ha^c animnm disciplina;, multorumque inventorum capacem reddit," &.c. &c. — Hugenii Opera Varia,\o\. II. p. 663. Lugd. Batav. 1724.
* Essays and Treatises, &c. Appendix, concerning Moral Sentiment.
6 ELEMENTS Or THE PHILOSOPHY
appear afterwards, that, in consequence of this circum- stance, some controversies, which have been keenly agitated about the principles of morals, resolve entirely into verbal disputes ; or, at most, into questions of ar- rangement and classification, of Uttle comparative mo- ment to the points at issue.*
Another ambiguity in the word reason it is of still greater consequence to point out at present ; an ambi- guity which leads us to confound our rational powers in general, with that particular branch of them, known among logicians by the name of the Discursive faculty. The affinity between the words reason and reasoning sufficiently accounts for this inaccuracy in common and popular language ; although it cannot fail to appear ob- vious, on the shghtest reflection, that in strict propriety, reasoning only expresses one of the various functions or operations of reason ; and that an extraordinary capaci- ty for the former by no means affords a test by which the other constituent elements of the latter may be measured-! Nor is it to common and popular language that this inaccuracy is confined. It has extended itself to the systems of some of our most acute philosophers, and has, in various instances produced an apparent diversity of opinion where there was little or none in reality.
"No hypothesis," says Dr. Campbell, "hitherto in- vented, hath shown that, by means of the discursive facul- ty, without the aid of any other mental power, we could ever obtain a notion of either the beautiful or the good." J
* In confirmation of this remark, I shall only quote at present a few sentences from an excellent discourse, by Dr. Adams of Oxford, on the nature and obligations- of virtue. " Nothing can bring us under an obligation to do what .appears to our moral judgment wrong. It may be supposed our interest to do this ; but it cannot be supposed our duty. — Power may compel, interest may biibe, pleasure may per- suade ; but REASON only can oblige. This is the only authority which rational be- ino-s can own, and to which they owe obedience."
It must appear perfectly obvious to every reader, that the apparent difference of opinion between this writer and Mr. Hume, turns chiefly on the different degrees of latitude with which they have used the word reason. Of the two, there cannot be a doubt that Dr. Adams has adhered by far the most faithfully, not only to its ac- ceptation in the works ot our best English authors, but to the acceptation of the corresponding term in the ancient languages. " Est quidem vera lex, recta ratio — quae vocet ad officium, jubendo ; vetando, a fraude dcterreat," &c. &c.
\ " The two most different things in the world, says Locke, are, a logical chicaner, and a man of reason." — Conduct of the Understanding, § 3.
I Philosophy of Rhetoric, Vol. I. p. 204.
OF THE HUMAN MIJ^D. 7
The remark is undoubtedly true, and may be applied to all those system^s which ascribe to reason the origin of our moral ideas, if the expressions reason and discursive faculty be used as synonymous. But it was assuredly not in this restricted acceptation, that the word reason was understood by those ethical writers at whose doc- trines this criticism seems to have been pointed by the ingenious author. That the discursive faculty alone is sufficient to account for the origin of our moral ideas, I do not know that any theorist, ancient or modern, has yet ventured to assert.
Various other philosophical disputes might be men- tioned, which would be at once brought to a conclusion, if this distinction between reason and the power of reasoning were steadily kept in view.*
In the use which I make of the word reason, in the title of the following disquisitions, I employ it in a man-
* It is cuiious, that Dr. Johnson has assi2;ned to this veiy limited, and (according to present usage) very doubtful interpretation of the word reaann, ihe first place in his enumeration of its various meanings, as if he had thought it the sense in which it is most properly and correctly employed. "Reason," he tells us, "is the power by which man deduces one proposition from another, or proceeds from premises to consequences.'' The authoiity which he has quoted for this definition is slill more curious, being manifestly altogether inapplicable to his purpose. " Reason is the director of man's will, discoveiing in action what is good ; for the laws of well-doing are the dictates of right reason." — Hooker.
In the si:cth article of the same enumeration, he states as a distinct meaning of the same word, ratiocination, discursive pou)er. What possible difference could he conceive between this signification and that above quoted .' The authoiity, however, which he produces for this last explanation, is worth transcribing. It is a passao-e from Sir John Uavis, where that fanciful writer states a distinction between reason and understanding: to which he seems to have been led by a conceit founded on their respective etymologies.
" When she rates tilings, and moves from ground to ground, The name of Reason she obtains by this ; But wlien by Reason she the truth hath found. Anil standoth lixt, slie Understanding is."
The adjective reasonable, as'employcd in our language, is not liable to the same ambiguity with the substantive from which is derived. It denotes a character in wliich reaso?i (taking that word in its largest acceptation) possesses a decided as- cendant over the temper and tl'.e i)assions ; and implies no particular propensity to a display of the discursive power, if, indeed, it does not exclude the idea of such a propensity. In the following stanza, Pope certainly had no view to the logical tal- ents of the lady whom he celebrates :
"I know a thing that '3 most uncommon, (Envy be silent and attend) I know a reasonable woman, Handsome and witty, yet a friend."
Of this reasonable woman, we may venture to conjecture, with some confidence, that she did not belong to the class of those femmes raisonnenses, so happily described bj"^ Moliere :
"Raisonncr est I'emjdoi de toule ma maison, £t lo ruisouuoincnt un baonit la rabun."
8 ELEMENTS OF THE PHILOSOPHY
ner to which no philosopher can object — to denote merely the power by which we distinguish truth from falsehood, and combine means for the attainment of our ends : omitting for the present all consideration of that function which many have ascribed to it, of distinguishing right from wrong : without, however, presuming to call in question the accuracy of those by whom the term has been thus explained. Under the title of Reason, I shall consider also whatever faculties and operations appear to be more immediately and essentially connect- ed with the discovery of truth, or the attainment of the objects of our pursuit, more particularly the Power of Reasoning or Deduction ; but distinguishing, as carefully as I can, our capacity of carrying on this logical, process, from those more comprehensive powers which Reason is understood to imply.
The latitude with which this word has been so uni- versally used, seemed to recommend it as a convenient one for a general title, of which the object is rather comprehension than precision. In the discussion of particular questions, I shall avoid the employment of it as far as I am able ; and shall endeavour to select other modes of speaking, more exclusively significant of the ideas which I wish to convey.*
* Mr. Locke too has prefixed the same title, Of Reason, to the I7th chapter of his Fourth Book, using the word in a sense nearly coinciding with that very exten- sive one which I wish my readers to annex to it here.
After observing, that by reason he means " that faculty whereby man is supposed to be distinguished from brutes, and wherein it is evident he much surpasses them ; " he adds, that " we may in reason consider these four degrees ;^the first and highest is the discovering and finding out of proofs ; the second, the regular and methodi- cal disposition of them, and laying them in a clear and fit order, to make their con- nexion and force be plainly and easily perceived ; the third is the perceiving their connexion ; and the fourth is making a right conclusion."
Dr. Reid's authority for this use of the word is equally explicit : " The power of reasoning is very nearly allied to that of judging. We include both under the name o{ reason." — Intellect. Powers, p. 671, 4to edit.
Another authority to the same puipose is furnished by Milton :
" Whence the soul
Reason receives ; and Reason is hek being, Discursive or intuitive."
Par. Lost, B. V. 1. 488,
I presume that Milton, who was a logician as well as a poet, means by the words her being, her essential or characteristical endowment.
To these quotations I shall only add a sentence from a very judicious French writer ; which I am tempted to introduce here, less on account of the sanction which it gives to my own phraseology, than of the importance of the truth which it con- veys. " Reason is commonly employed as an instrument to acquire the sciences ; whereas, on the contrary, the sciences ought to be made use of as an instrument to give reason its perfection." LVIrt cle Penser, translated by Ozell, p. 2. London, 1717.
OF THE HUMAN MIIfD. 9
Another instance of the vagueness and indistinctness of the common language of logicians, in treating of this part of the Philosophy of the Human Mind, occurs in the word imderstanding. In its popular sense it seems to be very nearly synonymous with reason, when that word is used most comprehensively ; and is seldom or never apphed to any of our faculties, but such as are immediately subservient to the investigation of truth, or to the regulation of our conduct. In this sense, it is so far from being understood to comprehend the powers of Imagination, Fancy, and Wit, that it is often stated in di- rect opposition to them ; as in the common maxim, that a sound understanding and a warm imagination are sel- dom united in the same person. But philosophers, without rejecting this use of the word, very generally employ it, with far greater latitude, to comprehend all the powers which I have enumerated under the title of intellectual ; referring to it Imagination, Memory, and Perception, as well as the faculties to which it is appro- priated in popular discourse, and which it seems indeed most properly to denote. It is in this manner that it is used by Mr. Locke in his celebrated Essay : and by all the logicians who follow the common division of our mental powers into those of the Understanding and those of the Will.
In mentioning this ambiguity, I do not mean to cavil at the phraseology of the writers from whom it has de- rived its origin, but only to point it out as a circumstance which may deserve attention in some of our future dis- quisitions. The division of our powers which has led to so extraordinary an extension of the usual meaning of language, has an obvious foundation in the constitution of our nature, and furnishes an arrangement which seems indispensable for an accurate examination of the subject : nor was it unnatural to bestow on those facul- ties, which are all subservient in one way or another to the right exercise of the Understanding, the name of that power, from their relation to which their chief value arises.
As the word understancUng, however, is one of those which occur very frequently in philosophical arguments,
VOL. 11. 2
10 ELEMENTS OF THE PHILOSOPHY
it may be of some use to disengage it from the ambigui- ty just remarked ; and it is on this account that I have followed the example of some late writers, in distin- guishing the two classes of powers which were former- ly referred to the Understanding and to the Will, by calling the former intellectual, and the latter active. The terms cognitive and motive were long ago proposed for the same purpose by Hobbes ; but they never appear to have come into general use, and are indeed liable to ob- vious objections.
It has probably been owing to the very comprehensive meaning annexed in philosophical treatises to the word understandings, that the use of it has so frequently been supplied of late by intellect. The two words, as they are commonly employed, seem to be very nearly, if not exactly, synonymous : and the latter possesses the ad- vantage of being quite unequivocal, having never acquir- ed that latitude of apphcation of which the former ad- mits. The adjective intellectual, indeed, has had its meaning extended as far as the substantive understand- ing ; but, as it can be easily dispensed with in our par- ticular arguments, it may, without inconvenience, be adopted as a distinctive epithet, where nothing is aimed at but to mark, in simple and concise language, a very general and obvious classification. The word intellect can be of no essential use whatever, if the am.biguity in the signification of the good old English word under- standing be avoided ; and as to intellection, which a late very acute writer * has attempted to introduce, I can see no advantage attending it, which at all compensates for the addition of a new and uncouth term to a phraseolo- gy which, even in its most simple and unaffected form, is so apt to revolt the generality of readers.
The only other indefinite word which I shall take no- tice of in these introductory remarks, is judgment ; and, in doing so, I shall confine myself to such of its ambi- guities as are more pecuharly connected with our pres- ent subject. In some cases, its meaning seems to ap- proach to that of understanding ; as in the nearly synon-
* Dr. Campbell. See his Philosophy of Rhetoric, Vol. I. p. 103. 1st. edit.
OF THE HUMAW MIIfD. 1 1
ymous phrases, a sound understanding, and a sound judgment. If there be any difference between these two modes of expression, it appears to me to consist chiefly in this, that the former imphes a greater degree of positive abihty than the latter ; which indicates rath- er an exemption from those biases which lead the mind astray, than the possession of any micommon reach of capacity. To understanding we apply the epithets strong, vigorous, comprehensive, profound : to judg- ment, those of correct, cool, unprejudiced, impartial, solid. It was in this sense that the word seems to have been understood by Pope in the following couplet :
" 'T is with our judgments as our watches ; none Go just alike, yet each believes his own."
For this meaning of the word, its primitive and literal apphcation to the judicial decision of a tribunal accounts sufficiently.
Agreeably to the same fundamental idea, the name of judgment is given, with pecuhar propriety, to those ac- quired powers of discernment which characterize a skil- ful critic in the fme arts ; powers which depend, in a very great degree, on a temper of mind free from the undue influence of authority and of casual associa- tions. The power of Taste itself is frequently denoted by the appellation oi judgment ; and a person who pos- sesses a more than ordinary share of it is said to be a judge in those matters which fall under its cognizance.
The meaning annexed to the word by logical writers is considerably different from this ; denoting one of the simplest acts or operations of which we are conscious, in the exercise of our rational powers. In this accepta- tion, it does not admit of definition any more than sen- sation, will, or belief. All that can be done, in such ca- ses, is to describe the occasions on which the operation takes place, so as to direct the attention of others to their own thoughts. With this view, it may be observed, in the present instance, that when we give our assent to a mathematical axiom ; or when, after perusing the de- monstration of a theorem, we assent to the conclusion ; or, in general, when we pronounce concerning the truth
12 ELEMENTS OF THE PHILOSOPHY
or falsity of any proposition, or the probability or im- probability of any event, the power by which we are en- abled to perceive what is true or false, probable or im- probable, is called by logicians the faculty of judgment. The same word, too, is frequently used to express the particular acts of this power, as when the decision of the understanding on any question is called a judgment of the mind.
In treatises of logic, judgment is commonly defined to be an act of the mind, by which one thing is affirmed or denied of another ; a definition which, though not un- exceptionable, is perhaps less so than most that have been given on similar occasions. Its defect (as Dr. Reid has remarked) consists in this, — that, although it be by affirmation or denial that we express our judg- ments to others, yet judgment is a solitary act of the mind, to which this affirmation or denial is not essential ; and, therefore, if the definition be admitted, it must be understood of mental affirmation or denial only ; in which case, we do no more than substitute, instead of the thing defined, another mode of speaking perfectly synonymous. The definition has, however, notwith- standing this imperfection, the merit of a conciseness and perspicuity, not often to be found in the attempts of logicians to explain our intellectual operations.
Mr. Locke seems disposed to restrict the word judg- ment to that faculty which pronounces concerning the verisimilitude of doubtful propositions ; employing the word knoioledge to express the faculty which perceives the truth of propositions, either intuitively or demon- stratively certain. " The faculty which God has given man to supply the want of clear and certain knowledge in cases where that cannot be had, is judgment; where- by the mind takes its ideas to agree or disagree ; or, which is the same thing, any proposition to be true or false, without perceiving a demonstrative evidence in the proofs.
" Thus, the mind has two faculties, conversant about truth and falsehood.
" First, knowledge, whereby it certainly perceives, and is undoubtedly satisfied of the agreement or disa- greement of any ideas.
OF THE HUMAN MIND. 13
" Secondly, judgment, which is the putting ideas to- gether, or separating them from one another in the mind, when their agreement or disagreement is not per- ceived, but presumed to be so ; wliich is, as the word imports, taken to be so, before it certainly appears. And if it so unites, or separates them, as in reahty things are, it is right judgment^ *
For this limitation in the definition of judgment, some pretence is afforded by the hteral signification of the word, when applied to the decision of a tribunal; and also, by its metaphorical apphcation to the decis- ions of the mind, on those critical questions which fall under the province of Taste. But, considered as a technical or scientific term of Logic, the practice of our purest and most correct writers sufficiently sanctions the more enlarged sense in which I have explained it ; and, if I do not much deceive myself, this use of it will be found more favorable to philosophical distinctness than Mr. Locke's language, which leads to an unneces- sary multiplcation of our intellectual powers. What good reason can be given for assigning one name to the faculty which perceives truths that are certain, and an- other name to the faculty which perceives truths that are probable ? Would it not be equally proper to dis- tinguish, by different names, the power by which we perceive one proposition to be true, and another to be false ?
As to knowledge, I do not think that it can, with pro- priety, be contrasted with judgment ; nor do I appre- hend that it is at all agreeable, either to common use or to philosophical accuracy, to speak of knowledge as a faculty. To me it seems rather to denote the posses- sion of those truths about which our faculties have been previously employed, than any separate power of the understanding by which truth is perceived.f
* Essay on tbe Human UntlerstanflinEf, Book iv. Chap. 14.
•j- In attempting thus to fix the logical impoit of various words in our language, which are apt to be confoumled, in popular speech, with reason, ami also with lea- soning, some of my readers may be surprised, that 1 have said nolhing about the wovd icisdom. The truth is, that the notion expressed by this teim, as it is em- ployed by 'Our best writers, seems to presuppose tlie influence of some principles, the consideration of which belongs to a diflerent part of my work. In confnniation
14 ELEMENTS OF THE PHILOSOPHY
Before concluding these preliminary remarks, I can- not help expressing my regret, that the subject on which I am about to enter will so frequently lay me un- der the necessity of criticising the language, and of disputing the opinions of my predecessors. In doing so, I am not conscious of being at all influenced by a wish to indulge myself in the captiousness of contro- versy ; nor am I much afraid of this imputation from any of my readers who shall honor these speculations with an attentive perusal. My real aim is, in the first place, to explain the grounds of my own deviations from the track which has been commonly pursued, and, secondly, to facilitate the progress of such as may fol- low me in the same path, by directing their attention to those points of divergency in the way, which may sug- gest matter for doubt or hesitation. I know, at the same time, that, in the opinion of many, the best mode of unfolding the principles of a science is to state them systematically and concisely, without any historical re- trospects whatever ; and I beheve the opinion is well founded, in those departments of knowledge, where the
of this, it may be remarked, that whereas the province of our reasoning powers (in their application to the business of life) is limited to the choice of means, wisdom denotes a power of a more comprehensive nature, and of a higher order; a power which implies a judicious selection both of means and of ends. It is very precisely defined by Sir William Temple to be " that which makes men judge what are the best ends and what the best means to attain them."
Of these two modifications of wisdom, the one denotes a power of the mind which obviously falls under the view of the logician ; the examination of the other, as obviously, belongs to ethics.
A distinction similar to this was plainly in the mind of Cudworth, when he wrote the following passage, which, although drawn from the purest sources of ancient philosophy, will, I doubt not, from the uncouthness of the phraseology, have the appearance of extravagance, to many in the present times. To myself it appears to point at 3, fact of the highest importance in the moral constitution of man.
"We have all of us by nature ^avTsu/^a -n (as both Plato and Aristotle call it, a certain divination, presage, and parturient vaticination in our minds, of some high- er good and perfection, than eiiher power or knowledge. Knowledge is plainly to be preferred before power, as being that which guides and directs its blind force and impetus ; but Aristotle himself declares, that therrj is Xoyou n x^urrov, which is Xoyou a^X'^ ; something better than reason and k7ioivleds;e, which is the principle and original of it. For saith he Xoyou a.^x}i oh x'oyos, aXXd. n x^iTrrov. The principle of reason is not reason, hut something better." — Intellectual System, p. 203.
Lord Shaftesbury has expressed the same truth more simply and perspicuously in that beautiful sentence which occurs more than once in his wiitings : " True wisdom comes more from the heart than from the head." — Numbcrless'iilustrations of this profound maxim must immediately crowd on the memory of all who are conversant with the most enlightened works on the theory of legislation ; more particularly, with those which appeared, during the eighteenth century, on the science of political economy.
OF THE HUMAN MIND. 15
difficulty arises less from vague ideas and indefinite terms, than from the length of the logical chain which the student has to trace. But, in such disquisitions as we are now engaged in, it is chiefly from the gradual correction of verbal ambiguities, and the gradual detec- tion of unsuspected prejudices, that a progressive though slow approximation to truth is to be expected. It is in- deed a slow approximation, at best, that we can hope to accomphsh at present, in the examination of a subject where so many powerful causes (particularly those con- nected with the imperfections of language) conspire to lead us astray. But the study of the human mind is not, on that account to be abandoned. Whoever compares its actual state with that in which Bacon, Des Cartes, and Locke, found it, must be sensible how amply their ef- forts for its improvement have been repaid, both by their own attainments, and by those of others who have since profited by their example. I am wilhng to hope, that some useful hints for its farther advancement, may be derived even from my own researches ; and, distant as the prospect may be of raising it to a level with the physical science of the Newtonian school, by uniting the opinions of speculative men about fundamental principles, my ambition as an author will be fully gratifi- ed, if, by the few who are competent to judge, I shall be allowed to have contributed my share, however small, towards the attainment of so great an object.
In the discussions which immediately follow, no ar- gument will, I trust, occur beyond the reach of those who shall read them with the attention which every in- quiry into the human mind indispensably requires. I have certainly endeavoured, to the utmost of my abili- ties, to render every sentence which I have written, not only intelhgible but perspicuous ; and, where I have failed in the attempt, the obscurity will, I hope, be im- puted, not to an affectation of mystery, but to some er- ror of judgment. I can, without much vanity, say, that with less expense of thought, I could have rivalled the obscurity of Kant ; and that the invention of a new technical language, such as that which he has introdu- ced, would have been an easier task, than the communi-
16 ELEMENTS OF THE PHILOSOPHY
cation of clear and precise notions, (if I have been so . fortunate as to succeed in this communication,) without departing from the estabhshed modes of expression.
To the following observations of D'Alembert (with some trifling verbal exceptions) I give my most cordial assent ; and, mortifying as tbey may appear to the pre- tensions of bolder theorists, I should be happy to see them generally recognised as canons of philosophical criticism : " Truth in metaphysics resembles truth in matters of taste. In both cases, the seeds of it exist in every mind ; though few think of attending to this latent treasure, till it be pointed out to them by more curious inquirers. It should seem that every thing we learn from a good metaphysical book is only a sort of reminiscence of what the mind previously knew. The obscurity, of which we are apt to complain in this science, may be always justly ascribed to the author ; because the information which he professes to communicate requires no technical language appropriated to itself Accordingly, we may apply to good metaphys- ical authors what has been said of those who excel in the art of writing, that, in reading them, every body is apt to imagine, that he himself could have written in the same manner.
" But, in this sort of speculation, if all are qualified to understand, all are not fitted to teach. The merit of accommodating easily to the apprehension of others, no- tions which are at once simple and just, appears, from its extreme rarity, to be much greater than is commonly imagined. Sound metaphysical principles are truths which every one is ready to seize, but which few men have the talent of unfolding ; so difficult is it in this, as well as in other instances, to appropriate to one's self what seems to be the common inheritance of the human race." *
* " Le vrai en metaphysique ressemble au viai en matiere de gout; c'est un vrai dont tons les esprits ont le geime en eux-memes, auquel la plupart ne font point d'attention, mail qu'ijs reconnoissent des qu'on le leur montre. n'semble que tout ce qu'on apprend dans un bon livre de metaphysique, ne soit qu'une espece de re- iTiiniscence de ce que notre ame a deja su ; I'obscuiite, quand il y en a, vient tou- jouis de la faute de I'auteur, parce que la science qu'il se piopose d'enseigner n'a point d'autre langue que lalanguc commune. Aussi peut-on appliquer aux bons au-
OF THE HUMAN MIND. 17
I am, at the same time, fully aware, that whoever, in treating of the hmiian mind, aims to be understood, must lay his account with forfeiting, in the opinion of a very large proportion of readers, all pretensions to depth, to subtilty, or to invention. The acquisition of a new nomenclature is, in itself, no inconsiderable reward to the industry of those, who study only from motives of Uterary vanity ; and, if D'Alembert's idea of this branch of science be just, the wider an author deviates from truth, the more likely are his conclusions to assume the appearance of discoveries. I may add, that it is chiefly in those discussions which possess the best claims to originality, where he may expect to be told by the mul- titude, that they have learned from him nothing but what they knew before.
The latitude with which the w^ord metaphysics is fre- quently used, makes it necessary for me to remark, with respect to the foregoing passage from D'Alembert, that he limits the term entirely to an account of the origin of our ideas. " The generation of our ideas," he tells us, " belongs to metaphysics. It forms one of the principal objects, and perhaps ought to form the sole object of that science." * If the meaning of the word be extended, as it too often is in our language, so as to comprehend all those inquiries which relate to the theory and to the improvement of our mental powers, some of his obser- vations must be understood with very important restric- tions. What he has stated, however, on the inseparable connexion between perspicuity of style and soundness of investigation in metaphysical disquisitions, will be found to hold equally in every research to which that epithet can, with any color of propriety, be applied.
teurs de metaphysique ce qu'on a dit des bons ecrivains, qu'il n'y a personne qui, en les lisant, ne croie pouvoir en dire autant qu'eux.
" Mais si dans ce genre tons soni: faits pour entendre, tous ne sont pas faits pour in- struire. Le merite de faire entrer avec facilite dans les esprits des notions vraies et simples, est beaucoup plus grand qu'on ne pense, puisque rexpericnce nous prouve conibien il est rare ; les saiues idees nieta]ihysiques sont des verites comniunea que chacun saisit, mais que peu d'hommes ont le talent de developpcr ; tant il est difficile, dans quelque sujet que se puisse etre, de so reudre propre cc qui appartient a tout le raonde." — Elemens de Philosophic.
* " La generation de nos idces appartient a la metaphysiquo ; c'cst un do ses ob- jets principaux,etpeut-etre dcvroit elle s'y borncr." — Ibid.
VOL. II. 3
18 ELEMENTS OF THE PHILOSOPHY
CHAPTER FIRST.
GP THE FUNDAMENTAL LAWS OF HUMAN BELIEF ; OR THE PRIMARY ELEMENTS OF HUMAN REASON.
The propriety of the title prefixed to this Chapter will, I trust, be justified sufficiently by the speculations which are to follow. As these differ, in some essential points, from the conclusions of former writers, I found myself under the necessity of abandoning, in various in- stances, their phraseology ; — but my reasons for the par- ticular changes which I have made, cannot possibly be judged of, or even understood, till the inquiries by which I was led to adopt them be carefully examined.
I begin with a review of some of those primary truths, a conviction of which is necessarily implied in all our thoughts and in all our actions ; and which seem, on that account, rather to form constituent and essential elements of reason, than objects with which reason is conversant.
The import of this last remark will appear more clear- ly afterwards.
The primary truths to which I mean to confine my attention at present are, 1. Mathematical Axioms: 2. Truths (or more properly speaking, Laws of BeUef,) inseparably connected with the exercise of Conscious- ness, Perception, Memory, and Reasoning. — Of some additional laws of Behef, the truth of which is tacitly recognised in all our reasonings concerning contingent events, I shall have occasion to take notice under a dif- ferent article.
SECTION I.
Of Mathematical Axioms.
I HAVE placed this class of truths at the head of the enumeration, merely because they seem likely, from the
OF THE HUMAN MITfD. 19
place which they hold in the elements of geometry, to present to my readers a more interesting, and at the same time, an easier subject of discussion, than some of the more abstract and latent elements of our knowledge, afterwards to be considered. In other respects, a dif- ferent arrangement might perhaps have possessed some advantages, in point of strict logical method.
I.
On the evidence of mathematical axioms it is unne- cessary to enlarge, as the controversies to which they have given occasion are entirely of a speculative, or rath- er scholastic description ; and have no tendency to af- fect the certainty of that branch of science to which they are supposed to be subservient.
It must at the same time be confessed, with respect to this class of proposidons (and the same remark may be extended to axioms in general,) that some of the lo- gical questions connected with them continue still to be involved in much obscurity. In proportion to their ex- treme simplicity is the difficulty of illustrating or of de- scribing their nature in unexceptionable language : or even of ascertaining a precise criterion by which they may be distinguished from other truths which approach to them nearly. It is chiefly owing to this, that, in ge- ometry, there are no theorems of which it is so difficult to give a rigorous demonstradon, as those, of which per- sons, unacquainted with the nature of mathematical evi- dence, are apt to say, that they require no proof what- ever. But the inconveniences arising from these cir- cumstances are of trifling moment ; occasioning, at the worst, some embarrassment to those mathematical wri- ters, who are studious of the most finished elegance in their exposition of elementary principles ; or to meta- physicians, anxious to display their subtilty upon points which cannot possibly lead to any practical conclusion.
It was long ago remarked by Locke, of the axioms of geometry, as stated by Euclid, that although the proposi- tion be at first enunciated in general terms, and after-
20 ELEMENTS OF THE PHILOSOPHY
wards appealed to, m its particular applications, as a prin- ciple previously examined and admitted, yet that the truth is not less evident in the latter case than in the former. He observes farther, that it is in some of its particular applications, that the truth of every axiom is originally perceived by the mind ; and, therefore, that the general proposition, so far from being the ground of our assent to the truths which it comprehends, is only a verbal generalization of what, in particular instances, has been already acknowledged as true.
The same author remarks, that some of these axioms " are no more than bare verbal propositions, and teach us nothing but the respect and import of names one to another. The lohole is equal to all its parts : what real truth, I beseech you, does it teach us ? What more is contained in that maxim, than what the signification of the word totum, or the lohole, does of itself import 1 And he that knovv^s that the word whole stands for what is made up of all its parts, knows very little less, than that ' the whole is equal to all its parts.' And upon the same ground, I think, that this proposition, A hill is higher than a valley, and several the hke, may also pass for maxims."
Notwithstanding these considerations, Mr. Locke does not object to the form which Euchd has given to his ax- ioms, or to the place which he has assigned to them in his Elements. On the contrary, he is of opinion, that a collection of such maxims is not ivithout reason prefixed to a mathematical system ; in order that learners, " hav- ing in the beginning perfectly acquainted their thoughts with these propositions made in general terms, may have them ready to apply to all particular cases as formed rules and sayings. Not that, if they be equally weigh- ed, they are more clear and evident than the instances they are brought to confirm ; but that, being more famil- iar to the mind, the very naming them is enough to sat- isfy the understanding." In farther illustration of this, he adds, very justly and ingeniously, that, " although our knowledge begins in particulars, and so spreads itself by degrees to generals ; yet afterwards, the mind takes quite the contrary course, and having drawn its know-
OF THE HUMAN MIND. 21
ledge into as general propositions as it can, makes them familiar to its thoughts, and accustoms itself to have re- course to them, as to the standards of truth and false- hood."
But although, in mathematics, some advantage may be gained, without the risk of any possible inconvenience, from this arrangement of axioms, it is a very dangerous example to be followed in other branches of knowledge, where our notions are not equally clear and precise ; and where the force of our pretended axioms (to use Mr. Lockf^'s words) " reaching only to the sound, and not to the signification of the words, serves only to lead us into confusion, mistakes, and error." For the illus- tration of this remark, I must refer to Locke.
Another observation of this profound writer deserves our attention, while examining the nature of axioms ; — " that they are liot the foundations on which any of the sciences is built ; nor at all useful in helping men for- ward to the discovery of unknown truths." * This ob- servation I intend to illustrate afterwards, in treating of the futility of the syllogistic art. At present I shall only add, to what Mr. Locke has so well stated, that, even in mathematics, it cannot with any propriety be said, that the axioms are the foundation on which the science rests ; or the first principles from which its more recon- dite truths are deduced. Of this I have little doubt that Locke was perfectly aware ; but the mistakes which some of the most acute and enhghtened of his disciples have committed in treating of the same subject, con- vince me, that a further elucidation of it is not altogeth- er superfluous. With this view I shall here introduce a few remarks on a passage in Dr. Campbell's Philosophy of Rhetoric, in which he has betrayed some misappre- hensions on this very point, which a little more attention to the hints already quoted from the Essay on Human Understanding might have prevented. These remarks will, I hope, contribute to place the nature of axioms, more particularly of mathematical axioms, in a different .nd clearer light than that in which they have been com- monly considered.
* Book iv. chap. 7. § 11.— 2, 3.
22 ELEMENTS OF THE PHILOSOPHY
" Of intuitive evidence," says Dr. Campbell, " that of the following propositions may serve as an illustration : * One and four make five. Things equal to the same thing are equal to one another. The whole is greater than a part ; ' and, in brief, all axioms in arithmetic and geometry. These are, in effect, but so many exposi- tions of our own general notions, taken in different views. Some of them are no more than definitions, or equivalent to definitions. To say, ' One and four make five,^ is precisely the same thing as to say, ' We give the name of five to one added to four.' In fact, they are all in some respects reducible to this axiom, ' Whatever is, is.' I do not say they are deduced from it, for they have in like manner that original and intrinsic evidence, which makes them, as soon as the terms are understood, to be perceived intuitively. And, if they are not thus per- ceived, no deduction of reason will ever confer on them any additional evidence. Nay, in point of time, the dis- covery of the less general truths has the priority, not from their superior evidence, but solely from this con- sideration, that the less general are sooner objects of perception to us. But I affirm, that though not dedu- ced from that axiom, they may be considered as partic- ular exemplifications of it, and coincident with it, inas- much as they are all implied in this, that the properties of our clear and adequate ideas can be no other than what the mind clearly perceives them to be.
" But, in order to prevent mistakes, it will be neces- sary further to illustrate this subject. It might be thought that, if axioms were propositions perfectly iden- tical, it would be impossible to advance a step by their means, beyond the simple ideas first perceived by the mind. And it must be owned, if the predicate of the proposition were nothing but a repetition of the subject, under the same aspect, and in the same or synonymous terms, no conceivable advantage could be made of it for the furtherance of knowledge. Of such propositions, for instance, as these * Seven are seven," Eight are eight,' and ' Ten added to eleven are equal to ten added to elev- en,' \i is manifest that we could never avail ourselves for the improvement of science. Nor does the change of
OF THE HUMAN MIND. 23
the term make any alteration in point of utility. The propositions, ' Twelve are a dozen,' ' Twenty are a score,' unless considered as explications of the words doze7i and score, are equally insignificant with the former. But when the thing, though in effect coinciding, is con- sidered under a different aspect, when what is single in the subject is divided in the predicate, and conversely ; or when what is a whole in the one is regarded as a part of something else in the other ; such propositions lead to the discovery of innumerable and apparently re- mote relations. One added to four may be accounted no other than a definition of the word Jive, as was re- marked above. But when I say, ' Two added to three are equal to five,' I advance a truth which, though equally clear, is quite distinct from the preceding. Thus, if one should affirm, that ' Twice fifteen make thirty,' and again, that ' Thirteen added to seventeen make thirty,' nobody would pretend that he had repeat- ed the same proposition in other words. The cases are entirely similar. In both cases, the same thing is predi- cated of ideas which, taken severally, are different. From these again result other equations, as, ' One added to four are equal to two added to three,' and ' Twice fif- teen are equal to thirteen added to seventeen.'
" Now, it is by the aid of such simple and elementa- ry principles, that the arithmetician and algebraist pro- ceed to the most astonishing discoveries. Nor are the operations of the geometrician essentially different."
I have little to object to these observations of Dr. Campbell, as far as they relate to arithmetic and to alge- bra ; for, in these sciences, all our investigations amount to nothing more than to a comparison of different ex- pressions of the same thing. Our common language, indeed, frequently supposes the case to be otherwise ; as when an equation is defined to be, " A proposition asserting the equality of two quantities." It would, however, be much more correct to define it, " A propo- sition asserting the equivalence of two expressions of the same quantity ; " for algebra is merely a universal arithmetic ; and the names of numbers are nothing else than collectives, by which we are enabled to express
24 ELEMENTS OF THE PHILOSOPHY
ourselves more concisely than could be done by enume- rating all^'the units that they contain. Of this doctrine, the passage now quoted from Dr. Campbell shows, that he entertained a sufficiently just and precise idea.
But if Dr. Campbell perceived that arithmetical equations, such as " one and four make five," are no other than definitions, why should he have classed them with the axioms he quotes from Euchd, " That the whole is greater than a part," and that " Things equal to the same thing, are equal to one another ; " proposi- tions which, however clearly their truth be imphed in the meaning of the terms of which they consist, cannot certainly, by any interpretation, be considered in the hght of definitions at all analogous to the former? The former, indeed, are only explanations of the relative import of particular names ; the latter are universal propositions, applicable alike to an infinite variety of instances.*
Another very obvious consideration might have satis- fied Dr. Campbell, that the simple arithmetical equations which he mentions, do not hold the same place in that science which Euchd's axioms hold in geometry. What I allude to is, that the greater part of these axioms are equally essential to all the different branches of mathe- matics. That " the whole is greater than a part," and that " things equal to the same thing are equal to one another," are propositions as essentially connected with our arithmetical computations, as with our geometrical reasonings ; and, therefore, to explain in what manner
* D'Alembert also has confounded these two classes of propositions. " Vi^hat do the greater part of those axioms on which geometry prides itself amount to, but to an expression, by means of two different words or signs, of the same simple idea ? He who says that two and two make four, what more does he know than another who should content himself with saying, that two and two make two and two ? " — Here a simple arithmetical equation (which is obviously a mere definition) is brought
to illustrate a remark on the nature of geometrical axioms. With respect to
these last (I mean such axioms as Euclid has prefixed to his Elements) D'Alembert's opinion seems to coincide exactly with that of Locke, already mentioned. " I would not be understood, nevertheless, to condemn the use of them altogether : I wish only to remark, that their utility rises no higher than this, that they render our simple ideas more familiar by means of habit, and better adapted to the different purposes to which we may have occasion to apply them." — " Je ne pretends point cependant en condamner absolument I'usage : je veux seulcment faire observer, a quoi il sc reduit ; c'est a nous rendre les idees simples plus familieres par I'habitude, et plus propres aux differens usages auxquels nous pouvons les appliquer. — Discours Preliminaire, &c. &c.
OF THE HUMAM" MIWD. 25
the mind makes a transition, in the case of numbers, from the more simple to the more comphcatecl equations, throws no hght whatever on the question, how the tran- sition is made, either in arithmetic, or in geometry, from what are properly called axioms, to the more remote conclusions in these sciences.
The very fruidess attempt thus made by this acute writer to illustrate the importance of axioms as the ba- sis of mathematical truth, was probably suggested to him by a doctrine which has been repeatedly inculcated of late, concerning the grounds of that pecuhar evidence which is allowed to accompany mathematical demon- stration. " All the sciences," it has been said, " rest ultimately on first principles, which we must take for granted without proof; and whose evidence determines, both in kind and degree, the evidence which it is possi- ble to attain in our conclusions. In some of the scien- ces, our first principles are intuitively certain ; in others, they are intuitively probable ; and such as the evidence of these principles is, such must that of our conclusions be. If our first principles are intuitively certain, and if we reason from them consequentially, our conclusions will be demonstratively certain : but if our principles be only intuitively probable, our conclusions will be only demonstratively probable. In mathematics, the first principles from which we reason are a set of axioms which are not only intuitively certain, but of w^hich we find it impossible to conceive the contraries to be true : And hence the peculiar evidence which belongs to all the conclusions that follow from these principles as ne- cessary consequences."
To this view of the subject Dr. Reid has repeatedly given his sanction, at least in the most essential points ; more particularly, in controverting an assertion of Locke's, that " no science is, or hath been built on maxims.'''' — " Surely," says Dr. Reid, " Mr. Locke was not ignorant of geometry, which hath been built upon maxims prefixed to the Elements, as far back as we are able to trace it. But though they had not been prefixed, which was a matter of utility rather than necessity, yet it must be granted, that every demonstration in geome-
VOL. II. 4
26 ELEMENTS OF THE PHILOSOPHY
try is grounded, either upon propositions formerly de- monstrated, or upon self-evident principles." *
On another occasion, he expresses himself thus : " I take it to be certain, that whatever can by just reason- ing, be inferred from a principle that is necessary, must be a necessary truth. Thus, as the axioms in mathe- matics are all necessary truths, so are all the conclu- sions drawn from them ; that is, the whole body of that science."!
That there is something fundamentally erroneous in these very strong statements with respect to the relation which Euclid's axioms bear to the geometrical theorems which follow, appears sufficiently from a consideration which was long ago mentioned by Locke, — that from these axioms it is not possible for human ingenuity to deduce a single inference. "It was not," says Locke " the influence of those maxims which are taken for principles in mathematics, that hath led the masters of that science into those wonderful discoveries they have made. Let a man of good parts know all the maxims generally made use of in mathematics never so perfect- ly, and contemplate their extent and consequences as much as he pleases, he will, by their assistance, I sup- pose, scarce ever come to know, that ' the square of the hypothenuse in a right-angled triangle, is equal to the squares of the two other sides.' The knowledge that * the whole is equal to all it parts,' and, ' if you take equals from equals, the remainders will be equal,' help- ed him not, I presume, to this demonstration. And a man may, I think, pore long enough on those axioms, without ever seeing one jot the more of mathematical truths." X But surely, if this be granted, and if, at the same time, by the first principles of a science be meant those fundamental propositions from which its remoter truths are derived, the axioms cannot, with any consis- tency, be called the First Principles of Mathematics. They have not (it will be admitted) the most distant analogy to what are called the first principles of Natural
* Essays on Intell. Powers, p. (547, 4to edit, t Ibid. p. 577. See also pp. 560, 561, 606. X Essay on Human Understanding, Book IV. chap. xii. § 15.
OF THE HUMAN MIND. 27
Philosophy ; — to those general facts, for example, of the gravity and elasticity of the air, from which may be de- duced, as consequences, the suspension of the mercury in the Torricellian tube, and its fall when carried up to an eminence. According to this meaning of the word, the principles of mathematical science are, not the axi- oms but the definitions ; which definitions hold, in math- ematics, precisely the same place that is held in natural philosophy by such general facts as have now been re- ferred to.*
From what principle are the various properties of the circle derived, but from the definition of a circle ? From what principle the properties of the parabola or ellipse, but from the definitions of these curves ? A similar ob- servation may be extended to all the other theorems which the mathematician demonstrates : And it is this observation (which, obvious as it may seem, does not appear to have occurred, in all its force, either to Locke, to Reid, or to Campbell) that furnishes, if I mistake not, the true explanation of the pecuharity already remarked in mathematical evidence. f
The prosecution of this last idea properly belongs to the subject of mathematical demonstration, of which I
* In order to prevent cavil it may be necessary for me to remark here, that, when I speak of matliematical axioms, I have in view only such as are of the same descrip- tion with ihe first nine of those which are prefixed to the Elements of Euclid ; for, in that list, it is well known, that there are several which belong to a class of ])ropo- sitions altogether different from the others. That " all right angles (for example) are equal to one another ; " that " when one straight line falling on two other straight lines makes the two interior angles on the same side less than two right angles, these two straight lines, if produced, shall meet on the side, where are the two" an- gles less than two right angles ; " are manifestly principles which bear no analogy to such barren truisms as these, " Things that are equal to one and the same thing are equal to one another." " If equals be added to equals, the wholes are equal." " If equals be taken from equals, the remainders are equal." Of these propositions, the two former (the 10th and 11th axioms, to wit, in Euclid's list) are evidently theo- rems which, in point of strict logical accuracy, ought to be demonstrated ; as may be easily done, with respect to the first, in a single sentence. That the second has not yet been proved in a simple and satisfactory manner, has been long considered as a sort of reproach to mathematicians ; and I have little doubt that this reproach will continue to exist, till the basis of the science be somewhat enlarged, by the introduc- tion of one or two new definitions, to serve as additional principles of geometrical reasoning.
For some farther remarks on Euclid's Axioms, see note (A.)
The edition of Euclid to which I uniformly refer, is that of David Gregory. Oxon. 1713.
t D'Alembert, although lie sometimes seems (o speak a difTerent language, ap- proached nearly to this view of the subject when he wrote the following passage :
" Finally, it is not without reason thatmathcmalicians cousider definitions tus prin-
28 ELEMENTS OF THE PHILOSOPHY
intend to treat afterwards. In the mean time, I trust, that enough has been said to correct those misapprehen- sions 9f the nature of axioms, which are countenanced by the speculations, and still more by the phraseology, of some late eminent writers. On this article, my own opinion coincides very nearly with that of Mr. Locke — both in the view which he has given of the nature and use of axioms in geometry, and in what he has so forci- bly urged concerning the danger, in other branches of knowledge, of attempting a similar list of maxims, with- out a due regard to the circumstances by which differ- ent sciences are distinguished from one another. With Mr. Locke, too, I must beg leave to guard myself against the possibility of being misunderstood in the illustrations which I have offered of some of his ideas : And for this purpose, I cannot do better than borrow his words. " In all that is here suggested concerning the httle use of axioms for the improvement of knowledge, or dangerous use in undetermined ideas, I have been far enough from saying or intending they should be laid aside, as some have been too forward to charge me. I affirm them to be truths, self-evident truths ; and so cannot be laid aside. As far as their influence will reach, it is in vain to endeavour, nor w^ould I attempt to abridge it. But yet, wihout any injury to truth or knowledge, I may have reason to think their use is not answerable to the great stress which seems to be laid on them, and I may warn men not to make an ill use of them, for the con- firming themselves in error." *
After what has been just stated, it is scarcely neces- sary for me again to repeat, with regard to mathematical axioms ; that although they are not the principles of our reasoning, either in arithmetic or in geometry, their truth is supposed or impUed in all our reasonings in both ; and, if it were called in question, our further progress would
ciples ; since it is on clear and precise definitions that our knowledge rests in those sciences, where our reasoning fpowers have the widest field opened for their exer- cise."— " Au reste, ce n'est pas sans raison que les mathematiciens regardcnt les definitions comme des principes, puisque, dans les sciences o\\ le raisonnement a la meillcure part, c'est sur des definitions ncttes et exactes que nos connoissances sont appuyces." — Elcmens de Phil. p. 4.
* Locke's Essay, Book IV. ch. vii. § 14. ,
OF THE HUMAN MIJVD. 29
be impossible. In both of these respects, we shall find them analogous to the other classes of primary or ele- mental truths which remain to be considered.
Nor let it be imagined, from this concession, that the dispute turns merely on the meaning annexed to the word principle. It turns upon an important question of fact ; Whether the theorems of geometry rest on the axioms, in the same sense in which they rest on the definitions 7 or (to state the question in a manner still more obvious) Whether axioms hold a place in geometry at all analo- gous to what is occupied in natural philosophy, by those sensible phenomena which form the basis of that sci- ence 1 Dr. Reid compares them sometimes to the one set of propositions and sometimes to the other.* If the foregoing observations be just, they bear no analogy to either.
Into this indistinctness of language Dr. Reid was prob- ably led in part by Sir Isaac Newton, who, with a very illogical latitude in the use of words, gave the name of axioms to the laws of motion,^ and also to those general
* " Mathematics, once fairly established on the foundation of a few axioms and definitions, as upon a rock, has grown from age to age, so as to become the loftiest and the most solid fabric that human reason can boast." — Essays on Int. Powers, p. 561, 4to edition.
" Lord Bacon first delineated the only solid foundation on which natural philosophy can be built ; and Sir Isaac Newton reduced the principles laid down by Bacon into three or four axioms, which he calls reguloe philosophandi. From these, together with the phenomena observed by the senses, which he likewise lays down as first principles, he deduces, by strict reasoning, the propositions contained in the third book of his Principia, and in his Optics ; and by this means has raised a fabric, which is not liable to be shaken by doubtful disputation, but stands immoveable on tlie basis of self-evident principles." — Ibid. See also pp. 647, 648.
t Axionaata, sive leges motias. Vide Philosophice JVaturalis Principia Mathe- matica.
At the beginning, too, of Newton's Optics, the title of axioms is given to the follow- ing propositions :
Axiom I.
" The angles of reflection and refraction lie in one and the same plane with the angle of incidence.
Axiom II.
" The angle of reflection is equal to the angle of incidence.
Axiom III.
" If the refracted ray be turned directly back to the point of incidence, it shall be refracted into the line before described by the incident ray.
Axiom IV.
" Refraction out of the rarer medium into the denser, is made towards the perpen- dicular ; that is, so that the angle of refraction be less than the angle of incidence.
Axiom V.
" The sine of incidence is either accurately, or veiy nearly in a given ratio to the sine of refraction."
30 ELEMENTS OF THE PHILOSOPHY
experimental truths which form the ground-work of our general reasonings in catoptrics and dioptrics. For such a misapphcation of the technical terms of mathematics some apology might perhaps be made, if the author had been treating on any subject connected with moral sci- ence ; but surely, in a work entitled " Mathematical Prin- ciples of Natural Philosophy," the word axiom might reasonably have been expected to be used in a sense somewhat analogous to that which every person liberally educated is accustomed to annex to it, when he is first initiated into the elements of geometry.
The question to which the preceding discussion re- lates is of the greater consequence, that the prevaihng mistake with respect to the nature of mathematical axi- oms, has contributed much to the support of a very erroneous theory concerning mathematical evidence, which is, I believe, pretty generally adopted at present, — that it all resolves ultimately into the perception of identi- ty ; and that it is this circumstance which constitutes the pecuhar and characteristical cogency of mathematical demonstration.
Of some of the other arguments which have been al- leged in favor of this theory, I shall afterwards have occasion to take notice. At present it is sufficient for me to remark, (and this I flatter myself I may venture to do with some confidence, after the foregoing reasonings,) that in so far as it rests on the supposition that all geo- metrical truths are ultimately derived from Euclid's axi- oms, it proceeds on an assumption totally unfounded in fact, and indeed so obviously false, that nothing but its antiquity can account for the facihty with which it con- tinues to be admitted by the learned.*
When the word axiom is understood by one writer in the sense annexed to it by Euclid, and by his antagonist in the sense here given to it by Sir Isaac Newton, it is not surprising that there should be apparently a wide diversity between their opinions concerning the logical importance of this class of propositions.
* A late mathematician, of considerable ingenuity and learning, doubtful, it should seem, whether Euclid had laid a sufliciently broad foundation for mathematical sci- ence in the axioms prefixed to his Elements, has thought proper to introduce several now ones of his own invention. The first of these is, that " Every quantity is equal to itself; " to which he adds afterwards, that " A quantity ex|)ressed one way is equal to itself expressed any other way." — See Elements of Mathematical Analysis, by Professor Vilant of St. Andrew's. We are apt to smile at the formal statement of these propositions ; and yet, according to the theory alluded to in the text, it is in
OF THE HUMAN MIND. 31
II.
Continuation of the same Subject.
The difference of opinion between Locke and Reid, of which I took notice in the foregoing part of this sec- tion, appears greater than it really is, in consequence of an ambiguity in the wOrd principle, as employed by the latter. In its proper acceptation, it seems to me to de- note an assumption (whether resting on fact or on hypothesis) upon which, as a datum, a train of reasoning- proceeds ; and for the falsity or incorrectness of which no logical rigor in the subsequent process can compen- sate. Thus the gravity and the elasticity of the air are prhiciples of reasoning in our speculations about the barometer. The equality of the angles of incidence and reflection ; the proportionality of the sines of inci- dence and refraction ; are principles of reasoning in ca- toptrics and in dioptrics. In a sense perfectly analogous to this, the definitions of geometry (all of which are merely hypothetical) are the first principles of reasoning in the subsequent demonstrations, and the basis on which the whole fabric of the science rests.
I have called this the proper acceptation of the word, because it is that in which it is most frequently used by the best writers. It is also most agreeable to the lit- eral meaning which its etymology suggests, expressing the original point from which our reasoning sets out or commences.
Dr. Reid often uses the word in this sense, as, for example, in the following sentence, already quoted: "From three or four axioms, which he calls regidm phi- losophandi, together with the phenomena observed hij the senses, ivhich he likewise lays down as first principles, Newton deduces, by strict reasoning, the propositions
truths of this very description that the whole science of mathematics not only begins but ends. " Omncs mathematicorum propositiones sunt identicfe, et repnescntantur hac formula, a:=a," This sentence, which I quote from a dissertation, published at Berlin about fifty years ago, expresses, in a few words, what seems to be now the prevailing opinion (more particularly on the Continent) concerning the nature of mathematical evidence. The remarks which I have to offer upon it, 1 delay till some other questions shall be previously considered.
32 ELEMENTS OF THE PHILOSOPHY
contained in the third book of his Principia, and in his Optics."
On other occasions, he uses the same word to de- note those elemental truths (if I may use the expression) which are virtually taken for granted or assumed, in every step of our reasoning ; and without which, al- though no consequences can be directly inferred from them, a train of reasoning would be impossible. Of this kind in mathematics, are the axioms, or (as Mr. Locke and others frequently call them) the maxims; in physics, a belief of the continuance of the Laws of JYature ; — in all our reasonings without exception, a belief in our own identity., and in the evidence of mem- ory. Such truths are the last elements into which reasoning resolves itself, when subjected to a meta- physical analysis ; and which no person but a metaphy- sician or a logician ever thinks of stating in the form of propositions, or even of expressing verbally to himself. It is to truths of this description that Locke seems in general to apply the name of maxims; and, in this sense, it is unquestionably true, that no science (not even geometry) is founded on maxims as its first prin- ciples.
In one sense of the word principle, indeed, maxims may be called principles of reasoning ; for the words principles and elements are sometimes used as synony- mous. Nor do I take upon me to say that this mode of speaking is exceptionable. All that I assert is, that they cdiViRoihQ c2[\q^ principles of reasoning, m. the sense which has just now been defined ; and that accuracy requires, that the word, on which the whole question hinges, should not be used in both senses, in the course of the same argument. It is for this reason that I have em- ployed the phrase principles of reasoning on the one oc- casion, and elements of reasoning on the other.
It is difficult to find unexceptionable language to mark distinctions so completely foreign to the ordinary purposes of speech ; but, in the present instance, the line of separation is strongly and clearly drawn by this criterion, — that from principles of reasoning consequen- ces may be deduced ; from what I have called elements of reasoning, none ever can.
OF THE HUMAN MIND. 33
A process of logical reasoning has been often liken- ed to a chain supporting a weight. If this simihtude be adopted, the axioms or elemental truths now mention- ed, may be compared to the successive concatenations which connect the different links immediately with each other; the principles of our reasoning resemble the hook, or rather the beam, from which the whole is sus- pended.
The foregoing observations, I am inclined to think, coincide with what was, at bottom, Mr. Locke's opinion on this subject. That he has not stated it with his usual clearness and distinctness, it is impossible to de- ny ; at the same time, I cannot subscribe to the follow- ing severe criticism of Dr. Reid :
" Mr. Locke has observed, ' That intuitive knowledge is necessary to connect all the steps of a demonstration.'
"From this, I think, it necessarily follows, that in every branch of knowledge, we must make use of truths that are intuitively known, in order to deduce from them such as require proof.
" But I cannot reconcile this with what he says, (section 8th of the same chapter ;) * The necessity of this intuitive knowledge in every step of scientifical or demonstrative reasoning, gave occasion, I imagine, to that mistaken axiom, that all reasoning was ex prcecog- nitis et prcBConcessis^ which how far it is mistaken I shall have occasion to show more at large when I come to consider propositions, and particularly those propo- sitions which are called maxims, and to show that it is by a mistake that they are supposed to be the founda- tion of all our knowledge and reasonings.' " *
The distinction which I have already made between elements of reasoning, and first principles of reasoning, appears to myself to throw much light on these apparent contradictions.
That the seeming difference of opinion on this point between these two profound writers, arose chiefly from the ambiguities of language, may be inferred from the
* Essays on Int. Powers, p. G43, 4to. edit. VOL. II. 5
34 ELEMEIVTS OF THE PHILOSOPHY
following acknowledgment of Dr. Reid, which immedi- ately follows the last quotation :
" I have carefully examined the chapter on maxims, which Mr. Locke here refers to, and though one would expect, from the quotation last made, that it should run contrary to what I have before delivered concerning first principles, I find only two or three sentences in it, and those chiefly incidental, to which I do not assent." *
Before dismissing this subject, I must once more re- peat, that the doctrine which I have been attempting to establish, so far from degrading axioms from that rank which Dr. Reid would assign them, tends to identify them still more than he has done with the exercise of our reasoning powers ; inasmuch as, instead of compar- ing them with the data, on the accuracy of which that of our conclusion necessarily depends, it considers them as the vincula which give coherence to all the particular links of the chain ; or (to vary the metaphor) as component elem.ents, without which the faculty of rea- soning is inconceivable and impossible, f
• Essays on Int. Powers, p. 643, 4to edit.
t D'Alembert has delined the word principle exactly in the sense in which I have used it; and has expressed himself (at least on one occasion) nearly as I have done, on the subject of- axioms. He seems however on this, as well as on some other logical and metaphysical questions, to have varied a little in his views (proba- bly from mere forgetfulness) in different parts of his writings.
" What then are the truths which are entitled to have a place in the elements of philosophy .' They are of two kinds ; those which form the head of each part of the chain, and those which are to be found at the points where different branches of the chain unite together.
" Truths of the first kind are distinguished by this — that they do not depend on any other truths, and that they possess within themselves the whole grounds of their evidence. Some of my readers will be apt to suppose, that I here mean to speak of axioms ; but these are not the truths which I have at present in view. With respect to this last class oi principles, I must refer to what I have elsewhere said of them ; that, notwithstanding their truth, they add nothing to our information; and that the palpable evidence which accompanies them, amounts to nothing more than to an expression of the same idea by means of two different terms. On such occasions, the mind only turns to no purpose about its own axis, without advancing forward a single step. Accordingly, axioms are so far from holding the highest rank in philosophy, that they scarcely deserve the distinction of being formally enunciated."
" Or quelles sent les verites qui doivent entrer dans des elemens de philosophie ? II y en a de deux sortes ; celles qui forment la tete de chaque partie de la chatne, et celles qui se trouvent au point de reunion de plusieurs branches.
" Les verites du premier genre ont pour caractere distinctif de ne dependre d'aucune autre, et de n'avoir de preuves que dans elles-raemes. Plusieurs lecteurs croiront que nous voulons parler des axioms, et ilS se tromperont ; nous les renvoy- ons a ce que nous en avons dit ailleurs, que ces sortes de principes ne nous appren- ncnt rien a force d'etre vrais, et que lour evidence palpable ct grossiere se reduit a exprimer la meme idee par deux termes differens ; I'esprit ne fait alors autre chose que tourner inutilement sur lui-meme sans avancer d'un seul pas. Ainsi les axioms,
OP THE HUMAN MIND. 35
SECTION II.
Of certain Laws of Belief, inseparably connected with the Exeicise of Consciousness, Memory, Perception, and Reasoning,
1. It is by the immediate evidence of consciousness that we are assured of the jwesent existence of our vari- ous sensations, whether pleasant or painful ; of all our affections, passions, hopes, fears, desires, and vohtions. It is thus too we are assured of the present existence of those thoughts which, during our waking hours, are continually passing through the mind, and of all the dif- ferent effects which they produce in furnishing employ- ment to our intellectual faculties.
According to the common doctrine of our best phi- losophers,* it is by the evidence of consciousness we are assured that we ourselves exist. The proposition, how- ever, when thus stated, is not accurately true ; for our own existence (as I have elsewhere observed,!) is not a direct or immediate object of consciousness, in the
bien loin de tenir en philosophie le premier rang, n'ontpasmeme besoin d'etre enon- ces." — Elem de Phil. pp. 24, 25.
Although in the foregoing passage, D'Alembert, in compliance with common phraseology, has bestowed the name of principles upon axioms, it appears clearly, from a question which occurs afterwards, that he did not consider them as well enti- tled to this appellation. " What are then," he asks, " in each science, the true prin- ciples from which we ought to set out ? " (" Quels sont done dans chaque science \qs vrais principes A' OU.V on do'ii partir?") The answer he gives to this question agrees with the doctrine I have stated in every particular, excepting in this, that it represents (and in my opinion very incorrectly) the principles of geometrical science to be (not definitions or hypotheses, but) those simple and acknowledged facts, which our senses perceive with respect to the properties of extension. " The true principles from which we ought to set out in the different sciences, are simple and acknowledged /ac^s, which do not presuppose the existence of any others, and which of course it is equally vain to attempt explaining or confuting ; in physics, the famil- iar phenomena which daily experience presents to every eye ; in geometry the sen- sible properties of extension; in mechanics, the impenetrability of bodies, upon which their mutual actions depend ; in metaphysics, the results of our sensations ; in morals, the original and conunon afiections of the human race." — " Les vrais principes d'ou I'on doit partir dans chaque science, sont des fails simples et reconnus, qui n'en supposcnt point d'autres, et qu'on ne puisse par consequent ni expliquer ni contester; en physique les phenomenes journaliers que I'observation decouvre a tons les yeux ; in geometrie les proprietcs sdnsibles de V 6t endue ; en mecanique, I'impenctrabilite des corps, source de leur action mutuelle ; en metaphysique, le re- sultat de nos sensations ; en morale, les aflections premieres et communes a tous les horames." — pp. 26, 27.
In cases of this sort, where so much depends on extreme precision and nicety in the use of words, it appears to me to be proper to verify the lidelity of my transla- tions by sul)joining the original passages.
* See, in particular, Campbell's Philosophy of Rhetoric.
t Philosophical Essays, 4to edit. p. 7.
36 ELEMENTS OF THE PHILOSOPHY
strict and logical meaning of that term. We are con- scious of sensation, thought, desire, volition: but we are not conscious of the existence of mind itself ; nor would it be possible for us to arrive at the knowledge of it (supposing us to be created in the full possession of all the intellectual capacities which belong to human nature,) if no impression were ever to be made on our external senses. The moment that, in consequence of such an impression, a sensation is excited, we learn two facts at once ; — the existence of the sensation, and our own existence as sentient beings ; — in other words, the very first exercise of consciousness necessarily implies a behef, not only of the present existence of what is felt, but of the present existence of ^^a/ which feels and thinks ; or (to employ plainer language) the present existence of that being which I denote by the words / and myself. Of these facts, however, it is the former alone of which we can properly be said to be conscious, agreeably to the rigorous interpretation of the expres- sion. A conviction of the latter, although it seems to be so inseparable from the exercise of consciousness, that it can scarcely be considered as posterior to it in the order of time, is yet (if I may be allowed to make use of a scholastic distinction) posterior to it in the or- der of nature ; not only as it supposes consciousness to be already awakened by some sensation, or some other mental affection ; but as it is evidently rather a judg- ment accompanying the exercise of that power, than one of its immediate intimations concerning its appro- priate class of internal phenomena. It appears to me, therefore, more correct to call the belief of our own existence a concomitant or accessory of the exercise of consciousness, than to say, that our existence is a fact falling under the immediate cognizance of conscious- ness, like the existence of the various agreeable or pain- ful sensations which external objects excite in our minds.
2. That we cannot, without a very blameable latitude in the use of words, be said to be conscious of our personal identity, is a proposition still more indisputable; inasmuch as the very idea of personal identity involves
OF THE HUMAN^ MIND.
37
the idea of time, and consequently presupposes the ex- ercise not only of consciousness but of memory. The belief connected with this idea is impUed in every thought and every action of the mind, and may be justly regarded as one of the simplest and most essential ele- ments of the understanding. Indeed it is impossible to conceive either an intellectual or an active being to ex- ist without it. It is, however, extremely worthy of re- mark, with respect to this belief, that, universal as it is among our species, nobody but a metaphysician ever thinks of expressing it in words, or of reducing into the shape of a proposition the truth to which it relates. To the rest of mankind, it forms not an object of knowl- edge : but a condition or supposition, necessarily and un- consciously involved in the exercise of all their faculties. On a part of our constitution, which is obviously one of the last or primordial elements at which it is possible to arrive in analyzing our intellectual operations, it is plain- ly unphilosophical to suppose, that any new light can be thrown by metaphysical discussion. All that can be done with propriety, in such cases, is to state the fact. And here, I cannot help taking notice of the absurd and inconsistent attempts which some ingenious men have made, to explain the gradual process by which they suppose the mind to be led to the knowledge of its own existence, and of that continued identity which our constitution leads us to ascribe to it. How (it has been asked) does a child come to form the very abstract and metaphysical idea expressed by the pronoun / or moi 1 In answer to this question, I have only to observe, that when we set about the explanation of a phenome- non, we must proceed on the supposition that it is pos- sible to resolve it into some more general law or laws with which we are already acquainted. But, in the case before us, how can this be expected, by those who con- sider that all our knowledge of mind is derived from the exercise of reflection ; and that every act of this power implies a conviction of our own existence as re- flecting and intelhgent beings ? Every theory, therefore, which pretends to account for this conviction, must ne- cessarily involve that sort of paralogism which logicians
38 ELEMENTS OF THE PHILOSOPHY
call a pefitio principii ; inasmuch as it must resolve the thing to be explained into some law or laws, the evi- dence of which rests ultimately on the assumption in question. From this assumption, which is necessarily imphed in the joint exercise of consciousness and mem- ory, the philosophy of the' human mind, if we mean to study it analytically, must of necessity set out ; and the very attempt to dig deeper for its foundation, betrays a total ignorance of the logical rules, according to which alone it can ever be prosecuted with any hopes of suc- cess.
It was, I beheve, first remarked by M. Prevost of Geneva, (and the remark, obvious as it may appear, reflects much honor on his acuteness and sagacity,) that the inquiries concerning the mind, founded on the hypothesis of the animated statue — inquiries which both Bonnet and Condillac professed to carry on analytically, — were in truth altogether synthetical. To this criti- cism it may be added, that their inquiries in so far as they had for their object to explain the origin of our belief of our own existence, and of our personal identity, assumed, as the principles of their synthesis, facts at once less certain and less familiar than the problem which they were employed to resolve.
Nor is it to the metaphysician only, that the ideas of identity and of personality are familiar. Where is the individual who has not experienced their powerful influ- ence over his imagination, while he was employed in re- flecting on the train of events which have filled up the past history of his life ; and on that internal world, the phe- nomena of which have been exposed to his own inspec- tion alone 1 On such an occasion, even the wonders of external nature seem comparatively insignificant ; and one is tempted (with a celebrated French writer) in contemplating the spectacle of the universe, to adopt the words of the Doge of Genoa when he visited Ver- sailles— " Ce qui m'etonne le plus ici, c'est de m'y
3. The belief which aU men entertain of the exist-
' D'Alembert, Apologie de FEtude.
OF THE HUMAN MIND. 39
ence of the material world, (I mean their behef of its existence independenly of that of percipient beings,) and their expectation of the continued uniformity of the laws of nature, belong to the same class of ultimate or elemental laws of thought, with those which have been just mentioned. The truths which form their ob- jects are of an order so radically different from what are commonly called truths, in the popular acceptation of that word, that it might perhaps be useful for logicians to distinguish them by some appropriate appellation, such, for example, as that of metaphysical or transcenden- tal truths. They are not principles or data (as will after- wards appear) from which any consequence can be deduced ; but form a part of those original stamina of human reason, which are equally essential to all the pursuits of science, and to all the active concerns of life.
4. I shall only take notice farther, under this head, of the confidence which we must necessarily repose in the evidence of memory (and I may add, in the continuance of our personal identity) when we are employed in car- rying on any process of deduction or argumentation ; in following out, for instance, the steps of a long mathe- matical demonstration. In yielding our assent to the conclusion to which such a demonstration leads, we evi- dently trust to the fidelity with which our memory has connected the different links of the chain together. The reference which is often made, in the course of a de- monstration, to propositions formerly proved, places the same remark in a light still stronger ; and shows plainly that, in this branch of knowledge, which is justly con- sidered as the most certain of any, the authority of the same laws of belief which are recognised in the ordinary pursuits of life, is tacitly acknowledged. Deny the evi- dence of memory as a ground of certain knowledge, and you destroy the foundations of mathematical science, as completely as if you were to deny the truth of the axioms assumed by EucHd.
The foregoing examples sufficiently illustrate the na- ture of that class of truths which I have called Funda- mental Laws of Human Belief, or Primary Elements of Human Reason. A variety of others, not less important,
40 ELEMENTS OF THE PHILOSOPHY
might be added to the list ; * but these I shall not at present stop to enumerate, as my chief object, in intro- ducing the subject here, was to explain the common relation in which they all stand to deductive evidence. In this point of view two analogies, or rather coinci- dences, between the truths which we have been last considering, and the mathematical axioms which were treated of formerly, immediately present themselves to our notice.
1. From neither of these classes of truths can any direct inference be drawn for the farther enlargement of our knowledge. This remark has been already shown to hold universally with respect to the axioms of geom- etry ; and it applies equally to what I have called Fun- damental Laws of Human Belief. From such proposi- tions as these, I exist; I am the same pe^'son to-day that I was yesterday ; the material world has an existence inde- pendent of my mind ; the general laws of nature will con- tinue in future^ to operate uniformly as in time past, no inference can be deduced, any more than from the intui- tive truths prefixed to the Elements of Euclid. Abstract- ed from other data, they are perfectly barren in them- selves ; nor can any possible combination of them help the mind forward, one single step, in its progress. It is for this reason, that, instead of calling them, with some other writers, first principles, I have distinguished them by the title oi fundamental laws of belief ; the former word seeming to me to denote, according to common usage, some/ac^, or some supposition, from which a series of consequences may be deduced.
If the account now given of these laws of belief be just, the great argument which has been commonly urged in support of their authority, and which manifestly con- founds them with what are properly called principles of reasoning,] is not at all applicable to the subject ; or at
* Such for example, as our belief of the existence oi efficient causes ; our belief of the existence of other intelligent beings besides ourselves, &c. &c.
f Aristotle himself has more than once made this remark ; more particularly, in dis- cussing the absurd question, Whether it be ])ossible for the same thing to be and not to be ? ' K^toufft 31 xa) rouro oiTtoBtiKvivat rivls S;' a,7roiiotiiiriav • %ari yap ec^aiScua'icc, to fin yivcitrictiv rivav ii7 'i*irtTv a^oSti^iVf x.a) fivuv oh Ssr. o\us (Jt'h ya,^ oc^rivruv u^uvurov iiVO"
OF THE HUMAN MIND. 41
least does not rest the point in dispute upon its right foundation. If there were no first principles (it has been said) or, in other words, if a reason could be given for every thing, no process of deduction could possibly be brought to a conclusion. The remark is indisputably true ; but it only proves (what no logician of the present times will venture to deny) that the mathematician could not demonstrate a single theorem, unless he were first allowed to lay down his definitions ; nor the natural philosopher explain or account for a single phenomenon, unless he w^ere allowed to assume, as acknowledged facts, certain general laws of nature. Wliat inference does this afford in favor of that particular class of truths to which the preceding observations relate, and against which the ingenuity of modern sceptics has been more particularly directed ? If I be not deceived, these truths are still more intimately connected with the operations of the reasoning faculty than has been generally imagin- ed ; not as the principles (dg^^al) from which our reason- ings set out, and on which they ultimately depend ; but as the necessary co7iditions on which every step of the deduction tacitly proceeds ; or rather (if I may use the expression) as essential elements which enter into the composition of reason itself.
2. In this last remark, I have anticipated, in some measure, what I had to state with respect to the second coincidence alluded to, between mathematical axioms, and the other propositions which I have comprehended under the general title of fundamental laws of human be- lief As the truth of axioms is virtually presupposed or
Ss/^/v iivat u; afu^ev ya^ an fiai'i^et • acrt (t.'nS ovrcas iJvai ci^oSti^it. — Aristot. Meta- phi/s. Vol. II, p. 873. Edit. Da V';il.
" But there are some who, through ignorance, malcc an attempt to prove even this principle, (that it is impossible for the same thing to be and not to be.) For it is a mark of ignorance, not to be able to distinguish those things which ought to be de- monstrated from things cf which no demonstration should be attempted. In truth, it is altogether impossible that every thing should be susccptil)Ic of demonstration ; otherwise the process would extend to infinity, and, after all our labor, nothing would be gained." In the sentence immediately preceding this quotation, Aristotle calls the maxim in question, (itSaiorccTn tuv a^x'^^ ^a<rav, " the most certain of all principles."
To the same purpose Dr. Reid has said : " I hold it to be certain and even demon- strable, that all knowledge got by reasoning must be built on first principles. This," he adds, " is as certain as that every house must have a foundation." — Essays on Int. Powers, p. 558. 4to edit.
VOL. I. 6
42 ELEMENTS OF THE PHILOSOPHY
implied in the successive steps of every demonstration, so, in every step of our reasonings concerning the order of Nature, we proceed on the supposition, that the laws by which it is regulated will continue uniform as in time past; and that the material universe has an existence independent of our perceptions. I need scarcely add, that, in all our reasonings whatever, whether they relate to necessary or to contingent truths, our own personal identity, and the evidence of memory, are virtually taken for granted. These different truths all agree in this, that they are essentially involved in the exercise of our rational powers : although, in themselves, they furnish no principles or data by which the sphere of our knowledge can, by any ingenuity, be enlarged. They agree farther in being tacitly acknowledged by all men, learned or ignorant, without any formal enunciation in words, or even any conscious exercise of reflection. It is only at that period of our intellectual progress when scientific arrangements and metaphysical refinements begin to be introduced, that they become objects of attention to the mind, and assume the form of propositions.
In consequence of these two analogies or coinciden- ces, I should have been inclined to comprehend, under the general title of axioms, all the truths which have been hitherto under our review, if the common usage of our language had not, in a great measure, appropriated that appellation to the axioms of mathematics ; and if the view of the subject which I have taken, did not render it ne- cessary for me to direct the attention of my readers to the wide diversity between the branches of knowledge to which they are respectively subservient.
I was anxious also to prevent these truths from being all identified, in point of logical importance, under the same name. The fact is, that the one class, (in conse- quence of the relation in which they stand to the demon- strative conclusions of geometry, are comparatively of so little moment, that the formal enumeration of them was a matter of choice rather than of necessity ; where- as the other class have unfortunately been raised, by the sceptical controversies of modern times, to a conspicuous rank in the philosophy of the human mind. I have
OF THE HUMAN MIND. 43
thought it more advisable, therefore, to bestow on the latter an appropriate title of their own ; without, howev- er, going so far, as to reject altogether the phraseology of those who have annexed to the word axiom a more enlarged meaning than that which I have usually given to it. Little inconvenience, indeed, can arise from this latitude in the use of the term ; provided only it be always confined to those ultimate laws of belief, which, although they form the first elements of human reason, cannot vt^ith propriety be ranked among the principles from which any of our scientific conclusions are de- duced.
Corresponding to the extension which some late wri- ters have given to axioms, is that of the province which they have assigned to intuition ; a term which has been apphed, by Dr. Beattie and others, not only to the power by which we perceive the truth of the axioms of geom- etry, but to that by which we recognise the authority of the fundamental laws of behef, when we hear them enunciated in language. My only objection to this use of the word is, that it is a departure from common prac- tice ; according to which, if I be not mistaken, the proper objects of intuition are propositions analogous to the axioms prefixed to Euchd's Elements. In some other respects, this innovation might perhaps be regarded as an improvement on the very limited and imperfect vo- cabulary of which we are able to avail ourselves in our present discussions.*
To the class of truths which I have here called laws of belief, or elements of reason, the title of principles of common sense was long ago given by Father Buffier,
* According to Locke, we have the knowledge of our own existence by intuition ; of the existence of God by demonstration ; and of other things by sensation. Book iv. Chap. 9. § 2. ■
Xiiis use of the word intuition seems to be somewhat arbitrary. The reality of our own existence is a truth which bears as little analogy to the axioms of mathematics, as any other primary truth whatever. If the province of intuition, therefore, be ex- tended as far as it has been carried by Locke in the foregoing sentence, it will not be easy to give a good reason why it should not be enlarged a little farther. The words intuition and demonstration, it must not be forgotten, have, both of them, an ety- mological reference to the sense of seeing ; and when we wish to express, in the strongest terms, the most complete evidence which can be set before the mind, we compare it to the light of noon-day : — in other words, we compare it to what Mr. Locke here attempts to degrade, by calling it the evidence of sensation.
44 ELEMENTS OF THE PHILOSOPHY
whose language and doctrine concerning them bears a very striking resemblance to those of some of our later Scotish logicians. This, at least, strikes me as thfe meaning which these writers in general annex to the phrase ; although all of them have frequently employed it with a far greater degree of latitude. When thus limited in its acceptation, it is obviously hable, in point of scientific accuracy, to two very strong objections, both of which have been already sufficiently illustrated. The first is, that it applies the appellation of principles to laws of behef from which no inference can be dedu- ced ; the second, that it refers the origin of these laws to common sense.* Nor is this phraseology more agreeable to popular use than to logical precision. If we were to suppose an individual, whose conduct be- trayed a disbehef of his own existence, or of his own identity, or of the reality of surrounding objects, it would by no means amount to an adequate description of his condition to say, that he was destitute of common sense. We should at once pronounce him to be destitute of reason, and would no longer consider him as a fit subject of discipline or of punishment. The former expression, indeed, would only imply that he was apt to fall into ab- surdities and improprieties in the common concerns of life. To denominate, therefore, such laws of belief as we have now been considering, constituent elements of human reason, while it seems quite unexceptionable in point of technical distinctness, cannot be justly censured as the shghtest deviation from our habitual forms of speech. On the same grounds, it may be fairly ques- tioned, whether the word reason would not on some occasions, be the best substitute which our language affords for intuition, in that enlarged acceptation which has been given to it of late. If not quite so definite and precise as might be wished, it would be at least employed in one of those significations in which it is already fa- miliar to every ear : whereas the meaning of intuition, when used for the same purpose, is stretched very far
* See the preceding part of this section, with respect to the word principle ; and the Account of Hold's Life, for some remarks on the proper meaning of the phrase common sense.
OF THE HU3IAN MIND. 45
beyond its ordinary limits. And in cases of this sort, where we have to choose between two terms, neither of which is altogether unexceptionable, it will be found much safer to trust to the context for restricting, in the reader's mind, what is too general, than for enlarging what use has accustomed us to interpret in a sense too narrow.
I must add too, in opposition to the high authorities of Dr. Johnson and Dr. Beattie,* that for many years past, reason has been very seldom used by philosophical wri- ters, or, indeed, by correct writers of any description, as synonymous with the power of reasoning. To ap- peal to the light of human reason from the reasonings of the schools, is surely an expression to which no good objection can be made, on the score either of vague- ness or of novelty. Nor has the etymological affinity between these two words the slightest tendency to throw any obscurity on the foregoing expression. On the contrary, this affinity may be of use in some of our future arguments, by keeping constantly in view the close and inseparable connexion which will be after- wards shown to exist between the two different intellec- tual operations which are thus brought into immediate contrast.
The remarks which I have stated in the two preced- ing sections, comprehend every thing of essential im- portance which I have to offer on this article of logic. But the space which it has occupied for nearly half a century, in some of the most noted philosophical works which have appeared in Scotland, lays me under the necessity, before entering on a new topic, of introdu- cing in this place, a few critical strictures on the doc- trines of my predecessors.
• Dr. Johnson's definition of Reason was before quoted. The following is that given by Dr. Beattie.
" Reason is used by those who are most accurate in distinguishing, to signify that power of the human mind by which we draw inferences, or by which we are con- vinced, that a relation belongs to two ideas, on account of our having found that these ideas bear certain relations to other ideas. In a word, it is that faculty which enables us, from relations or ideas that are known, to investigate such as are un- known, and without which we never could proceed in the discovery of truth a sin- gle step beyond first principlca or intuitive axioms." — Essaij oil Truth, Part I. Chap. i.
46 ELEMENTS OF THE PHILOSOPHY
SECTION III.
Continuation of the Subject. — Critical Remarks on some late Controversies to which it has given rise. — Of the Appeals which Dr. Reid and some other Modern Writers have made, in their Philosophical Discussions, to Common Sense, as a Criterion of Truth,
I OBSERVED, in a former part of this work, that Dr. Reid acknowledges the Berkeleian system to be a logi- cal consequence of the opinions universally admitted by the learned at the time when Berkeley wrote. In the earlier part of his own life, accordingly, he informs us, that he was actually a convert to the scheme of im- materialism ; a scheme which he probably considered as of a perfectly inoffensive tendency, as long as he conceived the existence of the material world to be the only point in dispute. Finding, however, from Mr. Hume's writings, that along with this paradox, the ideal theory necessarily involved various other consequences of a very different nature, he was led to a careful ex- amination of the data on which it rested ; when he had the satisfaction to discover that its only foundation was a hypothesis, unsupported by any evidence whatever but the authority of the schools.*
From this important concession of a most impartial and competent judge, it may be assumed as a fact, that, till the refutation of the ideal theory in his own " In- quiry into the Human Mind," the partisans of Berkeley's system remained complete masters of the controver- sial field ; and yet, during the long period which inter- vened, it is well known how httle impression that system
* It was not therefore, (as has very generally been imagined by the followers of Berkeley,) from any apprehension of danger in his argument against the existence of matter, that Reid was induced to call in question the ideal theory ; but because he thought that Mr. Hume had clearly shown, by turning Berkeley's weapons against himself, that this theory was equally subversive of the existence of mind. The ultimate object of Berkeley and of Reid was precisely the same ; the one assert- ing the existence of matter from the very same motive which led the other to deny it.
When I speak of Reid's asserting the existence of matter, I do not allude to any new proofs which he has produced of the fact. This he rests on the evidence of sense, as he rests the existence of the mind on the evidence of consciousness. All that he professes to have done is, to show the inconclusiveness of Berkeley's argu- ment ao^ainst the former, and that of Hume against the latter, by refuting the ideal l)ypothesis which is the common foundation of both.
OF THE HUMAN MIND. 47
made on the belief of our soundest philosophers. Many answers to it were attempted, in the mean time, by various authors, both in this country and on the Continent ; and by one or other of these, the generahty of the learned professed themselves to be convinced of its futihty ; — the evidence of the conclusion (as in many other cases) supporting the premises, and not the premises the con- clusion.* A very curious anecdote, in illustration of this, is mentioned in the life of Dr. Berkeley. After the pubhcation of his book, it appears that he had an interview with Dr. Clarke ; in the course of which, Clarke, it is said, discovered a manifest unwillingness to enter into the disscussion, and was accused by Berke- ley of a want of candor.f The story (which, if I re- collect right, rests on the authority of Whiston) has every appearance of authenticity ; for as Clarke, in common with his antagonist, regarded the princi- ples of the ideal theory as incontrovertible, it was per- fectly impossible for him, with all his acuteness, to de- tect the flaw to which Berkeley's paradox owed its plausibihty. In such circumstances, would it have been unphilosophical in Clarke to have defended himself, by saying : " Your conclusion not only contradicts those perceptions of my senses, the evidence of which I feel to be irresistible ; but, by annihilating space itself as an external existence, bids defiance to a conviction insep- arable from the human understanding ; and, therefore,, although I cannot point out the precise oversight which has led you astray, there must necessarily be some er- ror, either in your original data, or in your subsequent
* The impotent, though ingenious attempt of Beikeley (not many years after the date of liis metaphysical publications) to shake the foundation? of the newly invented method of Fluxions, cicatcd, in the public mind, a strong prejudice against him, as a sophistical and paradoxical disputant; and operated as a more powerful antidote to the scheme of imniatcrialism, than all the reasonings which his contem- poraries were able to oppose to it. This unfavorable impression was afterwards not a little confirmed, by the ridicule which he incurred in consequence of his pamphlet on the virtues of Tar-water; a performance, however, of which it is but justice to add, that it contains a great deal more both of sound philosophy and of choice learn- ing, than could have been expected from the subject.
t Philosophical Essays, Note F.
That Clarke would look upon the Berkelelan theory with more than common feel- ings of suspicion and alarm, may be easily conceived, when it is recollected that, by denying the independent existence both of space and of time, it put an end at once to his celebrated argument a priori, for the existence of God.
48 ELEMENTS OF THE PHILOSOPHY
reasoning." Or, supposing Clarke to have perceived, as clearly as Reid, that Berkeley's reasoning was per- fectly unexceptionable, might he not have added ; " The conclusion which it involves is a demonstration in the form of a reductio ad ahsurdum, of the unsoundness of the ideal theory, on which the whole of your argu- ment is built." *
I am far from supposing that Berkeley would have admitted this consideration as decisive of the point in dispute. On the contrary, it appears from his writings, that the scheme of immateriahsm was, in his opinion, more agreeable to popular behef, than the received theories of philosophers concerning the independent existence of the external world ; nay, that he consider- ed it as one of the many advantages likely to result from the universal adoption of his system, that " men would thereby be reduced from paradoxes to common sense."
The question, however, if not decided by this dis- cussion, would at least have been brought to a short and simple issue ; for the paramount authority of the common sense or common reason of mankind, being equally recognised by both parties, all that remained for their examination was whether the belief of the ex- istence, or that of the non-existence of matter, was sanctioned by this supreme tribunal? For ascertaining this point, nothing more was necessary, than an accu-
* I acknowledge, very readily, that the force of this indirect mode of reasoning is essentially different in mathematics, from what it is in the other branches of know- ledge ; for the object of mathematics (as will afterwards more fully appear) not being truth, but systematical connexion and consistency, whenever two contradictory propositions occur, embracing evidently the only possible suppositions on the point in question, if the one can be shown to be incompatible with the definitions or hy- potheses on which the science is founded, this may be regarded as perfectly equiv- alent to a direct proof of the legitimacy of the opposite conclusion. In other scien- ces, the force of a reductio ad ahsurdum depends entirely on the maxim, " That truth is always consistent with itself ; " a maxim which, however certain, rests evi- dently on grounds of a more abstract and metaphysical nature than the indirect demonstrations of geometry. It is a maxim, at the same time, to which the most sceptical writers have not been able to refuse their testimony. " Truth," says Mr. Hume himself, " is one thing, but errors are numberless, and every man has a differ- ent one."
The wni^y, or systematical consistency of truth, is a subject which well deserves to be farther prosecuted. It involves many important consequences, of which Mr. Hume does not, from the general spirit of his philosophy, seem to have been suffi- ciently aware.
OF THE HUMAjV MIND. 49
rate analysis of the meaning annexed to the word exis- tence ; which analysis w^ould have at once shown, not only that we are irresistibly led to ascribe to the mate- rial world all the independent reality which this w^ord expresses, but that it is from the material world that our first and most satisfactory notions of existence are drawn. The mathematical affections of matter (exten- sion and figure) to which the constitution of the mind imperiously forces us to ascribe an existence, not only independent of our perceptions, but necessary and eternal, might more particularly have been pressed upon Berkeley, as proofs how incompatible his notions were with those laws of belief, to which the learned and the unlearned must in common submit.*
But farther, (in order to prevent anj^ cavil about the foregoing illustration,) we shall suppose that Clarke had anticipated Hume in perceiving that the ideal theory went to the annihilation of mind as w^ell as of matter ; and that he had succeeded in proving, to the satisfac- tion of Berkeley, that nothing existed in the universe but impressions and ideas. Is it possible to imagine, that Berkeley would not immediately have seen and acknow- ledged, that a theory which led to a conclusion directly contradicted by the evidence of consciousness, ought not, out of respect to ancient authority, to be rashly admitted ; and that, in the present instance, it was much more philosophical to argue from the conclusion against the hypothesis, than to argue from the hypothesis in proof of the conclusion ? No middle course, it is evident, was left him between such an acknowledgment, and an un- quahfied acquiescence in those very doctrines wdiich it was the great aim of his system to tear up by the roots.
The two chief objections which I have heard urged against this mode of defence, are not perfectly consist- ent with each other. The one represents it as a pre- sumptuous and dangerous innovation in the established rules of philosophical controversy, calculated to stifle entirely a spirit of liberal inquiry : while the other char- ges its authors with all the meanness and guilt of litera-
*See Note (B.) VOL. II. ' 7
50 ELEMENTS OF THE PHILOSOPHY
ry plagiarism. I shall offer a few slight remarks on each of these accusations.
1. That the doctrine in question is not a new one, nor even the language in which it has been recently stated an innovation in the received phraseology of logical sci- ence, has been shown by Dr. Reid, in a collection of very interesting quotations, which may be found in dif- ferent parts of his Essays on the Intellectual Powers of Man, more particularly in the second chapter of the sixth essay. Nor has this doctrine been generally re- jected even by those writers who, in their theories, have departed the farthest from the ordinary opinions of the world. Berkeley has sanctioned it in the most explicit manner, in a passage already quoted from his works, in which he not only attempts the extraordinary task of re- conciling the scheme of immaterialism with the common sense of mankind, but alleges the very circumstance of its conformity to the unsophisticated judgment of the human race as a strong argument in its favor, when con- trasted with the paradoxical doctrine of the independ- ent existence of matter. The ablest advocates, too, for the necessity of human actions, have held a similar lan- guage ; exerting their ingenuity to show, that there is nothing in this tenet which does not perfectly accord with our internal consciousness, when our supposed feel- ings of liberty, with all their concomitant circumstances, are accurately analyzed, and duly weighed.* In this re- spect, Mr. Hume forms almost a solitary exception, avowing, with the greatest frankness, the complete re- pugnance between his philosophy and the laws of be- lief to which all men are subjected by the constitution of their nature. " I dine ; I play a game at backgam- mon ; I converse, and am happy with my friends ; and when, after three or four hours of amusement, I would
• This, I own, appears to me the only argument for the scheme of necessity, which deserves a moment's consideration, in the present state of the controversy : and it is certainly possible to state it in such a form as to give it some degree of plau- sibility to a superficial inquirer. On this point, however, as on many others, our ^rsf and third thoughts will be found perfectly to coincide ; a more careful and profound examination of the question infallibly bringing back to their natural impressions, those who reflect on the subject with candor and with due attention. Having allu- ded to so very important a controversy, I could not help throwing out this hint here. The farther prosecution of it would be altogether foreign to my present purpose.
OF THE HUMAN MIND. 51
return to these speculations, they appear so cold, so strained, and so ridiculous, that I cannot find in my heart to enter into them any further. Here, then, I find my- self absolutely and necessarily determined to live, and talk, and act, hke other people, in the common affairs of life." *
Even Mr. Hume himself, however, seems at times to forget his sceptical theories, and sanctions, by his own authority, not only the same logical maxims, but the same mode of expressing them, which has been so se- verely censured in some of his opponents. " Those," he observes, " who have refused the reahty of moral distinctions, may be ranked among the disingenuous dis- putants. The only way of converting an antagonist of this kind is, to leave him to himself ; for, finding that no- body keeps up the controversy with him, 't is probable he will at last, of himself, from mere weariness, come over to the side of common sense and reason." f
To the authorities which have been already produced by Reid and his successors, in vindication of that mode of arguing which is now under our review, I shall beg leave to add another, which, as far as I know, has not yet been remarked by any of them ; and which, while it effectually removes from it the imputation of novelty, states, in clear and forcible terms, the grounds of that respect to which it is entitled, even in those cases where it is opposed by logical subtilties which seem to baffle all our powers of reasoning.
" What is it," said some of the ancient sophists, " which constitutes what we call httle, much, long, broad, small, or great? Do three grains of corn make a heap 1 The answer must be — No. Do four grains make a heap ? You must make the same answer as be- fore.— They continued their interrogations from one grain to another, without end ; and if you should hap- pen at last to answer. Here is a heap, they pretended your answer was absurd, inasmuch as it supposed, that one single grain makes the difference between what is a
* Treatise of Human Nature, Vol. I. p. 467. t Inquiry concerning the Principles of Morals.
52 ELEMENTS OF THE PHILOSOPHY
heap, and what is not. I might prove, by the same method, that a great drinker is never drunk. Will one drop of wine fuddle him ? — No. Two drops, then 1 By no means ; neither three nor four. I might thus continue my interrogations from one drop to another : and if, at the end of the 999th drop, you answered he is not fuddled, and at the 1000th he is, I should be enti- tled to infer, that one single drop of wine makes the difference between being drunk and being sober ; which is absurd. If the interrogations went on from bottle to bottle, you could easily mark the difference in question. But he who attacks you with a sorites, is at liberty to choose his own weapons : and, by making use of the smallest conceivable increments, renders it impossible for you to name a precise point which fixes a sensible limit between being drunk and being sober ; between what is httle and what is great ; between what is enough and what is too much. A man of the world would laugh at these sophistical quibbles, and would appeal to comraon sense ; to that degree of knowledge which, in common life, is sufficient to enable us to es- tabhsh such distinctions. But to this tribunal a pro- fessed dialectician was not permitted to resort ; he was obliged to answer in form ; and if unable to find a solution according to the rules of art, his defeat was un- avoidable. Even at this day, an Irish Tutor,* who should harass a Professor of Salamanca with similar subtUties, and should receive no other answer but this, — Common sense, and the general consent of mankind, suffi- ciently show that your inferences are false, — would gain the victory ; his antagonist having declined to defend himself with those logical weapons with which the as- sault had been made."
* It is remarkable of this ingenious, eloquent, and gallant nation, that it has been for ages distinguished, in the universities on the Continent, for its proficiency in the school logic. Le Sage (who seems to have had a very just idea of the value of this accomplishment) alludes to this feature in the Irish character, in the account given by Gil Bias of his studies at Oviedo. " Je m'appliquai aussi a la logique, qui ■ni'ap- prit a raisonner beaucoup. J'aimois lant la dispute, que j'arretois les passans, con- nus ou inconnus, pour leur proposer des argumens. Je m'addressois quelquefois a des FIGURES HiBERNoisEs, qui nc demandoient pas mieux, et il falloit alors nous voir disputer. Quels gestes, quelles grimaces, quellcs contorsions ! nos yeux etoient pleins de fureur, ct nos bouches ^cumantes. On nous devoit plutot prendre pour flos possedes que pour des philosophes."
OF THE HUMAN MIND.
53
Had the foregoing passage been read to the late Dr. Priestley, while he was employed in combating the wri- tings of Reid, Oswald, and Beattie, he would, I appre- hend, without hesitation, have supposed it to be the pro- duction of one of their disciples. The fact is, it is a translation from Mr. Bayle, an author who w^as never accused of an undue deference for estabhshed opinions, and who was himself undoubtedly one of the most sub- tile disputants of modern times.*
From this quotation it clearly appears, not only that the substance of the doctrine maintained by these philo- sophers is of a much earlier date than their writings ; but that, in adopting the phrase common sense, to express that standard or criterion of truth to which they appeal- ed, they did not depart from the language previously in use among the least dogmatical of their predecessors.
In the passage just quoted from Bayle, that passion for disputation which, in modern Europe, has so often subjected the plainest truths to the tribunal of metaphys- ical discussion, is, with great justness, traced to the unlimited influence which the school logic maintained for so many ages over the understandings of the learned. And although, since the period when Bayle wrote, this influence has every where most remarkably declined, it has yet left traces behind it, in the habits of thinking and judging prevalent among speculative men, which are but too discernible in all the branches of science con- nected with the philosophy of the mind. In illustration of this remark, it would be easy to produce a copious hst of examples from the literary history of the eigh- teenth century ; but the farther prosecution of the sub- ject here would lead me aside from the conclusions which I have at present in view. I shall therefore con- tent myself with opposing, to the contentious and scep- tical spirit bequeathed by the schoolmen to their succes- sors, the foHowing wise and cautious maxims of their master, — maxims which, while they illustrate his anxiety to guard the principles of the demonstrative sciences
*See Bayle's Dictionary, article Chrysippc. I have availed myself, in the above translation, (with a few retrenchments and corrections,) of that which ia given in the English Biographical and Critical Dictionary.
54 ELEMENTS OF THE PHILOSOPHY
against the captiousness of sophists, evince the respect which he conceived to be due by the philosopher to the universal reason of the human race.
" Those things are to be regarded as first truths, the credit of which is not derived from other truths, but is inherent in themselves. As for probable truths, they are such as are admitted by all men, or by the generality of men, or by wise men ; and, among these last, either by all the wise, or by the generahty of the wise, or by such of the wise as are of the highest authority." *
The argument from Universal Consent, on which so much stress is laid by many of the ancients, is the same doctrine with the foregoing, under a form somewhat different. It is stated with great simplicity and force by a Platonic philosopher in the following sentences :
" In such a contest, and tumult, and disagreement, (about other matters of opinion,) you may see this one law and language acknowledged by common accord. This the Greek says, and this the barbarian says ; and the inhabitant of the continent, and the islander; and the wise, and the unwise." f
It cannot be denied, that against this summary spe- cies of logic, when employed without any collateral lights, as an infallible touchstone of philosophical truth, a strong objection immediately occurs. By what test (it may be asked) is a principle of common sense to be distinguished from one of those prejudices to which the whole human race are irresistibly led, in the first in- stance, by the very constitution of their nature ? If no test or criterion of truth can be pointed out but univer- sal consent, may not all those errors which Bacon has
*'EaTi 8s aX7]-d-ij fisv xal ngwra, ra jxr] d^ hsQav, alia dt avxwv s/ovra Tr)V Tilariv. "Evdo^a ds, zee Soxovvtu naaiv, tj ToUg nkdoToig, i] rdlg aocpdig ' xal TOVToig, rj xdlg naaiv, ij jdlg nXsloToig, ij rdig fidXiara yvojgi^ot,g, nai ivdo^oig.—Aristot. Top. Lib. I. cap. i. (Vol. I. p. 180, ed. Du Val.)
t Ev TooovTco de noldfiw :tal araast xal diaqxovln tva i'doig av iv naai] yij o^ocpuivov vo/iiov aal loyov, &lc. Tavxa ds 6 "Elh]v Uyu, xal 6 BaqSaqog Xsysi, xal o ^jTisigcari^g, xal 6 &alaTxiog, xal 6 aocpbg, xal o aao(pog. — Maz. Tyr. ^speaking of the existence of the Deity) Dis. I.
" Una in re consensio omnium gentium lex naturae putanda est." — Cic. 1. Tusc.
*' Multum dare solenms prsesumptioni omnium hominum : Apud nos veritatis argu- joaeatum est, aliquid omnibus videri," &,c. &,c. — Sen. Ep. 117.
OF THE HUMAN MIND. 55
called idola tribus claim a right to admission among the incontrovertible axioms of science ? And might not the popular cavils against the supposition of the earth's mo- tion, which so long obstructed the progress of the Co- pernican system, have been legitimately opposed, as a reply of paramount authority, to all the scientific rea- sonings by which it was supported 7
It is much to be wished that this objection, of which Dr. Reid could not fail to be fully aware, had been more particularly examined and discussed in some of his pub- lications, than he seems to have thought necessary. From different parts of his works, however, various im- portant hints towards a satisfactory answer to it might be easily collected.* At present, I shall only remark, that, although universality of belief is one of the tests by which (according to him) a principle of common sense is characterized, it is not the only test which he repre- sents as essential. Long before his time. Father Huf- fier, in his excellent treatise on First Truths, had laid great stress on two other circumstances, as criteria to be attended to on such occasions ; and although I do not recollect any passage in Reid where they are so expli- citly stated, yet the general spirit of his reasonings plainly shows, that he had them constantly in view in all the practical applications of his doctrine. The first cri- terion mentioned by Buffier is, " That the truths assumed as maxims of common sense should be such, that it is impossible for any disputant either to defend or to attack them, but by means of propositions which are neither more manifest nor more certain than the propositions in question." The second criterion is, " That their practi- cal influence should extend even to those individuals who affect to dispute their authority."
To these remarks of Bufiier, it may not be altogether superfluous to add, that, wherever a prejudice is found to obtain universally among mankind in any stage of so- ciety, this prejudice must have some foundation in the general principles of our nature, and must proceed upon some truth or fact inaccurately apprehended, or errone-
• See, in particular, Essays on the Int. Powers, p. 565, at seq. 4to. edit.
56 ELEMENTS OF THE PHILOSOPHY
ously applied. The suspense of judgment, therefore, which is proper with respect to particular opinions, till they be once fairly examined, can never justify scepti- cism with respect to the general laws of the human mind. Our beUef of the sun's motion is not a conclu- sion to which we are necessarily led by any such law, but an inference rashly drawn from the perceptions of sense, which do not warrant such an inference. All that we see is, that a relative change of position be- tween us and the sun takes place ; and this fact which is made known to us by our senses, no subsequent dis- covery of philosophy pretends to disprove. It is not, therefore, the evidence of perception which is overturn- ed by the Copernican system, but a judgment or infer- ence of the understanding, of the rashness of which every person must be fully sensible, the moment he is made to reflect with due attention on the circumstances of the case ; and the doctrine which this system substi- tutes instead of our first crude apprehensions on the subject, is founded, not on any process of reasoning a priori, but on the demonstrable inconsistency of these apprehensions with the various phenomena which our perceptions present to us. Had Copernicus not only asserted the stability of the Sun, but, with some of the Sophists of old, denied that any such thing as motion exists in the universe, his theory would have been pre- cisely analogous to that of the non-existence of matter; and no answer to it could have been thought of more pertinent and philosophical, than that which Plato is said to have given to the same paradox in the mouth of Ze- no, by rising up and walking before his eyes.
2. If the foregoing observations be just, they not only illustrate the coincidence between Dr. Reid's general ar- gument against those metaphysical paradoxes which re- volt common sense, and the maxims of philosophical dis- cussion previously sanctioned by our soundest reason- ers ; but they go far, at the same time, to refute that charge of plagiarism in which he has been involved, in common with two other Scotish writers, who have made theu^ stand in opposition to Berkeley and Hume, nearly on the same ground. This charge has been stated, in
OF THE HUMAN MIND. 57
all its force, in the preface to an English translation of Buffier's Premieres Verites, printed at London, in the year 1780 ; and it cannot be denied, that some of the proofs alleged in its support are not without plausibility. But why suppose Reid to have borrowed from this leEirn- ed Jesuit, a mode of arguing which has been famihar to men in all ages of the world ; and to which, long before the publication of Buffier's excellent book, the very same phraseology had been appHed by numberless other authors. On this point, the passage already quoted from Bayle is of itself decisive. The truth is, it is a mode of arguing likely to occur to every sincere and enlight- ened inquirer, when bewildered by sceptical sophistry ; and which, during the long interval between the publica- tion of the Berkeleian theory, and that of Reid's Inqui- ry, was the only tenable post on which the conclusions of the former could be combated. After the length to which the logical consequences of the same principles were subsequently pushed in the Treatise of Human JYature, this must have appeared completely manifest to all who were aware of the irresistible force of the ar- gument, as it is there stated ; and, in fact, this very ground was taken as early as the year 1751, in a private correspondence with Mr. Hume, by an intimate friend of his own, for whose judgment, both on philosophical and literary subjects, he seems to have felt a pecuhar deference.* I mention this, as a proof that the doctrine in question was the natural result of the state of sci- ence at the period when Reid appeared ; and, conse- quentl}', that no argument against his originality in adopt- ing it, can reasonably be founded on its coincidence with the views of any preceding author.
A still more satisfactory reply to the charge of plagia- rism may be derived from this consideration, that, in Buffier's Treatise, the doctrine which has furnished the chief ground of accusation is stated with far greater precision and distinctness than in Dr. Reid's ^rs/ publi- cation on the Human Mind ; and that, in his subsequent performances, after he had perused the writings of Buf-
* See Note (C.) VOL. II. 8
58 ELEMENTS OF THE PHILOSOPHY
fier, his phraseology became considerably more guarded and consistent than before.
If this observation be admitted in the case of Dr. Reid, it will be found to apply with still greater force to Dr. Beattie, whose language in various parts of his book, is so loose and unsettled, as to afford demonstrative proof that it was not from Buffier he derived the idea of his general argument. In confirmation of this, I shall only mention the first chapter of the first part of his Essay, in which he attempts to draw the line between common sense and reason ; evidently confounding (as many other authors of high reputation have done) the two very different words, reason and reasoning. His account of common sense in the following passage, is liable to cen- sure in almost every line : " The term common sense hath, in modern times, been used by philosophers, both French and British, to signify that power of the mind which perceives truth, or commands belief, not by pro- gressive argumentation, but by an instantaneous, instinc- tive, and irresistible impulse ; derived neither from edu- cation nor from habit, but from nature ; acting inde- pendently on our will, whenever its object is presented, according to an established law, and therefore properly called SENSE,* and acting in a similar manner upon all,
* The doctrine of the schooUnen (revived in later times under a form somewhat modified by Locke) which refers to sensation the origin of all our ideas, has given rise to a very unwarrantable extension of the word sense, in the writings of modern philosophers. When it was first asserted, that " there is nothing in the intellect which does not come to it through the medium of sense," there cannot be a doubt that, by this last term, were understood exclusively our powers of external percep- tion. In process of time, however, it came to be discovered, that there are many ideas which cannot possibly be traced to this source ; and which, of consequence, afford undeniable proof that the scholastic account of the origin of our ideas is ex- tremely imperfect. Such was certainly the logical inference to which these discov- eries should have led ; but, instead of adopting it, philosophers have, from thd first, shown a disposition to save, as much as possible, the credit of the maxims in which they had been educated, by giving to the word sense so great a latitude of meaning, as to comprehend all the various sources of our simple ideas, whatever these sources may be. " All the ideas," says Dr. Hutcheson, " or the mateiials of our reasoning and judging, are received by some imm diate powers of perception, internal or ex- ternal, which we may call senses." Under the title of internal senses, accordingly, many writers, particularly of the medical profession, contiiuie to this day to compre- hend memory and imagination, and other faculties, both intellectual and active. — (Vide Haller, Element. Physiologias, lAh. xvii.) FTencc abo the phras.-SOT.9raZ sense, the senses of beauty and harmony, and many of the other peculiarities of Dr. Hutcheson's language ; a mode of speaking which was afterwards caiiied to a much more blameable excess by Lord Kaimes. Dr. Beattie, in the passage quoted above, has indirectly given his sanction to the same abu&e of words ; plainly supposing the phrase coOTwion. 8e»iS(5, not only to moan something quite distinct from reason, biit
or THE HUMAN MIND. 59
or at least upon a great majority of mankind, and there- fore properly called common sense."*
" Reason," on the other hand, (we are told by the same author,) " is used by those who are most accurate in distinguishing, to signify that power of the human mind by which we draw inferences, or by which we are con- vinced that a relation belongs to two ideas, on account of our having found that these ideas bear certain rela- tions to other ideas. In a word, it is that faculty which enables us, from relations or ideas that are known, to investigate such as are unknown ; and v/ithout which we never could proceed in the discovery of truth a single step beyond first principles or intuitive axioms. "f " It is in this last sense," he adds, " that we are to use the word reason in the course of this inquiry."
These 'two passages are severely, and, I think, justljv, animadverted on, in the preface to the English transla tion of Buffier's book, where they are contrasted with the definition of common sense given by that profound and original philosopher. From this definition it appears, that, far from opposing common sense and reason to each other, he cons-iders them either as the same faculty, or as faculties necessarily and inseparably connscted to- gether. " It is a faculty," he says, " which appears in all men, or at least in the far greater number of them, when they have arrived at the age of reason, enabling them to form a common and uniform judgment, on sub- jects essentially connected with the ordinary concerns of life."
That this contrast turns out greatly to the advantage of Buffier J must, I think, be granted to his very acute
sotnethins; which hears so close an analogy to the powers of external senso, as to be not improperly called by the same name. »
* Essay on Truth, p. 40. 2d edit. ^
t Ihid. pp, .36, 37. 2d edit.
X It is remarkable how little attention the writings of BufTier have attracted in his own country, and hTw very inadequate to his real eminence has been the rank cOm- moidy assio-ned to him amonuj French Philo-iophers. This has perhaps been partly owino; to an unfortunate combination wliich he thought proper to make of a variety of nii-icellaneous treatises, of very unequal merit, into a large woik, to which hj gave the name of a Course of the Sciences. Some of those treatises, however, are of great value: particularly that on First Truths, which contains (along witii souie erroneous notions, easily to be accounted for by the perio;! when the author wrote, and the religious society with which he was connected) many original and important views' concerning the foundation? of human knowledge, and the first principles of a ra-
60 ELEMENTS OF THE PHILOSOPHY
and intelligent translator. But while I make this conces- sion in favor of his argument, I must be allowed to add, that, in the same proportion in which Dr. Beattie falls short of the clearness and logical accuracy of his prede- cessor, he ought to stand acquitted, in the opinion of all men of candor, of every suspicion of a dishonorable plagiarism from his writings.
It is the doctrine itself, however, and not the compar- ative merits of its various abettors, that is likely to inter- est the generahty of philosophical students ; and as I have always thought that this has suffered considerably in the public estimation, in consequence of the state- ment of it given in the passage just quoted from the Essay on Truth, I shall avail myself of the present op- portunity to remark, how widely that statement differs from the language, not only of Buffier, but of the author's contemporary and friend, Dr. Reid. This circumstance I think it necessary to mention, as it seems to have been through the medium of Dr. Beattie's Essay, that most English writers have derived their imperfect information concerning Reid's philosophy.
" There is a certain degree of smse," says this last author, in his Essays on the Intellectual Powers of man, " which is necessary to our being subjects of law and government, capable of managing our own affairs, and answerable for our conduct to others. This is called common sense, because it is common to all men with whom we can transact business."
" The same degree of understanding," he afterwards
tional logic. Voltaire, in his catalogue of the illustrious writers who adorned the reip.n of Louis XIV. is one of the very few French authors who have spoken of Bu.'Tier vviih due respect. " II y a dans ses traites de metaphysique des morceaux que LocV;e n'aurait pas desavoues, et c'est le seul jesnite qui ait nus une philosophie raisonnable dans ses ouvrages." Another French philosopher, too, of a very different school, and certainly not disposed to overrate the talents of Buffiei-, has, in a work published as lately as 1805, candidly acknowledged the lights which he might have derived from the labors of his predecessor, if he had been acquainted with (hem in an earlier stage of his studies. Condillac, he also observes, might have profited greatly by the sanic lights, if he had availed himself of their guidance in his inquiries con- cerning tlie human understanding. " Du nioins est il certain, que pour ma part, je suis (ort fache de ne connoitrc que depuis tres peu de temps, ces opinions du Pere Buffier; si je les avais vues plulot enoncccs quelque part, eiles m'auraicnt epargne
beaucoup de pcines et d'hesitations." " .le regrette bcaucoup que Condillac, dans
ses i)rofondcs et sagaces meditations sur rintelligcnce humaine, n'ait pas fiiit plus d'attention aux ideesdu Pere Buffier," &,c. &c. — JElcmens d' Ideologic, par M. JDes^ tuU-Tracy, Tom. IIL pp. 1.36, 137.
OF THE HUMAN MIJTD. 61
observes, " which makes a man capable of acting with common prudence in life, makes him capable of discern- ing what is true and what is false, in matters that are self-evident, and which he distinctly apprehends." In a subsequent paragraph, he gives his sanction to a passage from Dr. Bentley, in which commoii sense is expressly used as synonymous with natural light and reason.*
It is to be regretted, as a circumstance unfavorable to the reception of Dr. Beattie's valuable essay among ac- curate reasoners, that, in the outset of his discussions, he did not confine himself to some such general expla- nation of this phrase as is given in the foregoing extracts from Buffier and Reid, without affecting a tone of logic- al precision in his definitions and distinctions, which, so far from being necessary to his intended argument, were evidently out of place, in a work designed as a popular antidote against the illusions of metaphysical scepticism. The v6ry idea, indeed, of appealing to common sense, virtually implies that these words are to be understood in their ordinary acceptation, unrestricted and unmodifi- ed by any technical refinements and comments. This part of his essay, accordingly, which is by far the most vulnerable part of it, has been attacked with advantage, not only by the translator of Buffier, but by Sir James Steuart, in a very acute letter published in the last edi- tion of his works. f
While I thus endeavour, -however, to distinguish Dr. Reid's definition oi common sense from that of Dr. Beattie, I am far from considering even the language of the for-
* Pages 522, 524, 4to edit. In the following verse? cf Prior, the word reason is em- ployed in an accei)i§tion exactly coincident with the idea whicli is, on most occasions, annexed by Dr. Reid to the phrase common sense : " Noti? hero, Lucret'ius dares to leach,
(As all our youth may learn from Uref.ch,)
That eyes were marie, but could not view,
Nor hands embrace, nor feet pursue,
But heedless nature did produce
The members lirst, and then the use ;
What each must act was yet unknown,
Till all was moved by Chance alone.
Blest for his sake bo human reaso!*,
Which came at last, tho' late, in season." — Alma, Canto I.
I To the honor of Dr. Beattie it must be remarked, that his reply to this letter, (which may be found in Sir James Steuart's worl<s,) is written in a strain of forbear- ance and of good humor, which few authors would have been able to maintain, after being handled so roughly.
62 ELEMENTS OF THE PHILOSOPHY
mer on this subject, as in every instance unexceptionable ; nor do I think it has been a fortunate circumstance, (notwithstanding the very high authorities which may be quoted in his vindication,) that he attempted to incorpo- rate so vague and ambiguous a phrase with the appro- priate terms of logic. My chief reasons for this opinion I have stated at some length, in an account pubhshed a few years ago of Dr. Reid's Life and Writings.*
One \erj unlucky consequence has unquestionably resulted from the coincidence of so many writers con- nected with this northern part of the island, in adopting, about the same period, the same phrase, as a sort of phi- losophical watch-word ; — that, although their views differ widely in various respects, they have in general been classed together as partisans of a new sect, and as mu- tually responsible for the doctrines of each other. It is easy to perceive the use likely to be made of this acci- dent by an uncandid antagonist.
All of these writers have, in my opinion, been occa- sionally misled in their speculations, by a want of atten- tion to the distinction between first principles, properly so called, and the fundamental laws of human belief. Buffier himself has fallen into the same error ; nor do I know of any one logician, from the time of Aristotle downwards, who has entirely avoided it.
The foregoing critical remarks will, I hope, have their use in keeping this distinction more steadily in the view
* In consequence of the ambiguous meanins; of this phrase, Dr. Raid sometimes falls into a sort ot play on words, which I have often regretted. " If this be philoso- phy," says he, on one occasion, " 1 renounce her guidance. Let my soul dwell with common sense." (Inquiry into the Hwnan Mind, Chap. i. §3. See also § 4. of ihe same chapter.) And in another passage, after quoting the not#d saying of Hobbes, that " when reason is against a man, a man will be agamst reason ; " he adds, " This is equally applicable to common sense." (Essays on the Intellectual Poioers, p. 530. 4to edition.) In both of these instances, and, indeed, in the general strain of argument which runs through his works, he understands common sense in its ordi- nary acceptation, as synonymous, or very nearly synonymous, with the word reason, as it is now most frequently employed. In a few cases, however, he seems to have annexed to the same phrase a technical meaning of his own, and has even spoken of this meaning as a thing not generally understood. Thus, after illustrating the differ- ent classes of natural signs, he adds the following sentence : " It may be observed, that as the first class of natural signs I have mentioned is the foundation of true phi- losophy, and the second of the fine arts or of taste, so the last is the foundation of common sense ; a part of human nature which hath never been explained," Jnqui' ry, Chap. v. § 3.
See Note (D.)
OF THE HUMAN MIWD. 63
of future inquirers ; and in preventing some of the read- ers of the publications to which they relate, from con- ceiving a prejudice, in consequence of the looseness of that phraseology which has been accidentally adopted by their authors, against the just and important conclusions which they contain.
64' ELEMENTS OF THE PHILOSOPHY
CHAPTER SECOND.
OF REASONING AND OP DEDUCTIVE EVIDENCE.
SECTION I.
Doubts with respect to Locke's Distinction between the Powers of Intuition and of
Reasoning.
Although, in treating of this branch of the Philoso- phy of the Mind, I have followed the example of pre- ceding writers, so far as to speak of intuition and reasoning as two different faculties of the understand- ing, I am by no means satisfied that there exists between them that radical distinction which is commonly appre- hended. Dr. Beattie, in his Essay on Truth, has at- tempted to show, that, how closely soever they may in general be connected, yet that this connexion is not necessary ; insomuch, that a being may be conceived endued with the one, and at the same time destitute of the other.* Something of this kind, he remarks, takes place in dreams and in madness ; in both of which states of the system, the power of reasoning appears occa- sionally to be retained in no inconsiderable degree, while the power of intuition is suspended or lost. But this doctrine is hable to obvious and to insurmountable ob- jections ; and has plainly taken its rise from the vague- ness of the phrase common sense, which the author employs through the whole of his argument, as synony- mous with the power of intuition. Of the indissoluble connexion between this last power and that of reasoning, no other proof is necessary than the following consider- ation, that, " In every step which reason makes in demonstrative knowledge, there must be intuitive cer- tainty;" a proposition which Locke has excellently
* Beattie's Essay p. 41, 2d edit.
OF THE HUMAN MIND. 65
illustrated, and which, since his time, has been acquies- ced in, so far as I know, by philosophers of all descrip tions. From this proposition (which when properly interpreted, appears to me to be perfectly just) it obvi- ously follows, that the power of reasoning presupposes the power of intuition ; and, therefore, the only ques- tion about which any doubt can be entertained is, Whe- ther the power of intuition (according to Locke's idea of it) does not also imply that of reasoning? My own opinion is decidedly, that it does ; at least, when com- bined with the faculty of memory. In examining those processes of thoughtwhichconduct themind by a series of consequences from premises to a conclusion, I can detect no intellectual act whatever, which the joint op- eration of intuition and of memory does not sufficiently explain.
Before, however, proceeding farther in this discus- sion, it is proper for me to observe, by way of comment on the proposition just quoted from Locke, that although, " in a complete demonstration, there must be intuitive evidence at every step," it is not to be supposed, that, in every demonstration, all the various intuitive judg- ments leading to the conclusion are actually presented to our thoughts. In by far the greater number of in- stances, we trust entirely to judgments resting on the evidence of memory ; by the help of which faculty, we are enabled to connect together the most remote truths, with the very same confidence as if the one were an immediate consequence of the other. Nor does this diminish, in the smallest degree, the satisfaction we feel in following such a train of reasoning. On the contrary, nothing can be more disgusting than a demonstration where even the simplest and most obvious steps are brought forward to view ; and where no appeal is made to that stock of previous knowledge which memory has identified with the operations of reason. Still, howev- er, it is true, that it is by a continued chain of intuitive judgments, that the whole science of geometry hangs together; inasmuch as the demonstration of any one proposition virtually includes all the previous demon- strations to which it refers.
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Hence it appears, that, in mathematical demonstra- tions, we have not, at every step, the immediate evidence of intuition, but only the evidence of memory. Every demonstration, however, may be resolved into a series of separate judgments, either formed at the moment, or remembered as the results of judgments formed at some preceding period ; and it is in the arrangement and concatenation of these different judgments or media of proof, that the inventive and reasoning powers of the mathematician find so noble a field for their exercise.
l¥ith respect to these powers of judgment and of reasoning, as they are here combined, it appears to me that the results of the former may be compared to a collection of separate stones prepared by the chisel for the purposes of the builder ; upon each of which stones, while lying on the ground, a person may raise himself, as upon a pedestal, to a small elevation. The same judgments, when combined into a train of reason- ing, terminating in a remote conclusion, resemble the formerly unconnected blocks^ when converted into the steps of a staircase leading to the summit of a tower, which would be otherwise inaccessible. In the de- sign and execution of this staircase, much skill and in- vention may be displayed by the architect ; but, in order to ascend it, nothing more is necessary than a repeti- tion of the act by which the first step was gained. The fact I conceive to be somewhat analogous, in the relation between the power of judgment, and what logicians call the discursive processes of the understanding.
Mr. Locke's language, in various parts of his Essay, seems to accord with the same opinion. " Every step in reasoning," he observes, " that produces knowledge, has intuitive certainty ; which, when the mind perceives^ there is no more required hut to remember it, to make the agreement or disagreement of the ideas, concerning which we inquire, visible and certain. This intuitive perception of the agreement or disagreement of the intermediate ideas, in each step and progression of the demonstration, must also be carried exactly in the mind, and a man must be sure that no part is left out ; which, in long deductions, and in the use of many proofs, the
OF THE HUMAN MIND. 67
memory does not always so readily and exactly retain : therefore it comes to pass, that this is more imperfect than intuitive knowledge, and men embrace often false- hood for demonstrations." *
The same doctrine is stated elsewhere by Mr. Locke, more than once in terms equally exphcit ; f and yet his language occasionally favors the supposition, that, in its deductive processes, the mind exhibits some modification of reason essentially distinct from intuition. The account, too, which he has given of their respective provinces, af- fords evidence that his notions concerning them were not sufficiently precise and settled. " When the mind," says he, " perceives the agreement or disagreement of two ideas immediately by themselves, without the interven- tion of any other, its knowledge may be called intuitive. When it cannot so bring its ideas together, as, by their immediate comparison, and, as it were, juxta-position, or apphcation one to another, to perceive their agree- ment or disagreement, it is fain, by the intervention of other ideas (one or more as it happens) to discover the agreement or disagreement, which it searches ; and this is that which we call reasoning." J According to these definitions, supposing the equality of two fines A and B to be perceived immediately in consequence of their coincidence ; the judgment of the mind is intuitive : Supposing A to coincide with B, and B with C ; the relation between A and C is perceived by reasoning. Nor is this a hasty inference from Locke's accidental language. That it is perfectly agreeable to the forego- ing definitions, as understood by their author, appears from the following passage, which occurs afterwards : " The principal act of ratiocination is the finding the agreement or disagreement of tw^o ideas, one with anoth- er, by the intervention of a third. As a man, by a yard, finds two houses to be of the same length, which could not be brought together to measure their equality by juxta-position." §
* B. IV. Ciiap. ii. § 7. See also B. IV. Chap xvii. § 15. t B. IV. Chap. xvii. § 2. B. IV. Chap. xvii. § 4. § 14. X B. IV. Chap. ii. §§ 1 and 2. §B. IV. Chap. xvii. §18.
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This use of the words intuition and reasoning, is sure- ly somewhat arbitrary. The truth of mathematical axi- oms has always been supposed to be intuitively obvious ; and the first of these, according to EucHd's enumera- tion, affirms. That if A be equal to B, and B to C, A and C are equal. Admitting, however, Locke's defini- tion to be just, it only tends to confirm what has been already stated with respect to the near affinity, or rather the radical identity, of intuition and of reasoning. When the relation of equahty between A and B has once been perceived, A and B are completely identified as the same mathematical quantity ; and the two letters may be regarded as synonymous wherever they occur. The faculty, therefore, which perceives the relation be- tween A and C, is the same with the faculty which perceives the relation between A and B, and between B and C*
In farther confirmation of the same proposition, an appeal might be made to the structure of syllogisms. Is it possible to conceive an understanding so formed as to perceive the truth of the major and of the minor propositions, and yet not to perceive the force of the conclusion ? The contrary must appear evident to every person who knows what a syllogism is ; or rather, as in this mode of stating an argument, the mind is led from universals to particulars, it must appear evident, that in the very statement of the major proposition, the truth of the conclusion is presupposed ; insomuch, that it was not without good reason Dr. Campbell hazarded the epigrammatic, yet unansv/erable remark that, " there is always some radical defect in a syllogism, which is not chargeable with that species of sophism known among logicians by the name of petitio principii,jor a begging of the question.''^ f
* Dr Reid's notions, as well as those of Mr. Locke, seem to^have been somewhat Tinsettled with respect to the precise line which separates intuition from reasoning. That the axioms of geometry are intuitive truths, he has;^remarked in^numberless pas- sages of his works : and yet, in speaking of the application of the syllogistic theory to mathematics, he makes use of the following expression : " The simple reasoning, * A is equal to B, and B to C, therefore A is equal to C,' cannot be brought into any syllogism in figure and mode." — Sec his Analysis of Aristotle's Logic.
t Phil, of Rhet. Vol. I. p. 174.
OF THE HUMAN MI]S^D. 69
The idea which is commonly annexed to intuition, as opposed to reasoning, turns, I suspect, entirely on the circumstance of time. The former we conceive to be instantaneous ; whereas the latter necessarily involves the notion of succession, or of progress. This distinc- tion is sufficiently precise for the ordinary purposes of discourse ; nay, it supphes us, on many occasions, w^ith a convenient phraseology : but in the theory of the mind, it has led to some mistaken conclusions, on which I intend to offer a few remarks in the second part of this section.
So much with respect to the separate provinces of these powers, according to Locke : — a point on which I am, after all, inclined to think, that my own opinion does not differ essentially from his, whatever inferences to the contrary may be drawn from some of his casual expressions. The misapprehensions into which these have contributed to lead various writers of a later date, will, I hope, furnish' a sufficient apology for the attempt which I have made, to place the question in a stronger light than he seems to have thought requisite for its illustration.
In some of the foregoing quotadons from his Essay, there is another fault of still greater moment ; of which, although not immediately connected with the topic now under discussion, it is proper for me to take notice, that I may not have the appearance of acquiescing in a mode of speaking so extremely exceptionable. What I allude to is, the supposition which his language, con- cerning the powers both of intuition and of reasoning, \nYo\ves, that knowledge consists solely in the perception of the agreement or the disagreement of our ideas. The im- propriety of this phraseology has been sufficiently ex- posed by Dr. Reid, Avhose animadversions I would beg leave to recommend to the attention of those readers, who, from long habit, may have familiarized their ear to the peculiarities of Locke's philosophical diction. In this place, I think, it sufficient for me to add to Dr. Reid's strictures, that Mr. Locke's language has, in the present instance, been suggested to him by the partial view which he took of the subject ; his illustrations
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being chiefly borrowed from mathematics, and the re- lations about which it is conversant. When appUed to these relations, it is undoubtedly possible to annex some sense to such phrases as compariiig ideas, — the juxta- position of ideas, — the perception of the agreements or disagreements of ideas, but, in most other branches of knowledge, this jargon will be found on examination, to be altogether unmeaning; and, instead of adding to the precision of our notions, to involve plain facts in technical and scholastic mystery.
This last observation leads me to remark farther, that even when Locke speaks of reasoning in general, he seems, in many cases, to have had a tacit reference, in his own mind, to mathematical demonstration ; and the same criticsism may be extended to every logical writer whom I know, not excepting Aristotle himself. Per- haps it is chiefly owing to this, that their discussions are so often of very httle practical utihty : the rules which result from them being wholly superfluous, when apphed to mathematics ; and, when extended to other branches of knowledge, being unsusceptible of any pre- cise, or even intelligible interpretation.
II.
Conclusions obtained by a Process of Deduction often mistaken for Intuitive
Judgments.
It has been frequently remarked, that the justest and most efficient understandings are often possessed by men who are incapable of stating to others, or even to them- selves, the grounds on which they proceed in forming their decisions. In some instances, I have been dis- posed to ascribe this to the faults of early education ; but, in other cases, I am persuaded, that it was the ef- fect of active and imperious habits in quickening the evanescent processes of thought, so as to render them untraceable by the memory ; and to give the appear- ance of intuition to what was in fact the result of a train- of reasoning so rapid as to escape notice. This I conceive to be the true theory of what is generally
OF THE HUMAN MIND. 71
called common sense, in opposition to book-learning ; and it serves to account for the use which has been made of this phrase, by various writers, as synonymous with intuition.
These seemingly instantaneous judgments have al- ways appeared to me as entitled to a greater share of our confidence than many of our more deliberate conclusions; inasmuch as they have been forced, as it were, on the mind, by the lessons of long experience ; and are as little hable to be biassed by temper or passion, as the estimates we form of the distances of visible objects. They constitute, indeed, to those who are habitually engaged in the busy scenes of hfe, a sort of peculiar faculty, analogous, both in its origin and in its use, to the coup (i'cBi/ of the mihtary engineer, or to the quick and sure tact of the medical practitoner, in marking the diagnostics of disease.
For this reason, I look upon the distinction between our intuitive and deductive judgments as, in many ca- ses, merely an object of theoretical curiosity. In those simple conclusions which all men are impelled to form by the necessities of their nature, and in which we find an uniformity not less constant than in the acquired perceptions of sight, it is of as httle consequence to the logician to spend his time in efforts to retrace the first steps of the infant understanding, as it would be to the sailor or the sportsman to study, with a view to the improvement of his eye, the Berkeleian theory of vis- ion. In both instances, the original faculty and the acquired judgment are equally entided to be considered as the work of 'nature ; and in both instances we find it equally impossible to shake off" her authority. It is no wonder, therefore, that, in popular language, such words as common sense and reason should be used with a considerable degree of latitude ; nor is it of much importance to the philosopher to aim at extreme nicety in defining their province, where all mankind, whether wise or ignorant, think and speak ahke.
In some rare and anomalous cases, a rapidity of judg- ment in the more complicated concerns of life, appears in individuals who have had so few opportunities of
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profiting by experience, that it seems, on a superficial view, to be the immediate gift of heaven. But in all such instances, (although a great deal must undoubtedly be ascribed to an inexplicable aptitude or predisposition of the intellectual powers,) we may be perfectly assured, that every judgment of the understanding is preceded by a process of reasoning or deduction, whether the individual himself be able to recollect it or not. Of this I can no more doubt, than I could bring myself to beheve that the Arithmetical Prodigy, who has, of late, so justly attracted the attention of t]ie curious, is able to extract square and cube roots by an instinctive and instantaneous perception, because the process of men- tal calculation, by which he is led to the result, eludes all his efforts to recover it.*
It is remarked by Mr. Hume, with respect to the elo- cution of Ohver Cromwell, that " it was always confus- ed, embarrassed, and unintelligible." — " The great de- fect, however," he adds, " in Oliver's speeches consist- ed, not in his want of elocution, but in his want of ideas ; the sagacity of his actions and the absurdity of his dis- course, forming the most prodigious contrast that ever was known." — " In the great variety of human genius- es," says the same historian, upon a different occasion, " there are some which, though they see their object clearly and distinctly in general ; yet, when they come to unfold its parts by discourse or writing, lose that lu- minous conception which they had before attained. All accounts agree in ascribing to Cromwell, a tiresome, dark, uninteUigible elocution, even when he had no in- tention to disguise his meaning : Yet, no man's actions were ever, in such a variety of difficult incidents, more decisive and judicious."
The case here described may be considered as an ex- treme one ; but every person in common observation must recollect facts somewhat analogous, which have fallen under his own notice. Indeed, it is no more than we should expect a priori, to meet with, in every indi- vidual whose early habits have trained him more to the
* Sec Note (E.)
OF THE HUMAN MIND. 73
active business of the world, than to those pursuits which prepare the mind for communicating to others its ideas and feehngs, Avith clearness and effect.
An anecdote which I heard, many years ago, of a late very eminent Judge (Lord Mansfield) has often recur- red to my memory, while reflecting on these apparent inconsistencies of intellectual character. A friend of his, who possessed excellent natural talents, but who had been prevented, by his professional duties as a naval officer, from bestowing on them all the cultivation of which they were susceptible, having been recently ap- pointed to the government of Jamaica, happened to ex- press some doubts of his competency to preside in the Court of Chancery. Lord Mansfield assured him, that he would find the difficulty not so great as he apprehend- ed. " Trust," he said, " to your own good sense in forming your opinions ; but beware of attempting to state the grounds of your judgments. The judgment will probably be right ; — the argument will infallibly be wrong."
From what has been said, it seems to follow, that al- though a man should happen to reason ill in support of a sound conclusion, we are by no means entitled to infer, with confidence, that he judged right merely by accident. It is far from being impossible that he may have commit- ted some mistake in stating to others (perhaps in retra- cing to himself) the grounds upon which his judgment was really founded. Lideed, this must be the case, wherever a shrewd understanding in business is united with an incapacity for clear and luminous reasoning ; and something of the same sort is incident, more or less, to all men (more particularly to men of quick parts) when they make an attempt, in discussions concerning human affairs, to remount to first pi^inciples. It may be added, that in the old, this correctness of judgment of- ten remains, in a surprising degree, long after the dis- cursive or argumentative power would seem, from some decay of attention, or confusion in the succession of ideas, to have been sensibly impaired by age or by dis- ease.
In consequence of these views, as well as of various
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others, foreign to the present subject, I am led to enter- tain great doubts about the soHdity of a very specious doctrine laid down by Condorcet, in his "Essay on the Application of Mathematical Analysis to the Probabili- ties of Decisions resting upon the Votes of a Majority." " It is extremely possible," he observes, " that the de- cision which unites in its favor the greatest number of suffrages, may comprehend a variety of propositions, some of which, if stated apart, would have had a plural- ity of voices against them ; and, as the truth of a system of propositions, supposes that each of the propositions composing it is true, the probabihty of the system can be rigorously deduced only from an examination of the probability of each proposition separately consider- ed." *
When this theory is apphed to a court of law, it is well known to involve one of the nicest questions in practical jurisprudence ; and, in that hght, I do not pre- sume to have formed any opinion with respect to it. It may be doubted, perhaps, if it be not one of those prob- lems, the solution of which, in particular instances, is more safely entrusted to discretionary judgment, than to the rigorous apphcation of any technical rule founded on abstract principles. I have introduced the quotation here, merely on account of the proof which it has been supposed to afford, that the seeming diversities of hu- man behef fall, in general, greatly short of the reahty. On this point the considerations already stated, strongly incline me to entertain an idea directly contrary. My reasons for thinking so may be easily collected from the tenor of the preceding remarks.
It is time, however, to proceed to the examination of those discursive processes, the different steps of which admit of being distinctly stated and enunciated in the form of logical arguments ; and which, in consequence of this circumstance, furnish more certain and palpable
* Essai sur I'AppIication de I'Analyse a la Probabilite des Decisions rendues a, la Pluralite des Voix. Disc. Prel. pp. 46, 47.
Some of the expressions in the above quotation are not agreeable to the idiom of ourlang;uao;e ; but I did not think myself entitled to depart from the phraseology of the original , The meaning is sufficiently obvious.
OF THE HUMAN MIND. 75
data for our speculations. I begin with some remarks on the Power of General Reasoning ; for the exercise of which, (as I formerly endeavoured to show,) the use of language, as an instrument of thought, is indispensa- bly requisite.
SECTION II.
OP GENERAL KEA30NING.
I.
Illustrations of some Remarks formerly stated in treating of Abstraction.
I SHOULD scarcely have thought it necessary to re- sume the consideration of Abstraction here, if I had not neglected, in my first volume, to examine the force of an objection to Berkeley's doctrine concerning abstract general ideas, on which great stress is laid by Dr. Reid, in his Essays on the Intellectual Powers of Man ; and which some late writers seem to have considered as not less conclusive against the view of the question which I have taken. Of this objection I was aware from the first ; but was unwilling, by replying to it in form, to lengthen a discussion which savoured so much of the schools ; more especially, as I conceived that I had guarded my own argument from any such attack, by the cautious terms in which I had expressed it. Having since had reason to beheve that I was precipitate in form- ing this judgment, and that Reid's strictures on Berke- ley's theory of General Signs have produced a deeper impression than I had expected,* I shall endeavour to obviate them, at least as far as they apply to myself, before entering on any new speculations concerning our reasoning powers ; and shall, at the same time, introduce
* See a book entitled, Elements of Intellectual Philosophy, by the late learned and justly regretted Mr. Scott, of King's College, Aberdeen, p. US. ct seq. (Edin- burgh, 1803.) I have not thought it necessary to reply to Mr. Scoti's own reason- ings, which do not appear to mc to throw much new light on the question; but 1 thought it right to refer to them here, that the reader may, if he pleases, have an opportunity of judging for himseil.
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some occasional illustrations of the principles which I formerly endeavoured to establish.
To prevent the possibihty of misrepresentation, I state Dr. Reid's objection in his own words.
" Berkeley, in his reasoning against abstract general ideas, seems unwillingly or unwaringly to grant all that is necessary to support abstract and general concep- tions.
"A man," says Berkeley, "may consider a figure merely as triangular, without attending to the particular quahties of the angles, or relations of the sides. So far he may abstract. But this will never prove that he can frame an abstract general inconsistent idea of a trian- gle."
Upon this passage Dr. Reid makes the following re- mark : " ifa man may consider a figure merely as triangu- lar, he must have some conception of this object of his con- sideration; for no man can consider a thing which he does not conceive. He has a conception, therefore, of a trian- gular figure, merely as such. I know no more that is meant by cm abstract general conception of a triangle,"
" He that considers a figure merely as triangular," continues the same author, " must understand what is meant by the word triangular. If to the conception he joins to this word, he adds any particular quahty of an- gles or relation of sides, he misunderstands it, and does not consider the figure merely as triangular. Whence I think it is evident, that he who considers a figure mere- ly as triangular, must have the conception of a triangle, abstracting from any quality of angles or relations of sides." *
For what appears to myself to be a satisfactory an- swer to this reasoning, I have only to refer to the first volume of these Elements. The remarks to which I allude are to be found in the third section of chapter fourth ; f and I must beg leave to recommend them to the attention of my readers as a necessary preparation for the following discussion.
* Reid's Intellectual Powers, p. 483, 4to. ed. t V, 195. 3d. cd.
OF THE HUMAN MIJfD. 77
In the farther prosecution of the same argument, Dr. Reid lays hold of an acknowledgment which Berkeley has made, " That we may consider Peter so far forth as man, or so far forth as animal, inasmuch as all that is perceived is not considered." — " It may here," says Reid, " be observed, that he who considers Peter so far forth as man, or so far forth as animal, must conceive the meaning of those abstract general words man and ani- mal; and he who conceives the meaning of them, has an abstract general conception."
According to the definition of the word conception, which I have given in treating of that faculty of the mind, a general conception is an obvious impossibility. But, as Dr. Reid has chosen to annex a more extensive meaning to the term than seems to me consistent with precision, I would be far from being understood to ob- ject to his conclusion, merely because it is inconsistent with an arbitrary definition of my own. Let us consid- er, therefore, how far his doctrine is consistent with it- self; or rather, since both parties are evidently so nearly agreed about the principal fact, which of the two have adopted the more perspicuous and philosophical mode of stating it.
In the first place, then, let it be remembered as a thing admitted on both sides, " that we have a power of rea- soning concerning a figure considered merely as trian- gular, without attending to the particular qualities of the angles, or relations of the sides ; " and also, that " we may reason concerning Peter or John, considered so far forth as man, or so far forth as animal." About these facts there is but one opinion ; and the only question is, Whether it throws additional light on the subject, to tell us, in scholastic language, that " we are enabled to carry on these general reasonings, in consequence of the pow- er which the mind has of forming abstract general con- ceptions." To myself, it appears, that this last state- ment (even on the supposition that the word conception is to be understood agreeably to Dr. Reid's own explan- ation) can serve no other purpose than that of involving a plain and simple truth in obscurity and mystery. If it be used in the sense in which 1 have invariably em-
■^8 ELEMENTS OF THE PHILOSOPHY
ployed it in this work, the proposition is altogether ab- surd and incomprehensible.
For the more complete illustration of this point, I must here recur to a distinction formerly made between the abstractions which are subservient to reasoning, and those which are subservient to imagination. " In every instance in which imagination is employed in forming new wholes, by decompounding and combining the per- ceptions of sense, it is evidently necessary that the poet or the painter should be able to state or represent to him- self the circumstances abstracted, as separate objects of conception. But this is by no means requisite in every case in which abstraction is subservient to the power of reasoning ; for it frequently happens, that we can reason concerning the quahty or property of an object ab- stracted from the rest, while, at the same time, we find it impossible to conceive it separately. Thus, I can reason concerning extension and figure, without any re- ference to color, although it may be doubted, if a per- son possessed of sight can make extension and figure steady objects of conception, without connecting with them the idea of one color or another. Nor is this al- ways owing (as it is in the instance just mentioned) merely to the association of ideas ; for there are cases, in which we can reason concerning things separately, which it is impossible for us to suppose any mind so constituted as to conceive apart. Thus we can reason concerning length, abstracted from any other dimension ; although, surely, no understanding can make length, without breadth, an object of conception." * In like manner, while I am studying Euchd's demonstration of the equality of the three angles of a triangle to two right angles, I find no difficulty in following his train of reasoning, although it has no reference whatever to the specific size or to the specific form of the diagram be- fore me. I abstract, therefore, in this instance, from both of these circumstances presented to my senses by the immediate objects of my perceptions ; and yet it is manifestly impracticable for me either to dehneate on
* Vol. I. p 119.
OF THE HUMAN MIND. 79
paper, or to conceive in the mind, such a figure as shall not include the circumstances from which I abstract, as well as those on which the demonstration hinges.
In order to form a precise notion of the manner in which this process of the mind is carried on, it is necessa- ry to attend to the close and inseparable connexion which exists between the faculty of general reasoning, and the use of artificial language. It is in consequence of the aids which this lends to our natural faculties, that we are furnished with a class of signs, expressive of all the cir- cumstances which we wish our reasonings to compre- hend ; and, at the same time, exclusive of all those which we wish to leave out of consideration. The word triangle, for instance, when used without any additional epithet, confines the attention to the tlwee angles and three sides of the figure before us ; and reminds us, as we proceed, that no step of our deduction is to turn on any of the specific varieties which that figure may ex- hibit. The notion, however, which we annex to the word triangle, while we are reading the demonstration, is not the less 'dparticular notion, that this word, from its partial or abstracted import, is equally applicable to an infinite variety of other individuals.*
These observations lead, in my opinion, to so easy an explanation of the transition from jjarticular to general reasoning, that I shall make no apology for prosecuting the subject a little farther, before leaving this branch of my argument.
* " By this imposition of names, some of larger, some of stricter signification, we turn the reckoning of tlie consequences of things imagined in the mind, into a reck- oning of the consequences of appellations. For example, a man that hath no use of speech at all (such as is born and remains perfectly deaf and dumb,) if he set be- fore his eyes a triangle, and by it two right angles (such as are the corners of a square figure,) he may by meditation compare and find, that the three angles of that triangle, are equal to those right angles that stand by it. But if another triangle be shown him, different in shape from the former, he cannot know, without a new la- bor, whether the three angles of that also be equal to the same. But he that hath the use of words, when he observes that such equality was consequent, not to the length of the sides, nor to any particular thing in this triangle ; but only to this, that the sides were straight, and the angles three ; and that that was all for which he named it a triangle ; will boldly conclude universally, that such equality of angles is in all triangles whatsoever ; and register his invention in these general terms, " Ev- ery triangle hath its three angles equal to two right angles. And thus the conse- quence found in one particular, comes to be registered and remembered as an univer- sal rule ; and discharges our mental reckoning of time and place ; and delivers us from all labor of the mind, saving the first ; and makes that which was found true here, and now, to be tiue in all times and places." — Hobbes, 0/ Man, Part. I. Chap. iv.
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It will not, I apprehend, be denied, that when a learn- er first enters on the study of geometry, he considers the diagrams before him as individual objects, and as in- dividual objects alone. In reading, for example, the de- monstration just referred to, of the equality of the three angles of every triangle to two right angles, he thinks only of the triangle which is presented to him on the margin of the page. Nay, so completely does this par- ticular figure engross his attention, that it is not without some difficulty he, in the first instance, transfers the demonstration to another triangle whose form is very different, or even to the same triangle placed in an in- verted position. It is in order to correct this natural bias of the mind, that a judicious teacher, after satisfy- ing himself that the student comprehends perfectly the force of the demonstration, as applicable to the particu- lar triangle which Euclid has selected, is led to vary the diagram in different w^ays, with a view to show him, that the very same demonstration expressed in the very same form of words, is equally apphcable to them all. In this manner he comes, by slow degrees, to comprehend the nature of general reasoning, establishing insensibly in his mind this fundamental logical principle, that when the enunciation of a mathematical proposition involves only a certain portion of the attributes of the diagram which is employed to illustrate it, the same proposition must hold true of any other diagram involving the same attributes, how much soever distinguished from it by other specific pecuUarities.*
* In order to impress the mind still more forcibly with the same conviction, some have supposed that it might be useful, in an elementary work, such as that oi" Fuclid, to omit the diagrams altogether, leaving the student to delineate them for himself, agreeably to the terms of the enunciation and of the construction. And were the study of geometry to be regarded merely as subservient to that of logic, much might be alleged in confirmation of this idea. Where, however, it is the main purpose of the teacher (as almost always happens) to familiarize the mind of his pupil with the fundamental principles of the science, as a preparation for the study of physics, and of the other parts of mixed mathematics, it cannot be denied, that such a practice would be far less favorable to the memory, than the plan which Euclid has adopted, of annexing to each theorem an appropriate diagram, with which the general truth comes very soon to be strongly associated. Nor is this circumstance found to be at- tended in practice with the inconvenience it may seem to threaten ; inasmuch as the student, without any reflection whatever on logical principles, generalizes the particular example, according to the different cases which may occur, as easily and unconsciously as he could have applied to these cases the general enunciation.
The same remark may be extended to the other departments of our knowledge ;
OF THE HUMAN MIND. 81
Of all the generalizations in geometry, there are none into which the mind enters so easily as those which relate to diversities in point of size or magnitude. Even in reading the very first demonstrations of Euchd, the learner almost immediately sees, that the scale on which the diagram is constructed, is as completely out of the question as the breadth or the colo7' of the lines which it presents to his external senses. The demonstration, for example, of the fourth proposition, is transferred without any conscious process of reflection, from the two trian- gles on the margin of the page, to those comparatively large ones which a public teacher exhibits on his board or slate to a hundred spectators. I have frequently, however, observed in beginners, while employed in copy- ing such elementary diagrams, a disposition to make the copy, as nearly as possible, both in size and figure, afac simile of the original.
The generahzations which extend to varieties oiform and oi position, are accomplished much more slowly ; and for this obvious reason, that these varieties are more strongly marked and discriminated from one another, as objects of vision and of conception. How difficult (comparatively speaking) in such instances, the gene- ralizing process is, appears manifestly from the embar- rassment which students experience, in applying the fourth proposition to the demonstration of the fifth. The inverted position, and the partial coincidence of the two little triangles below the base, seem to render their mutual relation so difl'erent from that of the two separate triangles which had been previously familiarized to the eye, that it is not surprising this step of the reasoning
in all of which it will be found useful to associate with every important general con- clusion some particular example or illustration, calculated, as much as possible, to present an impressive image to the power of conception. By this means, while (he example gives us a firmer hold, and a readier command of the general theorem, the theorem, in its turn, serves to correct the errors into which the judgment might be led by the specific pecularitics of the example. Hence, by the way, a strong argu- ment in favor of the practice recommended by Bacon, of connecting emblems with prccnot'wris, as the most powerful of all adminicles to the f.icully of memory; and hence the aid which this faculty may be expected to receive, in point of prompti- tude, if not of correctness, from a lively imagination. Nor is it the least advan- tage of this practice, that it supplies us at all times with ready and apposite illus- trations to facilitate the conimimication of our general conclusions to others. But the prosecution of these hints would lead me too far astray from the subject of this section.
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should be followed, by the mere novice, with some de- gree of doubt and hesitation. Indeed, where nothing of this sort is manifested, I should be more incHned to as- scribe the apparent quickness of his apprehension to a retentive memory, seconded by implicit faith in his in- structer ; than to regard it as a promising symptom of mathematical genius.
Another, and perhaps a better illustration of that nat- ural logic which is exemplified in the generalization of mathematical reasonings, may be derived from those instances where the same demonstration apphes, in the same words, to what are called, in geometry, the diifer- ent cases oi a proposition. In the commencement of our studies, we read the demonstration over and over, applying it successively to the different diagrams ; and it is not without some wonder we discover, that it is equally adapted to them all. In process of time, we learn that this labor is superfluous ; and if we find it sat- isfactory in one of the cases, can anticipate with confi- dence the justness of the general conclusion, or the modifications which will be necessary to accommodate it to the diff"erent forms of which the hypothesis may admit.
The algebraical calculus, however, when applied to geometry, places the foregoing doctrine in a point of view still more striking ; " representing," to borrow the words of Dr. Halley, " all the possible cases of a problem at one view ; and often in one general theorem compre- hending whole sciences ; which deduced at length into propositions, and demonstrated after the manner of the ancients, might well become the subject of large treati- ses."* Of this remark, Halley gives an instance in a formula, which, when he first published it, was justly regarded " as a notable instance of the great use and comprehensiveness of algebraic solutions." I allude to his formula for finding universally the foci of optic lenses ; an example which I purposely select, as it cannot fail to be famiharly known to all who have the slightest tincture of mathematical and physical science.
* PhUos. Transact. No. 205. Miscell. Cur. Vol. I. p. 348.
OF THE HUMAN MIND. 83
In such instances as these, it will not surely be sup- posed, that while we read the geometrical demonstration, or follow the successive steps of the algebraical process, our general conceptions embrace all the various possible cases to which our reasonings extend. So very differ- ent is the fact, that the wide grasp of the conclusion is discovered only by a sort of subsequent induction ; and, till habit has familiarized us with similar discoveries, they never fail to be attended with a certain degree of unex- pected delight. Dr. Halley seems to have felt this strong- ly when the optical /ormw/a already mentioned first pre- sented itself to his mind.
In the foregoing remarks, I have borrowed my exam- ples from mathematics, because, at the period of life when we enter on this study, the mind has arrived at a sufficient degree of maturity to be able to reflect accu- rately on every step of its own progress ; whereas, in those general conclusions to which we have been habitua- ted from childhood, it is quite impossible for us to ascer- tain, by any direct examination, what the processes of thought were, which originally led us to adopt them. In this point of view, the first doubtful and unassured steps of the young geometer, present to the logician a peculiarly interesting and instructive class of phenomena, for illustrating the growth and developement of our rea- soning powers. The true theory, more especially of general reasoning, may be here distinctly traced by every attentive observer ; and may hence be confidently appli- ed (under due limitations) to all the other departments of human knowledge.*
* The view of general reasoning which is given above, appears to myself to af- ford, (without any comment) a satisfactory answer to the following argument of the late wortliy and learned Dr. Price : " That the universality consists in the idea, and not merely in the name, as used to signify a number of particulars, resembling that which is the immediate object of reflection, is plain ; because, was the idea to which the name answers, and which it recalls into the mind, only a particular one, we could not know to what other ideas to apply it, or what particular objects had the resemblance necessary to bring them within the meaning of the name. A person, in reading over a mathematical demonstration, certainly is conscious that it relates to somewhat else, than just that precise figure presented to him in the diagram. But if he knows not what else, of what use can the demonstration be to him ? How is his knowledge enlarged by it ? Or how shall he know afterwards to what to apply it ? "
In a note upon this passage. Dr. Price observes, that, " according to Dr. Cudworth, abstract ideas arc implied iu the cognodcitive jtower oj the mind ,■ which, he says,
84 ELEMENTS OF THE PHILOSOPHY
From what has been now said, it would appear, that, in order to arrive at a general conclusion jn mathemat- ics, (and the same observation holds with respect to other sciences,) tioo different processes of reasoning are necessary. The one is the demonstration of the propo- sition in question.; in studying which we certainly think of nothing but the individual diagram before us. The other is, the train of thought by which we transfer the particular conclusion to which we have been thus led, to any other diagram to which the same enunciation 4s equally applicable. As this last train of thought is, in all cases, essentially the same, we insensibly cease to re- peat it when the occasion for employing it occurs, till we come at length, without any reflection, to generalize our particular conclusion, the moment it is formed ; or, in other words, to consider it as a proposition compre- hending an indefinite variety of particular truths. When this habit is established, we are apt to imagine, — forget- ting the slow steps by which the habit was acquired, — that the general conclusion is an immediate inference from a general demonstration ; and that, although there was only one particular diagram present to our external senses, we must have been aware, at every step, that our thoughts were really conversant, not about this dia- gram, but BboMt general ideas ^ or, in Dr. Reid's language, general conceptions. Hence the familiar use among logi- cians of these scholastic and mysterious phrases, which,
contains in itself virtually (as the future plant or tree is contained in the seed) general notions or exemplars of all things, which are exei ted by it, or unfold and discover themselves, as occasions invite, and proper circumstances occur." " This, no doubt," Dr. Price adds, " many will very freely condemn as whimsical and ex- travagant. I have, I own, a different opinion of it ; but yet I should not care to be obliged to defend it," — Review of the Principal Questions in Morals, pp. 38, 3d, 2d edit.
For my own part, I have no scruple to s'ay, that I consider this fancy of Cudworth as not only whimsical and extravagant, but as altogether unintelligible ; and yet it appears to me, that some confused analogy , of the same sort must exist in the mind of every person who imagines that he has the power of forming general conceptions without the intermediation of language.
In the continuation of the same note, Dr. Price seems disposed to sanction another remark of Dr. Cudworth : in which he pronounces the opinion of the nominalists to be so ridiculous and false, as to deserve no confutation. I suspect that when Dr. Cudworth wrote this splenetic and oracular sentence, he was out of humor with some argument of Hobbes, which he found himself unable to answer. It is not a little re- markable, that the doctrine which he here treats with so great contempt, should, with a very few exceptions, have united the suffrages of all the soundest philosophers of the eighteenth century.
OF THE HUMAN MIND. 85
/
whatever attempts may be made to interpret them in a
manner not altogether inconsistent with good sense,
;L have unquestionably the effect of keeping out of view the
real procedure of the human mind in the generahzation
idioi its knowledge.
Dr. Reid seems to be of opinion, that it is by the pow- er of forming general conceptions that man is distinguish- ed from the brutes ; for he observes, that " Berkeley's system goes to destroy the barrier between the rational and animal natures." I must own I do not perceive the justness of this remark, at least in its application to the system of the nominalists, as I have endeavoured to ex- plain and to limit it in the course of this work. On the contrary, it appears to me, that the account which has been just given of general reasoning, by ascribing to a process of logical deduction (presupposing the previous exercise of abstraction or analysis) what Dr. Reid at- tempts to explain by the scholastic, and not very intelli- gible phrase oi general conceptions, places the distinction between man and brutes in a far clearer and stronger light than that in which philosophers have been accus- tomed to view it. That it is to the exclusive possession of the faculty of abstraction, and of the other powers subservient to the use of general signs, that our species is chiefly indebted for its superiority over the other ani- mals, I shall afterwards endeavour to show.
It still remains for me to examine an attempt which Dr. Reid has made, to coiivict Berkeley of an inconsis- tency, in the statement of his argument against abstract general ideas. " Let us now consider," says he, " the Bishop's notion of generahzing. An idea (he tells us) which, considered in itself, is particular, becomes gen- eral, by being made to represent or stand for all other particular ideas of the same sort. To make this plain by an example : Suppose (says Berkeley) a geometri- cian is demonstrating the method of cutting a line into two equal parts. He draws, for instance, a black hne of an inch in length. This, which is in itself a particular Hne, is nevertheless, with regard to its s-ignification, general, since, as it is there used, it represents all par- ticular lines whatsoever, so that what is demonstrated of
86 ELEMENTS OF THE PHILOSOPHY
it, is demonstrated of all lines, or, in other words, of a line in general. And as that particular Hne becomes general by being made a sign, so the name line, which, taken absolutely, is particular, by being a sign, is made general.
" Here," continues Dr Reid, " I observe, that when a particular idea is made a sign to represent and stand for all of a sort, this supposes a distinction of things into sorts or species. To be of a sort, imphes having those attributes which characterize the sort, and are common to all the individuals that belong to it. There cannot therefore, be a sort without general attributes ; nor can there be any conception of a sort without a conception of those general attributes which distinguish it. The conception of a sort, therefore, is an abstract general conception.
" The particular idea cannot surely be made a sign of a thing of which we have no conception. I do not say, that you must have cm idea of the sort ; but surely you ought to understand or conceive what it means when you make a particular idea a representative of it ; oth- erwise your particular idea represents you know not what." *
Although I do not consider myself as called upon to defend all the expressions which Berkeley may have employed in support of his opinion on this question, I must take the liberty of remarking, that, in the present instance, he appears to me to have been treated with an undue severity. By ideas of the same sort, it is plain he meant nothing more than things called by the same name, and, consequently, (if our illustrations are to be borrow- ed from mathematics,) comprehended under the terms of the same definition. In such cases, the individuals thus classed together, are completely identified as subjects of reasoning ; insomuch, that what is proved with respect to one individual, must hold equally true of all the oth- ers. As it is an axiom in geometry, that things which are equal to one and the same thing, are equal to one another ; so it may be stated as a maxim in logic, that
* Pages 484, 485.
OF THE HUMAN MIND. 87
whatever things have the same name apphed to them, in consequence of their being comprehended in the terms of the same definition, may all be considered as the same identical subject, in every case where that defini- tion is the principle on which our reasoning proceeds. In reasoning, accordingly, concerning any sort or species of things, our thoughts have no occasion to wander from the individual sign or representative to which the attention happens to be directed or to attempt the fruit- less task of grasping at those specific varieties which are avowedly excluded from the number of our premises. As every conclusion which is logically deduced from the definition must, of necessity, hold equally true of all the individuals to which the common name is appli- cable, these individuals are regarded merely as so many units, which go to the composition of the multitude comprehended under the collective or generic term. Nor has the power of conception any thing more to do in the business, than when we think of the units, expressed by a particular number in an arithmetical computation.
The word sort is evidently transferred to our intellec- tual arrangements, from those distributions of material objects into seperate heaps or collections, which the common sense of mankind universally leads them to make for the sake of the memory; or (which is perhaps nearly the same thing) with a view to the pleasure aris- ing from the perception of order. A familiar instance of this presents itself in the shelves, and drawers, and parcels, to which every shopkeeper has recourse for assorting, according to their respective denominations and prices, the various articles which compose his stock of goods. In one parcel (for example) he collects and incloses under one common envelope, all his gloves of a particular size and quality ; in another, all his gloves of a different size and quality ; and, in like manner, he proceeds with the stockings, shoes, hats, and the various other commodities with which his warehouse is filled. By this means, the attention of his shop-boy, instead of being bewildered among an infinitude of particulars, is confined to parcels or assortments of particulars ; of each
88 ELEMENTS OF THE PHILOSOPHY
of which parcels a distinct idea may be obtained from an examination of any one of the individuals contained in it. These individuals, therefore are, in his apprehen- sion, nothing more than so many units in a multitude, any one of which units is perfectly equivalent to 'any other; while, at the same time, the parcels themselves, notwithstanding the multitude of units of which they are made up, distract his attention, and burden his memory as Uttle, as if they were individual articles. The truth is, that they become to his mind individual objects of thought, like a box of counters, or rouleau of guineas, or any ,of the other material aggregates with which his sen- ses are conversant ; or, to take an example still more apposite to our present purpose, like the phrases one thousand, or one milhon, when considered merely as simple units entering into the composition of a numeric- al sum.
The task which I have here supposed the tradesman to perform, in order to facihtate the work of his shop- boy, is exactly analogous, in its effect, to the aid which is furnished to the infant understanding by the structure of its mother-tongue ; the generic words which abound in language assorting and (if I may use the expression) packing up, under a comparatively small number of com- prehensive terms, the multifarious objects of human knowledge.* In consequence of the generic terms to which, in civilized society, the mind is early familiarized, the vast multiphcity of things which compose the furni- ture of the globe are presented to it, not as they occur to the senses of the untaught savage, but as they have been arranged and distributed into parcels or assortments by the successive observations and reflections of our predecessors. Were these arrangements and distribu- tions agreeable, in every instance, to sound philosophy, the chief source of the errors to which we are hable in all our general conclusions would be removed : but it would be too much to expect (with some late theorists) that, even in the most advanced state, either of phisycal
* The same analogy had occured to Locke. " To shorten its way to knowledge, and make each perception more comprehensive, the mind binds them into bundles."
OF THE HUMAN MIND. 89
or of moral science, this supposition is ever to be real- ized in all its extent. At the same time, it must be re- membered, that the obvious tendency of the progressive reason and experience of the species, is to diminish, more and more, the imperfections of the classifications which have been transmitted from ages of comparative ignorance ; and of consequence, to render language, more and more, a safe and powerful organ for the in- vestigation of truth.
The only science which furnishes an exception to these observations is mathematics ; a science essentially distinguished from every other by this remarkable cir- cumstance, that the precise import of its generic terms is fixed and. ascertained by the definitions which form the basis of all our reasonings, and in which, of conse- quence, the very possibiUty of error in our classifica- tions, is precluded, by the virtual identity of all those hypothetical objects of thought to which the same gen- eric term is applied.
I intend to prosecute this subject farther, before con- cluding my observations on general reasoning. At present, I have only to add to the foregoing remarks, that, in the comprehensive theorems of the philosopher, as well as in the assortments of the tradesman, I cannot perceive a single step of the understanding, which im- phes any thing more than the notion of number, and the use of a common name.
Upon the whole, it appears to me, that the celebrated dispute concerning abstract general ideas, which so long divided the schools, is now reduced, among correct thinkers, to this simple question of fact, Could the hu- man mind, without the use of signs of one kind or another, have carried on general reasonings, or formed general conclusions ? Before arguing with any person on the subject, I should wish for a categorical explanation on this preliminary point. Indeed, every other controversy connected with it turns on little more than the meaning of words.
A difference of opinion with respect to this question oi fact (or rather, I suspect, a want of attention in some of the disputants to the great variety of signs of which
VOL. II. 12
90 ELEMENTS OF THE PHILOSOPHY
the mind can ayail itself, independently of words) still continues to keep up a sort of distinction between the Nominahsts and the Conceptuahsts. As for the Real- ists, they may, I apprehend, be fairly considered, in the present state of science, as having been already forced to lay down their arms.
That the doctrine of the Nominalists has been stated by some writers of note in very unguarded terms, I do not deny,* nor am I certain it was ever delivered by any one of the schoolmen in a form completely unexception- able ; but after the luminous, and, at the same time, cautious manner in which it has been unfolded by Berkeley and his successors, I own it appears to me not a little surprising that men of talents and candor should still be found inclined to shut their eyes against the light, and to shelter themselves in the darkness of the middle ages. For my own part, the longer and the more attentively that I reflect on the subject, the more am I disposed to acquiesce in the eulogium be- stowed on Roscelinus and his followers by Leibnitz ; one of the very few philosophers, if not the only phi- losopher, of great celebrity, who seems to have been
* Particularly by Hobbes, some of whose incidental remarks and expressions would certainly, if followed strictly out to their logical consequences, lead to the com- plete subversion of truth, as a thing real and independent of human opinion. It is to this, I presume, that Leibnitz alludes when he says of him, " Thomas Hobbes, qui, ut verumfatear, mihiplus quam nomlnalis videtur."
I shall afterwards point out the mistake by which Hobbes seems to me to have been misled. In the mean time, it is but justice to him to say, that I do not think he had any intention to establish those sceptical conclusions which, it must be owned, may be fairly deduced as corollaries from some of his principles. Of this I would not wish for a stronger proof than his favorite maxim, that, " words are the counters of wise men, but the money of fools ; " a sentence which expresses, with marvellous conciseness, not only the proper function of language, as an instrument of reasoning, but the abuses to which it is liable when in unskilful hands.
Dr. Gillies, who has taken much pains to establish Aristotle's claims to all that is valuable in the doctrine of the Nominalists, has, at the same time, represented him as the only favorer of this opinion, by whom it has been taught without any admixture of those errors which are blended with it in the works of its modern revivers. Even Bishop Berkeley himself is involved with Hobbes and Hume in the same sweeping sentence of condemnation. " The language of the Nominalists seems to have been extremely liable to be perverted to the purposes of scepticism, as taking away the specific distinctions of things ; and is in fact thus perverted by Hobbes, Berkeley, Hume, and their innumtrahle followers. But Aristotle's language is not liable to this abuse." — Gillies'' s Aristotle, Vol. 1. p. 71, 2d. ed.
Among these sceptical followers of Berkeley, we must, I presume, include the late learned and ingenious Dr. Campbell : whose remarks on this subject, I will, nevertheless, venture to recommend to the particular attention of my readers. In- deed, I do not know of any writer who has treated it with more acuteness and per- spicuity. {'&^ic Philosophy of Rhetoric, Boo\i\\. chA.\i. Mil.)
OF THE HUMAN MIND. 91
fully aware of the singular merits of those by whom this theory was originally proposed : " secta nominali-
UM, OMNIUM INTER SCHOLASTICAS PROFUNDISSIMA, ET HODIERN^ REFORMATiE PHILOSOPHANDI RATIONI CON-
GRUENTissiMA." It is a theory, indeed, much more con- genial to the spirit of the eighteenth than of the elev- enth century ; nor must it be forgotten, that it w as pro- posed and maintained at a period when the algebraical art (or to express myself more precisely universal arith- metic) from which we now borrow our best illustrations in explaining and defending it, was entirely unknown.
II.
Continuation of the Subject. — Of Language considered as an Instrument of Thought.
Having been led, in defence of some of my own opinions, to introduce a few additional remarks on the controversy with respect to the theory of general rea- soning, I shall avail myself of this opportunity to illus- trate a little farther another topic, (intimately connected with the foregoing argument,) on which the current doctrines of modern logicians seem to require a good deal more of explanation and restriction than has been commonly apprehended. Upon this subject I enter the more willingly, that, in my first volume, I have alluded to these doctrines in a manner which may convey, to some of my readers, the idea of a more complete acqui- escence, on my part, in their truth, that I am disposed to acknowledge.
In treating of abstraction, I endeavoured to show that we think, as well as speak, by means of words, and that, without the use of language, our reasoning faculty (if it could have been at all exercised) must necessarily have been hmited to particular conclusions alone. The effects, therefore, of ambiguous and indefinite terms are not confined to our communications with others, but extend to our private and sohtary speculations. Dr. Campbell, in his Philosophy of Rhetoric, has made some judicious and important observations on this sub-
92 ELEMENTS OF THE PHILOSOPHY
ject ; and, at a much earlier period, it drew the attention of Des Cartes ; who, in the course of a very valuable discussion with respect to the sources of our errors, has laid particular stress on those to w^hich we are exposed from the employment of language as an instrument of thought. " And, lastly, in consequence of the habitual use of speech, all our ideas become associated with the words in which we express them ; nor do we ever com- mit these ideas to memory, without their accustomed signs. Hence it is, that there is hardly any one subject, of which we have so distinct a notion as to be able to think of it abstracted from all use of language ; and, indeed, as we remember words more easily than things, our thoughts are much more conversant with the former than with the latter. Hence, too, it is, that we often yield our assent to propositions, the meaning of which we do not understand ; imagining that we have either examined formerly the import of all the terms involved in them, or that we have adopted these terms on the authority of others upon whose judgment we can rely." *
* " Et denique propter loquelae usum, conceptos omnes nostros verbis, quibus eos exprimimus, alligamus, nee eos, nisi simul cum istis verbis, memorice mandamus. Cumque facilius postea verboium quam rerum recoidemur, vix unquam uUius rei conceptum habemus tam distinctum, ut ilium ab omni verboium conceptu separe- mus ; cogitationesque hominum fere omnium, circa verba magis quam circa res versantur ; adeo ut persaepe vocibus non intellectis prajbeant assensum, quia putant se illos olim intellexisse, vel ab aliis, qui eas recte intelligebant, accepisse." — Princ. Phil. Pars Prima, Ixxiv.
I have quoted a very curious passage nearly to the same purpose, from Leibneitz, in a note annexed to my first volume (see note L.) I was not then aware of the previous attention which had been given to this source of error by Des Cartes ; nor did I expect to find so explicit an allusion to it in the writings of Aristotle, as I have since observed in the following paragraph ;
/lib y ocl toJv naqa ttjv le^iv oiiTog o Tgoiiog -d-STsog' ngcorov fisv, ow uuXXov rj anaTTi ylvsrai /xst aXlwv aKonov^ivoig rj ya& eavjovg ' -r] filv yaq u£t aXXwv axe^ig dm loyn' ij ds )ca& avxovg, i^/rjxrovdi avra tov ng«y- uaxog ' sha, xal xa& uviovg anajua&ai, avu^aivsi, oxav ml tov loyov •jioiriaavrr]V axiipiV tzi,-)] (.isv unaTrj tx Ti]g of.wiOTtjrog ' r] 8s ofioioxrjg, ex T^? U^fag. De. Sophist. Elenchis, Lib. 1. Cap. 7.
" Quocirca inter eos (paralogismos) qui in dictione consistunt, hicfallendi modus est ponendus. Primum, quia magis decipimur considerantes cum aliis, quam apud nosmelipsos : nam consideratio cum aliis per sermonem instituitur ; apud nosmetip- sos autem non minus fit per rem ipsam. Deinde et per nosmetipsos ut fallamur accidit, cum in rebus considerandis sermo adhibetur. Prseterea deceptio est ex similitudine : sirailitudo autem ex dictione." — Edit. Du Vol. Vol. 1. p. 289.
J^est it should be concluded, however, from this detached remark, that Aristotle had completely anticipated Locke and Condillac in their speculations with respect to language, considered as an instrument of thought, 1 must beg of my readers to com- pare it with the previous enumeration given by the same author, of those paralogisms
OF THE HUMAN MIND. 93
To these important considerations it may be worth while to add, that whatever improvements may yet be made in language, by philosophers, they never can re- heve the student from the indispensable task of analyz- ing, with accuracy, the complex ideas he annexes to the terms employed in his reasonings. The use of general terms, as Locke has remarked, is learned, in many cases, before it is possible for us to comprehend their meaning ; and the greater part of mankind continue to use them through life, without ever being at the trouble to examine accurately the notions they convey. This is a study which every individual must carry on for himself; and of which no rules of logic (how useful soever they may be in directing our labors) can super- sede the necessity.
Of the essential utility of a cautious employment of words, both as a medium of communication and as an instrument of thought, many striking illustrations might be produced from the history of science during the time that the scholastic jargon was current among the learned ; a technical phraseology, which was not only ill-calculated for the discovery of truth, but which was dexterously contrived for the propagation of error ; and which gave to those who were habituated to the use of it, great advan- tages in controversy (at least in the judgment of the multitude) over their more enlightened and candid oppo- nents. " A blind wrestler, by fighting in a dark cham- ber," to adopt an allusion of Des Cartes, " may not only conceal his defect, but may enjoy some advantages over those who see. It is the hght of day only that can dis- cover his inferiority." The imperfections of this phi-
or fallacies which lie in the diction (De Sophist. Elenchis, Lib. 1, Cap. 4.) — recom- mending to them, at the same time, as a useful comment on the original, the twen- tieth chapter of the third book of a v/ork entitled Insiitiitio Logica, by the learned and justly celebrated Dr. Wallis of Oxford. I select this work in preference to any other modern one on the same subject, as it has been lately pronounced, by an au- thority lor which I entertain a sincere respect, to be " a complete and accurate trea- tise of logic, strictly according to the Aristotelian method ;" and as we are farther told, that it is " still used by many in the university to which Wallis belonged, as the lecture-book in that department of study." I intend to quote part of this chap- ter on another occasion. At present I shall only observe, that it does not contain the slightest reference to the passage which has led me to introduce these obscrs'ations ; and which, I believe, will be now very generally allowed to be of greater value than all those puerile distinctions put together, which Dr. Wallis has been at so much pains to illustrate and to exemplify.
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losophy, accordingly, have been exposed by Des Car- tes and his followers, less by the force of their reason- ings, than by their teaching men to make use of their own faculties, instead of groping in the artificial dark- ness of the schools ; and to perceive the folly of ex- pecting to advance science by ringing changes on words to which they annexed no clear or precise ideas.
In consequence of the influence of these views, the attention of our soundest philosophers was more and more turned, during the course of the last century, to the cultivation of that branch of logic which relates to the use of words. Mr. Locke's observations on this subject form, perhaps, the most valuable part of his writings ; and, since his time, much additional hght has been thrown upon it by Condillac and his successors.
Important, however, as this branch of logic is in its practical applications ; and highly interesting, from its intimate connexion with the theory of the human mind, there is a possibility of pushing, to an erroneous and dangerous extreme, the conclusions to which it has led. Condillac himself falls, in no inconsiderable a de- gree, under this censure ; having, upon more than one occasion, expressed himself as if he conceived it to be possible, by means of precise and definite terms, to reduce reasoning, in all the sciences, to a sort of mechanical operation, analogous, in its nature, to those which are practised by the algebraist, on letters of the alphabet. " The art of reasoning," he repeats over and over, " is nothing more than a language well-arranged." — " L'art de raisonner se reduit a une langue bien faite."
One of the first persons, as far as I know, who ob- jected to the vagueness and incorrectness of this pro- position, was M. De Gerando ; to whom we are farther indebted for a clear and satisfactory exposition of the very important fact to which it relates. To this fact Condillac approximates nearly in various parts of his works ; but never, perhaps, without some degree of in- distinctness and of exaggeration. The point of view in which it is placed by his ingenious successor, strikes me as so just and happy, that I cannot deny myself the
OF THE HUMAN MIND, 95
pleasure of enriching my book with a few of his obser- vations.
" It is the distinguishing characteristic of a hvely and vigorous conception, to push its speculative conclusions somewhat beyond their just limits. Hence, in the logi- cal discussions of this estimable writer, these maxims (stated without any explanation, or restriction,) ' That the study of a science is nothing more than the acquisition of a language ; ' and ' that a science properly treated is only a language loell contrived.'' Hence the rash asser- tion, ' That mathematics possess no advantage over other sciences, but ivhat they derive from a better phraseology ; and that all of these might attain to the same characters of simplicity and of certainty, if loe knew hoiv to give them signs equally perfectJ* " *
" The same task which must have been executed by those who contributed to the first formation of a lan- guage, and which is executed by every child when he learns to speak it, is repeated over in the mind of every adult when he makes use of his mother-tongue ; for it is only by the decomposition of his thoughts that he can learn to select the signs which he ought to employ, and to dispose them in a suitable order. Accordingly, those external actions which we call speaking or icriting, are always accompanied with a philosophical process of the understanding, unless we content ourselves, as too often happens, with repeating over mechanically what has been said by others. It is in this respect that languages, with their forms and rules, conducting (so to speak) those who use them, into the path of a regu- lar analysis ; tracing out to them, in a well-ordered dis- course, the model of a perfect decomposition, may be regarded, in a certain sense, as ancdyticcd methods — But I stop short ; Condillac, to whom this idea belongs, has developed it too well to leave any hope of improving upon his statement."
In a note upon this passage, however, M. De Gerando has certainly improved not a little on the statement of Condillac. " In asserting," says he, " that languages
* Des Signes et de Vkvi de Penser, &c. Introd. pp. xx. xxi.
96 ELEMENTS OF THE PHILOSOPHY
may be regarded as analytical methods, I have added the quahfying phrase, in a certain sense, for the word method cannot be employed here with exact propriety. Languages furnish the occasions and the means of analy- sis ; that is to say, they afford us assistance in following that method ; but they are not the method itself. They resemble signals or finger-posts placed on a road to en- able us to discover our way ; and if they help us to analyze, it is because they are themselves the results, and as it were, the monuments of an analysis which has been previously made ; nor do they contribute to keep us in the right path, but in proportion to the degree of judgment with which that analysis has been conduct- ed." *
I was the more solicitous to introduce these excellent remarks, as I suspect that I have myself indirectly con- tributed to propagate in this country the erroneous opinion which it is their object to correct. By some of our later writers it has not only been implicitly adopted, but has been regarded as a conclusion of too great value to be suffered to remain in the quiet possession of the moderns. " Aristotle," says the author of a very valu- able analysis of his works " well knew that our know- ledge of things chiefly depending on the proper appli- cation of language as an instrument of thought, the true art of reasoning is nothing but a language accu- rately defined and skilfully arranged ; an opinion which, after many idle declamations against his barren general- ities and verbal trifling, philosophers have begun very generally to adopt." f
* Des Signes et de I'Art de Penser, &c. pp. 158, 159, Tom. I.
t Aristotle's Ethics, &c. by Dr. Gillies, Vol. I. p. 94, '2d. edit.
The passage in my first volume, to which I suspect an allusion is here made, is as follows :
" The technical terms, in the different sciences, render the appropriate language of philosophy a still more convenient instrument of thought, than those langua- ges which have originated from popular use ; and in proportion as these technical terms improve in point of precision and of comprehensiveness, they will contribute to render our intellectual progress more certain and more rapid. ' While engaged,' says Mr. Lavoisier, ' in the composition of my Elements of Chemistry, I perceived, better than I had ever done before, the truth of an observation of Condillac, that we think only through the medium of words, and that languages are true analytic methods. Algebra, which, of all our modes of expression, is the most simple, the most exact, and the best adapted to its purpose, is, at the same time, a language and an analytical method. The art of reasoning is nothing more than a language
OF THE HUMAN MIND. 97
After this strong and explicit assertion of the priority of Aristotle's claim to the opinion which we are here told "philosophers begin venj generally to adopt,^^ it is to be hoped, that M. De Gerando will be in future allowed to enjoy the undisputed honor of having seen a little far- ther into this fundamental article of logic than the Sta- girite himself.'
III.
Continuation of the Subject. — Visionary Theories of some Logicians, occasioned by their Inattention to the Essential Distinction between Mathematics and other Sci-
In a passage already quoted from De Gerando, he takes notice of what he justly calls a rash assertion of Co7idillac, " that mathematics possess no advantage over other sciences, but wh^tt they derive from a better phraseology ; and that all of them might attain to the same characters of simplicity and of certainty, if we knew how to give them sig7is equally perfect."
Leibnitz seems to point at an idea of the same sort, in those obscure and enigmatical hints (not altogether worthy, in my opinion, of his powerful and comprehen-^ sive genius) which he has repeatedly thrown out, about the miracles to be effected by a new art of his own in- vention ; to which art he sometimes gives the name of
well arranged.' The influence," I have added, " which these very enlightened and philosophical views have already had on the doctrines of chemistry, cannot fail to be known to most of my readers."
When this paragraph was first written, I was fully aware of the looseness and in- distinctness of Lavoisier's expressions ; hut as my only object in introducing the quotation was to illustrate the influence of general logical principles on the progress of particular sciences, 1 did not think it necessary, in the introduction to my work, to point out in what manner Condillac's propositions were to be limited and correct- ed. I am truly happy, for the sake of M. Dc Gerando, that [ happened to transcribe them in the same vague and very exccjitionable terras in which 1 found them sanc- tioned liy the names of Condillac, and of one of the most illustrious of his disciples.
It will not, I hope, be considered as altogether foreign to the design of this note, if I remark further, how easy it is ibr a translator of Aristotle (in consequence of the unparalleled brevity which lie sometimes affects) to accommodate the sense of the original, by the help of paraphrastical clauses, expressed in the phraseology of mod- ern science, to every progressive step in the history of human knowledge. In truth, there is not one philosopher of antiquity, whose opinions, when they are stated in any terms buthis own, are to be received with so great distrust.
The unsoundness of Condillac's assertion, that the art of reasoning is nothing more than a language loell arranged, was, I believe, first pointed out by M. Pre- vost. — Sec some acute and decisive objections to this proposition in his Treatise Dea Signes, Sac. Paris, An. VIII. p. 20.
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Ars Combinatoria Chm'acteristica, and sometimes of ^rs Comhinatoria Generalis ac Vera. In one of his letters to Mr. Oldenburg, he speaks of a plan he had long been meditating, of treating of the science of mind by means of mathematical demonstrations. " Many wondeful things," he adds, " of this kind have occurred to me ; which, at some future period, I shall explain to the pub- lic with that logical precision which the subject re- quires." * In the same letter, he intimates his behef in the possibility of inventing an art, " which, with an ex- actitude resembling that of mechanism, may render the operations of reason steady and visible, and, in their effects on the minds of others, irresistible."! After which he proceeds thus :
" Our common algebra, which we justly value so high- ly, is no more than a branch of that general art which I have here in view. But, such as it is, it puts it out of our power to commit an error, even although we should wish to do so ; while it exhibits truth to our eyes like a picture stamped on paper by means of a machine. It must at the same time be recollected, that algebra is in- debted for whatever it accomplishes in the demonstra- 'tion of general theorems to the suggestions of a higher science ; a science which I have been accustomed to call characteristical combination ; very different, howev- er, in its nature, from that which these words are likely, at first, to suggest to the hearer. The marvellous utility of this art I hope to illustrate, both by precepts and ex- amples, if I shall be so fortunate as to enjoy health and leisure.
" It is impossible for me to convey an adequate idea of it in a short description. But this I may venture to assert, that no instrument (or organ) could easily be im- agined of more powerful efficacy for promoting the im- provement of the human understanding ; and that, sup- posing it to be adopted, as the common method of philo- sophizing, the time would very soon arrive, when we
• " Multa in hoc genere mira a me sunt obseivata, qua; aliquando, quo par est ri- gore, exposita dabo."
t " Quod velut mechanjca ratione fixam et visibilera ct (utita dicara) irresistibilem reddat rationem."
OF THE HUMAN MIND. 99
should be able to form conclusions concerning God and the Mind, with not less certainty than we do at present concerning figures and numbers." *
The following passage is translated from another let- ter of Leibnitz to the same correspondent :
" The matter in question depends on another of much higher moment ; I mean, on a general and true art of combination, of the extensive influence of which I do not know that any person has yet been fully aware. This, in truth, does not differ from that sublime analysis, into the recesses of which Des Cartes himself, as far as I can judge, was not able to penetrate. But, in order to carry it into execution, an alphabet of human thoughts must be previously formed ; and for the invention of this alphabet, an analysis of axioms is indispensably ne- cessary. I am not, however, surprised, that nobody has yet sufficiently considered it ; for we are, in general, apt to neglect what is easy ; and to take many things for granted, from their apparent evidence ; faults which, while they remain uncorrected, will for ever prevent us from reaching the summit of things intellectual, by the aid of a calculus adapted to moral as well as to mathe- matical science."!
In these extracts from Leibnitz, as well as in that quoted from Condillac, in the beginning of this article, the essential distinction between mathematics and the other sciences, in point of phraseology, is entirely over- looked. In the former science, where the use of an ambiguous word is impossible, it may be easily conceiv- ed how the solution of a problem may be reduced to something resembling the operation of a mill, — the conditions of the problem, when once translated from the common language into that of algebra, disappearing entirely from the view ; and the subsequent process
* Wallisli Opera, Vol. HI. p. 621.
t Wallisii Opera, Vol. III. p. 6.33.
As these reveries of this truly great man arc closely connected with tlio suhseqiient history of logical speculation in more than one country of Europe, I have hccu indu- ced to incorporate them, in an English version, with my own disquisitions. Some expressions, which, I am sensible, are not altogether agreeable to the idiom of ,our language, might have been easily avoided, if I had not felt it incumbent on me, in translating an author whose meaning, in this instance, I was able but vciy imperfect- ly to comprehend, to deviate as little as possible from his own words.
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being almost mechanically regulated by general rules, till the final result is obtained. In the latter the whole of the words about which our reasonings are conver- sant, admit, more or less, of different shades of mean- ing ; and it is only by considering attentively the rela- tion in which they stand to the immediate context, that the precise idea of the author in any particular instance is to be ascertained. In these sciences, accordingly, the constant and unremitting exercise of the attention is indispensably necessary, to prevent us, at every step of our progress, from going astray.
On this subject I have made various remarks in a vol- ume lately pubhshed ; to which I beg leave here to refer, in order to save the trouble of unnecessary repetitions.* From what I have there said, I trust it appears that, in following any train of reasoning, beyond the circle of the mathematical sciences, the mind must necessarily carry on, along with the logical deduction expressed in words, another logical process of a far nicer and more difficult nature ; — that of fixing, with a rapidity which escapes our memory, the precise sense of every word which is ambiguous, by the relation in which it stands to the general scope of the argument. In proportion as the language of science becomes more and more exact, the difficulty of this task will be gradually dimin- ished ; but let the improvement be carried to any con- ceivable extent, not one step will have been gained in accelerating that era, so sanguinely anticipated by Leib- nitz and Condillac, when our reasonings in morals and poUtics shall resemble, in their mechanical regularity, and in their demonstrative certainty, the investigations of algebra. The improvements which language re- ceives, in consequence of the progress of knowledge, consisting rather in a more precise distinction and clas- sification of the various meanings of words, than in a reduction of these meanings in point of number, the task of mental induction and interpretation may be ren- dered more easy and unerring; but the necessity of this task can never be superseded, till every word which
* Philosophical Essays, p, 153 et seq. 4to edit.
OF THE HUMAN MIND. 101
we employ shall be as fixed and invariable in its significa- tion as an algebraical character, or as the name of a geometrical figure.
In the mean time, the intellectual superiority of one man above another, in all the different branches of mor- al and political philosophy, will be found to depend chiefly on the success with which he has cultivated these silent habits of inductive interpretation, — much more, in my opinion, than on his acquaintance with those rules which form the great objects of study to the professed logician. In proof of this, it is sufficient for me to re- mind my readers, that the whole theory of syllogism proceeds on the supposition that the same word is al- ways to be employed precisely in the same sense, (for otherwise, the syllogism would be vitiated by consisting of more than three terms,) and, consequently, it takes for granted, in every rule which it furnishes for the guidance of our reasoning powers, that the nicest, and by far the most difficult part of the logical process, has been previously brought to a successful termination.
In treating of a different question, I have elsewhere remarked, that although many authors have spoken of the wonderful mechanism of speech, none has hitherto attended to the far more wonderful mechanism which it puts into action behind the scene. A similar obser- vation will be found to apply to what is commonly call- ed the Art of Reasoning. The scholastic precepts which profess to teach it, reach no deeper than the ve- ry surface of the subject ; being all of them confined to that part of the intellectual process which is embodied in the form of verbal propositions. On the most favor- able supposition which can be formed with respect to them, they are superfluous and nugatory ; but, in many cases, it is to be apprehended, that they interfere with the right conduct of the understanding, by withdrawing the attention from the cultivation of that mental logic on which the soundness of our conclusions essentially depends, and in the study of which (although some general rules may be of use) every man must be, in a great measure, his own master.*
* Tliose who ail- interested in this discussion, will enter more coiupletcly into my
102 ELEMENTS OF THE PHILOSOPHY
In the practical application of the foregoing conclu- sions, it cannot fail to occur, as a consideration equally obvious and important, that, in proportion as the objects of our reasoning are removed from the particular details with which our senses are conversant, the difficulty of these latent inductive processes must be increased. This is the real source of that incapacity for general speculation, which Mr. Hume has so well described as a distinguishing characteristic of uncultivated minds. " General reasonings seem intricate, merely because they are general ; nor is it easy for the bulk of man- kind to distinguish, in a great number of particulars, that common circumstance in which they all agree, or to extract it, pure and unmixed, from the other super- fluous circumstances. Every judgment or conclusion with them is particular. They cannot enlarge their views to those universal propositions which comprehend under them an infinite number of individuals, and in- clude a whole science in a single theorem. Their eye is confounded with such an extensive prospect, and the conclusions deduced from it, even though clearly ex- pressed, seem intricate and obscure." *
Difficult, however, and even impossible as the task of general speculation is to the bulk of mankind, it is nev- ertheless true, that it is the path which leads the cautious and skilful reasoner to all his most certain, as well as most valuable conclusions in morals and pohtics. If a theorist, indeed, should expect that these conclusions are, in every particular instance, to be reahzed, he would totally misapprehend their nature and appUcation ; inas- much as they are only to be brought to an experimental test, by viewing them on an extensive scale, and contin- uing our observations during a long period of time. " When a man deliberates," says Mr. Hume, "concerning his conduct in any particular diffair and forms schemes in pohtics, trade, economy, or any business in hfe, he never ought to draw his arguments too fine, or connect too
views, if they take the trouble to combine what is here stated with some observa- tions I have introduced in the first volume of this work. See p. 177, et seq. 3d edit.
* Essay on Commerce.
OF THE HUMAN MIND. 103
long a chain of consequences together. Something is sure to happen that will disconcert his reasoning, and produce an event different from what he expected. But when we reason upon general subjects, one may justly affirm, that our speculations can scarcely ever be too fine, provided they be just ; and that the difference between a common man and a man of genius is chiefly seen in the shallowness or depth of the principles on which they proceed." The same author afterwards ex- cellently observes, " That general principles, however intricate they may seem, must always prevail, if they be just and sound, in the general course of things, though they may fail in particular cases ; and that it is the chief business of philosophers to regard the general course of things." — " I may add," continues Mr. Hume, " that it is also the chief business of pohticians, especially in the do- mestic government of the state, where the public good, which is, or ought to be, their object, depends on the con- currence of a multitude of causes ; not as in foreign politics, on accidents and chances, and the caprices of a few persons." *
To these profound reflections of Mr. Hume, it may be added (although the remark does not bear directly on our present argument) that, in the systematical apphca- tion of general and refined rules to their private con- cerns, men frequently err from calculating their measures upon a scale disproportionate to the ordinary duration of human fife. This is one of the many mistakes into which projectors are apt to fall ; and hence the ruin which so often overtakes them, while sowing the seeds of a har- vest which others are to reap. A few years more might have secured to themselves the prize which they had in view ; and changed the opinion of the world (which is always regulated by the accidental circumstances of
• Essay on Commerce.
This contrast between the domestic and the foreign policy of a state, occurs more than once in Mr. Hume's writings ; (see in particular the first paragraphs of his Essay on tlio Rise of Arts and Sciences.) A similar observation had long before been made by Polybius. " There are two ways by whicli every kind of government is destroyed : either by some accident that liappens from without ; or some evil that arises within itself. When the first will be, it is not always easy to foresee ; but the latter is certain and determinate." — Book VI. Ex. 3. (Hampton's Trans- lation.)
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failure or of success) from contempt of their folly, into admiration of their sagacity and perseverance.
It is observed by the Comte de Bussi, that " time remedies all mischances ; and that men die unfortunate, only because they did not live long enough. Mareschal d'Estree, who died rich at a hundred, would have died a beggar, had he hved only to eighty." The maxim, like most other apothegms, is stated in terms much too un- quahfied ; but it may furnish matter for many interesting reflections, to those who have surveyed with attention the characters which have passed before them on the stage of life ; or who amuse themselves with marking the trifling and fortuitous circumstances by which the multi- tude are decided, in pronouncing their verdicts of fore- sight or of improvidence.
IV.
Continuation of the Subject. — Peculiar and supereminent Advantages possessed by Mathematicians, in consequence of their definite Phraseology.
If the remarks contained in the foregoing articles of this section be just, it will follow, that the various artifi- cial aids to our reasoning powers which have been pro- jected by Leibnitz and others, proceed on the supposi- tion (a supposition which is also tacitly assumed in the syllogistic theory) that, in all the sciences, the words which we employ have, in the course of our previous studies, been brought to a sense as unequivocal as the phraseology of mathematicians. They proceed on the supposition, therefore, that by far the most difficult part of the logical problem has been already solved. Should the period ever arrive, when the language of morahsts and pohticians shall be rendered as perfect as that of geometers and algebraists, then, indeed, may such con- trivances as the ^i^s Combinatoria and the Alphabet of human thoughts, become interesting subjects of philo- sophical discussion ; although the probability is, that, even were that era to take place, they would be found nearly as useless in morals and pohtics, as the syllogistic
OF THE HUMAN MIND. 105
art is acknowledged to be at present, in the investigations of pure geometry.
Of the pecuhar and siipereminent advantage possess- ed by mathematicians, in consequence of those fixed and definite relations which form the objects of their science, and the correspondent precision in their language and reasonings, I can think of no illustration more striking than what is afforded by Dr. Halley's Latin version from an Arabic manuscript, of the two books of Apollonius Pergaeus de Sectione Rationis. The extraordinary cir- cumstances under which this version was attempted and completed (which I presume are little known beyond the narrow circle of mathematical readers) appear to me so highly curious, considered as a matter of literary his- tory, that I shall copy a short detail of them from Halley's preface.
After mentioning the accidental discovery in the Bod- leian library, by Dr. Bernard, Savilian Professor of As- tronomy, of the Arabic version of Apollonius, negl loys djtoTOfzijg, Dr. Halley proceeds thus :
" Dehghted, therefore, with the discovery of such a treasure, Bernard applied himself diligently to the task of a Latin translation. But before he had finished a tenth part of his undertaking, he abandoned it altogeth- er, either from his experience of its growing difficulties, or from the pressure of other avocations. Afterwards, when, on the death of Dr. Wallis, the Savilian profes- sorship was bestowed on me, I was seized with a strong desire of making a trial to complete what Bernard had begun ; — an attempt, of the boldness of which the reader may judge, when he is informed, that, in addition to my OAvn entire ignorance of the Arabic language, I had to contend with the obscurities occasioned by innumerable passages which were either defaced or altogether oblit- erated. With the assistance, however, of the sheets which Bernard had left, and which served me as a key for investigating the sense of the original, I began first with making a list of those words, the signification of which his version had clearly ascertained ; and then pro- ceeded, ])y comparing these words, wherever they oc- curred, with the train of reasoning in which they were
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involved, to decypher, by slow degrees, the import of the context ; till at last I succeeded in mastering the vv^hole work, and in bringing my translation (without the aid of any other person) to the form" in which I now give it to the public." *
When a similar attempt shall be made, with equal success, in decyphering a moral or a political treatise, written in an unknown tongue, then, and not till then, may we think of comparing the phraseology of these two sciences with the simple and rigorous language of the Greek geometers ; or with the more refined and abstract, but not less scrupulously logical system of signs, employ- ed by modern mathematicians.
It must not, however, be imagined, that it is solely by the nature of the ideas which form the objects of its rea- sonings, even when combined with the precision and unambiguity of its phraseology, that mathematics is dis- tinguished from the other branches of our knowledge. The truths about which it is conversant, are of an order altogether peculiar and singular ; and the evidence of which they admit resembles nothing, either in degree or in kind, to which the same name is given, in any of our other intellectual pursuits. On these points also, Leibnitz and many other great men have adopted very incorrect opinions ; and, by the authority of their names, have given currency to some logical errors of fundamen- tal importance. My reasons for so thinking, I shall state, as clearly and fully as I can, in the following section.
SECTION III.
OF MATHEMATICAL DEMONSTRATION.
I.
Of the Circumstance on which Demonstrative Evidence essentially depends.
The pecuharity of that species of evidence which is called demonstrative, and which so remarkably distin-
* ApoUon. Perg. de Sectionc Rationis, &c. Opera et Studio Edm. Halley. Oxon. 1706. In Prsefat.
* OF THE HUMAN MIND. 107
guishes our mathematical conclusions from those to which we are led in other branches of science, is a fact which must have arrested the attention of every person who possesses the shghtest acquaintance with the elements of geometry. And yet I am doubtful if a satisfactory ac- count has been hitherto given of the circumstances from which it arises. Mr. Locke tells us, that " what consti- tutes a demonstration is intuitive evidence at every step ;" and I readily grant, that if, in a single step, such evidence should fail, the other parts of the demonstra- tion would be of no value. It does not, however, seem to me that it is on this consideration that the demon- strative evidence of the conclusion depends, — not even when we add to it another which is much insisted on by Dr. Reid, — that, " in demonstrative evidence, our first principles must be intuitively certain." The inaccuracy of this remark I formerly pointed out when treating of the evidence of axioms ; on which occasion I also ob- served, that the first principles of our reasonings in mathematics are not axioms, but definitions. It is in this last circumstance (I mean the pecuharity of reasoning from definitions) that the true theory of mathematical demonstraUon is to be found ; and I shall accordingly endeavour to explain it at considerable length, and lo state some of the more important consequences to which it leads.
That I may not, however, have the appearance of claiming, in behalf of the following discussion, an undue share of originality, it is necessary for me to remark, that the leading idea which it contains has been repeat- edly started, and even to a certain length prosecuted, by different writers, ancient as well as modern ;' but that, in all of them, it has been so blended with collateral considerations, altogether foreign to the point in ques- tion, as to divert the attention both of writer and reader, from that single principle on which the solution of the problem hinges. The advantages which mathematics derives from the peculiar nature of those relations about which it is conversant ; from its simple and definite phraseology ; and from the severe logic so admirably dis- played in the concatenation of its innumerable theorems,
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are indeed immense, and well entitled to a separate and ample illustration ; but they do not appear to have any necessary connexion with the subject of this section. How far J am right in this opinion, my readers will be enabled to judge by the sequel.
It was already remarked, in the first chapter of this Part, that whereas, in all other sciences, the propositions which we attempt to establish, express facts real or sup- posed,— in mathematics the proposidons which we de- monstrate only assert a connexion between certain sup- positions and certain consequences. Our reasonings, therefore, in mathematics, are directed to an object es- sentially different from what we have in view, in any other employment of our intellectual faculties ; — not to ascertain truths with respect to actual existences, but to trace the logical fihation of consequences which follow from an assumed hypothesis. If from this hypothesis we reason with correctness, nothing, it is manifest, can be wanting to complete the evidence of the result ; as this result only asserts a necessary connexion between the supposition and the conclusion. In the other sciences, admitting that every ambiguity of language were re- moved, and that every step of our deductions were rigor- ously accurate, our conclusions would still be attended with more or less of uncertainty ; being ultimately found- ed on principles which may, or may not, correspond exactly with the fact.*
Hence it appears, that it might be possible, by devis- ing a set of arbitrary definitions, to form a science, which, although conversant about moral, pohtical, or physical ideas, should yet be as certain as geometry. It is of no moment, whether the definidons assumed cor- respond with facts or not, provided they do not express impossibihties, and be not inconsistent with each other.
* This distinction coincides with one which has been very ino;cniously illustrated by M. Prevost in his ])bilosophical essays. See his remarks on those sciences which have for their oliject absolute truth, considered in contrast with those which are oc- cupied only about conditional or hypothetical tniths. Mathematics is a science of the latter (lescri|)tion ; and is therefore called by M. Prevost a science of pure rea- soning.— Essais de Philosophie, Tom. II, p. 9. et seq. See also his Memoirc surles Signes. Paris, Baudoin, ISOO, pp. 1.5, 16. In what respects my opinion on this subject ditlers from his, will appear afterwards.
OF THE HUMAN MIZ^D. 109
From these principles, a series of consequences may be deduced by the most unexceptionable reasoning ; and the results obtained will be perfectly analogous to math- ematical propositions. The terms true and /a/se, cannot be applied to them ; at least in the sense in which they are apphcable to propositions relative to facts. All that can be said is, that they are or are not connected with the definitions which form the principles of the science ; and, therefore, if we choose to call our conclusions true in the one case, and/a/se in the other, these epithets must be understood merely to refer to their connexion with the data, and not to their correspondence with things actually existing, or with events which we expect to be reahzed in future. An example of such a science as that which I have now been describing, occurs in what has been called by some writers theoretical mechanics ; in which, from arbitrary hypotheses concerning physical laws, the consequences are traced which zt*ot<M follow, if such was really the order of nature.
In those branches of study which are conversant about moral and political propositions, the nearest ap- proach which I can imagine to a hypothetical science, analogous to mathematics, is to be found in a code of municipal jurisprudence ; or rather might be conceived to exist in such a code, if systematically carried into execution, agreeably to certain general or fundamental principles. Whether these principles should or should not be founded in justice and expediency, it is evidently possible, by reasoning from them consequentially, to create an artificial or conventional body of know- ledge, more systematical, and, at the same time, more complete in all its parts, than, in the present state of our information, any science can be rendered, which ulti- mately appeals to the eternal and immutable standards of truth and falsehood, of right and wrong. This con- sideration seems to me to throw some light on the fol- lowing very curious parallel which Leibnitz has drawn (with what justness I presume not to decide) between the works of the Roman civilians and those of the Greek geometers. Few writers certainly have been so fully qualified as he was to pronounce on the characteristical merits of both.
110 ELEMENTS OF THE PHILOSOPHY
" I have often said, that, after the writings of geome- tricians, there exists nothing which, in point of force and of subtilty, can be -compared to the works of the Roman lawyers. And, as it would be scarcely possible, from mere intrinsic evidence, to distinguish a demon- stration of Euchd's from one of Archimedes or of Apol- lonius, (the style of all of them appearing no less uniform than if reason herself was speaking through their organs,) so also the Roman lawyers all resemble each other like twin-brothers ; insomuch that, from the style alone of any particular opinion or argument, hard- ly any conjecture could be formed with respect to the author. Nor are the traces of a refined and deeply meditated system of natural jurisprudence any where to be found more visible, or in greater abundance. And, even in those cases where its principles are departed from, either in compliance with the language consecra- ted by technical forms, or in consequence of new stat- utes, or of ancient traditions, the conclusions which the assumed hypothesis renders it necessary to incorporate with the eternal dictates of right reason, are deduced with the soundest logic, and with an ingenuity which excites admiration. Nor are these deviations from the law of nature so frequent as is commonly imagined." *
I have quoted this passage merely as an illustration of the analogy already alluded to, between the systematical unity of mathematical science, and that which is conceiv- able in a system of municipal law. How far this unity is exemplified in the Roman code, I leave to be determin- ed by more competent judges, f
As something analogous to the hypothetical or condi- tional conclusions of mathematics may thus be fancied to take place in speculations concerning moral or political subjects, and actually does take place in theoretical me-
* Leibnitz, Op. Tom. IV. p. 254.
t It is not a little curious, that the same code which furnished to this very learned and philosophical jurist, the subject of the eulogium quoted above, should have been lately stigmatized by an English lawyer, eminently distinguished for his acuteness and originality, as " an enormous mass of confusion and inconsistency." Making all due allowances for the exaggerations of Leibnitz, it is difficult to conceive that his opinion, on a subject which he had so profoundly studied, should be so very widely at variance with the truth.
OF THE HUMAN MIND. Ill
chanics ; so, on the other hand, if a mathematician should affirm, of a general property of the circle, that it applies to a particular figure described on paper, he would at once degrade a geometrical theorem to the lev- el of a fact resting ultimately on the evidence of our im- perfect senses. The accuracy of his reasoning could never bestow on his proposition that pecuUar evidence which is properly called mathematical^ as long as the fact remained uncertain, whether all the straight lines drawn from the centre to the circumference of the figure were mathematically equal.
These observations lead me to remark a very common misconception concerning mathematical definitions ; which are of a nature essentially different from the de- finitions employed in any of the other sciences. It is usual for writers on logic, after taking notice of the er- rors to which we are hable in consequence of the ambi- guity of words, to appeal to the example of mathemati- cians, as a proof of the infinite advantage of using, in our reasonings, such expressions only as have been care- fully defined. Various remarks to this purpose occur in the writings both of Mr. Locke and of Dr. Reid. But the example of mathematicians is by no means ap- plicable to the sciences in which these eminent philoso- phers propose that ic should be followed ; and, indeed, if it were copied as a model in any other branch of hu- man knowledge, it would lead to errors fully as danger- ous as any which result from the imperfections of lan- guage. The real fact is, that it has been copied much more than it ought to have been, or than would have been attempted, if the pecuHarities of mathematical ev- idence had been attentively considered.
That in mathematics there is no such thing as an am- biguous word, and that it is to the proper use of defini- tions we are indebted for this advantage, must unques- tionably be granted. But this is an advantage easily se- cured, in consequence of the very hmited vocabulary of mathematicians, and the distinctness of the ideas about which their reasonings are employed. The difference, besides, in this respect, between mathematics and the other sciences, however great, is yet only a difference in
112 ELEMENTS OF THE PHILOSOPHY
degree ; and is by no means sufficient to account for the essential distinction which every person must perceive between the irresistible cogency of a mathematical de- monstration, and that of any other process of reasoning.
From the foregoing considerations it appears, that in mathematics, definitions answer two purposes ; first. To prevent ambiguities of language ; and, secondly, To serve as the principles of our reasoning. It appears further, that it is to the latter of these circumstances (I mean to the employment of hypotheses instead of facts, as the data on which we proceed) that the peculiar force of demonstrative evidence is to be ascribed. It is how- ever only in the former use of definitions, that any par- allel can be drawn between mathematics and those branches of knowledge which relate to facts ; and, therefore, it is not a fair argument in proof of their g-m- era/ utility, to appeal to the unrivalled certainty of math- ematical science, — a pre-eminence which that science derives from a source altogether different, though com- prehended under the same name, and which she will for ever claim as her own exclusive prerogative.*
Nor ought it to be forgotten, that it is in pure mathe- matics alone, that definitions can be attempted with pro- priety at the outset of our investigations. In most other instances, some previous discussion is necessary to show, that the definitions which we lay down correspond with facts ; and, in many cases, the formation of a just defi- nition is the end to which our inquiries are directed. It is very judiciously observed by Mr. Burke, in his Essay on Taste, that " vv^hen we define, we are in danger of circumscribing nature within the bounds of our own no- tions, which we often take up by hazard, or embrace on trust, or form out of a limited and partial consideration of the object before us, instead of extending our ideas to take in all that nature comprehends, according to her manner of combining. We are limited in our inquiry by the strict laws to which we have submitted at our set- ting out." ,
* These two classes of definitions are very o-enerally confounded by logicians ; among others, by the Abbe de Condillac. See La Logique, ou Ici^ Premiers Dcve- loppemena de I'Jiri de Penser, Chap. VL
OF THE HUMAN MIND. 113
The same author adds, that " a definition may be very exact, and yet go but a very httle way towards inform- ing us of the nature of the thing defined ; " and that, " in the order of things a definition (let its virtue be what it will) ought rather to follow than to precede our inquiries, of which it ought to be considered as the re- sult."
From a want of attention to these circumstances, and from a blind imitation of the mathematical arrangement, in speculations where facts are involved among the principles of our reasonings, numberless errors in the writings of philosophers might be easily traced. The subject is of too great extent to be pursued any farther here ; but it is well entitled to the examination of all who may turn their thoughts to the reformation of logic. That the ideas of Aristotle himself, with respect to it, were not very precise, must, I think, be granted, if the following statement of his ingenious commentator be admitted as correct.
" Every general term," says Dr. GiHies, " is considered by Aristotle as the abridgment of a definition ; and every definition is denominated by him a collection, be- cause it is the result always of observation and compar- ison, and often of many observations and of many comparisons." *
These two propositions will be found, upon examina- tion, not very consistent with each other. The first, " That every general term is the abridgment of a de- finition," applies, indeed, admirably to mathematics ; and touches with singular precision on the very circum- stance which constitutes (in my opinion) the peculiar cogency of mathematical reasoning. But it is to math- ematics that it applies exclusively. If adopted as a log- ical maxim in other branches of knowledge, it would prove an endless source of sophistry and error. — The second proposition, on the other hand, " That every definition is the result of observation and comparison and often of many observations and many compari- sons ; " however applicable to the definitions of natural
• Gillies's Aristotle, Vol. I. p. 92, 2d edit.
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114 ELEMENTS OF THE PHILOSOPHY
history, and of other sciences which relate to facts, cannot, in one single instance, apply to the definitions of geometry ; inasmuch as these definitions are neither the result of observations nor of comparisons, but the hypotheses, or first principles, on which the whole sci- ence rests.
If the foregoing account of demonstrative evidence be just, it follows, that no chain of reasoning whatever can deserve the name of a demonstration (at least in the mathematical sense of that word) which is not ulti- mately resolvable into hypotheses or definitions.* It has been already shown, that this is the case with geom- etry ; and it is also manifestly the case with arithmetic, another science to which, in common with geometry, we apply the word mathematical. The simple arith- metical equations 2 + 2= 4 ; 2 + 3 = 5, and other ele- mentary propositions of the same sort, are (as was for- merly observed) mere definitions ; f perfectly analogous, in this respect, to those at the beginning of Euchd ; and it is from a few fundamental principles of this sort, or at least from principles which are essentially of the same description, that all the more complicated results in the science are derived.
To this general conclusion, with respect to the na- ture of mathematical demonstration, an exception may perhaps be, at first sight, apprehended to occur, in our reasonings concerning geometrical problems : all of these reasonings (as is well known) resting ultimately upon a particular class of principles c2X[e.di postulates, which are commonly understood to be so very nearly akin to axioms, that both might, without impropriety, be
* Although the account given by Locke of what constitutes a demonstration he different from that which I have here proposed, he admits the converse of this doc- trine as manifest ; viz. That if we reason accurately from our own definitions, our conclusions will possess demonstrative evidence ; and " hence," he observes with great truth, " it comes to pass, that one may often meet with very clear and coherent discourses, that amount yet to nothing." He afterwards remarks, that " one may make demonstrations and undoubted propositions in words, and yet thereby advance not one jot in the knowledge of the truth of things." " Of this sort," he adds, " a man may find an infinite number of propositions, reasonings, and conclusions, in books of metaphysics, school-divinity, and some sort of natural philosophy; and, after all, know as little of God, spirits, or bodies, as he did before he set out." — JEssay on Human Understanding, Book IV. chap. viii.
t See page 22.
OF THE HUMAN MIND. 115
comprehended under the same name. " The defini- tion of a postulate," says the learned and ingenious Dr. Hutton, " will nearly agree also to an axiom, which is a self-evident theorem, as a postulate is a self-evident problem." * The same author, in another part of his work, quotes a remark from Dr. Barrow, that " there is the same affinity between postulates and problems, as between axioms and theorems." f Dr. Walhs, too, ap- pears, from the following passage, to have had a decid- ed leaning to this opinion : " According to some, the difference between axioms and postulates is analogous to that between theorems and problems ; the former expressing truths which are self-evident, and from which other propositions may be deduced ; the latter, opera- tions which may be easily performed, and by the help of which more difficult constructions may be effected." He afterwards adds, " This account of the distinction between postulates and axioms seems not ill-adapted to the division of mathematical propositions into problems and theorems. And, indeed, if both postulates and axi- oms were to be comprehended under either of these names, the innovation would not, in my opinion, afford much ground for censure." |
In opposition to these very high authorities, I have no hesitation to assert, that it is with the definitions of Eu- clid, and not with the axioms, that the postulates ought to be compared, in respect of their logical character and importance ; — inasmuch as all the demonstrations in plane geometry are ultimately founded on the former, and all the constructions which it recognises as legiti- mate, may be resolved ultimately into the latter. To this remark it may be added, that, according to Euclid's view of the subject, the problems of geometry are not less hypothetical and speculative than the theorems ; the possibility of drawing a mathematical straight line, and of describing a mathematical circle, being assumed in the construction of every problem, in a way quite analogous to that in which the enunciation of a theorem
* Mathematical Diclionary, Art. Postulate.
t Ibid. Art. Hypothesis.
t Wallisii Opera. Vol. II. i)p. 667, 668.
116 ELEMENTS OF THE PHILOSOPHY
assumes the existence of straight Hnes and of circles cor- responding to their mathematical definitions. The rea- soning, therefore, on which the solution of a problem rests, is not less demonstrative than that which is em- ployed in proof of a theorem. Grant the possibility of the three operadons described in the postulates, and the correctness of the solution is as mathematically certain, as the truth of any property of the triangle or of the circle. The three postulates of Euchd are, indeed, nothing more than the definitions of a circle and a straight fine thrown into a form somewhat different ; and a simi- lar remark may be extended to the corresponding dis- tribution of propositions into theorems and problems. Notwithstanding the many conveniences with which this distribudon is attended, it was evidently a matter of choice rather than of necessity ; all the truths of geometry easily admitting of being moulded into either shape, according to the fancy of the mathematician. As to the axioms, there cannot be a doubt, (whatever opin- ion may be entertained of their utihty or of their insig- nificance) that they stand precisely in the same relation to both classes of propositions.*
* In farther illustration of what is said above, on the subject of postulates and of problems, I transcribe with pleasure, a short passage from a learned and interesting memoir, just published, by an author intimately and critically conversant with the classical remains of Greek geometry.
" The description of any geometrical line from the data by which it is defined, must always be assumed as possible, and is admitted as the legitimate means of a geo- metrical construction ; it is therefore properly regarded as a postulate. Thus, the description of a straight line and of a circle are the postulates of plane geometry as- sumed by Euclid. The description of the three conic sections, according to the de- finitions of them, must also be regarded as postulates ; and though not formally stated like those of Euclid, are in truth admitted as such by Apollonius, and all other writers on this branch of geometry. The same principle must be extended to all superior lines.
" It is true, however, that the properties of such superior lines may be treated of, and the description of them may be assumed in the solution of problems, without an actual delineation of them. — For it must be observed, that no lines whatever, not even the straight line or circle, can be truly represented to the senses according to the strict mathematical definitions ; but this by no means affects the theoretical con- clusions which are logically deduced from such definitions. It is only when geome- try is applied to practice, either in mensuration, or in the arts connected with geo- metrical principles, that accuracy of delineation becomes important." — See an Ac- count of, the Life and Writings of Robert Simson, M. D. By the Rev. William Trail, LL, D. Published by G. and W. Nicol, London, 1812.
OF THE HUMAN MIJVD. 117
II.
Continuation of the Subject. — How far it is true that all Mathematical Evidence is resolvable into Identical Propositions.
I HAD occasion to take notice, in the first section of the preceding chapter, of a theory with respect to the nature of mathematical evidence, very different from that which I have been now attempting to explain. According to this theory (originally, I beheve, proposed by Leibnitz) we are taught, that all mathematical evi- dence ultimately resolves into the perception of identi- ty ; the innumerable variety of propositions which have been discovered, or which 7'emain to be discovered in the science, being only diversified expressions of the simple formula, a= a.* A writer of great eminence, both as a mathematician and a philosopher, has lately given his sanction, in the strongest terms, to this doc- trine : asserting, that all the prodigies performed by the geometrician are accomphshed by the constant repeti- tion of these words, — the same is the same, " Le geom- etre avance de supposition en supposition. Et retour- nant sa pensee sous mille formes, c'est en repetant sans cesse, le meme est le meme, qu'il opere tons ses pro- diges."
As this account of mathematical evidence appears to me quite irreconcilable with the scope of the foregoing observations, it is necessary, before proceeding farther, to examine its real import and amount ; and what the circumstances are from which it derives that plausibiHty which it has been so generally supposed to possess. f
* It is more than probable, that this theory was susgested to Leibnitz by some very curious observations in Aristotle's Metaphysics, Book IV. chap. iii. and iv.
t I must here observe, in justice to my friend M. Prevost, that the two doctrines which I have represented in the above paragraph as quite irreconcilable, seem to be regarded by him as not only consistent with each other, but as little more than dif- ferent modes of slating the same proposition. Tlie remarks with which he has fa- vored me on this point will be found in the Appendix annexed to this volume. At present, it may suffice to mention, that none of the following reasonings apply to that particular view of the question which he has taken. Indeed, I consider tho difference of opinion between us, as to the subject now under consideration, as chiefly verbal. On the subject of the preceding article, our opinions arc exactly the same. See Appendix.
118 ELEMENTS OF THE PHILOSOPHY
That all mathematical evidence resolves ultimately in- to the perception of identity, has been considered by some as a consequence of the commonly received doc- trine, which represents the axioms of Euchd as the first principles of all our subsequent reasonings in geometry. Upon this view of the subject I have nothing to offer, in addition to what I have already stated. The argu- ment which I mean to combat at present is of a more subtile and refined nature ; and, at the same time, in- volves an admixture of important truth, which contri- butes not a httle to the specious verisimihtude of the conclusion. It is founded on this simple consideration, that the geometrical notions of equality and of coinci- dence are the same ; and that, even in comparing togeth- er spaces of different figures, all our conclusions ulti- mately lean, with their whole weight, on the imaginary application of one triangle to another ;— the object of which imaginary apphcation is merely to identify the two triangles together, in every circumstance connected both with magnitude and figure.*
Of the justness of the assumption on which this argu- ment proceeds, I do not entertain the slightest doubt. Whoever has the curiosity to examine any one theorem in the elements of plane geometry, in which different spaces are compared together, will easily perceive, that the demonstration, when traced back to its first princi- ples, terminates in the fourth proposition of Euclid's first book : a proposition of which the proof rests entirely on a supposed apphcation of the one triangle to the other. In the case of equal triangles which differ in figure, this expedient of ideal superposition cannot be
* It was probably with a view to the establishment of this doctrine, that some foreign elementary writers have lately given the name of identical triangles to such as agree with each other, both in sides, in angles, and in area. The differences which may exist between them in respect of place, and of relative position (differ- ences which do not at all enter into the reasonings of the geometer) seem to have been considered as of so little account in discriminating them as separate objects of thought, that it has been concluded they only form one and the same triangle, in the contemplation of the logician.
This idea is veiy explicitly stated, more than once, by Aristotle : ?»■« Sv ro vroffov 'iv ; " Those things arc equal whose quantity is the same ; " (Met. iv. c. 16.") and still more precisely in these remarkable words, Iv rourois h i<rSrtis horug ; " In math- ematical quantities, equality is identity." (Met. x. c. 3.)
For some remarks on this last passage, See Note (F.)
OF THE HUMAN MIND. 1 19
directly and immediately employed to evince their equality ; but the demonstration will nevertheless be found to rest at bottom on the same species of evidence. In illustration of this doctrine, I shall only appeal to the thirty-seventh proposition of the first book, in which it is proved that triangles on the same base, and between the same parallels, are equal ; a theorem which appears, from a very simple construction, to be only a few steps removed from the fourth of the same book, in which the supposed apphcation of the one triangle to the other, is the only medium of comparison from which their equal- ity is inferred.
In general, it seems to be almost self-evident, that the equality of two spaces can be demonstrated only by showing, either that the one might be applied to the other, so that their boundaries should exactly coincide ; or that it is possible, by a geometrical construction, to divide them into compartments, in such a manner, that the sum of parts in the one may be proved to be equal to the sum of parts in the other, upon the principle of superposition. To devise the easiest and simplest con- structions for attaining this end, is the object to which the skill and invention of the geometer is chiefly direct- ed.
Nor is it the geometer alone who reasons upon this principle. If you wish to convince a person of plain understanding, who is quite unacquainted with mathe- matics, of the truth of one of Euclid's theorems, it can only be done by exhibiting to his eye, operations exact- ly analogous to those which the geometer presents to the understanding. A good example of this occurs in the sensible or experimental illustration which is some- times given of the forty -seventh proposition of Euclid's first book. For this purpose, a card is cut into the form of a right-angled triangle, and square pieces of card are adapted to the different sides ; after which, by a simple and ingenious contrivance, the different squares are so dissected, that those of the two sides are made to cover the same space with the square of the hypothenuse. In truth, this mode of comparison by a superposition, actu- al or ideal, is the only test of equahty which it is possi-
120 ELEMEJfTS OF THE PHILOSOPHY
ble to appeal to : and it is from this (as seems from a passage in Proclus to have been the opinion of Apol- lonius) that, in point of logical rigor, the definition of geometrical equality should have been taken.* The subject is discussed at great length, and with much acuteness, as well as learning, in one of the mathemati- cal lectures of Dr. Barrow ; to which I must refer those readers who may wish to see it more fully illustrated.
I am strongly inclined to suspect, that most of the writers who have maintained that all mathematical evi- dence resolves ultimately into the perception of identity, have had a secret reference, in their own minds, to the doctrine just stated ; and that they have imposed on themselves by using the words identity and equality as Uterally synonymous and convertible terms. This does not seem to be at all consistent, either in point of ex- pression or of fact, with sound logic. When it is affirm- ed (for instance) that " if two straight lines in a circle intersect each other, the rectangle contained by the seg- ments of the one is equal to the rectangle contained by the segments of the other ; " can it with any propriety be said, that the relation between these rectangles may be expressed by the formula a = a ? Or, to take a case yet stronger, when it is affirmed, that " the area of a circle is equal to that of a triangle having the circumfer- ence for its base, and the radius for its altitude ; " would it not be an obvious paralogism to infer from this propo-
* I do not think, however, that it would be fair, on this account, to censure Euclid for the arrangement which he has adopted, as he has thereby most ingeniously and dexterously contrived to keep out of the view of the student some very puzzling questions, to which it is not possible to give a satisfactory answer till a considerable progress has been made in the elements. When it is stated io the form of a self-ev- ident truth, that magnitudes which coincide, or which exactly fill the same space, are equal to one another, the beginner readily yields his assent to the proposition ; and this assent, without going any farther, is all that is required in any of the demon- strations of the first six books, whereas, if the proposition were converted into a de- finition by saying, " Equal magnitudes are those which coincide, or which exactly fill the same space ; " the question would immediately occur. Are no magnitudes equal, but those to which this test of equality can be applied ? Can the relation of equality not subsist between magnitudes which differ from each other in figure ? In reply to this question, it would be necessary to explain the definition, by adding, That those magnitudes likewise are said to be equal, which are capable of being divi- ded or dissected in such a manner that the parts of the one may severally coincide with the parts of the other ; — a conception much too refined and complicated for the generality of students at their first outset ; and which, if it were fully and clearly apprehended, would plunge them at once into the profound speculation concerning the comparison of rectilinear with curvilinear figures.
OF THE HUMAN MIND. 121
sition, that the triangle and the circle are one and the same thing ? In this last instance, Dr. Barrow himself has thought it necessary, in order to reconcile the lan- guage of Archimedes with that of Euchd, to have re- course to a scholastic distinction between actual and potential coincidence ; and, therefore, if we are to avail ourselves of the principle of superposition, in defence of the fashionable theory concerning mathematical evidence, we must, I apprehend, introduce a correspondent dis- tinction between actual and potential identity*
That I may not be accused, however, of misrepresent- ing the opinion which I am anxious to refute, I shall state it in the words of an author, who has made it the sub- ject of a particular dissertation ; and who appears to me to have done as much justice to his argument as any of its other defenders.
" Omnes mathematicorum propositiones sunt identicae, et repraesentantur hac formula, a = a. Sunt veritates identicae, sub varia forma expressae, imo ipsum, quod dicitur contradictionis principium, vario modo enuncia- tum et involutum ; siquidem omnes hujus generis propo- sitiones revera in eo continentur. Secundum nostram autem intelligendi facultatem ea est propositionum dif- ferentia, quod quaedam longa ratiociniorum serie, alia autem breviore via, ad primum omnium principium re- ducantur, et in illud resolvantur. Sic v. g. propositio 2 +2 r= 4 statim hue cedit i + i + i + i-i + i + i + i; i. e. idem est idem ; et proprie loquendo, hoc modo enunciari debet. Si contingat, adesse vel existere qua- tuor entia, tum existunt quatuor entia ; nam de existen- tia non agunt geometrae, sed ea hypothetice tantum sub- intelligitur. Inde summa oritur certitudo ratiocinia
* " Cum dernonstravit Archimedes circulum apqiiari rectans^ulo tiian^ulo cujus ba- sis radio circuli, cathetiis pcripheria; exa^quetiir, nil illc, siquis propius altendat, aliud quicqiiam quam aream circuli ecu poiyso'i' rc2;ularis indefinite multa latcra habenlis, in tot dividi posse minutissima trianojuia, qutR totidem exilissiniis dicti triani^uli trigo- nis a;qucntur; eorum vero trianoulonirti a;qualitas e sola con^rucntia. demonstralurin dementis. Unde consequenter Archimedes circuli cinn trianpitdo (sil)i quanlunivis dissimili) congruentiam demonstravit. — Ita congnienti^c nihil obstat figuiainm di.ssim- ilitudo ; verum sen similes sive dissimiles sint, modo requales, semper poterunt, sem- per posse dehebunt congruere. Igitur octavuin axioina vel nulio modo conversuin valet, aut universaliter convcrti potest ; nuUo modo, si quae isthic habetur congruenlia designet ac.tualem congruentiam ; universim, si de potentiali tantum accipialur." — Lectiones Mathematicm, Lect. V.
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perspicienti ; observat nempe idearum identitatem ; et haec est evidentia assensum immediate cogens, quam mathematicam aut geometricam vocamus. Mathesi tamen sua natura priva non est et propria ; oritur etenim ex identitatis perceptione, quae locum habere potest, eti- amsi ideae non repraesentent extensum." *
With respect to this passage I have only to remark, that the author confounds two things essentially different ; — the nature of the truths which are the objects of a sci- ence, and the nature of the evidence by which these truths are estabhshed. Granting, for the sake of argu- ment, that all mathematical propositions may be repre- sented by the formula a = a, it would not therefore fol- low, that every step of the reasoning leading to these conclusions was a proposition of the same nature ; and that, to feel the full force of a mathematical demonstra- tion, it is sufficient to be convinced of this maxim, that every thing may he truly predicated of itself; or, in plain Enghsh, that the same is the same. A paper written in cypher, and the interpretation of that paper by a skilful decypherer, may, in like manner, be considered as, to all intents and purposes, one and the same thing. They are so, in fact, just as much as one side of an algebraical equation is the same thing with the other. But does it therefore follow, that the whole evidence upon which the art of decyphering proceeds, resolves into the percep- tion of identity?
It may be fairly questioned, too, whether it can, with strict correctness, be said even of the simple arithmeti- cal equation 2 + 2 = 4, that it may be represented by the formula a = a. The one is a proposition asserting the equivalence of two different expressions ; — to ascertain which equivalence may, in numberless cases, be an ob- ject of the highest importance. The other is altogether unmeaning and nugatory, and cannot, by any possible
* The above extract (from a dissertation printed at Berlin in 1764) has long had a very extensive circulation in this country, in consequence of its being quoted by Dr. Beattie, in his Essay on Truth, (see p. 221, 2d edit.) As the learned author of the essay has not given the slightest intimation of his own opinion on the subject, the doctrine in question has, I suspect, been considered as in some measure s.inctioned by his authority. It is only in this way that I can account for the facility with which it has been admitted by so many of our northern logicians. ,
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supposition, admit of the slightest application of a prac- tical nature. What opinion, then, shall we form of the proposition a = a, when considered as the representative of such di formula as the binomial theorem of Sir Isaac Newton ? When apphed to the equation 2 + 2=4 (which, from its extreme simplicity and familiarity, is apt to be regarded in the light of an axiom) the paradox does not appear to be so manifestly extravagant ; but, in the other case, it seems quite impossible to annex to it any meaning whatever.*
I should scarcely have been induced to dwell so long on this theory of Leibnitz concerning mathematical evidence, if I had not observed among some late logi- cians (particularly among the followers of Condillac) a growing disposition to extend it to all the different sorts of evidence resulting from the various employments of our reasoning powers. Condillac himself states his own opinion on this point with the most perfect confi- dence. " Uevidence de raison consists uniquement dans Videntite : c'est ce que nous avons demontre. II faut que cette verite soit bien simple pour avoir echappe a tons les philosophes, quoiqu'ils eussent tant d'interet a s'as- surer de I'evidence, dont ils avoient continuellement le mot dans la bouche." f
* The foregoino- reasonings are not meant as a refutation of the arguments urged by any one author in support of the doctrine in question ; but merely as an examinatioa of those by which I have cither hoard it defended, or from whicli I conceived that it might possibly derive its verisimilitude in the judgment of those who have adopted it. The arguments which I have supposed to be alleged by its advocates, are so completely independent of each other, that instead of being regarded as different premises leading to the same conclusion, tiiey amount only to so many different in- terpretations of the saine veibal proijosilion : — a circumstance which, I cannot help thinking, affords of itself no slight proof, that this proposition has been commonly staled in terms too general and too ambiguous for a logical principle. What a strange inference has been drawn from it by no less a philosopher than Diderot ! " Interrogez des mathematiciens de bonne foi, et ils vous avoueront que leurs propositions sont toutes identiques, et que tant de volumes sur le cercle, par exemple, se reduisent a. nous repeter en cent mille farons differentes, que c'est une figure oii toutes leslignes tirees du centre a la circonference sont egales. JYousne savons doncpresque rien." — Lcttre sur les Aveugles.
t La Logiquc, Chap. IX.
On another occasion, Condillac expresses himself thus : " Tout le systeme des connoissances humaines pcut etre rendu par une expression plus abregee et tout-a-fait identique : les sensations sont des sensations. Si nous pouvions, dans toutes les sciences, suivre egalement la generation des idee*, et saisirle vrai systetne des choses, nous verrions d'une verite naitre toutes les autrcs, etnous trouverions i'expression a- bregee de tout ce que nous saurions, dans cette proposition identique : le mime est le mime."
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The demonstration here alluded to is extremely con- cise ; and if we grant the two data on which it proceeds, must be universally acknowledged to be irresistible. The first is, " That the evidence of every mathematical equation is that of identity : " The second, " That what are called, in the other sciences, propositions or judg- ments, are, at bottom, precisely of the same nature with equations.^^ — But it is proper, on this occasion, to let our author speak for himself.
" Mais, dira-t-on, c'est ainsi qu'on raisonne en mathe- matiques, ou le raisonnement se fait avec des equations. En sera-t-il de meme dans les autres sciences, ou le raisonnement se fait avec des propositions ? Je reponds qu' equations, propositions, jugemens, sont au fond la meme chose, et que par consequent on raisonne de la meme maniere dans toutes les sciences."*
Upon this demonstration I have no comment to offer. The truth of the first assumption has been already ex- amined at sufficient length; and the second (which is only Locke's very erroneous account oi judgment, stated in terms incomparably more exceptionable) is too puerile to admit of refutation. It is melancholy to reflect, that a writer who, in his earlier years, had so admirably un- folded the mighty influence of language upon our spec- ulative conclusions, should have left behind him, in one of his latest publications, so memorable an illustration of his own favorite doctrine.
It was manifestly with a view to the more complete establishment of the same theory, that Condillac under- took a work, which has appeared since his death, under the title of La Langue des Calculs ; and which, we are told by the editors, was only meant as a prelude to other labors, more interesting and more difficult. From the circumstances which they have stated, it would seem that the intention of the author was to extend to all the other branches of knowledge, inferences similar to those which he has here endeavoured to estabhsh with respect to mathematical calculations ; and much regret is ex- pressed by his friends, that he had not lived to accom-
'' La Logique, Chap. VIII.
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plish a design of such incalculable importance to human happiness. I believe I may safely venture to assert, that it was fortunate for his reputation he proceeded no far- ther; as the sequel must, from the nature of the subject, have afforded, to every competent judge, an experimental and palpable proof of the vagueness and fallaciousness of those views by which the undertaking was suggested. In his posthumous volume, the mathematical precision and perspicuity of his details appear to a superficial reader to reflect some part of their own hght on the general reasonings with which they are blended ; while, to better judges, these reasonings come recommended with many advantages, and with much additional authori- ty, from their coincidence with the doctrines of the Leib- nitzian school.
It would probably have been not a little mortifying to this most ingenious and respectable philosopher, to have discovered, that, in attempting to generalize a very celebrated theory of Leibnitz, he had stumbled upon an obsolete conceit, started in this island upwards of a cen- tury before. " When a man reasoneth," says Hobbes, " he does nothing else but conceive a sum total, from addition of parcels ; or conceive a remainder from sub- traction of one sum from another ; which (if it be done by words) is conceiving of the consequence of the names of all the parts, to the name of the whole ; or from the names of the whole and one part, to the name of the other part. These operations are not incident to numbers only, but to all manner of things that can be added together, and taken one out of another. In sum, in what matter soever there is place for addition and subtraction, there also is place for reason ; and where these have no place, there reason has nothing at all to do.
" Out of all which we may define what that is which is meant by the word reason, when we reckon it amongst the faculties of the mind. For reason, in this sense, is nothing but reckoning (that is adding and subtracting) of the consequences of general names agreed upon, for the marking and signifying of our thoughts ; — I say marking them, when we reckon by ourselves ; and signi-
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fying, when we demonstrate, or approve our reckonings to other men." *
Agreeably to this definition, Hobbes has given to the first part of his elements of philosophy, the title of CoMPUTATio, sive Logica; evidently employing these two words as precisely synonymous. From this tract I shall quote a short paragraph, not certainly on account of its intrinsic value, but in consequence of the interest which it derives from its coincidence with the specula- tions of some of our contemporaries. I transcribe it from the Latin edition, as the antiquated Enghsh of the au- thor is apt to puzzle readers not familiarized to the pe- culiarities of his philosophical diction.
" Per ratiocinationem autem intelligo computationem. Computare vero est plurium 7'erum simul additarum sum- mam colligere, vel una re ah alia detractd, cognoscere re- siduum. Ratiocinari igitur idem est quod addere et sub- trahere, vel si quis adjungat his multiplicare et divider e, non abnuam, cum multiplicatio idem sit quod aequalium additio, divisio quod aequalium quoties fieri potest sub- tractio. Recidit itaque ratiocinatio omnis ad duas ope- rationes animi, additionem et suhtr actionem.] How wonderfully does this jargon agree with the assertion of Condillac, that all equations are propositions, and all propositions equations !
These speculations, however, of Condillac and of Hobbes relate to reasoning in general ; and it is with m.athematical reasoning alone, that we are immediately concerned at present. That the pecuhar evidence with which this is accompanied is not resolvable into the per- ception of identity, has, I flatter myself, been sufficient- ly proved in the beginning of this article ; and the plausible extension by Condillac of the very same theory to our reasonings in all the diff"erent branches of moral science,
* Leviathan, Chap. v.
t The Logica of Hobbes has been lately translated into French under the title of Calcul, ou Logique, byM. Destutt-Tracy. It is annexed to the third volume of his Elemens iTIdeologie, where it is honored with the highest eulogies by the ingen- ious translator. " L'ouvrage en masse," he observes in one passage, " merite d'etre regarde comme un produit precieux des meditations de Bacon et de Des Cartes sur le systeme d'Aristote, et comme le germe des progres ultericures de la science." Disc. Prtl. p. 117.
OF THE HUMAN MIND. 127
affords a strong additional presumption in favor of our conclusion.
From this long digression, into which I have been in- sensibly led by the errors of some illustrious foreigners concerning the nature of mathematical demonstration, I now return to a further examination of the distinction between sciences which rest ultimately on facts, and those in which definitions or hypotheses are the sole prin- ciples of our reasonings. •
III.
Continuation of the Subject. — Evidence of the Mechanical Philosophy, not to be confounded with that which is properly called Demonstrative or Mathematical. — Opposite Error of some late Writers.
Next to geometry and arithmetic, in point of evi- dence and certainty, is that branch of general physics which is now called mechanical philosophy ; — a science in which the progress of discovery has been astonish- ingly rapid, during the course of the last century ; and which, in the systematical concatenation and fihation of its elementary principles, exhibits every day more and more of that logical simplicity and elegance which we ad- mire in the works of the Greek mathematicians. It may, I think, be fairly questioned, whether, in this department of knowledge, the affectation of mathematical method has not been already carried to an excess ; the essen- tial distinction between mechanical and mathematical truths being, in many of the physical systems which have lately appeared on the Continent, studiously kept out of the reader's view, by exhibiting both, as nearly as possible, in the same form. A variety of circumstan- ces, indeed, conspire to identify in the imagination, and, of consequence, to assimilate in the mode of their state- ment, these two very different classes of propositions ; but as this assimilation (beside its obvious tendency to involve experimental facts in metaphysical mystery) is apt occasionally to lead to very erroneous logical con- clusions, it becomes the more necessary, in proportion as it arises from a natural bias, to point out the causes
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in which it has originated, and the hmitations with which it ought to be understood.
The following slight remarks will sufficiently explain my general ideas on this important article of logic.
1. As the study of the mechanical philosophy is, in a great measure, inaccessible to those who have not re- ceived a regular mathematical education, it commonly happens, that a taste for it is, in the first instance, graft- ed on a previous attachment to the researches of pure or abstract mathematics. Hence a natural and insensi- ble tranference to physical pursuits, of mathematical habits of thinking ; and hence an almost unavoidable propensity to give to the former science, that systemat- ical connexion in all its various conclusions, which from the nature of its first principles, is essential to the latter, but which can never belong to any science, which has its foundations laid in facts collected from experience and observation.
2. Another circumstance, which has co-operated powerfully with the former in producing the same effect, is that proneness to simplification which has misled the mind, more or less, in all its researches ; and which, in natural philosophy, is peculiarly encouraged by those beautiful analogies which are observable among different physical phenomena ; — analogies, at the same time, which, however pleasing to the fancy, cannot always be resolved by our reason into one general law. In a remark- able analogy, for example, which presents itself between the equality of action and re-action in the colhsion of bo- dies, and what obtains in their mutual attractions, the co- incidence is so perfect, as to enable us to comprehend all the various facts in the same theorem : and it is difficult to resist the temptation which this theorem seems to offer to our ingenuity, of attempting to trace it, in both cases, to some common principle. Such trials of theoretical skill I would not be understood to censure indiscrimi- nately ; but, in the present instance, I am fully persuad- ed, that it is at once more unexceptionable in point of sound logic, and more satisfactory to the learner, to establish the fact, in particular cases, by an appeal to experiment ; and to state the law of action and re-action
OF THE HUMAN MIND. 129
in the collision of bodies, as well as that which regulates the mutual tendencies of bodies towards each other, merely as general rules which have been obtained by induction, and which are found to hold invariably as far as our knowledge of nature extends.*
An additional example may be useful for the illustra- tion of the same subject. . It is well known to be a gen- eral principle in mechanics, that when, by means of any machine, two heavy bodies counterpoise each other, and are then made to move together, the quantities of mo- tion with which one descends, and the other ascends perpendicularly, are equal. This equilibrium bears such a resemblance to the case of two moving bodies stop- ping each other when they meet together with equal quantities of motion, that, in the opinion of many writ- ers, the cause of an equihbrium in the several machines is sufficiently explained, by remarking, " that a body always loses as much motion as it communicates."
* It is observed by Mr. Robison, in his Elements of Mechanical Philosophy, that •• Sir Isaac Newton, in the general scholium on the laws of motion, seems to consid- er the equality of action and re-action, as an axiom deduced fiorn the relations of ideas. But this ,"' says Mr. Robison, " seems doubtful. Because a magnet causes the irbn to approach towards it, it does not appear that we necessarily sup])0?e that iron also attracts the magrnet." In confirmation of this, he remarks, that notwith- standing the previous conclusions of Wallis, Wren, and Huygens, about the mutual, equal, and contraiy action of solid bodies in their collisions, " Newton himself only presumed that, because the sun attracted the planets, these also attracted the sun ; and that he is at much pains to point out phenomena to astronomers, by which this may be proved, when the art of observation shall be sufficiently perfected." Ac- cordingly, Mr Robison, with great propriety, contents himself with stating this third law of motion, as a fact "with respect to all bodies on which we can make expeii- ment or observation fit for deciding the question."
In the very next paragraph, however, he proceeds thus : " As it is an univer?al law, we cannot rid ourselves of the persuasion that it depends on some general principle which influences all the matter in the universe ; " — to which observation he subjoins a conjecture or hypothesis concerning the nature of this principle or cause. For aa outline of his theory I must refer to his own statement. See Elements of Me- chanical Philosophy, Vol. I. pp. 124, 125, 126.
Of the fallaciousness of synthetical reasonings concerning physical phenomena, there cannot be a stionger proof, than the diversity of opinion among tlic most emi- nent philosophers with respect to the species of evidence on which the third law of motion rests. On this point, a direct opposition may bo remarked in the views of Sir Isaac Newton, and of his illustrious fiicnd and commentator, I\Ir. Maclauiin; the former seeming to lean to the supposition, that it is a corollory deducible a priori from abstract principley ; while the latter (manifestly considering it as the eflect of an arbitrary arrangement) strongly recommends it to the attention of those who de- light in the investigation of final causes. («) My own idea is, that, in the present state of our knowledge, it is at once more safe and more logical, to consider it merely as an experimental truth ; without ventuiing to decide positively on cither side of the question. As to the doctrine of final causes, it fortunately stands in need of no aid from such dubious speculations.
(a) Account of Nowton's I'liilosopliiral DLicoveries. Book II, Cliap. 2. $ 28. VOL. JI. 17
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Hence it is inferred, that when two heavy bodies are so circumstanced, that one cannot descend without cau- sing the other to ascend at the same time, and with the same quantity of motion, both of these bodies must necessarily continue at rest. But this reasoning, how- ever plausible it may seem to be at first sight, is by no means satisfactory ; for (as Dr. Hamilton has justly ob- served *) when we say, that one b.ody communicates its motion to another, we must suppose the motion to exist, first in the one, and aftervjards in the other ; whereas, in the case of the machine, the ascent of the one body cannot, by any conceivable refinement, he ascribed to a communication of motion from the body which is de- scending at the same moment ; and, therefore, (admit- ting the truth of the general law which obtains in the colhsion of bodies,) we might suppose, that in the ma- chine, the superior weight of the heavier body would overcome the lighter, and cause it to move upwards with the same quantity of motion with which itself moves dowmwards. In perusing a pretended demonstration of this sort, a student is dissatisfied and puzzled ; not from the difficulty of the subject, which is obvious to every capacity, but from the illogical and inconclusive reason- ing to which his assent is required, f
3. To these remarks it may be added, that even when one proposition in natural philosophy is logically deducible from another, it may frequently be expedient, in communicating the elements of the science, to illus- trate and confirm the consequence, as well as the prin- ciple, by experiment. This 1 should apprehend to be proper, wherever a consequence is inferred from a principle less familiar and intelligible than itself; a thing
* See Philosophical Essays, by Hugh Hamilton, D. D. Professor of Philosophy in the University of Dublin, p, 135. et seq. 3d edit. (London, 1772.)
•f The following- observation of Dr. Hamilton places this question in its true point of view. " However, as the theorem above mentioned is a very elegant one, it ought certainly to be taken notice of in every treatise of mechanics, and may serve as a very good index of an cequilihriuin in all machines ; but I do not think that we can from thenco, or from anyone general piinciplc, explain the nature and effects of all the mechanic powers in a safisfaclory manner."
To (he same purpose, it is remarked by Mr. Maclaurin, that " though it he useful and agreea!)le, to observe how unilbrirdy this piinciple prevails in engines of every sort, throughout tlie whole of mechanics, in all cases where an aquilibrhiin takes place ; yet tliat it would not be right to rest the evidence of so important a doctrine upon aproof of this kind only." — Account ofJVewton's Discoveries, B. 11. c. 3.
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which must occasionally happen in physics, from the complete incorporation (if 1 may use the expression) which, in modern times, has taken place between phys- ical truths, and the discoveries of mathematicians. The necessary effect of this incorporation was, to give to natural philosophy a mathematical form, and to systema- tize its conclusions, as far as possible, agreeably to rules suggested by mathematical method.
In pure mathematics, where the truths which we in- vestigate are all co-existent in point of time, it is univer- sally allowed, that one proposition is said to be a conse- quence of another, only with a reference to our estab- lished arrangements. Thus all the properties of the circle might be as rigorously deduced from any one generalproperty of the curve, as from the equality of the radii. But it does not, therefore, follow, that all these arrangements would be equally convenient; on the, contrary, it is evidently useful, and indeed necessary, to lead the mind, as far as the thing is practicable, from what is simple to what is more complex. The misfor- tune is, that it seems impossible to carry this rule uni- versally into execution : and, accordingly, in the most elegant geometrical treatises which have yet appeared, instances occur, in which censequences are deduced from principles more complicated than themselves. Such inversions, however, of what may justl}^ be regard- ed as the natural order, must always be felt by the au- thor as a subject of regret ; and, in proportion to their frequency, they detract both from the beauty and from the didactic simplicity of his general design.
The same thing often happens in the elementary doc- trines of natural philosophy. A very obvious example occurs in the different demonstrations given by writers on mechanics, from the resolution of forces, of the fun- damental proposition concerning the lever ; — demonstra- tions in which the proposition, even in the simple case when the directions of the forces are supposed to be parallel, is inferred from a process of reasoning involv- ing one of the most refined principles employed in the mechanical philosophy. I do not object to this ar- rangement as illogical ; nor do I presume to say that it
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is injudicious.* I would only suggest the propriety, in such instances, of confirming and illustrating the conclu- sion, by an appeal to experiment ; an appeal which, in natural philosophy, possesses an authority equal to that which is generally, but very improperly, considered as a mathematical demonstration of physical truths. In pure geometry, no reference to the senses can be admi- ted, but in the way of illustration ; and any such refer- ence, in the most trifling step of a demonstration, vitiates the whole. But, in natural philosophy, all our reason- ings must be grounded on principles for which no evi- dence but that of sense can be obtained ; and the prop- ositions which we estabhsh, diff'er from each other only as they are deduced from such principles immediately, or by the intervention of a mathematical demonstration. An experimental proof, therefore, of any particular physical truth, when it can be conveniently obtained, although it may not always be the most elegant or the most expedient way of introducing it to the knowledge of the student, is as rigorous and as satisfactory as any other ; for the intervention of a process of mathemati- cal reasoning can never bestow on our conclusions a
* In some of these demonstrations, however, there is a logical inconsistency so glaiing, that I cannot resist the temptation of pointing it out here, as a good instance of that undue predilection for mathematical evidence, in the exposition of physical principles, which is conspicuous in many elementary treatises. I allude to those demonstrations of the property of the lever, in which, after attempting to prove the Ejeneral theorem, on the supposition that the directions of the forces meet in a point, the same conclusion is extended to the simple case in which these directions are parallel, by the. fiction (for it deserves no other name) of conceiving parallel lines to meet at an infinite distance, or to form with each other an angle infinitely small. It is strange, that such a proof should ever have been thought more satisfactory than the direct evidence of our senses. How much more reasonable and pleasing to begin with the simpler case, (which may be easily brought to the test of experiment,) and then to deduce from it, by the resolution offerees, the general proposition ? Even Dr. Hamilton himself, who has treated of the mechanical powers with much ingenui- ty, seems to have imagined, that by demonstrating the theorem, in all its cases, from the composition and resolution of forces alone, he had brought the whole subject within the compass of pure geometry. It could scarcely, however, (one should think,) have escaped him, that every valid demonstration of the composition offerees must neces'^arily assume as a fact, that " when a body is acted upon by a force par- allel to a straight line given in position, this force has no elfect, either to accelerate or to retard the progress of the body towards that Hne." Is not this fact much forther removed from common observation than the fundamental property of the lever, which is familiar to every peasant, and even to eveiy savage ? And yet the same author objects to the demonstration of Huygens, that it depends upon a principle, which, (he says) ought not to be granted on this occasion, — that " when two equal bodies are placed on the arms of a lever, that which is farthest from the fulcrum will pre- ponderate."
OF THE HUMAN MIND. 133
greater degree of certainty than our principles pos- sessed.*
I have been led to enlarge on these topics by that un- qualified application of mathematical method to physics, which has been fashionable for many years past among foreign writers ; and which seems to have originated chiefly in the commanding influence which the genius and learning of Leibnitz have so long maintained over the scientific taste of most European nations.f In an
* Several of the foregoing remarks were suggested by certain peculiarities of opin- ion relative to the distinct provinces of experimental and of mathematical evidence in the study of physics, which were entertained by my learned and excellent friend, the late Mr. Robison. Though himself a most enlightened and zealous advocate for the doctrine of final causes, he is well known to have formed his scientific taste chiefly upon the mechanical philosophers of the Continent, and, in consequence of this circumstance, to have undervalued experiment, wherever a possibility offered of introducing mathematical, or even metaphysical reasoning. Of this bias various tra- ces occur, both in his Elements of Mechanical Philosophy, and in the valuable arti- cles which he furnished to the Encyclopaedia Britannica.
t The following very extraordinary passage occurs in a letter from Leibnitz to Mr. Oldenburg.
" Ego id agere constitui, ubi primum otium nactus ero, ut rem omnem mechani- cam reducam ad puram geometriam ; problemataque circa elateria, et aquas, et pen- dula, et projecta, et solidorum resistentiam, et frictiones, &c. definiam. Quse hacte- iius attigit nemo. Credo autem rem omnem nunc esse in potestate ; ex quo circa regulas motuum mihi penitus perfectis demonstrationibus satisfeci ; neque quicquatu amplius in eo genere desidero. Tota autem res, quod mireris, pendet ex axiotnate metaphysico pulchenimo, quod non minoris momenii est circa motum, qiiam hoc to- lum esse majus parte, circa magiiitudinem.' — Wallisii Opera, Vol. III. p. 633.
The beautiful metaphysical axiom here referred to by Leibnitz, is plainly the principle of the sufficient reason ; and it is not a little remarkable that the highest praise which he had to bestow upon it was, to compare it to Euclid's axiom " That the whole is greater than its part." Upon this principle of the sufficient reason Leibnitz, as is well known, conceived that a complete systetn of pliysical science might be built, as he thought the whole of mathematical science resolvable into the principles of identity and of contradiction. — By the first of these principles (it may not be altogether superfluous to add) is (o be understood the maxim, " Whatever is is ; " by the second, the maxim, that " It is iinpossible for the same thins to be, and rot to be : " — two maxims which, it is evident, are only different expressions of the same proposition.
In the remarks made by Locke on the logical inutility of mathematical axioms, and on the logical danger of assuming metaphysical axioms as the principles of our reasonings in other sciences, I think it highly probable, that he had a secret reference to the philosophical writings and epistolary correspondence of Leibnitz. This ap- pears to me to furnish a key to some of Locke's observations, the scope of which Dr. Reid professes his inability to discover. One sentence, in particular, on which he has animadverted with some severity, is, in my opinion, distinctly pointed at the letter to Mr. Oldenburg, quoted in the beginning of this note.
" Mr. Locke farther says (I borrow Dr. Rcid's own statement) that maxims arc not of use to help men forward in the advancement of the sciences, or new discoveries of yet unknown truths: that Newton, in the discoveries he has made in his never enough to be admired book, has not been assisted by the general maxim, wliatever is, is ; or the whole is greater than a part, or the like."
As the letter to Oldenburg is dated in 1676, (twelve years before the publication of the Essay on Human Understanding,) and as Leibnitz expresses a desire that it may be communicated to Mr. Newton, there can scarcely he a doubt that Locke had read it ; and it reflects infinite honor on his sagacity, that he seems, at that early pe-
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account, lately published, of the Life and Writings of Dr. Reid, I have taken notice of some other inconven- iences resulting from it, still more important than the in- troduction of an unsound logic into the elements of nat- ural philosophy ; in particular, of the obvious tendency v^^hich it has to withdraw the attention from that unity of design which it is the noblest employment of philo- sophy to illustrate, by disguising it under the semblance of an eternal and necessary order, similar to what the mathematician delights to trace among the mutual rela- tions of quantities and figures. The consequence has been, (in too many physical systems,) to level the study of nature, in point of moral interest, with the investiga- tions of the algebraist ; — an effect too, which has taken place most remarkably, where, from the sublimity of the subject, it was least to be expected, — in the application of the mechanical philosophy to the phenomena of the heavens. But on this very extensive and important topic, I must not enter at present.
In the opposite extreme to the error which I have now been endeavouring to correct, is a paradox which was broached, about twenty years ago, by the late in- genious Dr. Beddoes ; and which has since been adopt- ed by some writers whose names are better entitled, on
riod, to have foreseen the extensive influence vphich the errors of this illustrious man were so long to maintain over the opinions of the learned world. The truth is, that even then he prepared a reply to some reasonine;s which, at the distance of a cen- tury, were to mislead, both in physics and in logic, the first philosophers in Europe.
If these conjectures be well founded, it must he acknowledged that Dr. Reid has not only failed in his defence of maxims against Locke's attack : but that he has to- tally misapprehended the aim of Locke's argument.
" I answer," says he, in the paragraph immediately following that which was quo- ted above, " the first of these maxims (whatever is, is) is an identical proposition, of no use in mathematics or in any other science. The second (that the whole is greater than a part) is often used by Newton, and by all mathematicians, and many demonstrations rest upon it. In general, Newton, as well as all other mathemati- cians, grounds his demonstrations of mathematical propositions upon the, axioms laid down by Euclid, or upon propositions which have been before demonstrated by help of these axioms.
" But it deserves to be particular]}' observed, that Newton, intending in the third book of his Principia to give a more scientific form to the physical part of astrono- my, which he had at first composed in a popular form, thought proper to follow the example of Euclid, and to lay down first, in what he calls Regukc Philosophandi, and in his Phenomena, the first princijjles whicli he assumes in his reasoning. Noth- ing, therefore, could have been more unluckily adduced by Mr. Locke to support his aversion to first principles, than the example of Sir Isaac Newton." — Essays on the Int. Powers, pp. 647, 648, 4to edit.
OF THE HUMAN MINB. 135
a question of this sort, to give weight to their opinions.* By the partisans of this nev/ doctrine it seems to be im- agined, that — so far from physics being a branch of mathematics, — mathematics, and more particularly ge- ometry, is, in reality, only a branch of physics. " The mathematical sciences," says Dr. Beddoes, " are scien- ces of experiment and observation, founded solely on the induction of particular facts ; as much so as mechan- ics, astronomy, optics, or chemistry. In the kind of ev- idence there is no difference ; for it originates from per- ception in all these cases alike ; but mathematical exper- iments are more simple, and more perfectly within the grasp of our senses, and our perceptions of mathemati- cal objects are clearer." f
A doctrine essentially the same, though expressed in terms not quite so revolting, has been lately sanctioned by Mr. Leslie ; and it is to his view of the argument that I mean to confine my attention at present. " The whole structure of geometry," he remarks, " is grounded on the simple comparison of triangles ; and all the fun- damental theorems which relate to this comparison, de- rive their evidence from the mere superposition of the triangles themselves ; a mode of proof which, in reality, is nothing but an ultimate appeal, though of the easiest and most familiar kind, to external observation." J And,
* I allude here more paiticulaiiv to my learned friend, Mr. Leslie, whose high and justly inerited reputation, hotli as a mathematician and an experimentalist, rcndeis it indispensably necessary for ino to take notice of some fundamental looical mistakes which he appears to me to have committed in the course of those inoenious excur- sions, in which he occasionally indulges himself, beyond the strict limits of his favor- ite studies.
t Into this train of thinking;, Dr. Beddoes informs us, he was first led by Mr, Home Tooke's speculations conct^rnino; language. " In whatever study you are en- gaged, to leave difficulties behind is distressing : and when these difficulties occur at your very entrance upon a science, professing to be so clear and certain as geometry, your feelings become slill more uncomfortable ; and you are dissatisfied vvit'i ^our own powers of comprehension. I therefore think it due to the author of EHEA IITEPOENTA, to acknowledge my obligations to him for relieving me from this sort (jf (ii-tiess. For although I had often made the attempt, I could never solve certain difficulties in Euclid, till my reflections were revived and assisted by Mr. Tooke's discoveries.''' — See Observations on the JVature of Demonstrative Evi- dence. Lonlon, 1793, pp. 5, and 1.5.
{ Elements of Geometry and of Geometrical Analysis, &c. By Mr. Leslie. Ed- inbi-rgh, 1809.
The assertion that the ichnle structure of geometry is founded on the comparison of triangles, is expressed in terms too unqualified. D'Alembcrt has mentioned another principle as not less fundanumtal, the measurement of angles by circular arches. " Lcs propositions fondamentales de geometric peuvent etre reduites a
136 ELEMENTS OF THE PHILOSOPHY
in another passage : " Geometry, like the other sciences which are not concerned about the operations of mind, rests ultimately on external observations. But those ul- timate facts are so few, so distinct and obvious, that the subsequent train of reasoning is safely pursued to un- limited extent, without ever appealing again to the evi- dence of the senses."*
Before proceeding to make any remarks on this theo- ry, it is proper to premise, that it involves two separate considerations, which it is of material consequence to distinguish from each other. The first is, that extension and figure (the subjects of geometry) are qualities of body which are made known to us by our external sens- es alone, and which actually fall under the consideration of the natural philosopher, as well as of the mathemati- cian. The second, that the whole fabric of geometrical science rests on the comparison of triangles, in forming which comparison, we are ultimately obliged to appeal (in the same manner as in estabhshing the first princi- ples of physics) to a sensible and experimental proof.
1. Inansv/er to the first of these allegations, it might perhaps be sufficient to observe, that in order to identi- fy two sciences, it is not enough to state, that they are both conversant about the same objects ; it is necessary farther to show, that, in both cases, these objects are considered in the same point of view, and give employ- ment to the same faculties of the mind. The poet, the painter, the gardener, and the botanist, are all occupied in various degrees and modes, with the study of the vegetable kingdom ; yet who has ever thought of con-
deux ; la mesure des angles par les arcs de cercle, et le principe de la superposition." — Elemens de Philosophie, Art. Geom6trie. — The same writer, however, justly ob- serves, in another part of his works, that the measure of angles by.circular arches, is itself dependent on the principle of superposition ; and that, consequently, however extensive and important in its application, it is entitled only to rank with what he calls principles of a seco7id order. " La mesure des angles par Ics arcs de cercle decrits de leur sommet, est elle-meine dependante du principe de la superposition. Car quand on dit que la mesure d'un angle est Tare circulaire decrit de son sommet, on veut dire que si deux angles sont egaux, les angles decrits de leur sommet a. nieme rayon, seront egaux ; verite qui se demontre par Ic piincipe de la superposi- tion, comme tout geometre tant soit peu initie dans cette science le sentira facile- rnent." — Eclairdssemens sur les Elemens de Philosophie, ^ IV.
Instead, therefore, of saying that the whole structure of geometry is grounded on the comparison of triangles, it would be more correct to say, that it is grounded on the principle of superposition.
* Elements of Geometry and of Geometrical Analysis, p. 453.
OF THE HUMAN MIND. 137
founding their several pursuits under one common name 1 The natural historian, the civil historian, the moralist, the logician, the dramatist, and the statesman, are all enga- ged in the study of man, and of the principles of human nature ; yet how widely discriminated are these various departments of science and of art ! how different are the kinds of evidence on which they respectively rest ! how different the intellectual habits which they have a tendency to form ! Indeed, if this mode of generaliza- tion were to be admitted as legitimate, it would lead us to blend all the objects of science into one and the same mass ; inasmuch as it is by the same impressions on our external senses, that our intellectual faculties are, in the first instance, roused to action, and all the first elements of our knowledge unfolded.
In the instance, however, before us, there is a very remarkable specialty, or rather singularity, which ren- ders the attempt to identify the objects of geometrical and of physical science, incomparably more illogical than it would be to classify poetry with botany, or the natural history of man with the political history of nations. This specialty arises from certain pecuharities in the metaphysical nature of those sensible qualities which fall under the consideration of the geometer ; and which led me, in a different work, to distinguish them from oth- er sensible qualities, (both primary and secondary,) by bestowing on them the title of mathematical affections of matter* Of these mathematical affections {magnitude im({ figure,) our first notions are, no doubt, derived (af5 well as of hardness, softness, roughness, and smooth- ness) from the exercise of our external senses; but it is equally certain, that whei;^ the notions of magnitude and figure have once been acquired, the mind is immediate- ly led to consider them as attributes of space no less than of body ; and (abstracting them entirely from the other sensible qualities perceived in conjunction with them) becomes impressed with an irresistible conviction, that their existence is necessary and eternal, and that it would remain unchanged if all the bodies in the uni-
* Philosophical Essays, pp. 94, 95. 4to edit.
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verse were annihilated. It is not our business here to inquire into the origin and grounds of this conviction. It is with the fact alone that we are concerned at pres- ent ; and this I conceive to be one of the most obvious- ly incontrovertible which the circle of our knowledge embraces. Let those explain it as they best can, who are of opinion, that all the judgments of the human un- derstanding rest ultimately on observation and experi- ence.
Nor is this the only case in which the mind forms conclusions concerning space, to which those of the natural philosopher do not bear the remotest analogy. Is it from experience we learn that space is infinite 1 or, (to express myself in more unexceptionable terms,) that no limits can be assigned to its immensity ? Here is a fact, extending not only beyond the reach of our personal observation, but beyond the observation of all created beings ; and a fact on which we pronounce with no less confidence, when in imagination we transport ourselves to the utmost verge of the material universe, than when we confine our thoughts to those regions of the globe which have been explored by travellers. How unUke those general laws which we investigate in physics, and which, how far soever we may find them to reach, may still, for any thing we are able to discov- er to the contrary, be only contingent, local, and tempo- rary !
It must indeed be owned, with respect to the conclu- sions hitherto mentioned on the subject of space, that they are rather of a metaphysical than of a mathematical nature ; but they are not, on that account, the less ap- plicable to our purpose ; for if the theory of Beddoes had any foundation, it would lead us to identify with physics the former of these sciences as well as the lat- ter; at least, all that part of the former which is employ- ed about space, or extension, — a favorite object of met- aphysical as well as of mathematical speculation. The truth, however, is, that some of our metaphysical con- clusions concerning space are more nearly allied to ge- ometrical theorems than we might be disposed at first to apprehend ; being involved or impUed in the most
OF THE HUMAN MIND. 139
simple and fundamental propositions which occur in Eu- cUd's Elements. When it is asserted, for example, that " if one straight line falls on two other straight lines, so as to make the two interior angles on the same side to- gether equal to two right angles, these two straight lines, though indefinitely produced, will never meet ; "—is not the boundless immensity of space tacitly assumed as a thing unquestionable 7 And is not a universal affirma- tion made with respect to a fact which experience is equally incompetent to disprove or to confirm 1 In like manner, when it is said, that " triangles on the same base, and betv^^een the same parallels are equal," do we feel ourselves the less ready to give our assent to the demonstration, if it should be supposed, that the one triangle is confined within the limits of the paper before us, and that the other, standing on the same base, has its vertex placed beyond the sphere of the fixed stars ? In various instances, we are led, with a force equally imperious, to acquiesce in conclusions, which not only admit of no illustration or proof from the perceptions of sense, but which, at first sight, are apt to stagger and confound the faculty of imagination. It is sufficient to mention, as examples of this, the relation between the hyperbola and its asymptotes ; and the still more obvi- ous truth of the infinite divisibility of extension. What analogy is there between such propositions as these, and that which announces, that the mercury in the Tor- riceUian tube will fall, if carried up to the top of a moun- tain ; or that the vibrations of a pendulum of a given length will be performed in the same time, while it re- mains in the same latitude ? Were there, in reality, that analogy between mathematical and physical propo- sitions, which Beddoes and his followers have fancied, the equality of the square of the hypothenuse of a right angled triangle to the squares described on the two other sides, and the proportion of 1,2, 3, between the cone and its circumscribed hemisphere and cylinder, might, with fully as great propriety, be considered in the light of physical phenomena, as of geometrical theo- rems : Nor would it have been at all inconsistent with the logical unity of his work, if Mr. Leslie had annexed
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to his Elements of Geometry, a scliolium concerning the final causes of circles and of straight lines, similar to that which, with such subhme effect, closes the Principia of' Sir Isaac Nev/ton.*
2. It yet remains for me to say a few words upon that superposition of triangles which is the ground-work of all our geometrical reasonings concerning the relations which different spaces bear to one another in respect of magnitude. And here I must take the liberty to remark, in the first place, that the fact in question has been stated in terms much too loose and incorrect for a logi- cal argument. When it is said, that " all the fundamen- tal theorems which relate to the comparison of triangles, derive their evidence from the mere superposition of the triangles themselves," it seems difficult, or rather impos-
*In the course of my own experience, I have met with one person, of no common ingenuity, who seemed seriously disposed to consider the truths of geometry very nearly in this light. The person I allude to was James Ferguson, author of the justly popular works on Astronomy and Mechanics. In the year 1768, he paid a visit to Edinburgh, when 1 had not only an opportunity of attending his public course of lectures, but of frequently enjoying, in private, the pleasme of his very interesting conversation. I remember distinctly to have heard him say, that he had more than once attempted to study the Elements of Euclid; but found himself quite unable to enter into that species of reasoning. The second proposition of the first book, he mentioned particu'aily as one of his stumbling-blocks at the very outset; — the cir- cuitous process by which Euclid sets about an operation which never could puzzle, for a single moment, any man who had seen a pair of compasses, appearing to him altogether capricious and ludicrous. He added, at the same time, that as there were various geometrical theorems of which he had dailj^ occasion to make use, he had satisfied himself of tlieir truth, either by means of his compasses and scale, or by some mechanical contrivances of his own invention. Of one of these I have still a perfect recollection ; — his mechanical or experimental demonstration of the 47th prop- osition of Euclid's first book, by cutting a card so as to afford an ocular proof, that ttie squares of the two sides actually filled the same space with the square of the hypothenuse.
To those who reflect on the disadvantages under which Mr. Ferguson had labored in point of education, and on the early and exclusive hold which experimental sci^ ence had taken of his mind, it will not perhaps seem altogether unaccountable, that the refined and scrupulous logic of Euclid should have struck him as tedious, and even unsatisfactory, in comparison of that more summary and palpable evidence on which his judgment was accustomed to rest. Considering, however, the great num- ber of years which have elapsed since this conversation took place, I should have hesitated about recording, solely on my own testimony, a fact so singular with respect to so distinguished a man, if I had not lately found, from Dr. Hutton's Matheuiatical Dictionary, that he also had heard from Mr. Ferguson's mouth, the most important of those particulars which I have now stated ; and of which my own recollection is probably the more lively and circumstantial, in consequence of the very early period of my life when they fell under ray notice.
" Mr. Ferguson's general mathematical knowledge," saj's Dr. Hutton, " was little or nothing. Of algebra, he understood little more than the notation ; and he has often told me he could never demonstrate one proposition in Euclid's Elements; his con- stant method being to satisfy himself, as to the truth of any problem, with a measure- ment by scale and compasses." — Hutton's Mathematical and Philosophical Diction- ary, Article Ferguson.
OF THE HUMAIV MIND. 141
sible, to annex to the adjective mere, an idea at all dif- ferent from what would be conveyed, if the word actual were to be substituted in its place ; more especially, when we attend to the assertion which immediately fol- lows, that " this mode of proof is, in reahty, nothing but an ultimate appeal, though of the easiest and most fa- miliar kind, to external observation.''^ But if this be, in truth, the sense in v/hich we are to interpret the state- ment quoted above, (and I cannot conceive any other interpretation of which it admits,) it must appear obvi- ous, upon the slightest reflection, that the statement pro- ceeds upon a total misapprehension of the principle of superposition ; inasmuch as it is not to an actual or mere superposition, but to an imaginary or ideal one, that any appeal is ever made by the geometer. Between these two modes of proof, the difference is not only wide, but radical and essential. The one would, indeed, level geometry with physics, in point of evidence, by building the whole of its reasonings on a fact ascertained by mechanical m.easurement : The other is addressed to the understanding, and to the understanding alone, and is as rigorously conclusive as it is possible for demonstration to be.*
* The same remark was, more than fifty years ago, made by D'Alembert, in reply to some mathematicinns on the Continent, who, it would appear, had then adopted a paradox very neaily approachinij to that which I am now combating. " Le prin- cipe de la superposition n'est point, comnie Font pretendu plusieurs geometres, une methode da demontrer peu exacto et purement mecanique. La superposition, telle que Ics mathematiciens la conroivent, ne consiste pas a appliquer grossiercraent une figure sur unc autre, pour juger par les yeux de Icur egalite ou de leur difference, comme un ouvrier applique son pie sur une ligne pour In mesurer ; elle consiste a. imaginer une figure transportce sur une autre, et a concliue de I'egalite supposee de certaincs parlies de deux figures, la coincidence de ces parties entr'clles, et de leur coincidence la coincidence du reste : d'ou resulte I'egalite et la similitude parfaites des figures entieres."
About a century Jjefore the time when D'Alembert wrote these observations, a similar view of the subject was taken by Dr. Barrow, a wiiter who, like D'Alembert, added to the skill and originality of an inventive mathematician, the most refined, and, at the same time, the justsst ideas concerning the theory of those intellectual processes which are subservient to mathematical reasoning. — " Unde merito vir acu- tissimus AVillcbrordus Sncllius liiculcntissimum appellat geometric supellcctilis in- strumentum banc ipsam \(pu^i/.o(nv. Earn igitur in dcmonstralionihus mathematicis quifastidiunt et respinuit, ut mechanical crassitudinis ac avrou^yia.? aliquid redo- lentem, ipsisfiinmm geomelricE basin lahefaclare student ; ast intprudenter etfrus- tra. Nam i(px^fioiM geornetra; suam non manu sed mente pcragunt, non oculi sensu, sed animi judicio Etstlmant. Supponunt (id quod nulla manus pra^stare, nullus sen- sus discernerc valet) accuratam et perfectam congiuentiaui, ex caque supposita justas et logicas eliciunt consequcntius. Nullus liic reguliE, circini, vei norma; usus, nullus brachiorutn labor, aut laterum contentio, rationis totum opus, artificium et
142 ELEMENTS OF THE PHILOSOPHY
That the resoning employed by Euchd m proof of the fourth proposition of his first book is completely demon- strative, will be readily granted by those who compare its different steps with the conclusions to which we were formerly led, when treating of the nature of mathemati- cal demonstration. In none of these steps is any ap- peal made to facts resting on the evidence of sense, nor, indeed, to any facts whatever. The constant appeal is to the definition of equahty.* " Let the triangle ABC," says Euclid, " be applied to the triangle D E F ; the point A to the point D, and the straight hne A B to the straight line D E ; the point B will coincide with the point E, because A B is equal to D E. And A B coin- ciding with D E, A C will coincide with D F, because the angle B A C is equal to the angle E D F" A simi- lar remark will be found to apply to every remaining step of the reasoning ; and, therefore, this resoning possesses the peculiar characteristic which distinguishes mathematical evidence from that af all the other scien- ces,— that it rests wholly on hypotheses and definitions, and in no respect upon any statement of facts, true or false. The ideas, indeed, of extension, of a triangle, and of equality, presuppose the exercise of our senses. Nay, the very idea of superposition involves that of mo- tion, and, consequently, (as the parts of space are im- moveable) of a material triangle. But where is there any thing analogous in all this, to those sensible facts, which are the principles of our reasoning in physics ; and which, according as they have been accurately or inaccurately ascertained, determine the accuracy or in- accuracy of our conclusions? The material triangle
machinatio est ; nil mechanicam sapiens auvou^yiav exigitur ; nil, inquam, mechani- cum, nisi quatenus omnis magnitudo sit aliquo modo mateiiaj involuta, sensibus exposita, visibilis et palpabilis, sic ut quod mens intelligi jubet, id manus quadante- nus exequi possit, et contemplationem praxis utcunque conetur ajmulaii. Quae tamen imitatio geometiica3 demonstiationis lobur ac dignitatem nedum non infirmat aut deprimit, at validius constabilit, etattollit altius," &c. — Lectiones Mathematics, Lect. in.
* It was before observed (see p. 119) that Euclid's eighth axiom (magnitudes which coincide with each other are equal) ought, in point of logical rigor, to have been stated in the form of a definition. In our present argument, however, it is not of material consequence whether this criticism be adopted or not. Whether we consider the proposition in question in the light of an axiom or of a definition, it is equally evident that it does not express a /ac< ascertained by observation or by experi- ment.
OF THE HUMAN MIND. 143
itself, as conceived by the mathematician, is the object, not of sense, but of intellect. It is not an actual measure, liable to expansion or contraction, from the influence of heat or of cold ; nor does it require, in the ideal use which is made of it by the student, the shghtest address of hand or nicety of eye. Even in explaining this de- monstration, for the first time, to a pupil, how slender soever his capacity might be, I do not believe that any teacher ever thought of illustrating its meaning by the actual application of the one triangle to the other. No teacher, at least, would do so, who had formed correct notions of the nature of mathematical science.
If the justness of these remarks be admitted, the demonstration in question must be allowed to be as well entitled to the name, as any other which the mathema- tician can produce ; for as our conclusions relative to the properties of the circle (considered in the hght of hy- pothetical theorems) are not the less rigorously and necessarily true, that no material circle may any where exist corresponding exactly to the definition of that fig- ure, so the proof given by EucUd of the fourth proposi- tion, would not be the less demonstrative, although our senses were incomparably less acute than they are, and although no material triangle continued of the same mag- nitude for a single instant. Indeed, when we have once acquired the ideas of equahty and of a common measure, our mathematical conclusions would not be in the least aifected, if all the bodies in the universe should vanish into nothing.
To many of my readers, I am perfectly aware, the foregoing remarks will be apt to appear tedious and su- perfluous. My only apolygy for the length to which they have extended is, my respect for the talents and learning of some of those writers who have lent the sanction of their authority to the logical errors which I have been endeavouring to correct ; and the obvious inconsis- tency of these conclusions with the doctrine concerning the characteristics of mathematical or demonstrative evi- dence, which it was the chief object of this section to establish.*
* This doctrine is concisely and clearly stated by a writer, whose acute and origin-
144 ELEMENTS OF THE PHILOSOPHY
SECTION IV.
OP OUR REASONINGS CONCERNING PROBABLE OR CONTINGENT TRUTHS.
I.
Narrow Field of demonstrative Evidence. — Of demonstrative Evidence, when com- bined with that of Sense, as in Practical Geometry; and with those of Sense, and of Induction, as in the Mechanical Philosophy. — Remarks on a Fundamental Law of Belief, involved in all our Reasonings concerning Contingent Truths.
If the account which has been given of the nature of demonstrative evidence be admitted, the province over which it extends must be hmited almost entirely to the objects of pure mathematics. A science perfectly anal- ogous to this, in point of evidence, may, indeed, be conceived (as I have already remarked) to consist of a series of propositions relating to moral, to pohtical, or to
al, though very eccentric genius, seldo-m fails to redeem his wildest paradoxes by the new lights which he strikes out in defending them. " Demonstratio est syllogismus vel syllogismorum series a nominum definitionibus usque ad conclusionem ultimam derivata." — Computatio sive Logica, cap. 6.
It will not, I trust, be inferred, from my having adopted, in the words of Hobbes, this detached proposition, that I am disposed to sanction any one of those conclusions which have been commonly supposed to be connected with it, in the mind of the au- thor:— I say, sup^Josec/, because I am by no means satisfied (notwithstanding the loose and unguarded manner in which he has stated some of his logical opinions) that justice has been done to his views and motives in this part of his works. My own notions on the subject of evidence in general, will be sufficiently unfolded in the progress of my speculations. In the mean time to prevent the possibility of any misapprehension of my meaning, I think it proper once more to remark, that the definition of Hobbes, quoted above, is to be understood (according to my interpre- tation of it) as applying solely to the word demonstration in pure mathematics. The extension of the same term by Dr. Clarke and others, to reasonings which have for their object, not conditional or hypothetical, but absolute truth, appears to me to have been attended with many serious inconveniences, which these excellent authors did not foresee. Of the demonstrations with which Aristotle has attempted to fortify his syllogistic rules, I shall afterwards have occasion to examine the validity.
The charge of unlimited scepticism brought against Hobbes, has, in my opinion, been occasioned, partly by his neglecting to draw the line between absolute and hypothetical truth, and partly by his applying the word demonstration to our rea- sonings in other sciences as well as in mathematics. To these causes may perhaps be added the offence which his logical writings must have given to the Realists of his time.
It is not, however, to Realists alone, that the charge has been confined. Leibnitz himself has given some countenance to it, in a dissertation prefixed to a work of Ma- rius Nizolius ; and Brucker, in referring to this dissertation, has aggravated not a little the censure of Hobbes, which it seems to contain. " Quin si ilhistrem Lcibnitzium audimus, Hobbesius quoque inter nominales referendus est, earn oh causam, quod ipso Occamo nominalior, rerum veritatern dicat in nominibus consistere, ac, quod majus est, pendere ab arbitrio humano." — Histor. PMlosph. de Ideis, p. 209. Augustte Vindelicorum, 1723.
OF THE HUMAN MIND. 145
physical subjects, but as h could answer no other pur- pose than to display the ingenuity of the inventor, hard- ly any thing of the kind has been hitherto attempted. The only exception which I can think of occurs in the speculations formerly mentioned under the title of theo- retical mechanics.
But, if the field of mathematical demonstration be limited entirely to hypothetical or conditional truths, whence (it may be asked) arises the extensive and the various utility of mathematical knowledge, in our phys- ical researches, and in the arts of life 7 The answer, I apprehend, is to be found in certain pecuharities of those objects to which the suppositions of the mathematician are confined ; in consequence of which peculiarities, real combinations of circumstances may fall under the examination of our senses, approximating far more near- ly to what his definitions describe, than is to be expect- ed in any other theoretical process of the human mind. Hence a corresponding coincidence between his ab- stract conclusions, and those facts in practical geometry and in physics which they help him to ascertain.
For the more complete illustration of this subject, it may be observed, in the first place, that although the peculiar force of that reasoning which is properly called mathematical, depends on the circumstance of its princi- ples being hypothetical, yet if, in any instance, the sup- position could be ascertained as actually existing, the conclusion might, with the very same certainty, be ap- phed. If I were satisfied, for example, that in a par- ticular circle drawn on paper, all the radii were exactly equal, every property which Euchd has demonstrated of that curve might be confidently affirmed to belong to this diagram. As the thing, however, here supposed, is rendered impossible by the imperfection of our senses, the truths of geometry can never, in their practical ap- plications, possess demonstrative evidence ; but only that kind of evidence which our organs of perception enable us to obtain.
But although, in the practical applications of mathe- matics, the evidence of our conclusions diff'ers essential- ly from that which belongs to the truths investigated in
VOL. II. 19
146 ELEMENTS OF THE PHILOSOPHY
the theory, it does not therefore follow, that these con- clusions are the less important. In proportion to the accuracy of our data, will be that of all our subsequent deductions ; and it fortunately happens, that the same imperfections of sense which limit what is physically attainable in the former, hmit also, to the very same extent, what is practically useful in the latter. The astonishing precision which the mechanical ingenuity of modern times has given to mathematical instruments, has, in fact, communicated a nicety to the results of practical geometry, beyond the ordinary demands of human life, and far beyond the most sanguine anticipa- tions of. our forefathers.*
This remarkable, and, indeed, singular coincidence of propositions purely hypothetical, with facts which fall under the examination of our senses, is owing, as I already hinted, to the peculiar nature of the objects about which mathematics is conversant ; and to the op- portunity which we have (in consequence of that men- surability f which belongs to all of them) of adjusting, with a degree of accuracy approximating nearly to the truth, the data from which we are to reason in our prac- tical operations, to those which are assumed in our the- ory. The only affections of matter which these objects comprehend are extension and figure ; affections which
* See a very interesting and able article, in the fifth volume of the Edinburgh Re- view, on Colonel Mudge's account of the operations carried on for accomplishing a trio-onornetrical survey of England and Wales. I cannot deny myself the pleasure of quoting a few sentences.
" In two distances that were deduced from sets of triangles, the one measured by General Roy in 1787, the other by Major Mudge, in 1794, one of 24,133 miles, and the other of 88,688, the two measures agree within a foot as'to the first distance, and 16 inches as to the second. Such an agreement where the observers and the in- etruments were both different, where the lines measured were of such extent, and deduced from such a variety of data, is probably without Jiny other example. Coin- cidences of this sort are frequent in the trigonometrical survey, and prove how much more good instruments, used by skilful and attentive observers, are capable of per- forming, than the most sanguine theorist could have ever ventured to foretell, —
" It is curious to compare the early essays of practical geometry with the perfec- tion to which its operations have now reached, and to consider that, while the artist had made so litde progress, the theorist had reached many of the sublimest heights of mathematical speculation ; that the latter had found out the area of the circle, and calculated its circumference to more than a hundred places of decimals, when the former could hardly divide an arch into minutes of a degree ; and that many ex- cellent treatises had been written on the properties of curve lines, before a straight line of considerable length had ever been carefully drawn, or exactly measured on the surface of the earth."
] See note (G.)
OF THE HUMAN MIND. 1 47
matter possesses in common with space, and which may, therefore, be separated in fact, as well as abstracted in thought, from all its other sensible quahties. In exam- ining, accordingly, the relations of quantity connected with these affections, we are not liable to be disturbed by those physical accidents, which, in the other applications of mathematical science, necessarily render the result, more or less, at variance with the theory. In measuring the height of a mountain, or in the survey of a country, if we are at due pains in ascertaining our data, and if we reason from them with mathematical strictness, the result may be depended on as accurate within very nar- row limits; and as there is nothing but the incorrectness of our data by which the result can be vitiated, the limits of possible error may themselves be assigned. But in the simplest apphcations of mathematics to me- chanics or to physics, the abstractions which are neces- sary in the theory, must always leave out circumstances which are essentially connected with the effect. In demonstrating, for example, the property of the lever, we abstract entirely from its own weight, and consider it as an inflexible methematical hne ; — suppositions with which the fact cannot possibly correspond ; and for which, of course, allowances (which nothing but physical experience can enable us to judge of) must be made in practice.*
Next to practical geometry, properly so called, one of the easiest apphcations of mathematical theory occurs in those branches of optics which are distinguished by the name of catoptrics and dioptrics. In these, the physical principles from which we reason are few and precisely definite, and the rest of the process is as purely geometrical as the Elements of Euchd.
In that part of astronomy, too, which relates solely to the phenomena, without any consideration of physical causes, our reasonings are purely geometrical. The data, indeed, on which we proceed must have been pre- viously ascertained by observation ; bat the inferences we draw from these are connected with them by math-
* See Note (H.)
148 ELEMENTS OF THE PHILOSOPHY
ematical demonstration, and are accessible to all who are acquainted with the theory of spherics.
In physical astronomy, the law of gravitation becomes also a principle or datum in our reasonings ; but as in the celestial phenomena, it is disengaged from the effects of the various other causes which are combined with it near the surface of our planet, this branch of physics, as it is of all the most sublime and comprehensive in its objects, so it seems, in a greater degree than any other, to open a fair and advantageous field for mathe- matical ingenuity.
In the instances which have been last mentioned, the evidence of our conclusions resolves ultimately not only into that of sense, but into another law of belief former- ly mentioned ; that which leads us to expect the con- tinuance in future of the estabUshed order of physical phenomena. A very striking illustration of this presents itself in the computations of the astronomer ; on the faith of which he predicts, with the most perfect assur- ance, many centuries before they happen, the appear- ances which the heavenly bodies are to exhibit. The same fact is assumed in all our conclusions in natural philosophy ; and something extremely analogous to it in all our conclusions concerning human affairs. They relate, in both cases, not to necessary connexions, but to probable or contingent events ; of which (how confidently soever we may expect them to take place) the failure is by no means perceived to be impossible. Such con- clusions, therefore, differ essentially from those to which we are led by the demonstrations of pure mathematics, which not only command our assent to the theorems they establish, but satisfy us that the contrary supposi- tions are absurd.
These examples may suffice to convey a general idea of the distinction between demonstrative and probable evidence; and I purposely borrowed them from scien- ces where the two are brought into immediate contrast with each other, and where the authority of both has hitherto been equally undisputed.
Before prosecuting any farther the subject of proba- ble evidence, some attention seems to be due, in the
OF THE HUMAN MIND. 149
first place, to the grounds of that fundamental supposi- tion on which it proceeds, — the stability of the order of nature. Of this important subject, accordingly, I pro- pose to treat at some length.
II.
Continuation of the Subject. — Of that Permanence or Stability in the Order of Na- ture, which is presupposed in our Reasonings concerning Contingent Truths.
I HAVE already taken notice of a remarkable princi- ple of the mind, (whether coeval with the first exercise of its powers, or the gradual result of habit, it is not at present material to inquire,) in consequence of which, we are irresistibly led to apply to future events the re- sults of our past experience. In again resuming the sub- ject, I do not mean to add any thing to what was then stated concerning the origin or the nature of this prin- ciple ; but shall confine myself to a few reflections on that established order in the succession of events, which it unconsciously assumes as a fact ; and which, if it were not real, would render human life a continued se- ries of errors and disappointments. In any incidental remarks that may occur on the principle itself, I shall consider its> existence as a thing universally acknow- ledged, and shall direct my attention chiefly to its prac- tical eff'ects ; — efl'ects which will be found to extend equally to the theories of the learned, and to the pre- judices of the vulgar. The question with regard to its origin is, in truth, a problem of mere curiosity ; for of its actual influence on our beUef, and on our conduct, no doubts have been suggested by the most sceptical writers.
Before entering, however, upon the following argu- ment, it may not be superfluous to observe, with respect to this expectation, that, in whatever manner it at first arises, it cannot fail to be mightily confirmed and strengthened by habits of scientific research ; the ten- dency of which is to familiarize us more and more with the simpHcity and uniformity of physical laws, by grad-
150 ELEMENTS OF THE PHILOSOPHY
ually reconciling with them, as our knowledge extends, those phenomena which we had previously been dispos- ed to consider in the light of exceptions. It is thus that, when due allowances are made for the different circumstances of the two events, the ascent of smoke appears to be no less a proof of the law of gravitation than the fall of a stone. This simplification and gene- rahzation of the laws of nature is one of the greatest pleasures which philosophy yields ; and the growing confidence with which it is anticipated, forms one of the chief incentives to philosophical pursuits. Few experiments, perhaps, in physics, afford more exquisite delight to the novice, or throw a stronger fight on the nature and object of that science, than when he sees, for the first time, the guinea and the feather drop to- gether in the exhausted receiver.
In the language of modern science, the estabhshed order in the succession of physical events is commonly referred (by a sort of figure or metaphor) to the general laws of nature. It is a mode of speaking extremely convenient from its conciseness, but is apt to suggest to the fancy a groundless, and, indeed, absurd analogy be- tween the material and the moral worlds. As the order of society results from the laws prescribed by the legis- lator, so the order of the universe is conceived to re- sult from certain laws established by the Deity. Thus, it is customary to say, that the fall of heavy bodies to- wards the earth's surface, the ebbing and flowing of the sea, and the motions of the planets in their orbits, are consequences of the laiv of gravitation. But although, in one sense, this may be abundantly accurate, it ought always to be kept in view, that it is not a literal but a metaphorical statement of the truth ; a statement some- what analogous to that poetical expression in the sacred writings, in which God is said " to have given his de- cree to the seas, that they should not pass his com- mandment." In those pohtical associations from which the metaphor is borrowed, the laws are addressed to rational and voluntary agents, who are able to compre- hend their meaning, and to regulate their conduct ac- cordingly ; whereas, in the material universe, the sub-
OF THE HUMAN MIND. 151
jects of our observation are understood by all men to be unconscious and passive, (that is, are understood to be unchangeable in their state, without the influence of some foreign and external force,) and, consequently, the order so admirably maintained, amidst all the various changes which they actually undergo, not only implies intelligence in its first conception, but implies, in its con- tinued existence, the incessant agency of power, exe- cuting the purposes of wise design. If the word law, therefore, be, in such instances, hterally interpreted, it must mean a uniform mode of operation, prescribed by the Deity to himself; and it has accordingly been ex- plained in this sense by some of our best philosophical writers, particularly by Dr. Clarke.* In employing, however, the word with an exclusive reference to ex- perimental philosophy, it is more correctly logical to consider it as merely a statement of some general fact with respect to the order of nature ; — a fact which has been found to hold uniformly in our past experience, and on the continuance of which, in future, the consti- tution of our mind determines us confidently to rely.
After what has been already said, it is hardly neces- sary to take notice of the absurdity of that opinion, or rather of that mode of speaking, which seems to refer the order of the universe to general laws operating as efficient causes. Absurd, however, as it is, there is rea- son to suspect, that it has, with many, had the effect of keeping the Deity out of view, while they were study- ing his works. To an incautious use of the same very equivocal phrase, may be traced the bewildering ob- scurity in the speculations of som^e eminent French writers, concerning its metaphysical import. Even the great Montesquieu, in the very first chapter of his prin- cipal work, has lost himself in a fruitless attempt to ex- plain its meaning, when, by a simple statement of the essential distinction between its literal and its metaphor- ical acceptations, he might have at once cleared up the
* So likewise Halley, in his Latin verses prefixed to Newton's Principia : "En tibi norma poli, et tlivtc libraniina molis, Computus on Jovig ; et qiias, dum primordla rerum Pavgcrr.t, omniparcns leges violare Creator JVolvit."
152 ELEMENTS OF THE PHILOSOPHY
mystery. After telling us that " laws, in their most ex- tensive signification, are the necessary relations {Us rappo7is necessaires) which arise from the nature of things, and that, in this sense, all beings have their laws ; — that the Deity has his laws ; the material world Us laws ; intelligences superior to man their laws ; the brutes their laws ; man his laws ; " — he proceeds to re- mark, " That the moral world is so far from being so well governed as the material ; for the former, although it has its laws, which are invariable, does not observe these laws so constantly as the latter." It is evident that this remark derives whatever plausibility it posesses from a play upon words ; from confounding moral laws with physical ; or, in plainer terms, from confounding laws which are addressed by a legi'slator to intelligent beings, with those general conclusions concerning the established order of the universe, to which, when legit- imately inferred from an induction sufficiently extensive, philosophers have metaphorically applied the title of Laivs of JYature. In the one case, the conformity of the law with the nature of things, does not at all de- pend on its being observed or not, but on the reasona- bleness and moral obligation of the law. In the other case, the very definition of the word law supposes that it apphes universally ; insomuch that, if it failed in one single instance, it would cease to be a law. It is, there- fore a mere quibble to say, that the laws of the mate- rial world are better observed than those of the moral ; the meaning of the word law, in the two cases to which it is here applied, being so totally different, as to ren- der the comparison or contrast, in the statement of which it is involved, altogether illusory and sophistical. Indeed, nothing more is necessary to strip the proposi- tion of every semblance of plausibihty, but an attention to this verbal ambiguity.*
* I do not recollect any instance in the writino-s of Montesquieu, where he has reasoned more vaguely than in this chapter ; and yet I am inclined to believe, that few chapters in the Spirit of Laws have been more admired. "Montesquieu," says a French writer, " paroissoit a Thomas le premier des ecrivains, pour la force et Petendue des idees, pour la multitude, la profondeur, la nouveaute des rapports. II est incroyable (disoit-il) tout ce que Montesquieu a fait apper^evoir dans ce mot si court, le mot Loi." — JVouveau Diction. Historique, Ait. Thomas. Lyon, 1804.
OF THE HUMAN MIJVD. 153
This metaphorical employment of the word law, to express a general fact, although it does not appear to have been adopted in the technical phraseology of an- cient philosophy, is not unusual among the classical wri- ters, when speaking of those physical arrangements, whether on the earth or in the heavens, which continue to exhibit the same appearance from age to age.
" Hie segetes, illic veniunt felicius uvse : Arborei fetus alibi, atque injussa virescunt Gramina. Nonne vides, croceos ut Tmolus odores, India mittit ebur, molles sua thura Sabaei 1 At Chalybes nudi ferrum, virosaque Pontus Castorea, Eliadum palmas Epiros equarum T - Continue has leges, seternaque federa certis Imposuit natura locis." *
The same metaphor occurs in another passage of the Georgics, where the poet describes the regularity which is exhibited in the economy of the bees :
" Solse communes natos, consortia tecta Urbis habent, magnisque agitant sub legibus aevum." t
The following hnes from Ovid's account of the Pytha- gorean philosophy, are still more in point :
" Et rerum causas, et quid natura, docebat ; Q,uid Deus : unde nives : quae fulminis qsset origo: Jupiter, an venti, discussa nube tonarent : Quid quateret terras, qua sidera lege mearent, Et quodcunque latet." |
For some important remarks on the distinction between moral and physical laws, see Dr. Ferguson's Institutes of Moral Philosophy, last edit.
* Virg. I. Georg. 60.
t Georg. IV. 153.
I Ovid. Met. XV. 6S.
I shall only add to these quotations the epigram of Claudian on the instrument said to be invented by Archimedes for representing the movements of the heavenly bo- dies, in which various expressions occur coinciding remarkably with the scope of the foregoing observdtions.
" Jupiter in parvo cum rorncret a^thera vitro,
Risit, et ail suporos talia dicta iledit. * Hucciiio mortal i?i pro^rressa potentia curaj .' Jam meus in frajili Uiditur orbe lalior. Jura Poll, rerumijuc filciii, Icgcsi/uc Deorum,
Ecce Syrai-u>ins iranstulit arte senex. Inclusus variis famulatur spirilus nstris,
Et vivum corlis motibus urget opus. Percurrit propriuni mcntilU3 Signitcr annum,
Et simulala novo Cynthia menso redii. Jamque suum volvens audax industria mundum,
Oaudet et humani sidera menle regit. Ciuid falso insontem tonitru Salmonea miror .' yEmula naturae parva reperta manus.' "
VOL. II. 20
154 ELEMENTS OF THE PHILOSOPHY
I have quoted these different passages from ancient authors, chiefly as an illustration of the strength and of the similarity of the impression which the order of na- ture has made on the minds of reflecting men, in all ages of the world. Nor is this wonderful : for, were things difl'erently constituted, it would be impossible for man to derive benefit from experience ; and the powers of observation and memory would be subservient only to the gratification of an idle curiosity. In consequence of those uniform laws by which the succession of events is actually regulated, every fact collected with respect to the past is a foundation of sagacity and of skill with respect to the future ; and, in truth, it is chiefly this ap- phcation of experience to anticipate what is yet to hap- pen, which forms the intellectual superiority of one in- dividual above another. The remark holds equally in all the various pursuits of mankind, whether speculative or active. As an astronomer is able, by reasonings founded on past observations, to predict those phenom- ena of the heavens which astonish or terrify the sav- age ; as the chemist, from his previous familiarity with the changes operated upon bodies by heat or by mix- ture, can predict the result of innumerable experiments, which to others furnish only matter of amusement and w^onder ; — so a studious observer of human afl'airs ac- quires a prophetic foresight (still more incomprehensible to the multitude) with respect to the future fortunes of mankind ; — a foresight which, if it does not reach, like our anticipations in physical science, to particular and definite events, amply compensates for what it wants in precision, by the extent and variety of the prospects which it opens. It is from this apprehended analogy between the future and the past, that historical know- ledge derives the whole of its value ; and were the anal- ogy completely to fail, the records of former ages
In the progress of philosophical refinement at Rome, this metaphorical application of the word law seems to have been attended with the same consequences which (as I already observed) have resulted from an incautious use of it among some philo- sophers of modern Europe. Pliny tells us, that, in his time, these consequences ex- tended both to the lettered, and to the unlettered multitude. " Pars alia astro sue evcntus assignat, et nascendi legibus ; semelque in oinnes futures unquam Deo de- cretum, in rcliquum vcro otium datum. Scdere capit scntcntia haec, pariterque et erudilum vulgus et rude in cam cursu vadit." — Plin. JVat. Hist. Lib. ii.
OF THE HUMAN MIND. 155
would, in point of utility, rank with the fictions of poet- ry. Nor is the case different in the business of common life. Upon what does the success of men in their pri- vate concerns so essentially depend as on their own prudence ; and what else does this word mean, than a wise regard, in every step of their conduct, to the les- sons which experience has taught them ? *
The departments of the universe, in which we have an opportunity of seeing this regular order displayed, ,are the three following: 1. The phenomena of inani- mate matter ; 2. The phenomena of the lower animals ; and, 3. The phenomena exhibited by the human race.
1. On the first of these heads, I have only to repeat what was before remarked, That, in all the phenomena of the material world, the uniformity in the order of events is conceived by us to be complete and infalhble ; insomuch that, to be assured of the same result upon a repetition of the same experiment, we require only to be satisfied, that both have been made in circumstances precisely similar. A single experiment, accordingly, if conducted with due attention, is considered, by the most cautious inquirers, as sufficient to estabhsh a general physical fact ; and if, on any occasion, it should be re- peated a second time, for the sake of greater certainty in the conclusion, it is merely with a view of guarding against the effects of the accidental concomitants which may have escaped notice, when the first result was ob- tained.
2. The case is nearly similar in the phenomena exhib- ited by the brutes ; the various tribes of which furnish a subject of examination so steady, that the remarks made on a few individuals may be extended, with little risk of error, to the whole species. To this uniformity in their instincts it is owing, that man can so easily maintain his empire over them, and employ them as agents or instruments for accomplishing his purposes ; advantages which would be wholly lost to him, if the operations of instinct were as much diversified as those of human reason. Here, therefore, we may plainly
* " Pnidentiam quodaminodo esse divinationem." Coiti. J\fep. in vild Miici.
156 ELEMENTS OF THE PHILOSOPHY
trace a purpose or design, perfectly analogous to that already remarked, with respect to the laws which regu- late the material world ; and the difference, in point of exact uniformity, which distinguishes the two classes of events, obviously arises from a certain latitude of ac- tion which enables the brutes to accommodate them- selves, in some measure, to their accidental situations ; — rendering them, in consequence of this power of ac- commodation, incomparably more serviceable to our race than they would have been, if altogether subject- ed, hke mere matter, to the influence of regular and as- signable causes. It is, moreover, extremely worthy of observation, concerning these two departments of the universe, that the uniformity in the phenomena of the latter presupposes a corresponding regularity in the phenomena of the former ; insomuch that, if the estab- lished order of the material world were to be essentially disturbed, (the instincts of the brutes remaining the same,) all their various tribes would inevitably perish. The uniformity of animal instinct, therefore, bears a re- ference to the constancy and immutability of physical laws, not less manifest, than that of the fin of the fish to the properties of the water, or of the wing of the bird to those of the atmosphere.
3. When from the phenomena of inanimate matter and those of the lower animals, we turn our attention to the history of our own species, innumerable lessons present themselves for the instruction of all who reflect seriously on the great concerns of human life. These lessons require, indeed, an uncommon degree of acute- ness and good sense to collect them, and a still more uncommon degree of caution to apply them to practice ; not only because it is difficull to find cases in which the combinations of circumstances are exactly the same ; but because the peculiarities of individual character are infinite, and the real springs of action in our fellow-crea- tures are objects only of vague and doubtful conjecture. It is, however, a curious fact, and one which opens a wide field of interesting speculation, that, in proportion as we extend our views from particulars to generals, and from individuals to communities, human affairs exhibit,
OF THE HUMAN MIND. 157
more and more, a steady subject of philosophical exam- ination, and furnish a greater number of general con- clusions to guide our conjectures concerning future contingences. To speculate concerning the character or talents of the individual who shall possess the throne of a pardcular kingdom, a hundred years hence, would be absurd in the extreme : But to indulge imagination in anticipating, at the same distance of time, the con- dition and character of any great nation, with whose manners and pohdcal situation we are well acquainted, (although even here our conclusions may be widely erroneous,) could not be justly censured as a misap- plication of our faculties equally vain and irrational with the former. On this subject, Mr. Hume has made some very ingenious and important remarks in the beginning of his Essay on the Rise and Progress of the Arts and Sciences.
The same observation is apphcable to all other cases, in which events depend on a multiphcity of circumstan- ces. How accidental soever these circumstances may appear, and how much soever they may be placed, w^hen individually considered, beyond the reach of our calcu- lations, experience shows, that they are somehow or other mutually adjusted, so as to produce a certain de- gree of uniformity in the result ; and this uniformity is the more complete, the greater is the number of circum- stances combined. What can appear more uncertain than the proportion between the sexes among the chil- dren of any one family ! and yet how wonderfully is the balance preserved in the case of a numerous society ! What more precarious than the duration of life in an in- dividual ! and yet, in a long hst of persons of the same age, and placed in the same circumstances, the mean duration of hfe is found to vary within very narrow lim- its. In an extensive district, too, a considerable degree of regularity may sometimes be traced for a course of years, in the proportion of births and of deaths, to the number of the whole inhabitants. Thus, in France, Necker informs us, that " the number of births is in pro- portion to that of the inhabitants as one to twenty-three and twenty-four, in the districts that are not favored by
158 ELEMENTS OF THE PHILOSOPHY
nature, nor by moral circumstances : this proportion is as one to twenty-five, twenty-five and a half, and twenty- six, in the greatest part of France : in cities, as one to twenty-seven, twenty-eight, twenty-nine, and even thirty, according to their extent and their trade." " Such pro- portions," he observes, " can only be remarked in dis- tricts where there are no settlers nor emigrants ; but even the differences arising from these," the same author adds, " and many other causes, acquire a kind of uniformity, when collectively considered, and in the immense extent of so great a kingdom." *
It may be worth while to remark, that on the princi- ple just stated, all the different institutions for Assuran- ces are founded. The object at which they all aim, in common, is, to diminish the number oi accidents to which human hfe is exposed; or rather, to counteract the in- conveniences resulting from the irregularity of individual events, by the uniformity of general laws.
The advantages which we derive from such general conclusions as we possess concerning the order of nature, are so great, and our propensity to believe in its exist- ence is so strong, that, even in cases where the succession of events appears the most anomalous, we are apt to suspect the operation of fixed and constant laws, though we may be unable to trace them. The vulgar, in all countries, perhaps, have a propensity to imagine, that, after a certain number of years, the succession of plen- tiful and of scanty harvests begins again to be repeated in the same series as before ; — a notion to which Lord Bacon himself has given some countenance in the fol- lowing passage : " There is a toy which I have heard, and I would not have it given over, but waited upon a little. They say it is observed in the low countries, (I know not in what part,) that every five and thirty years, the same kind and suite of years and weathers come about again ; as great frosts, great wet, great droughts, warm winters, summers with Httle heat, and the like ; and they call it the prime. It is a thing I do the
* Traite de rAdrainistration des Finances de France.
OF THE HUMAN MIND. 159
rather mention, because computing backwards, I have found some concurrence." *
Among the philosophers of antiquity, the influence of the same prejudice is observable on a scale still greater; many of them having supposed, that at the end of the annus magnus, or Platonic year, a repetition would com- mence of all the transactions that have occurred on the theatre of the world. According to this doctrine the predictions in Virgil's PoHio, will, sooner or later, be lite- rally accomplished :
" Alter erit turn Tiphys, et altera quae vehat Argo Delectcs Heroas ; erunt etiam altera bella ; Atque iterum ad Trojam magnus mittetur Achilles." t
The astronomical cycles which the Greeks borrowed from the Egyptians and Chaldeans, when combined with that natural bias of the mind which I have just re- marked, account suflSciently for this extension to the moral world, of ideas suggested by the order of physi- cal phenomena.
Nor is this hypothesis of a moral cycle, extravagant as it unquestionably is, without its partisans among modern theorists. The train of thought, indeed, by which they have been led to adopt it is essentially different ; but it probably received no small degree of countenance in their opinion, from the same bias which influenced the speculations of the ancients. It has been demonstrated by one of the most profound mathematicians of the present age,| that all the irregularities arising from the mutual action of the planets, are, by a combination of various arrangements, necessarily subjected to certain periodical laws, so as for ever to secure the stability and order of the system. Of this sublime conclusion, it has been justly and beautifully observed, that " after New-
• Essays, Art. 59.
I " Turn cfficitur," says Cicero, speaking of this period,' " cum solis ct lima;, et quinque enantium, ad eandciii inter se coiriparationcm confectis omnium spatiis, est facta convcrsio. Qu;e quam longa sit, ma2;na qiucstio est : esse vera certain et defi- nitam necesse est." — J)c J\''at. Deorwn, Lib. ii. 74. " Hoc iiitervallo," Clavius ob- serves, " quidam volunt, omnia qua^cmique in nmndo sunt, eodcm ordine esse rcditu- ra, quo nunc cernuntur." — Clav. Commentar.in Sjihxram Joannis dc Sacro JBoscu, p. 57. Rom;.', I(i07.
I M. de la Grange.
160 ELEMENTS OF THE PHILOSOPHY
ton's theory of the elhptic orbits of the planets, La Grange's discovery of their periodical inequaUties, is, without doubt, the noblest truth in physical astronomy ; while, in respect of the doctrine of final causes, it may truly be regarded as the greatest of all." * The theo- rists, however, to whom I at pi-esent allude, seem dis- posed to consider it in a very different light, and to employ it for purposes of a very different tendency. " Similar periods (it has been said) but of an extent that affright the imagination, probably regulate the modifica- tions of the atmosphere ; inasmuch as the same series of appearances must inevitably recur, whenever a coin- cidence of circumstances takes place. The aggregate labors of men, indeed, may be supposed, at first sight, to alter the operation of natural causes, by continually transforming the face of our globe ; but it must be re- collected that, as the agency of animals is itself stimula- ted and determined solely by the influence of external objects, the re-actions of hving beings are comprehend- ed in the same necessary system ; and, consequently, that all the events within the immeasurable circuit of the universe, are the successive evolution of an extended series, which, at the returns of some vast period, re- peats its eternal round during the endless flux of time."f
On this very bold argument, considered in its connex- ion with the scheme of necessity, I have nothing to observe here. I have mentioned it merely as an addi- tional proof of that irresistible propensity to believe in the permanent order of physical events, which seems to form an original principle of the human constitution ; — a belief essential to our existence in the world which we inhabit, as well as the foundation of all physical science ; but which we obviously extend far beyond the bounds authorized by sound philosophy, when we apply it, with- out any limitation, to that moral system, which is distin- guished by pecuHar characteristics, so numerous and
* Edinburgh Review, Vol. XL p. 264.
f The foregoing passage is transcribed from an article in the Monthly Review. I have neglected to mark the volume ; but I think it is one of those published since 1800. See Note (L)
OF THE HUMAN MIND. 161
important, and for the accommodation of which, so many reasons entitle us to presume, that the material universe, with all its constant and harmonious laws, was purposely arranged.
To a hasty and injudicious apphcation of the same belief, in anticipating the future course of human affairs, might be traced a variety of popular superstitions, which have prevailed, in a greater or less degree, in all nations and ages ; those superstitions, for example, which have given rise to the study of charms, of omens, of astrolo- gy, and of the different arts of divination. But the argument has been already prosecuted as far as its con- nexion with this part of the subject requires. For a fuller illustration of it, I refer to some remarks in my former volume, on the superstitious observances which, among rude nations, are constantly found blended with the practice of physic ; and which, contemptible and ludicrous as they seem, have an obvious foundation, during the infancy of human reason, in those important principles of our nature, which, when duly disciphnedby a more enlarged experience, lead to the sublime discov- eries of inductive science.*
Nor is it to the earlier stages of society, or to the lower classes of the people, that these superstitions are confined. Even in the most enhghtened and refined periods they occasionally appear ; exercising, not unfre- quently, over men of the highest genius and talents, an ascendant, which is at once consolatory and humiliating to the species.
" Ecce fulgurum monitus, oraculorum praescita, arus- picum prsedicta, atque etiam parva dictu in auguriis sternutamenta et offensiones pedum. Divus Augustus Icfivum prodidit sibi calceum praepostere inductum, quo die seditione militari prope afflictus est." f
" Dr. Johnson," says his affectionate and very com- municative biographer, " had another particularity, of which none of his friends ever ventured to ask an explanation. It appeared to me some superstitious habit,
* Vol I. pp. 355,356, 3ij7, 3(1 edit, t Plin. Nat. Hist. Lib. ii.
VOL. II. 21
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which he had contracted early, and from which he had never called upon his reason to disentangle him. This was, his anxious care to go out or in at a door or pas- sage, by a certain number of steps from a certain point, or at least so as that either his right or his left foot (I am not certain which) should constantly make the first ac- tual movement when he came close to the door or pas- sage. Thus I conjecture : for I have, upon innumerable occasions, observed him suddenly stop, and then seem to count his steps with a deep earnestness ; and when he had neglected or gone wrong in this sort of magical movement, I have seen him go back again, put himself in a proper posture to begin the ceremony, and, having gone through it, break from his abstraction, walk briskly on, and join his companion."*
The remark may appear somewhat out of place, but, after the last quotation, I may be permitted to say, that the person to whom it relates, great as his powers, and splendid as his accomplishments undoubtedly were, was scarcely entitled to assert, that " Education is as well known, and has long been as well known, as ever it can be." f What a hmited estimate of the objects of edu- cation must this great man have formed ! They who know the value of a well regulated and unclouded mind, would not incur the weakness and wretchedness exhib- ited in the foregoing description, for all his hterary ac- quirements and hterary fame.
III.
Continuation of the Subject. — General Remarks on the DifTerence between the Evi- dence of Experience, and that of Analogy.
According to the account of experience which has been hitherto given, its evidence reaches no farther than to an anticipation of the future from the past, in cases where the same physical cause continues to operate in exactly the same circumstances. That this statement is
* Boswell's Johnson, Vol. I. p. 264, 4to edit. f Boswell's Johnson, Vol I. p. 514, 4to edit.
OF THE HUMAN MIND. 163
agreeable to the strict philosophical notion of experi- ence, will not be disputed. Wherever a change takes place, either in the cause itself, or in the circumstances combined with it in our former trials, the anticipations which we form of the future cannot with propriety be referred to experience alone, but to experience co-ope- rating with some other principles of our nature. In common discourse, however, precision in the use of language is not to be expected, where logical or meta- physical ideas are at all concerned ; and, therefore, it is not to be wondered at, that the word experience should often be employed with a latitude greatly beyond what the former definition authorizes. When I transfer, for example, my conclusions concerning the descent of heavy bodies from one stone to another stone, or even from a stone to a leaden bullet, my inference might be said, with sufficient accuracy for the ordinary purposes of speech, to have the evidence of experience in its fa- vor ; if indeed it would not savour of scholastic affecta- tion to aim at a more rigorous enunciation of the propo- sition. Nothing, at the same time, can be more evident than this, that the slightest shade of difference which tends to weaken the resemblance, or rather to destroy the identity of two cases, invahdates the inference from the one to the other, as far as it rests on experience sole- ly, no less than the most prominent dissimilitudes which characterize the different kingdoms and departments of nature.
Upon what ground do I conclude that the thrust of a sword through my body, in a particular direction, would be followed by instant death ? According to the popu- lar use of language, the obvious answer would be, — up- on experience, and experience alone. But surely this account of the matter is extremely loose and incorrect ; for where is the evidence that the internal structure of my body bears any resemblance to that of any of the other bodies which have been hitherto examined by anatomists ? It is no answer to this question to tell me, that the experience of these anatomists has ascertained a uniformity of structure in every human subject which has as yet been dissected ; and that, therefore, I am
164 ELEMENTS OF THE PHILOSOPHY
justified in concluding, that myhodj forms no exception to the general rule. My question does not relate to the soundness of this inference, but to the principle of my nature, which leads me thus not only to reason from the past to the future, but to reason from one thing to anoth- er, which, in its external marks, bears a certain degree of resemblance to it. Something more than experience, in the strictest sense of that word, is surely necessary to explain the transition from what is identically the same, to vv^hat is only similar ; and yet my inference in this instance is made with the most assured and unqual- ified confidence in the infallibihty of the result. No in- ference, founded on the most direct and long-continued experience, nor, indeed, any proposition established by mathematical demonstration, coiild more imperiously command my assent.
In whatever manner the province of experience, strictly so called, comes to be thus enlarged, it is per- fectly manifest, that, without some provision for this purpose, the principles of our constitution would not have been duly adjusted to the scene in which we have to act. Were we not so formed as eagerly to seize the resembling features of different things and different events, and to extend our conclusions from the individ- ual to the species, fife would elapse before we had ac- quired the first rudiments of that knowledge which is essential to the preservation of our animal existence.
This step in the history of the human mind has been httle, if at all, attended to by philosophers ; and it is certainly not easy to explain in a manner completely satisfactory how it is made. The following hints seem to me to go a considerable way towards a solution of the difficulty.
It is remarked by Mr. Smith, in his considerations on the Formation of Languages, that the origin of genera and species, which is commonly represented in the schools as the effect of an intellectual process pecuHar- ly mysterious and unintelligible, is a natural consequence of our disposition to transfer to a new object the name of any other famihar object which possesses such a de- gree of resemblance to it, as to serve the memory for
OF THE HUMAN MIND. 165
an associating tie between them. It is in this manner, he has shown, and not by any formal or scientific exer- cise of abstraction, that, in the infancy of language, proper names are gradually transformed into appellatives ; or in other words, that individual things come to be re- ferred to classes or assortments.*
This remark becomes in my opinion, much more lu- minous and important, by being combined with another very original one, which is ascribed to Turgot by Con- dorcet, and which I do not recollect to have seen taken notice of by any later writer on the human mind. Ac- cording to the common doctrine of logicians, we are led to suppose that our knowledge begins in an accurate and minute acquaintance with the characteristical prop- erties of individual objects ; and that it is only by the slow exercise of comparison and abstraction, that we attain to the notion of classes or genera. In opposition to this idea, it was a maxim of Turgot's, that some of our most abstract and general notions are among the earliest which we form.f What meaning he annexed to this maxim, we are not informed ; but if he under- stood it in the same sense in which I am disposed to interpret it, he appears to m.e entitled to the credit of a very valuable suggestion with respect to the natural pro- gress of human knowledge. The truth is, that our first perceptions lead us invariably to confound together things which have very little in common ; and that the specifi-
* A writer of great learning and ability (Dr. Magee, of Dublin) who has done me the honor to animadvert on a few passages of my works, and who has softened his criticisms by some expressions of regard, by which I feel myself highly flattered, has started a very acute objection to this theory of Mr. Smith, which I think it incum- bent on me to submit to my readers, in his own words. As the quotation, however, with the remarks which I have to offer upon it, would extend to too great a length to be introduced here, I must delay entering on the subject till the end of this vol- ume. See Note (K.)
■f " M. Turgot croyoit qu'on s'etoit trompe en imaginant qu'en general I'esprit n'acquiert des idees generales ou abstraites que par la comparaison d'idees plus particulieres. Au contraire, nos premieres idees sont tres-generales, puisque ne voyant d'abord qu'un petit nombre de qualites, notre idee renfenne tous les etres auxquels cos qualites sont communes. En nous eclairant, enexaminant davantage, nos idees dcviennent plus particulieres sans jamais atteindro le dernier terme ; ct ce qui a pu tromper les metaphysiciens, c'est qu'alors precisement nous apprenons que ces idees sont plus generales que nous ne I'avions d'abord suppose." — Vie de Tur- got, p. 189. Berne, 1787.
I have searched in vain for some additional light on this interesting hint, in the complete edition of Turgot's works, published in Paris in 1808.
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cal differences of individuals do not begin to be marked with precision till the powers of observation and rea- soning have attained to a certain degree of maturity. To a similar indistinctness of perception are to be as- cribed the mistakes about the most familiar appearances which we daily see committed by those domesticated an- imals with whose instincts and habits we have an oppor- tunity of becoming intimately acquainted. As an in- stance of this, it is sufficient to mention the terror which a horse sometimes discovers in passing, on the road, a large stone, or the waterfall of a mill.
Notwithstanding, however, the justness of this max- im, it is nevertheless true, that every scientific classifica- tion must be founded on an examination and compari- son of individuals. These individuals must, in the first instance, have been observed with accuracy, before their specific characteristics could be rejected from the generic description, so as to limit the attention to the common quahties which it comprehends. What are usually called general ideas or general notions, are there- fore, of two kinds, essentially different from each other ; those which are general, merely from the vagueness and imperfection of our information ; and those which have been methodically generalized, in the way explained by logicians, in consequence of an abstraction founded on a careful study of particulars. Philosophical precision requires, that two sets of notions, so totally disimilar, should not be confounded together ; and an attention to the distinction between them will be found to throw much light on various important steps in the natural history of the mind.*
• The distinction above stated, furnishes what seems to me the true answer to an argument which Charron, and many other writers since his time, have drawn, in proof of the reasoning powers of brutes, from the universal conclusions which they appear to found on the observation of particulars. " Les bestes dcs singuliers con- cluent les universels, du regard d'un homme seul cognoissent tous hommes," &c. &c. De la Sagesse, Lib. 1. Chap. 8.
Instead of saying, that brutes generalize things, which are similar, would it not be nearer the truth to say, that they confound things which are different ?
Many years after these observations were written, I had the satisfaction to meet with the following experimental confirmation of them, in the Abbe Sicard's Course of Instruction for the Deaf and Dumb . " J'avois rcmarque que Massieu donnoit plus volontiers le meme nom, un nom commun, a plusicurs individus dans lesquels il trouvoit des traits de ressemblance ; les noma individuels supposoient des differences
OF THE HUMAN MIND. 167
One obvious effect of the grossness and vagueness in the perceptions of the inexperienced observer must necessarily be to identify, under the same common ap- pellations, immense multitudes of individuals, which the philosopher will afterwards find reason to distinguish carefully from each other ; and as language, by its un- avoidable re-action on thought, never fails to restore to it whatever imperfections it has once received, all the indistinctness which, in the case of individual observers, originated in an ill-informed judgment, or in a capricious fancy, comes afterwards, in succeeding ages, to be en- tailed on the infant understanding, in consequence of its incorporation with vernacular speech. These con- fused apprehensions produced by. language, must, it is easy to see, operate exactly in the same way as the unclistinguishing perceptions of children or savages ; the familiar use of a generic word, insensibly and irre- sistibly leading the mind to extend its conclusions from the individual to the genus, and thus laying the founda- tion of conclusions and anticipations which we suppose to rest on experience, when, in truth, experience has never been consulted.
In all such instances, it is worthy of observation, we proceed ultimately on the common principle, — that in similar circumstances, the same cause will produce the same effects ; and, when we err, the source of our error lies merely in identifying different cases which ought to be distinguished from each other. Great as may be the occasional inconveniences, arising from this general principle thus misapphed, they bear no proportion to the essential advantages resulting from the disposition in which they originate, to arrange and to classify ; a disposidon on which (as I have elsewhere shown) the intellectual improvement of the species in a great man- ner hinges. That the constitution of our nature in this respect is, on the whole, wisely ordered, as well as per- fectly conformable to the general economy of our frame, will appear from a shght survey of some other principles,
qu'il n'etoit pas encore temps de lui faire observer."-— i^card, pp. 30, 31. The whole of the passage is well worth consulting.
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nearly allied to those which are at present under our consideration.
It has been remarked by some eminent writers in this part of the island,* that our expectation of the continu- ance of the laws of nature has a very close affinity to our faith in human testimony. The parallel might per- haps be carried, without any over-refinement, a httle far- ther than these writers have attempted ; inasmuch as, in both cases, the instinctive principle is in the first in- stance unlimited, and requires, for its correction and regulation, the lessons of subsequent experience. As the credulity of children is originally without bounds, and is afterwards gradually checked by the examples which they occasionally meet with of human falsehood, so, in the infancy of our knowledge, whatever objects or events present to our senses a strong resemblance to each other, dispose us, without any very accurate exam- ination of the minute details by which they may be re- ally discriminated, to conclude with eagerness, that the experiments and observations which we make with re- spect to one individual, may be safely extended to the whole class. It is experience alone that teaches us caution in such inferences, and subjects the natural principle to the discipline prescribed by the rules of in- duction.
It must not, however, be imagined, that, in instances of this sort, the instinctive principle always leads us astray ; for the analogical anticipations which it disposes us to form, although they may not stand the test of a rig- orous examination, may yet be sufficiently just for all the common purposes of hfe. It is natural, for example, that a man who has been educated in Europe should €xpect, when he changes his residence to any of the other quarters of the globe, to see heavy bodies fall downwards, and smoke to ascend, agreeably to the gen- eral laws to which he has been accustomed ; and that he should take for granted, in providing the means of his subsistence, that the animals and vegetables which
* See Rcid's Inquiry into the Human Mind, Chap. VI. Sect. 24. Campbell's Dissertation on Miracles, Part. I. Sect. 1. Smith's Theory of Moral Sentiments, Vol. II. p. 382, sixth edition.
OF THE HUMAN MIND. 169
he has found to be salutary and nutritious in his native regions, possess the same quahties wherever they exhib- it the same appearances. Nor are such expectations less useful than natural ; for they are completely reali- zed, as far as they minister to the gratification of our more urgent wants. It is only when we begin to indulge our curiosity with respect to those nicer details which derive their interest from great refinement in the arts, or from a very advanced state of physical knowledge, that we discover our first conclusions, however just in the main, not to be mathematically exact ; and are led by those habits which scientific pursuits communicate, to investigate the diff"erence of circumstances to which the variety in the result is owing. After having found that heavy bodies fall downwards at the equator as they do in this island, the most obvious, and perhaps, on a super- ficial view of the question, the most reasonable inference would be, that the same pendulum which swings seconds at London, will vibrate at the same rate under the line. In this instance, however, the theoretical inference is contradicted by the fact ; — but the contradiction is at- tended with no practical inconvenience to the multitude, while, in the mind of the philosopher, it only serves to awaken his attention to the different circumstances of the two cases, and, in the last result; throws a new lus^ tre on the simplicity and uniformity of that law, from which it seemed, at first sight, an anomalous deviation.
To this uniformity in the laws which regulate the or- der of physical events, there is something extremely similar in the systematical regularity (subject indeed to many exceptions) which, in every language, however imperfect, runs trough the different classes of its words, in respect of their inflexions, forms of derivation, and other verbal fihations or affinities. PIov/ much this reg- ularity or analogy (as it is called by gi'ammarians) con- tributes to facilitate the acquisition of dead and foreign languages, every person, who has received a liberal ed- ucation, knows from his own experience. Nor is it less manifest, that the same circumstance must contribute powerfully to aid the memories of children in learning to speak their mother-tongue. It is not my present bu-
voL II. 22
170 ELEMENTS OF THE PHILOSOPHY
siness to trace the principles in the human mind by which it is produced. All that I would remark is, the very early period at which it is seized by children ; as is strongly evinced by their disposition to push it a great deal too far, in their first attempts towards speech. This disposition seems to be closely connected with that which leads them to repose faith in testimony ; and it also bears a striking resemblance to that which prompts them to extend their past experience to those objects and events of which they have not hitherto had any means of acquiring a direct knowledge. It is probable, indeed, that our expectation, in all these cases, has its origin in the same common principles of our nature ; and it is certain that, in all of them, it is subservient to the important purpose of facilitating the progress of the mind. Of this, nobody can doubt, who considers for a moment, that the great end to be first accomplished, was manifestly the communication of the general rule ; the acquisition of the exceptions (a knowledge of which is but of secondary importance) being safely entrusted to the growing dihgence and capacity of the learner.
The considerations now stated, may help us to con- ceive in what manner conclusions derived from experi- ence come to be insensibly extended from the individu- al to the species ; partly in consequence of the gross and undistinguishing nature of our first perceptions, and partly in consequence of the magical influence of a common name. They seem also to show, that this natu- ral process of thought, though not always justified by a sound logic, is not without its use in the infancy of hu- man knowledge.
In the various cases which have been hitherto under our review, our conclusions are said in popular, and even in philosophical language, to be founded on experience. And yet the truth unquestionably is, (as was formerly observed,) that the evidence of experience reaches no farther than to an anticipation of the future from the past, in instances where the same cause continues to operate in circumstances exactly similar. How much this vagueness of expression must contribute to mislead us in many of our judgments, will afterwards appear.
OF THE HUMAN MIND. 171
The observations which I have to offer upon analogy, considered as a ground of scientific conjecture and rea- soning, will be introduced with more propriety in a fu- ture chapter.
IV.
Continuation of the Subject. — Evidence of Testimony tacitly recognised as a Ground of Belief, in our most certain Conclusions concerning contingent Tiuths. — Difference between the Logical and the Popular Meaning of the word Proba- bility.
liV some of the conclusions which have been already under our consideration with respect to contingent truths, a species of evidence is admitted, of which no mention has hitherto been made ; I mean the evidence of testi- mony. In astronomical calculations, for example, how few are the instances in which the data rest on the evi- dence of our own senses ; and yet our confidence in the result, is not, on that account, in the smallest degree weakened. On the contrary, what certainty can be more complete, than that with which we look forward to an eclipse of the sun or the moon, on the faith of el- ements and of computations which we have never veri- fied, and for the accuracy of which we have no ground of assurance whatever, but the scientific reputation of the writers from whom we have borrowed them. An as- tronomer who should affect any scepticism with respect to an event so predicted, would render himself no less an object of ridicule, than if he were disposed to cavil about the certainty of the sun's rising to-morrow.
Even in pure mathematics, a similar regard to testimo- ny, accompanied with a similar faith in the faculties of others, is by no means uncommon. Who would scru- ple, in a geometrical investigation, to adopt, as a link in the chain, a theorem of Apollonius or of Archimedes, although he might not have leisure at the moment, to satisfy himself, by an actual examination of their demon- strations, that they had been guilty of no paralogism, either from accident or design, in the course of their reasonings ?
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In our anticipations of astronomical phenomena, as well as in those which we form concerning the result of any familiar experiment in physics, philosophers are ac- customed to speak of the event as only probable ; al- though our confidence in its happening is not less com- plete, than if it rested on the basis of mathematical de- monstration. The word probable, therefore, when thus used, does not imply any deficiency in the proof, but only marks the particular nature of that proof, as contradis- tinguished from another species of evidence. It is op- posed, not to what is certain, but to what admits of be- ing demonstrated after the manner of mathematicians. This differs widely from the meaning annexed to the same word in popular discourse ; according to which, whatever event is said to be probable, is understood to be expected with some degree of doubt. As certain as death — as certam as the rising of the sun — are proverbial modes of expression in all countries ; and they are, both of them, borrowed from events which, in philoso- phical language, are only probable or contingent. In like manner, the existence of the city of Pekin, and the reahty of Caesar's assassination, which the philosopher classes with probabilities, because they rest solely upon the evidence of testimony, are universally classed with certainties by the rest of mankind ; and in any case but the statement of a logical theory, the application to such truths of the word probable, would be justly regarded as an impropriety of speech. This difference between the technical meaning of the word probability, as employed by logicians, and the notion usually attached to it in the business of hfe ; together with the erroneous theories concerning the nature of demonstration, which I have already endeavoured to refute, — have led many authors of the highest name, in some of the most important ar- guments which can employ human reason, to overlook that irresistible evidence which was placed before their eyes, in search of another mode of proof altogether un- attainable in moral inquiries, and which, if it could be attained, would not be less liable to the cavils of scep- tics.
But although, in philosophical language, the epithet
OF THE HUMAN MIND. 173
probable be applied to events which are acknowledged to be certain, it is also applied to those events which are cdWed^ probable by the vulgar. The philosophical mean- ing of the word, therefore, is more comprehensive than the popular ; the former denoting that particular species of evidence of which contingent truths admit ; the lat- ter being confined to such degrees of this evidence as fall short of the highest. These different degrees of prob- ability the philosopher considers as a series, beginning with bare possibility, and terminating in that apprehend- ed infallibility, with which the phrase moral certainty is synonymous. To this last term of the series, the word probable is, in its ordinary acceptation, plainly inapplica- ble.
The satisfaction which the astronomer derives from the exact coincidence, in point of time, between his the- oretical predictions concerning the phenomena of the heavens, and the corresponding events when they actu- ally occur, does not imply the smallest doubt, on Aispart, of the constancy of the laws of nature. It resolves partly into the pleasure of arriving at the knowledge of the same truth or of the same fact by different media ; but, chiefly, into the gratifying assurance which he thus receives, of the correctness of his principles, and of the competency of the human faculties to these sublime in- vestigations. What exquisite delight must La Place have felt, when, by deducing from the theory of gravi- tation, the cause of the acceleration of the moon's mean motion — an acceleration which proceeds at the rate of little more than 11'' in a century, — he accounted, with such mathematical precision, for all the recorded obser- vations of her place from the infancy of astronomical sci- ence ? It is from the length and abstruseness, however, of the reasoning process, and from the powerful effect produced on the imagination, by a calculus, which brings into immediate contrast with the immensity of time, such evanescent elements as the fractional parts of a second, that the coincidence between the computation and the event appears in this instance so peculiarly striking. In other respects, our confidence in the future result rests on the same principle with our expectation that the sun
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will rise to-morrow at a particular instant ; and, accord- ingly, now that the correctness of the theory has been so wonderfully verified by a comparison with facts, the one event is expected with no less assurance than the other.
With respect to those inferior degrees of probability to which, in common discourse, the meaning of that word is exclusively confined, it is not my intention to enter into any discussions. The subject is of so great extent, that I could not hope to throw upon it any hghts satis- factory either to my reader or to myself, without en- croaching upon the space destined for inquiries more in- timately connected with the theory of our reasoning powers. One set of questions, too, arising out of it, (I mean those to which mathematical calculations have been apphed by the ingenuity of the moderns,) involve some very puzzHng metaphysical difficulties,* the considera- tion of which would completely interrupt the train of our present speculations. I proceed, therefore, in con- tinuation of those in which we have been lately enga- ged, to treat of other topics of a more general nature, tending to illustrate the logical procedure of the mind in the discovery of scientific truth. As an introduction to these, I propose to devote one whole chapter to some miscellaneous strictures and reflections on the logic of the schools.
* I allude more particularly to the doubts started on this subject by D'Alembert, in his Opuscules Mathematiques ; and in his Melanges de Litterature.
OF THE HUMAN MIIfD. 175
CHAPTER THIRD.
OF THE ARISTOTELIAN LOGIC.
SECTION I.
Of the Demonstrations of the Syllogistic Rules given by Aristotle and his Commen- tators.
The great variety of speculations which, in the pres- ent state of science, the AristoteHan logic naturally sug- gests to a philosophical inquirer, lays me, in this chapter, under the necessity of selecting a few leading questions, bearing immediately upon the particular objects which I have in view. In treating of these, I must, of course, suppose my readers to possess some previous acquaint- ance with the subject to which they relate ; but it is only such a general knowledge of its outhnes and phrase- ology, as, in all universities, is justly considered as an essential acccomplishment to those who receive a liber- al education.
I begin with examining the pretensions of the Aris- toteHan logic to that pre-eminent rank which it claims among the sciences ; professing, not only to rest all its conclusions on the immoveable basis of demonstration, but to have reared this mighty fabric on the narrow ground- work of a single axiom. " On the basis," says the latest of his commentators, " of one simple truth, Aristotle has reared a lofty and various structure of abstract science, clearly expressed and fully demonstrated." * Nor have these claim.s been disputed by mathematicians them- selves. " In logica," says Dr. Wallis, " structura syllo- gismi demonstratione nititur pure mathematica." f And, in another passage : " Sequiturinstitutio logica, commu- ni Usui accommodata. — Quo videant tirones, syllogis-
* Analysis of Aristotle's Works by Dr. Gillies, Vol. I. p. S3, 2d edit, f See the Moiiiliun pretixed to the Miscellaneous Treatises annexed to the third Volume of Dr. Wallis's Mathematical Works.
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morum leges strictissimis demonstrationibus plane math- ematicis ita fundatas, ut consequentias habeant irrefra- gabiles, quaeque offuciis fallaciisque detegendis sint ac- commodatae." * Dr. Reid, too, although he cannot be justly charged, on the whole, with any undue reverence for the authority of Aristotle, has yet, upon one occa- sion, spoken of his demo7istrations with much more re- spect than they appear to me entitled to. " I beheve," says he, " it will be difficult, in any science, to find so large a system of truths of so very abstract and so gen- eral a nature, all fortified by demonstration, and all in- vented and perfected by one man. It shows a force of genius, and labor of investigation, equal to the most ar- duous attempts." f
As the fact which is so confidently assumed in these passages would, if admitted, completely overturn all I have hitherto said concerning the nature both of axioms and of demonstrative evidence, the observations which follow seem to form a necessary sequel to some of the preceding discussions. I acknowledge, at the same time, that my chief motive for introducing them, was a wish to counteract the effect of those triumphant pane- gyrics upon Aristotle's Organon^ which of late have been pronounced by some writers, whose talents and learning justly add much weight to their literary opinions ; and an anxiety to guard the rising generation against a waste of time and attention, upon a study so little fitted, in my judgment, to reward their labor.
The first remark which I have to oiFer upon Aris- totle's demonstrations, is, That they proceed on the ob- viously false supposition of its being possible to add to the conclusiveness and authority of demonstrative evi- dence. One of the most remarkable circumstances which distinguishes this from that species of evidence which is commonly called moral or probable, is that it is not sus-
* Preface to the third Volume of Dr. Wallis's Mathematical Works,
t Analysis of Aristoile's Lo2;ic.
That Dr. Reid, however, was perfectly aware that these demonstrations are more Bpccious than solid, may be safely inferred from a sentence which afterwards occurs in the same tract. " When we go without the circle of the mathematical sciences, I know nothin<;- in which (here seems to he so much demonstration as in that part of logic which treats of the figures and modes of syllogisms."
OF THE HUMAN MIRTD. 177
ceptible of degrees ; the process of reasoning of which it is the result, being either good for nothing, or so per- fect and complete in itself, as not to admit of support from any adventitious aid. Every such process of rea- soning, it is v\^ell knov^n, may be resolved into a series of legitimate syllogisms, exhibiting separately and dis- tinctly, in a light as clear and strong as language can afford, each successive link of the demonstration. How far this conduces to render the demonstration more convincing than it was before, is not now the question. Some doubts may reasonably be entertained upon this head, when it is considered, that, among the various expedients employed by mathematical teachers to as- sist the apprehension of their pupils, none of them have ever thought of resolving a demonstration (as may always be easily done) into the syllogisms of which it is composed.* But, abstracting altogether from this consideration, and granting that a demonstration may be rendered more manifest and satisfactory by being syllo- gisticaily stated ; upon what principle san it be supposed possible, after the demonstration has been thus analysed and expanded, to enforce and corroborate, by any sub- sidiary reasoning, that irresistible conviction which de- monstration necessarily commands 7
It furnishes no valid reply to this objection, to allege, that mathematicians often employ themselves in invent- ing different demonstrations of the same theorem ; for, in such instances, their attempts do not proceed from any anxiety to swell the mass of evidence, by finding (as in some other sciences) a variet}'' of collateral argu- ments, all bearing, with their combined force, on the
• From a passage, indeed, in a memoir by Leibnitz, (printed in the sixtli volume of the Acta Eruditorum) it would seem, that a commentary oithis kind on the first six hooks of Euclid, had been actually carried into execution by two writers, whose names he mentions. " Firma autcm dcmonstratio est, quaj pra^scriptam a logica Ibrmam servat, non quasi semper ordinalis scholarum more syllogismis opus sit (qua- les Christianus HerUnits ct Conradus J)ns}/podiiis in sex priores Eiiclidis libros exhibuerunl,) sed ita saltcm ut argumentatio concludat vi formae," &c. &c. — Acta Eruditor. Lips. Vol. L p. 285. Venet. 1740.
I have not seen either of the works alluded to in the above sentence ; and, ui>on less respectable authority, should scarccly'havc conceived it to he credilile, that any person, capable of understanding Euclid, had ever seriously engaged in such an undertaking. It would have been diiricult to devise a more effectual expedient fov exposing, to the meanest understanding, tlic futility of the sj-ilogistic theory.
VOL. II. 23
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same truth ; — their only wish is, to discover the easiest and shortest road by which the truth may be reached. In point of simphcity, and of what geometers call elegance, these various demonstrations may differ wide- ly from each other ; but, in point of sound logic, they are all precisely on the same footing. Each of them shines with its own intrinsic light alone ; and the first which occurs (provided they be all equally understood) commands the assent not less irresistibly than the last.
The idea, however, on which Aristotle proceeded, in attempting to fortify one demonstration by another, bears no analogy whatever to the practice of mathema- ticians in multiplying proofs of the same theorem ; nor can it derive the slightest countenance from their exam- ple. His object Avas not to teach us how to demon- strate the same thing in a variety of different ways ; but to demonstrate, by abstract reasoning, the conclu- siveness of demonstration. By what means he set about the accomplishment of his purpose, will afterwards ap- pear. At present, I speak only of his design; which, if the foregoing remarks be just, it will not be easy to reconcile with correct views, either concerning the na- ture of evidence, or the theory of the human under- standing.
For the sake of those who have not previously turn- ed their attention to Aristotle's Logic, it is necessary, before proceeding farther, to take notice of a peculiari- ty (and, as appears to me, an impropriety) in the use which he makes of the epithets demonstrative and dia- lectical, to mark the distinction between the two great classes into which he divides syllogisms; a mode of speak- ing which, according to the common use of language, would seem to imply, that one species of syllogisms may be more conclusive and cogent than another. That this is not the case, is almost self-evident ; for, if a syl- logism be perfect in form, it must, of necessity, be not only conclusive, but demonstratively conclusive. Nor is this, in fact, the idea which Aristotle himself annexed to the distinction ; for he tells us, that it does not refer to the form of syllogisms, but to their matter ; — or, in plainer language, to the degree of evidence accompany-
OF THE HUMAN MIND. 179
ing the joremises on which they proceed.* In the two books of his last Analytics, accordingly, he treats of syl- logisms which are said to be demonstrative, because their premises are certain ; and in his Topics, of what he calls dialectical syllogisms, because their premises are only probable. Would it not have been a clearer and juster mode of stating this distinction, to have ap- plied the epithets demonstrative and dialectical to the truth of the conclusions resulting from these two classes of syllogisms instead of applying them to the syllogisms themselves ? The phrase demonstrative syllogism cer- tainly seems, at first sight, to express rather the com- plete and necessary connexion between the conclusion and the premises, than the certainty or the necessity of the truths which the premises assume.
To this observation it may be added, (in order to prevent any misapprehensions from the ambiguity of language,) that Aristotle's idea of the nature of demon- stration, is essentially different from that which I have already endeavoured to explain. " In all demonstra- tion," says Dr. Gilhes, who, in this instance, has very accurately and clearly stated his author's doctrine, " the first principles must be necessary, immutable, and there- fore eternal truths, because those qualities could not belong to the conclusion, unless they belonged to the premises, which are its causes." f According to the
* To the same purpose also Dr. Wallis: " Syllogismus Topicus (qui et Dialectl- cus dici solet) talis haberi solet syllogismus (seu syllogismoruin series) qui tirmara potius praesumptioncm, seu opinionem valde probabilem creat, quarn absolutam cer- titudinem. Non quidem ratione Formce, (nam syllogismi omnes, si in justa forma, sunt demonstrativi ; hoc est, si prajmissffi verae sint, vera erit et conclusio,) sed ra- tione Materice, seu Prcemissarum ; quK ipsoe, utplurimum, non sunt absolute cer- tas, et universaliter vera? ; sed saltern probabiles, atquc utplurimum veraj." — Wallis, Logica, Lib. iii. cap. 2.3.
t Aristotle's Ethics and Politics, &c. By Dr. Gillies. Vol I. p. 96.
I am much at a loss how to reconcile this account of demonstrative evidence with the view which is given by Dr. Gillies of the nature of syllogism, and of the princi- ples on which the syllogistic theory is founded. In one passage (p. 81.) he tells us, that " Aristotle invented the syllogism, to prevent imposition arising from the abuse ofwords;" in a second, (p. 83.) that "the simple truth on which Aristotle has reared a lofty and vavioiis structure of abstract science, clearly expressed and fully demonstrated — is itself founded in the natural and universal texture of language : " in a third, (p. 86.) that " the doctrines of Aristotle's Organon have been strangely perplexed by confounding the granmiatical piinciples on which that xoork is built with mathematical axioms." Is it possible, to suppose, that Aristotle could have ever thought of ajiplying to mcic grammatical principles, — to truths founded in the natural and universal texture of language — the epithets of necessary, immutable, and eternal ?
I am unwilling to lengthen this note, otherwise it might be easily shown, how
180 ELEMENTS OF THE PHILOSOPHY
account of demonstrative or mathematical evidence for- merly given, the first principles on which it rests are not eternal and immutable truths, but definitions or hypoth- eses ; and therefore, if the epithet demonstrative be understood, in our present argument, as descriptive of that peculiar kind of evidence which belongs to mathe- matics, the distinction between demonstrative and dia- lectical syllogisms is reduced to this ; that in the former, where all that is asserted is the necessary connexion between the conclusion and the premises, neither the one nor the other of these can with propriety be said to be either true or false, because both of them are entirely hypothetical : in the latter, where the premises are meant to express truths or facts, (supported on the most favor- able supposition, by a very high degree of probabihty,) the conclusion must necessarily partake of that uncer- tainty in which the premises are involved.
But what I am chiefly anxious at present to impress on the minds of my readers, is the substance of the two following propositions : First, That dialectical syllogisms (provided they be not sophistical) are not less demon- stratively conclusive, so far as the process of reasoning is concerned, than those to which this latter epithet is re- stricted by Aristotle ; and, secondhj, That it is td^the process of reasoning alone, and not to the premises on which it pToceed^s^ that Aristotle's demonstrations exclu- sively refer. The sole object, therefore, of these de- monstrations, is (as I already remarked) not to strength- en, by new proofs, principles which were doubtful, or to supply new links to a chain of reasoning which was im- perfect, but to confirm one set of demonstrations by means of another. The mistakes into which some of my readers might have been led by the contrast which Aris- totle's language impHes between dialectical syllogisms, and those which he honors with the title of demonstra- tive, will, I trust, furnish a sufficient apology for the length of this explanation.
utterly incconclleable, in the present instance, are the glosses of this ingenious commentator with the text of his author. Into some of these glosses it is probable that h(! has Ijeen unconsciously betrayed, by his anxiety to establish the claim of his favorite philosopher to the important ypcculations of Locke on the abuse of words, and to those of some later writers on langu;ige considered as an instrument of thought.
OF THE HUMAN MmD. 181
Having enlarged so fully on the| professed aim of Aristotle's demonstrations, I shall dispatch in a very few pages, what I have to offer on the manner in which he has carried his design into effect. If the design be as unphilosophical as I have endeavoured to show that it is, the apparatus contrived for its execution can be con- sidered in no other light than as an object of hterary curiosity. A process of reasoning which pretends to demonstrate the legitimacy of a conclusion which, of itself, by its own intrinsic evidence, irresistibly com- mands the assent, must, we may be perfectly assured, be at bottom unsubstantial and illusory, how specious soev- er it may at first sight appear. Supposing all its infer- ences to be strictly just, it can only bring us round again to the point from whence we set out.
The very acute strictures of Dr. Reid, in his Analysis of Aristotle's Logic, on this part of the Syllogistic The- ory, render it superfluous for me, on the present occa- sion, to enter into any details upon the subject. To this small, but valuable tract, therefore, I beg leave to refer my readers ; contenting myself with a short extract, which contains a general and compendious view of the conclusion drawn, and of the argument used, to prove it, in each of the three figures of syllogisms.
"In the first figure, the conclusion afhrms or denies something of a certain species or individual ; and the argument to prove this conclusion is, That the same thing may be affirmed or denied of the whole genus to which that species or individual belongs.
" In the second figure, the conclusion is, That some species or individual does not belong to such a genus ; and the argument is. That some attribute common to the whole genus does not belong to that species or indi- vidual.
" In the third figure, the conclusion is. That such an attribute belongs to part of a genus ; and the argument is, That the attribute in question belongs to a species or individual which is part of that genus.
" I apprehend that, in this short view, every conclu- sion that falls within the compass of the three figures, as well as the mean of proof, is comprehended. The
182 ELEMENTS OF THE PHILOSOPHY
rules of all the figures might be easily deduced from it ; and it appears that there is only one principle of reason- ing in all the three ; so that it is not strange, that a syl- logism of one figure should be reduced to one of another figure.
" The general principle in which the whole termin- ates, and of which every categorical syllogism is only a particular application, is this. That what is affirmed or denied of the whole genus may be affirmed or denied of every species and individual belonging to it. This is a principle of undoubted certainty indeed, but of no great depth. Aristotle and all the logicians assume it as an axiom, or first principle, from which the syllogistic system, as it were, takes its departure ; and after a tedi- ous voyage, and great expense of demonstration, it lands at last in this principle, as its ultimate conclusion. 0 curas hominum ! 0 quantum est in rebus inane .'" *
When we compare this mockery of science with the unrivalled powers of the inventor, it is scarcely possible to avoid suspecting, that he was anxious to conceal its real poverty and nakedness, under the veil of the ab- stract language in which it was exhibited. It is observed by the author last quoted, that Aristotle hardly ever gives examples of real syllogisms to illustrate his rules ; and that his commentators, by endeavouring to supply this defect, have only brought into contempt the theory of their master. " We acknowledge," says he, " that this was charitably done, in order to assist the concep- tion in matters so very abstract ; but whether it was prudently done for the honor of the art, may be doubt- ed." One thing is certain, that when we translate any of Aristode's demonstrations from the general and enig- matical language in which he states it, into more famihar and intelligible terms, by applying it to a particular ex- ample, the mystery at once disappears, and resolves into some self-evident or identical puerihty. It is surely a strange mode of proof, which would establish the truth of what is obvious, and what was never doubted of, by means of an argument which appears quite unintelligi-
* This axiom is called, in scholastic language, the dictum dc omni et dc nulla.
OF THE HUMAN MIND. 183
ble, till explained and illustrated by an instance perfectly similar to the very thing to be proved.
" If A," says Aristotle, " is attributed to every B, and B to every C, it follows necessarily, that A may be attributed to every C." * Such is the demonstration given of the first mode of the first figure ; and it is obviously nothing more than the axiom, called the dic- tum de omni, concealed under the disguise of an un- couth and cabalistical phraseology. The demonstrations given of the other legitimate modes are all of the same description.
In disproving the illegitimate modes, he proceeds after a similar manner ; condescending, however, in general, to supply us, by way of example, with three terms, such as bonum, habitus, prudentia ; album, eqims, cygnus ; — which three terms, we are left, for our own satisfaction, to form into illegitimate syllogisms of the particular figure and mode which may be under consideration. The manifest inconclusivenes of every such syllogism, he seems to have thought, might assist readers of slower apprehension in perceiving more easily the import of the general proposition. The inconclusiveness, for instance, of those modes of the first figure, in which the major is particular, is thus stated and explained. " If A is or is not in some B, and B in every C, no conclusion fol- lows. Take for the terms in the affirmative case, good, habit, prudence ; in the negative, good, habit, ignorance.''^ f With respect to such passages as this, Dr. Reid has per- fectly expressed my feeling, when he says : " That the laconic style of the author, the use of symbols not fa- miliar, and, in place of giving an example, his leaving us to form one from three assigned terms, give such em- barrassment to a reader, that he is like one reading a
* Analyt. Prior, cap. iv.
It is olDvious, that Aristotle's symbolical demonstrations mi£,ht be easily thrown in- to the form of symbolical syllogisms. The circumstance which induced him to pre- fer the former mode of statement, was probably that he might avoid the appearance of reasoning in a circle, by employing the syllogistic theory to demonstrate itself. It is curious how it should have escaped him, that, in attempting to shun this fallacy, he had fallen into another exactly of the same description ; — that of employing an ar- gument in the common form to demonstrate the legitimacy of syllogisms, after hav- ing represented a syllogistic analysis as the only infallible test of the legitimacy of a demonstration.
t Analyt. Prior, cap. iv.
184 ELEMENTS OF THE PHILOSOPHY
book of riddles." * Can it be reasonably supposed, that so great an obscurity in such a writer was not the effect of some systematical design 1
From the various considerations already stated, I might perhaps without proceeding farther, be entitled to conclude, that Aristotle's demonstrations amount to no- thing more than to a specious and imposing parade of words ; but the innumerable testimonies to their validity, from the highest names, and the admiration in which they continue to be held by men of distinguished learning, render it necessary for me, before dismissing the subject, to unfold a little more completely some parts of the fore- going argument.
It may probably appear to some of my readers super- fluous to remark, after the above-cited specimens of the reasonings in question, that not one of these demonstra- tions ever carry the mind forward, a single step, from one truth to another ; but merely from a general axiom to some of its particular exemplifications. Nor is this all ; they carry the mind in a direction opposite to that in which its judgments are necessarily formed. The meaning of a general axiom, it is well known, is seldom, if ever intelligible, till it has been illustrated by some example ; whereas Aristotle, in all his demonstrations, proceeds on the idea, that the truth of an axiom, in particular instances, is a logical consequence of its truth, as enunciated in general terms. Into this mistake, it must be owned, he was not unnaturally led by the place which is asssigned to axioms at the beginning of the ele- ments of geometry, and by the manner in which they are afterwards referred to in demonstrating the propositions. " Since A," it is said, "-is equal to B, and B to C, A is equal to C ; for, things which are equal to one and the same thing, are equal to one another." This place, I have little doubt, has been occupied by mathematical axioms, as far back, at least, as the foundation of the Pythagore- an school ; and Aristotle's fundamental axiom will be found to be precisely of the same description. Instead,
* Dr. Gillies has attempted a vindication of the use which Aristotle, in his demon- strations, has made of the letters of the alphabet. For some remarks on this attempt, see Note (L.)
OF THE HUMAN MIND. 185
therefore, of saying, with Dr. GilUes, that "on the basis of one single truth Aristotle has reared a lofty and vari- ous structure of abstract science," — it would be more correct to say, that the whole of this science is com- prised or implied in the terms of one single axiom. Nor must it be forgotten, (if we are to retain Dr. GilUes's metaphor,) that the structure may with much more pro- priety, be considered as the basis of the axiom, than the axiom of the structure.
When it is recollected, that the greater part of our best philosophers (and among the rest Dr. Reid) still persevere, after all that Locke has urged on the oppo- site side of the question, in considering axioms as the ground-work of mathematical science, it will not appear surprising, that Aristotle's demonstrations should have so long continued to maintain their ground in books of logic. That this idea is altogether erroneous, in so far as mathematics is concerned, has been already suffi- ciently shown ; the whole of that science resting ulti- mately, not on axioms, but on definitions or hypotheses. By those who have examined my reasonings on this last point, and who take the pains to combine them with the foregoing remarks, I trust it will be readily allowed, that the syllogisdc theory furnishes no exception to the gen- eral doctrine concerning demonstrative evidence, which I formerly endeavoured to estabUsh ; its pretended demonstrations being altogether nugatory, and terminat- ing at last (as must be the case with every process of thought involving no data but v>diat are purely axiomati- cal) in the very proposition from which they originally set out.
The idea that all demonstrative science 'must rest ultimately on axioms, has been borrowed, with many other erroneous maxims, from the logic of Aristotle ; but is now, in general, stated in a manner much more consistent (although perhaps not nearer to the truth) than in the works of that philosopher. According to Dr. Reid, the degree of evidence which accompanies our conclusions, is necessarily determined by the degree of evidence which accompanies our first principles ; so that, if the latter be only probable, it is perfectly impos-
voL. II. 24
186 ELEMENTS OF THE PHILOSOPHY
sible that the former should be certain. Agreeing there- fore, with Aristotle, in considering axioms as the basis of all demonstrative science, he was led, at the same time, in conformity with the doctrine just mentioned, to consider them as eternal and immutable truths, which are perceived to be such by an intuitive judgment of the understanding. This, however, is not the language of Aristotle ; for, while he tells us, that there is no de- monstration but of eternal truths,* he asserts, that the first principles which are the foundation of all demon- stration, are got by induction from the informations of sense.f In what manner this apparent contradiction is to be reconciled, I leave to the consideration of his fu- ture commentators.
For my own part, I cannot help being of opinion with Lord Monboddo, (who certainly was not wanting in a due respect for the authority of Aristotle,) that the syllogistic theory would have accorded much better with the doctrine of Plato concerning general ideas, than with that held on the same subject by the founder of the Peripatetic school. J To maintain that, in all demon- stration, we argue from generals to particulars, and, at the same time, to assert, that the necessary progress ,of our iaiowledge is from particulars to generals, by a grad- ual induction from the informations of sense, do not ap- pear, to an ordinary understanding, to be very congru- ous parts of the same system ; § and yet the last of
* (liaviQov 8ii y.al, luv waiv at TTQoruasiq y.a&oXov i^ av 6 aiOdoyiafiog, on uvayy.rj yal to avfiTtigaafia u'idiov dvai T^jg TOiavujg anodeliiwg, zal T^? [a7[),wg iinsiv) ajwdsl^tag ' ovy. lariv aga dnodEi^ig tiov (p&UQXbn', ov8 e7naTi]ix't] anXoiig, aXX' omag, waneg xara avfiOi&t^y.og. — Analyt. Post. Lib. i. cap. viii,
t 'Jm fitv ovv c.hr&rj(jib)g yiyviTUV f.iri]H7]. ax 8e |«j'>;^?;? 'no}^lay.tg xov avTOV yLVOfxivrig, if.tnsiQta. ai yuq noXlal fivrijxai tw agi&nw, fi.i7isigla fiia iaxLV' ix 8 ifXTieiglag 7] iy. navTog ijgsf.Djoavrog toil xixSolov tv tjj if^'Zlh ^^^ ivog naga tm fiolla, o av iv unuaiv iv ivfi txelroig to avio, xfyvr^g f>^QXH '*^' iniaiTifirig. lav ys negl yinaiv, xfX^'hi' ^^^ ^^ nfgl to ov, {■jTiaTi]firjg. (Analyt. Post. Lib. ii. cap. xix.) The vvholu chapter may be read with advantage by those who wish for a fuller explanation of Aristotle's opinion on this question. His illustration of (he intellectual process by which general principles are obtained from the perceptions of sense, and from reiterated acts of memory resolving into one experievce, is more particularly deservine; of attention.
t Ancient Metaphysics, Vol. V. pp. 184, 185.
§ It 0iay perhaps be afkcd, Is not this '.he very mode of philosophizing recommend-
OF THE HUMAN MIND. 187
these tenets has been eagerly claimed as a discovery of Aristotle, by some of the most zealous admirers of his logical demonstrations.*
In this point of view, Lord Monboddo has certainly conducted, with greater skill, his defence of the syllogis- tic theory ; inasmuch as he has entirely abandoned the important conclusions of Aristotle concerning the natu- ral progress of human knowledge ; and has attempted to entrench himself in (what w^as long considered as one of the most inaccessible fastnesses of the Platonic philosophy) the very ancient theory, which ascribes to general ideas an existence necessary and eternal. Had he, upon this occasion, after the example of Aristotle, confined himself solely to abstract principles, it might not have been an easy task to refute, to the satisfaction
ed by Bacon, first lo proceed analytically from particulars to generals, and then to reason synthetically from generals to particulars ? My \t:\)]y to this question (a ques- tion which will not puzzle any peison at all acquainted with the subject) I must de- lay, till I shall have an opportunity, in the progress of my work, of pointing out the essential difference between the meanings annexed to the word induction, in the Aristotelian and in the Baconian logic. — Upon the present occasion it is sufficient to observe, that Bacon's plan of investigation was never supposed to be applicable to the discoveiy of principles which are necessary and eternal.
* See Dr. tVillles's Analysis of Aristotle's -works, passim.
In this learned, and on the whole, very instructive performance, I find several doc- trines ascribed lo Aristotle, which appear not a little at variance wMth each other. The following passages (which 1 am led to select fiom their connexion with the present argument) strike ine as not only widely different, but completely contradic- tory, in their import.
" According lo Aristotle, definitions arc the foundations of all science ; but those fountains are pure only when they originate in an accurate examination, and patient comparison of the perceptible qualities of individual objects." Vol. I p. 77.
" Demonstrative truth can apply only to those things which necessarily exist after a certain manner, and whose state is unalterable : and we know those things when we know their causes : Thus wc know a mathematical pioposition, when we know the causes that make it true ; that is, when we krow all the intermediate proposi- tions, up to the first principles or axioms, on which it is ultimately built." Ibid, pp. 95. 96.
It is almost superfluous to ob.^ervc, that while the former of these quotations founds all dcnionstraiive evidence on deJinitio)is,{he latter founds it upon axioms. Nor is this all. The former (as is mani.'"est from the second clause of the sentence) can refer ordy lo contingent truths ; inasmuch as the most accurate examination of the perceptible qualities of individual objects can never lead to the knowledge of things which necessarily exist after a. certain manner. The latter as obviously refers (and exclusively refers) to truths wliich resemble mathematical theorems.
As to Aristotle's asserlion, that definitions are the first principles of all demonstra- tions, fal c^X"'' '^'^'' a'''«Sj/|s(uv ol 0(117(1,01,) it undoubtedly seems, at Hist view, to co- incide exactly with the docuine wiiich 1 was at so much pains lo inculcate, in treat- ing of that peculiar evidence which belongs to mathematics. I hope, however, I shall nol, on this account, he accused of plagiarism, when it is considereil, that the comuKiiiary upon these words, quoted above from Dr. Gillies, absolutely excludes mathematics from the number of those sciences to which tlicy are to be applied, — On this point, too, Ali^totle's own language is decisive. 'E$ amyxaiaiv x^a (ruXXt. yif/ioi 'iffriyi h a.Tohii'iii. — Analyt. Poster. Lib. i. cap. iv.
188 elemejyts of the philosophy
of common readers, his metaphysical arguments. For- tunately, however, he has favored us with some exam- ples and illustrations, v^'hich render this undertaking quite unnecessary ; and which, in my opinion, have given to the cause which he was anxious to support, one of the most deadly blows which it has ever received. The following panegyric in particular, on the utihty of logic, while it serves to show that, in admiration of the Aristo- telian demonstradons, he did not yield to Dr. Gillies, forms precisely such a comment as I myself could have wished for, on the leading propositions which I have noAV been attempting to establish.
" In proof of the utility of logic," * says Lord Mon- boddo, " I will give an example of an argument to prove that man is a substance ; which argument, put into the syllogistic form, is this :
" Every Ajiimal is a Substance ; Every Manis an Animal; Therefore ev^ry Man is a Substance.
" There is no man, I beheve, who is not convinced of the truth of the conclusion of this syllogism : But how he is convinced of this, and for what reason he believes it to be true, no man can tell, who has not learned, from the logic of Aristotle, to know what a proposition, and what a syllogism is. There he will learn, that every proposition affirms or denies something of some other thing. What is affirmed or denied is called the Predi- cate ; and that of which it is affirmed or denied, is called the Subject. The predicate being a more general idea than the subject of which it is predicated, must contain or include it, if it be an affirmative proposition ; or if it be a negadve proposition, it must exclude it. This is the nature of propositions : And as to syllogism, the use of it is to prove any proposition that is not self-evident. And this is done by finding out what is called a middle term ; that is, a term connected with both the predicate and the subject of the proposition to be proved. Now, the proposition to be proved here is, that man is a sub- stance ; or, in other words, that substance can be predi-
* Ancient Metaphysics, Vol. V. p. 152.
OF THE HUMAN MIND. 189
cated of mem : And the middle term, by which this con- nexion is discovered, is animal, of which substance is predicated and this is the major proposition of the syl- logism, by which the major term of the proposition to be proved, is predicated of the middle term. Then an- imal IS predicated of raan; and this is the minor propo- sition of the syllogism, by which the middle term is pre- dicated of the lesser term, or subject of the proposition to be proved. The conclusion, therefore, is, that as sub- stance contains animal, and man is contained in animal, or is part of animal, therefore substance contains man. And the conclusion is necessarily deduced from the axi- om I have mentioned, as the foundation of the truth of the syllogism, ' That the whole is greater than any of its parts, and contains them all.' So that the truth of the syllogism is as evident as when we say, that if A con- tain B, and B contain C, than A contains C.
" In this manner Aristotle has demonstrated the truth of the syllogism. But a man, who has not studied his logic, can no more tell why he believes the truth of the syllogism above mentioned, concerning man being a sub- stance, than a joiner, or any common mechanic, who ap- phes a foot or a yard to the length of two bodies, and finds that both agree exactly to that measure, and are neither longer nor shorter, can give a reason why he be- lieves the bodies to be equal, not knowing the axiom of Euclid, ' That two things, which are equal to a third thing, are equal to one another.' '
" By this discovery Aristotle has answered the ques- tion which Pontius Pilate, the Roman Governor, asked of our Saviour, fV/ial Truth is ? The answer to which appears nov/ to be so obvious, that I am persuaded Pi- late would not have asked it as a question, which he no doubt thought very difficult to be answered, if he had not studied the logic of Aristotle." *
* Ancient Metaphysics, Vol. V. pp. 152, 153, 154.
I liavc quoted this passfiujc at lcn<ith, becauso I consider it as an instructive exam- ple of the eftccts likely to be piodiicerl on the understanding hy scholastic studies, where they become a favorite and habitual object of pursuit. The author (whom I knew well, and for whose memory I entertain a sincere respect) was a man of no common mental powers. Besides possessinij a rich fund of what is commonly called learniii<;-, he was distinguished by natural acutcncss ; by a more than ordinary share of wit; and, in the discharge of his judicial functions, by the singular correctness,
190 ELEMENTS OF THE PHILOSOPHY
After perusing the above exposition of Aristotle's de- monstration, the reader, if the subject be altogether new to him, will be apt to imagine, that the study of logic is an undertaking of much less difficulty than he had been accustomed formerly to apprehend ; the whole resolving ultimately into this axiom, " That if A contains B, and B contains C, then A contains C." In interpreting this axiom, he will probably figure to himself A, B, and C, as bearing some resemblance to three boxes, the sizes of which are so adapted to each other, that B may be lit- erally put into the inside of A, and C into the inside of B. Perhaps it may be reasonably doubted, if there is one logician in a hundred, who ever dreamed of under- standing it in any other sense. When considered in this light, it is not surprising that it should instantly com- mand the assent of the merest novice : nor would he hesitate one moment longer about its truth, if, instead of being limited (in conformity to the three terms of a syl- logism) to the three letters. A, B, C, it were to be ex- tended from A to Z ; the series of boxes corresponding to the series of letters^ being all conceived. to |)e nestled, one within another, like those which we sometimes see exhibited in the hands of a juggler.
If the curiosity of the student, however, should lead him to inquire a little more accurately into Aristotle's meaning, he will soon have the mortification to learn, that when one thing is said by the logician, to he in another, or to he contained in another, these words are not to be understood in their ordinary and most obvious sense, but in a. particular and technical sense, known only to adepts ; and about which (we may remark by the way) adepts are not, to this day, unanimously agreed. " To those," says Lord Monboddo, " who know no more of logic nor
gravity, and dignit}' of his unpremeditated elocution ; — and yet, so completely had his faculties been subdued i)y l!ie vain abstractions and verbal distinctions of the schools, tliat he had brought himself seriously to regard such discussions as that which I have here transcribed h-oin his works, not only as containing much excellent sense, but as the quintessence of sound philosophy. As for the mathematical and physical discoveries of the Newtonians, he held them in comparative contempt, and was probably prevented, by this circumstance, from ever proceeding farther than the first elenients of these sciences. Indeed, his ignorance of both was wonderful, con- sidering the very liberal education which he had received, not only in his own coua- try, but at a foreign university.
OF THE HUMAN MIND. 191
of ancient philosophy than Mr. Locke did, it will be ne- cessary to explain in what sense one idea can be said to contain another, or the idea less general can be said to be a part of the more general. And, in the first place, it is not in the sense that one body is said to be a part of another, or the greater body to contain the lesser ; nor is it as one number is said to contain another ; but it is virtually or potentially that the more general idea con- tains the less general. In this way the genus contains the species ; for the genus may be predicated of every species under it, whether existing or not existing ; so that virtually \t contains all the specieses under it, which exist or may exist. And not only does the more gener- al contain the less general, but (what at first sight may appear surprising) the less general contains the more general, not virtually ov potentially, but actually. Thus, the genus animal contains virtually man, and every other species of animal either existing or that may exist : But the genus animal is contained in man, and in other ani- mals actually ; for man cannot exist without being in actuality, and not potentially only an animal."*
If we have recourse to Dr. Gilhes for a litde more light upon this question, we shall meet with a similar disap- pointment. According to him, the meaning of the phra- ses in question is to be sought for in the following defi- nition of Aristode : " To say that one thing is contained in another, is the same as saying, that the second can be predicated of the first in the full extent of its signification ; and one term is predicated of another in the full extent of its signification, when there is no particular denoted by the subject, to which the predicate does not apply." f In
* Ancient Mctapliy.sics, Vol. IV. p. 73.
For the distinction betwixt containing potentiality and actualh/. Lord Monboddo acltnowJedges himself indebted to a Greelc author then living, Eugenius Diaconus. {Jlnc. Met. Vol. IV. p. 7.3.) Of this author we arc elsewhere told, that he was a Professor in the Pati larch's Universitj^ at Constantinople ; and that he published, in pure Attic Greek, a sj'stoin of loinc, at Leipsic, in the year 1766. {Origin and Progress of Language, Vol. I. p. 45, 2d edit.) It is an extraordinary circumstance, that a discovery, on which, in Lord IMonboddo's opinion, the whole truth of the syllogism depends, should have been of .-;o very recent a date.
\ Gillics's Aristotle, Vol. I. p. 73. "This remark," says Dr. Gillies, "which is the foundation of all Aristotle's logic, has been sadly mistaken by many. Airong others. Dr. Rcid .iccuses Aristotle of using as synonymous phrases, the being in a subject, and the being truly predicated of a subject ; whereas the truth is, that, ac- cording to Aristotle, the meaning of the one phrase is directly the reverse of the meaning of the other." — Ibid.
192 ELEMENTS OF THE PHILOSOPHY
order, therefore, to make sure of Aristotle's idea, we must substitute the definition instead of the thing defin- ed ; that is, instead of saying that one thing is contained in another, we must say, that " the second can be predi- cated of the first in the full extent of its signification." In this last clause, I give Aristotle all the advantage of Dr. Gilhes's very paraphrastical version ; and yet, such is the effect of the comment, that it at once converts our axiom into a riddle. I do not say that, v/hen thus inter- preted, it is altogether uninteUigible ; but only that it no longer possesses the same sort of evidence which we ascribe to it, while we supposed that one thing was said by the logician to be contained in another, in the same sense in which a smaller box is contained in a greater.*
To both comments the same observation may be ap- plied ; that, the moment a person reads them, he must feel himself disposed to retract his assent to the axiom which they are brought to elucidate ; inasmuch as they must convince him, that what appeared to be, according to the common signification of words, httle better than a truism, becomes, when translated into the jargon of the schools, an incomprehensible, if not, at bottom, an un- meaning (Enigma,
I have been induced to enlarge, with more minute- ness than I could have wished, on this fundamental ar- ticle of logic, that I might not be accused of repeating those common-place generalities which have, of late, been so much complained of by Aristotle's champion. I must not, however, enter any farther into the details
While I readily admit the justness of this criticism on Br. Reid, I must take the liberty of adding, that I consider Reid's error as a mere oversioht, or slip of the pen. That "he miohc have accused Aristotle of confounding two things which, although different in fact, had yet a certain degree cf resemblance or affinity, is hy no means impossible : but it is scarcely conceivable, that he could be so careless as to accuse him of confounding two things which he invariably states in direct opposition to each other. I have not a doubt, therefore, that Reid"s idea was, that Aristotle used, as synonymous phrases, the being in a tiling, and the being a subject of which that thing can be truly predicated ; more especially, as either statement would equally well have answered his purjiose.
* It is worthy of observation, that Condillac has availed himself of the same met- aphorical and equivocal word which the foregoing comments profess to explain, in support of the theory which represents every process of sound reasoning as a series of identical proi)osilions. " L'Analyse est la meme dans toules Ics sciences, parce que dans toutes elle conduit du connu a Tinconnu par le raisonncment, c'est-a-dire, par une suite de jugemens qui sont renjermes les uns dans les autres." — La Logi- qve.
OF THE HUMAN MIFD. 193
of the system ; and shall therefore proceed, in the next section, to offer a few remarks of a more practical na- ture, on the object and on the value of the syllogistic art.
SECTION 11.
General Reflections on the Aim of the Aristotelian logic, and on the Intellectual Hab- its which the study of it has a tendency to form. — That the Improvement of the Power of Reasoning ought to be regarded as only a secondary Object in the culture of the Understanding.
The remarks which were long ago made by Lord Bacon on the inutility of the syllogism as an organ of scientific discovery, together with the acute strictures in Mr. Locke's Essay on this form of reasoning, are so decisive in point of argument, and, at the same time, so familiarly known to all who turn their attention to philo- sophical inquiries, as to render it perfectly unnecessary for me, on the present occasion, to add any thing in support of them. I shall, therefore, in the sequel, con- fine myself to a few very general and miscellaneous reflections on one or two points overlooked by these eminent writers ; but to which it is of essential impor- tance to attend, in order to estimate justly the value of the Aristotehan logic, considered as a branch of educa- tion.*
It is an observation which has been often repeated since Bacon's time, and which, it is astonishing, was so long in forcing itself on the notice of philosophers. That, in all our reasonings about the established order of the universe, experience is our sole guide, and knowl- edge is to be acquired only by ascending from particu- lars to generals ; whereas the syllogism leads us invari- ably from universals to particulars, the truth of which, instead of being a consequence of the universal proposi- tion, is implied and presupposed in the very terms of its
* To some of ray readers it may not be superfluous to recommend, as a valuable supplement to the discussions of Locke and Bacon concerning the : ylloiistic art, what has been since written on the same subject, in farther proscculiou of their views by Dr. Rcid in his Analysis of Aristotle's Logic, and by Dr. Campbell in his Philos- ophy of Rhetoric.
VOL. II. 25
194 ELEMENTS OF THE PHILOSOPHY
enunciation. The syllogistic art, therefore, it has been justly concluded, can be of no use in extending our knowledge of nature.*
To this observation it may be added. That, if there are any parts of science in which the syllogism can be advantageously appHed, it must be those where our judgments are formed, in consequence of an apphcation to particular cases of certain maxims which we are not at liberty to dispute. An example of this occurs in the practice of Law. Here, the particular conclusion must be regulated by the general principle, whether right or wrong. The case was similar in every branch of phi- losophy, as long as the authority of great names pre- vailed, and the old scholastic maxims were allowed, without examination, to pass as incontrovertible truths.f Since the importance of experiment and observation was fully understood, the syllogistic art has gradually fallen into contempt.
A remark somewhat similar occurs in the preface to the JYovum Organon. " They who attributed so much to logic," says Lord Bacon, " perceived very well and tru- ly, that it was not safe to trust the understanding to itself,
* On this point it would be a mere waste of time to enlarge, as it has been of late explicitly admitted by some of the ablest advocates for the Organon of Aristotle. " When Mr. Locke," I quote the words of a very judicious and acute logician, " when Mr. Locke says — ' I am apt to think that he who should employ all the force of his reason only in brandishing of syllogisms, will discover very little of that mass of knowledge, which lies yet concealed in the secret recesses of nature ; ' — he ex- presses himself with needless caution. Such a man will certainly not discover any of it. And if any imagined, that the mere brandishing of syllogisms could in- crease their knowledge (as some of the schoolmen seemed to think), they were indeed very absurd." ( Commentary on the Compendium of Logic used in the University of Dublin. By the Rev. John Walker. Dublin, 1805.)
To the same effect, it is remarked, by a later writer, with respect to Lord Bacon's assertion, " that discoveries in Natural Philosophy are not likely to be promoted by the engine of syllogism ; " — " that this is a proposition which no one of the present day disputes ; and which, when alleged by our adversaries, as their chief objection to the study of logic, only proves, that they are ignorant of the subject about which they are speaking, and of the manner in Avhichit is now taught." (See an Anony- mous Pamphlet printed at Oxford in 1810, p. 26.) Dr. Gillies has expressed him- self in terras extremely similar upon various occasions. (See, in particular, Vol. I. pp. 63, 64, 2d edit.)
This very important concession reduces the question about the utility of the Aris- totelian logic within a very narrow compass.
j- " Ce sera un sujet eternel d'etonncment pour les personnes qui savent bien ce que c'cst que philosopliie, que de voir que I'autorite d'Aristote a ete tellement re- spectcc dans les ecolcs pendant quelques siecles, que lors qu'un disputant citoit un passage dc ce pbilosophe, celui qui soutcnoit la these n'osoit point dire transeat ; il falloit qu'il niat Ic passage, ou qu'il I'cxpliquiat a sa maniere." Diet, de Bayle, Art. Jlristote.
OF THE HUMAN MIND. 195
without the guard of any rules. But the remedy reach- ed not the evil, but became a part of it : For the logic which took place, though it might do well enough in civil affairs, and the arts which consisted in talk and opinion, yet comes very far short of subtilty, in the real perform- ances of nature ; and, catching at what it cannot reach, has served to confirm and estabhsh errors, rather than open a way to truth." *
It is not, however, merely as a useless or inefiicient or- gan for the discovery of truth, that this art is excep- tionable. The importance of the very object at which it professedly aims is not a httle doubtful. To exercise with correctness the powers of deduction and of argu- mentation ; or, in other words, to make a legitimate infer- ence from the premises before us, would seem to be an intellectual process which requires but little assistance from rule. The strongest evidence of this is, the facil- ity with which men of the most moderate capacity learn, in the course of a few months, to comprehend the long- est mathematical demonstrations ; a facility which, when contrasted with the difficulty of enlightening their minds on questions of morals or of pohtics, afibrds a sufficient proof, that it is not from any inability to conduct a mere logical process, that our speculative errors arise. The fact is, that, in most of the sciences, our reasonings con- sist of a very few steps ; and yet, how liable are the most cautious and the most sagacious, to form erroneous con- clusions !
To enumerate and examine the causes of these false judgments is foreign to my purpose in this section. The
* As the above translation is by Mr. Locke, who has introduced it in the way of apology for the freedom of his own strictures on the school logic, the opinion'^which it expresses may be considered as also sanctioned by the authority of his name. — See the Introduction to his Treatise on the Conduct of the Understanding. I cannot forbear rernaiking, on this occasion, that wlien Lord Bacon speaks of thp school logic as " answering well enough in civil affairs, and the arts which consist in talk and opinion," his words can only z\^^\y io diaJectical syllogisms, and' cannot possibly be extended to those which Aristotle calls demonstrative. Whatever praise, therefore, it may be supposed to imply, must be confined to the Books of Topics. The same ol)servation will be found to hold with respect to the greater ]iart of what has been alleged in defence of the syllogistic art, by Dr. Gillies, and Iiy the other authors referred to in the beginning of this section. One of the ablest of these scons to assent to an assertion of J5acon, "That logic does not help towards the invention of arts and sciences, but only of arguments." If it only helps towards the invention of arguments, for what purpose has Aristotle treated so fully of dcnioustration and of science in tlie two books of the Last Analytics ?
196 ELEMENTS OF THE PHILOSOPHY
following (which I mention only by way of specimen) seem to be among the most powerful. 1. The imper- fections of language, both as an instrument of thought, and as a medium of philosophical communication. 2. The difficulty, in many of our most important inquiries, of as- certaining the facts on which our reasonings are to pro- ceed. 3. The partial and narrow views, which, from want of information, or from some defect in our intellec- tual comprehension, we are apt to take of subjects, which are pecuUarly complicated in their details, or which are connected, by numerous relations, with other questions equally problematical. And lastly, (what is of all per- haps, the most copious source of speculative error,) the prejudices which authority and fashion, fortified by early impressions and associations, create to warp our opinions.
To illustrate these and other circumstances by which the judgment is apt to be misled in the search of truth, and to point out the most effectual means of guarding a- gainst them, would form a very important article in a phi- losophical system of logic ; but it is not on such sub- jects that we are to expect information from the logic of Aristotle.*
The fundamental idea on which this philosopher evi- dently proceeded, and in which he has been too imphcitly followed by many even of those who have rejected his syllogistic theory, takes for granted, that the discovery of truth chiefly depends on the reasoning faculty, and that it is the comiparative strength of this faculty, which constitutes the intellectual superiority of one man above another. The similarity between the words reason and reasoning of which I formerly took notice, and the confu- sion which it has occasioned in their appropriate meanings, has contributed powerfully to encourage and to perpetu- ate this unfortunate mistake. If I do not greatly deceive myself, it will be found, on an accurate examination of the subject, that, of the different elements which enter into the composition of reason, in the most enlarged acceptation
* In the Logic oi Port- Royal, there is a chapter, entitled, Des sophismes iVamour propre, d^interSt, et de passion, which is well worthy/ of a caielul perusal. Some useful hints may he also collected from Gravesando's Introductio ad Philosophiam. See Book ii. Part ii. (J)c Causis Errorum.)
OF THE HUMAN MIND. 197
of that word, the power of carrying on long processes of reasoning or deduction, is, in point of importance, one of the least.*
The slightest reflection, indeed, may convince us, how very little connexion the mere reasoning faculty has with the general improvement of mankind. The wonders which it has achieved have been confined, in a great measure, to the mathematical sciences, — the only branches of human knowledge which furnish occasion for long concatenated processes of thought ; and even there, method, together with a dexterous use of the helps to our intellectual faculties which art has discov- ered, will avail more than the strongest conceivable ca- pacity, exercised solely and exclusively in habits of synthetic deduction. The tendency of these helps, it may be worthwhile to add, is so far from being always favor- able to the power of reasoning, strictly so called, that it may be questioned, whether, among the ancient Greek geometers, this power was not in a higher state of cul- tivation, in consequence of their ignorance of the alge- braical symbols, than it exists in at this day, among the profoundest mathematicians of Europe.
In the other sciences, however, the truth of the re- mark is far more striking. By whom was ever the art of reasoning so sedulously cultivated as by the school-
* It was before observed (pp. 147, 148.), " That the whole theory of syllogism proceeds on the supposition, that the same word is always to be employed in the same sense ; and that, consequently, it takes for granted, in every rule which it furnishes for the guidance of our reasoning powers, that the nicest, and by far the most difficult part of the logical process, has been previous^ brought to a successful termination."
In this remark ( which, obvious as it may seem, has been very generally overlook- ed,) I have found, since the foregoing sheets were printed, that I have been anticipa- ted by M. Turgot. " Tout I'artifice de ce calcul ingenieux, dont Aristote nous a donne les regies, tout I'art du syllogisrae est foude sur I'usage des mots dans le me- me sens ; I'cmploi d'un merae mot dans deux sens differcns fait de tout raisonne- ment un sophisme ; et ce genre de sophisme, peut-etrc le plus commun de tous, est une des sources les plus ordinaires de nos crreurs." (Euures de M. Turgot, Tom. III. p. 66.
Lord Bacon had manifestly the same conclusion in view, in the following aphorism : " Syllogism consists of propositions, propositions of words,'an(l words are the signs of notions ; therefore, if our notions, the basis of all, arc confined, and over hastily taken from things, nothing tiiat is built on them can be firm ; whence our only iiope rests upon genuine induction." JVov. Org. Part I. Sect. 1. Aph. 14. (Shaw's Translation.)
On wiiat grounds Dr. Gillies was led to hazard the assertion formerly ([uoted (j). 179), that " Aristotle invented the syllogism, to prevent imposition arising from the abuse of words," I am quite unable to form a conjecture.
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men, and where shall we find such monuments of what mere reasoning can accomphsh, as in their writings T Whether the same end might not have been attained without the use of their technical rules, is a different question; but that they cZic? succeed, to a great degree, in the acquisition of the accomphshments at which they aimed, cannot be disputed. And yet, I believe, it will be now very generally admitted, that never were labor and ingenuity employed for so many ages to so httle pur- pose of real utihty. The absurdity of expecting to rear a fabric of science by the art of reasoning alone, was re- marked, with singular sagacity, even amidst the darkness of the twelfth century, by John of Salisbury, himself a dis- tinguished proficient in scholastic learning, which he had studied under the celebrated Ahelard. " After a long absence from Paris" he tells us in one passage, " I went to visit the companions of my early studies. I found them, in every respect, precisely as I had left them ; not a single step advanced towards a solution of their old difl&culties, nor enriched by the accession of one new idea : — a strong experimental proof, that, how much soever logic may contribute to the progress of other sciences, it must for ever remain barren and life- less, while abandoned to itself." *
Among the various pursuits now followed by men lib- erally educated, there is none, certainly, which aff"ords such scope to the reasoning faculty, as the science and profession of law ; and, accordingly, it has been observ- ed by Mr. Burke, " That they do more to quickeji and invigorate the understanding, than all the other kinds of learning put together." The same author, however, adds, that " they are not apt, except in persons very happily born, to open and to liberalize the mind, exact- ly in the same proportion." Nor is this surprising ; for the ultimate standards of right and wrong to which they recognise the competency of an appeal, being convention- al rules and human authorities, no field is opened to that spirit of free inquiry which it is the boast of philosophy to cultivate. The habits of thought, besides, which the
*Meialog. Lib/ii. cap. 10.
OF THE HUMAN MIND. 199
long exercise of the profession has a tendency to form, on its appropriate topics, seem unfavorable to the quali- ities connected with what is properly called judgment ; or, in other words, to the qualities on which the justness or correctness of our opinions depends ; they accustom the mind to those partial views of things which are sug- gested by the separate interests of litigants ; not to a calm, comprehensive, and discriminating survey of de- tails, in all their bearings and relations. Hence the ap- parent inconsistencies which sometimes astonish us in the intellectual character of the most distinguished prac- titioners,— a talent for acute and refined distinctions ; powers of subtle, ingenious, and close argumentation ; inexhaustible resources of invention, of wit, and of elo- quence ; — combined, not only with an infantine imbe- cility in the affairs of life, but with an incapacity of form-, ing a sound decision, even on those problematical ques- tions which are the subjects of their daily discussion. The great and enlightened minds, whose judgments have been transmitted to posterity, as oracles of legal wis- dom, were formed (it may be safely presumed) not by the habits of their professional warfare, but by contend- ing with these habits, and shaking off their dominion.
The habits of a controversial writer are, in some re- spects, analogous to those of a lawyer ; and their effects on the intellectual powers, when engaged in the inves- tigation of truth, are extremely similar. They confine the attention to one particular view of the question, and, instead of training the understanding to combine together the various circumstances which seem to favor opposite conclusions, so as to hmit each other, and to guard the judgment against either extreme, — they are apt, by presenting the subjects sometimes wholly on the one side, and sometimes wholly on the other, to render the disputant the sceptical dupe of his own, ingenuity. Such seems to have been nearly the case with the re- doubtable Chillingworth ; a person to whose native can- dor the most honorable testimony has been borne by the most eminent of his contemporaries, and whose argu- mentative powers have almost become matter of pro- verbial remark. Dr. Reid has pronounced him the
200 ELEMEICTS or THE PHILOSOPHY
" best reasoner, as well as the acutest logician of his age ;" and Locke himself has said, " If you would have your son to reason well, let him read Chillingworth." To what consequences these rare endowments and at- tainments led, we may learn from Lord Clarendon.
" Mr. Chillingworth had spent all his younger time in disputations, and had arrived at so great a mastery, that he was inferior to no man in those skirmishes ; but he had, with his notable perfection in this exercise, con- tracted such an irresolution and habit of doubting, that by degrees he grew confident of nothing." — " Neither the books of his adversaries, nor any of their persons, though he was acquainted with the best of both, had ever made great impression on him ; all his doubts grew out of himself, when he assisted his scruples with all the strength of his own reason, and was then too hard for himself : but finding as little quiet and repose in those victories, he quickly recovered, by a new appeal to his own judgment ; so that, in truth, he was, in all his sal- lies and retreats, his own convert."
The foregoing observations, if well founded, conclude strongly, not merely against the form of the school logic, but against the importance of the end to which it is direct- ed. Locke and many others have already sufficiently shown, how inadequate the syllogistic theory is to its avowed purpose ; but few seem to be sufficiently aware, how very little this purpose, if it were attained, would advance us in the knowledge of those truths which are the most interesting to human happiness.
" There is one species of madman," says Father Buf- fier, " that makes an excellent logician." * — The remark has the appearance of being somewhat paradoxical; but it is not without a solid foundation, both in fact, and in the theory of the human understanding. Nor does it ap- ply merely (as Buffier seems to have meant it) to the scholastic defenders of metaphysical paradoxes : it ex- tends to all whose ruling passion is a display of argumen- tative dexterity, without much solicitude about the just- ness of their premises, or the truth of their conclusions.
*Traite des Prcrn. Verites. Part I. chap. xi.
OF THE HUM A?? 3I1ND. 201
It is observed by Lord Erskine, in one of his admirable pleadings lately published, that " in all the cases which have filled Westminister-Hall with the most comphca- ted considerations — the lunatics, and other insane per- sons, who have been the subjects of them, have not only had the most perfect knowledge and recollection of all the relations they stood in towards others, and of the acts and circumstances of their lives, but have, in general, been remarkable for subtlety and aciiteness." — "These," he adds, " are the cases which frequently mock the wis- dom of the wisest in judicial trials ; because such persons ofte7i reason loith a subtlety which puts in the shade the ordiyiary conceptions of mankind : their conclusions are just, and frequently profound ; but the premises from which they reason, when within the range of the malady, are uniformly false : — not false from any defect of knowledge or judgment ; but because a delusive im- age, the inseparable companion of real insanity, is thrust upon the subjugated understanding, incapable of resist- ance, because unconscious of attack.'
In the instances here alluded to, something, it is prob- able ought to be attributed to the physical influence of the disorder in occasioning, together with an increased propensity to controversy, a preternatural and morbid excitation of the power of attention, and of some other intellectual faculties ; but much more in my opinion, to its effects in removing the check of those collateral cir- cumstances by which, in more sober understandings, the reasoning powers are perpetually retarded and control- led in their operation. Among these circumstances, it is sufficient to specify, for the sake of illustration, 1. That distrust, which experience gradually teaches, of the accuracy and precision of the phraseology in which our reasonings are expressed ; — accompanied with a corresponding apprehension of involuntary mistakes from the ambiguity and vagueness of language ; 2. A latent suspicion, that we may not be fully in possession of all the elements on which the solution of the problem de- pends ; and, .3. The habitual influence of those first principles of propriety, of morality, and of common sense, which, as long as reason maintains her ascendant, exer-
voL. II, 26
202 ELEMENTS OF THE PHILOSOPHY
cise a paramount authority over all those speculative con- elusions which have any connexion with the business of life. Of these checks or restraints on our reas<oning processes, none are cultivated and strengthened, either by the rules of the logician, or by the habits of viva voce disputation. On the contrary, in proportion as their reg- ulating power is confirmed, that hesitation and suspense of judgment are encouraged, which are so congenial to the spirit of true philosophy, but such fatal incumbran- ces in contending with an antagonist whose object is not truth but victory. In madness, where their con- trol is entirely thrown off, the merely logical process (which never stops to analyze the meaning of words) is likely to go on more rapidly and fearlessly than before ; — producing a volubility of speech, and an apparent quickness of conception, which present to common ob- servers all the characteristics of intellectual superiority. It is scarcely necessary to add, that the same appear- ances, which in this extreme case of mental aberration, are displayed on so great a scale, may be expected to show themselves, more or less, wherever there is any deficiency in those qualities which constitute depth and sagacity of judgment.
For my own part, so Httle value does my individual experience lead me to place on argumentative address, when compared with some other endowments subservi- ent to our intellectual improvement, that I have long been accustomed to consider that promptness of reply and dogmatism of decision which mark the eager and practised disputant, as almost infallible symptoms of a limited capacity ; a capacity deficient in what Locke has called, (in very significant, though somewhat homely terms) large^ sound, roundabout sense* In all the higher endowments of the understanding, this intellectual qual- ity (to which nature as well as education must liberally contribute) may be justly regarded as an essential ingre- dient. It is this which, when cultivated by study, and directed to great objects or pursuits, produces an unpre- judiced, comprehensive, and efficient mind ; and, where
* Conduct of the Understanding, § 3.
OF THE HUMAN BIIi?fD. 203
it is wanting, though we may occasionally find a more than ordinary share of quickness and of information ; a plausibility and brilliancy of discourse ; and that passive susceptibility of pohsh from the commerce of the vvorld, which is so often united with imposing but secondary talents, — we may rest assured, that there exists a total incompetency for enlarged views and sagacious combi- nations, either in the researches of science or in the con- duct of affairs.*
If these observations hold with respect to the art of reasoning or argumentation, as it is cultivated by men undisciplined in the contentions of the schools, they will be found to apply with infinitely greater force to those disputants (if any such are still to be found) who, in the present advanced state of human knowledge, have been at pains to fortify themselves, by a course of persever- ing study, with the arms of the Aristotelian logic. Per- sons of the former description often reason conscien- tiously with warmth from false premises which they are led by passion, or by want of information, to mistake for truth. Those of the latter description proceed system- atically on the radical error of conceiving the reasoning process to be the most powerful instrument by which truth is to be attained ; combined with the secondary error of supposing that the power of reasoning may be strengthened and improved by the syllogistic art.
* The outlines of an intellectual character, approaching nearly to this description, is exhibited by Mann ontel in his highly finished (and I have been assured, very faithful) portrait of M. de Brienne. Among the other defects of that unfortunate Btatesman, he mentions particularly lai esprit d facetted ; by which expression he eeems, from the context, to mean a quality of mind precisely opposite to that describ- ed by Locke in the words quoted above : — " quelques lumicres, mais eparses ; iles apper^us plutot quedes vues ; et dans les grands objets, de lafacilite a saisir lea petits details, nulle capacHi pour embrasser Vensemble." A consciousness of some similar deficiency has suggested to Gibbon the following criticism on his own juvenile performance, entitled Essai stir VEtude. It is executed by an impartial and masterly hand ; and may, perhaps, without much'Mnjustice, be extended not on- ly to his Roman History, but to the distinguishing features of that peculiar cast of genius, which so strongly marks all his writings.
" The most serious defect of my essay is a kind of obscurity and abruptness which always fatigues, and may often elude the attention of the reader. The obscurity of many passages is often affected ; proceeding from the desire of expressing perhaps a common idea with sententious brevity : brevis esse laboro,^ obscurus fio. Alas ! how fatal has been the imitation of Montesquieu ! But this . obscurity sometimes proceeds from a mixture of light and darkness in the author's mind ; from apar- tialray which strikes upon an angle, instead of spreading itself over the surface of an object."
204 ELEMENTS OF THE PHILOSOPHY
In one of Lord Karnes's sketches, there is an amusing and instructive collection of facts to illustrate the pro- gress of reason ; a phrase, by which he seems to mean chiefly the progress of good seiise, or of that quahty of the intellect which is very significantly expressed by the epithet enlightened. To what is this progress (which has been going on with such unexampled rapidity during the two last centuries) to be ascribed ? Not surely to any improvement in the art of reasoning ; for many of the most melancholy weaknesses which he has recorded, were exhibited by men, distinguished by powers of dis- cussion, and a reach of thought, which have never been surpassed ; while, on the other hand, the same weakness would now be treated with contempt by the lowest of the vulgar. The principal cause, I apprehend, has been, the general diffusion of knowledge (and more especially of experimental knowledge) by the art of printing : in consequence of which, those prejudices which had so long withstood the assaults both of argument and of ridicule, have been gradually destroyed by their mutual collision, or lost in the infinite multiplicity of elementary truths which are identified with the operations of the infant understanding. To examine the process by which truth has been slowly and insensibly cleared from that admixture of error, with which, during the long night of Gothic ignorance, it was contaminated and disfigured, would form a very interesting subject of philosophical speculation. At present, it is sufficient to remark, how little we are indebted for our emancipation from this in- tellectual bondage, to those quahties which it was the professed object of the school logic to cultivate ; and that, in the same proportion in which liberality and light have spread over Europe, this branch of study has sunk in the general estimation.
Of the inefficacy of mere reasoning in bringing men to an agreement on those questions which, in all ages, have furnished to the learned the chief matter of controver- sy, a very just idea seems to have been formed by the ingenious author of the following lines ; who has, at the same time, hinted at a remedy against a numerous and important class of speculative errors, more hkely to
OF THE HUMAN MIND. 205
succeed than any which is to be derived from the most skilful application of Aristotle's rules ; or, indeed, from any direct argumentative refutation, how conclusive and satisfactory soever it may appear to an unbiassed judg- ment. It must, at the same time, be owned, that this remedy is not without danger ; and that the same habits which are so useful in correcting the prejudices of the monastic bigot, and so instructive to all whose principles are sufficiently fortified by reflection, can scarcely fail to produce pernicious effects, where they operate upon a character not previously formed and confirmed by a ju- dicious education.
" En parcourant au loin la planete ou nous sommes, due verrons nous ? les torts et les travers des hommes ! Ici c'est iin synode, et la c'est un divan, Nous verrons le Mufti, le Berviche, I'lman, Le Bonze, le Lama, le Talapoin, le Pope, Les antiques Rabbins et les Abbes d'Europe, Nos moines, nos prelats, nos docteurs agreges ; Etes vous disputeurs, mes amis ? voyagez." *
To these verses it may not be altogether useless to subjoin a short quotation from Mr. Locke ; in whose opinion the aid of foreign travel seems to be less neces- sary for enhghtening some of the classes of controver- sialists included in the foregoing enumeration, than was suspected by the poet. The moral of the passage (if due allowances be made for the satirical spirit which it breathes) is pleasing on the whole, as it suggests the probability, that our common estimates of the intellectu- al darkness of our own times are not a little exaggera- ted.
" Notwithstanding the great noise that is made in the world about errors and opinions, I must do mankind that right as to say, lliere arc not so many men in errors and wrong opinions, as is commonly supposed. Not that I think they embrace the truth ; but, indeed, because concerning those doctrines they keep such a stir about, they have no thought, no opinion at all. For if any one should a litde catechize the greatest part of the parti- zans of most of the sects in the world, he would not
• Discours sur les Disputes, par M. de Rulhiere.
U h. }^ h u f, r. f.
204
ELEMEA^TS OF THE PHILOSOPHY
In one of Lord Karnes's sketches, there is an amusing and instructive collection of facts to illustrate the pro- gress of reason ; a phrase, by which he seems to mean chiefly the progress of good sense, or of that quality of the intellect which is very significantly expressed by the epithet enlightened. To what is this progress (which has been going on with such unexampled rapidity during the two last centuries) to be ascribed 1 Not surely to any improvement in the art of reasoning ; for many of the most melancholy weaknesses' which he has recorded, were exhibited by men, distinguished by powers of dis- cussion, and a reach of thought, which have never been surpassed ; while, on the other hand, the same weakness would now be treated with contempt by the lowest of the vulgar. The principal cause, I apprehend, has been, the general diffusion of knowledge (and more especially of experimental knov^'ledge) by the art of printing : in consequence of which, those prejudices which had so long withstood the assaults both of argument and of ridicule, have been gradually destroyed by their mutual collision, or lost in the infinite multiplicity of elementary truths which are identified with the operations of the infant understanding. To examine the process by which truth has been slowly and insensibly cleared from that admixture of error, with which, during the long night of Gothic ignorance, it was contaminated and disfigured, would form a very interesting subject of philosophical speculation. At present, it is sufficient to remark, how little we are indebted for our emancipation from this in- tellectual bondage, to those quahties w^hich it was the professed object of the school logic to cultivate; and that, in the same proportion in which liberality and light have spread over Europe, this branch of study has sunk in the general estimation.
Of the inefficacy of mere reasoning in bringing men to an agreement on those questions which, in all ages, have furnished to the learned the chief matter of controver- sy, a very just idea seems to have been formed by the ingenious author of the following fines ; who has, at the same time, hinted at a remedy against a numerous and important class of speculative errors, more likely to
OF THE HUMAN MIND.
205
succeed than any which is to be derived from the most skilful application of Aristotle's rules ; or, indeed, from any direct argumentative refutation, how conclusive and satisfactory soever it may appear to an unbiassed judg- ment. It must, at the same time, be owned, that this remedy is not without danger ; and that the same habits which are so useful in correcting the prejudices of the monastic bigot, and so instructive to all v/hose principles are sufficiently fortified by reflection, can scarcely fail to produce pernicious effects, where they operate upon a character not previously formed and confirmed by a ju- dicious education.
" En parcourant au loin la planete ou nous sommes, Q.ue verrons nous 1 les torts et les travers des homraes ! Ici c'est iin synode, et la c'est un divan, Nous verrons le Mufti, le Cerviche, I'lman, Le Bonze, le Lama, le Talapoin, le Pope, Les antiques Rabbins et les Abbes d'Europe, Nos moines, nos prelats, nos docteurs agreges ; Etes vous disputeurs, mes amis ? voyagez." *
To these verses it may not be altogether useless to subjoin a short quotation from Mr. Locke ; in whose opinion the aid oi foreign travel seems to be less neces- sary for enlightening some of the classes of controver- sialists included in the foregoing enumeration, than was suspected by the poet. The moral of the passage (if due allowances be made for the satirical spirit which it breathes) is pleasing on the whole, as it suggests the probability, that our common estimates of the intellectu- al darkness of our own times are not a httle exaggera- ted.
" Notwithstanding the great noise that is made in the world about errors and opinions, I must do mankind that right as to say, There are not so many men in errors and wrong opinions, as is commonly supposed. Not that I think they embrace the truth ; but, indeed, because concerning those doctrines they keep such a stir about, they have no thought, no opinion at all. For if any one should a little catechize the greatest part of the parti- zans of most of the sects in the world, he would not
* Discours sur les Disputes, par M. de Rulbiere.
200 ELEMICNTS Ol-^ THE J'lIlLOSOIMiy
find, ronr(;rnin<jj 11u)S(; mat tors tlicy are so zealous for, llial iUcy liave any opinion ol" (heir own : niiieli less would \n) have reason to (hink thai; they toolc Iheni upon the: exarnin;ilion ol" ai'}i;unK;n(s and appearance of prob- ability. They are rcisolved lo slick to a jiai'ty that edu- (tation or interest li;is (uiji;a}i;(ul tluuri in ; and tliere, like the common soldi(MS oi" an army, show their courage and w;uintli as thcii- h^ach^i'S direct, without ever exam- ining, or so inucli as knowing, the cause they contend for. If a man's life shows tliat he has no serious regard for religion, for what reason should we think that ho Ix^ats his head abont tlu^ opinions of his church, and troubles himself to examine the grounds of this or that <loctrin(5? 'Tis enongh for him to obey his leader's, to liavci his haml and his tongue rcsady for tlie snpj)ort of the common cause, and thereby approve himself to those who can give him credit, jU'elerment, and ])rot(iction in that society. Thus mtMi become! combatants for those opinions they were never convinced of; no, nor ever had so nnich as Jloating in their heads; and though
ONK CANNOr SAY THIORIO AllF. VKVVICIl 1 M I'KOl? Ani/IC OR KKK()Ni:oi)S OI'INIONS JN THE WORLD THAN THERE ARE, VV/I' THIS IS CEUPMN, TIIKItE ARE EEWERTHAT ACTUALLY ASSENT TO I'MEM, AND MISTAKE THEM EOR TRUTHS, THAN IS IMAGINED."*
If llu^se remnrlvS of TiOclce were duly weighed, they would have a tendency to abridge Ihe number of con- troversial writers ; and to encourage philosophers to at- tempt the im|)rov(Mn(Mit of mankind, I'ather by adding to ihe stock of usehil knowledge, dian by waging a direct war with prejudices, which have less root in tlie under- standings than in the interests and passions of their abet- tors.
* Essay on Human Undoi'staoding. Rook tv. c. 20.
OF Tl/i: HUMAN MIND. 207
SIXJTKjN J II.
In what fCBpficts tho Htudy of the AriHtotclian Lo;(ic iriuy I)c iisoful to Disputants, — A j;;<;n(;ral ac,(jij;iiii1;iti(:i; will) il jiixdy w/^miU-A as an csseiitial a(-.(:oiii|j|ishiiiciit to thosf! who are )ib(;ially ediicatijd. — IJouhtH Hiigf^iisled hy Moriie late VV liters, coa- ccruing AriHlotlc'H clainiH to tlie invention of tlie Syllogistic 'I'heoiy.
The ^oricral result of tlio f'oregoinf^ reflections is, That neither the means employed by the school lo^ic for the assistance of" the discurswe facuHi/, nor the ac- complishment of that end, were it really attaijied, are of much consequence in promoting the enlargement of the mind, or in guarding it against the influ(ince of errone- ous opinions. It is, however, a very different question, how far this art may be of use to such as are led by profession or inclination to try their strength in polemi- cal warfare. My own opinion is, that, in (h(i j^rr^sent age, it would not give to the disputant, in the judgment of men whose suffrage is of any value, the slightest ad- vantage over his antagonist. \n earlier times, indeed, the case must have been different. While the scholas- tic forms continued to be kept up, and while schoolmen were the sole judges of the contest, an expert logician could not fail to obtain an easy vic;tory over an inferior proficient. JVov), hctwever, when the su})r(;me tribunal to which all parties must appeal, is to be found, noly/Uh- in but wilkoul the walls of universities ; and when the most learned dial(;ctician must, for his own credit, avoid all allusion to the technif:al terms and technical forms of his art, can it be imagined that the mere possession of its rules furnishes him with invisible aid for annoying his adversary, or renders him invuln(irable by some secret spell against the weapons of his assailant? * Were this
• An argument of this sort in favor of the Aristotelian logic, has, In fact, hecn lately all<;ge(l, in a treatise to whieh I Jiave alreaily had or^easion to refer.
" Mr. Loeke seerns througliout to iuiagine that no use can he made of the doc- trine of syllogisms, uidess by loen who deliver their rf;asonirigs in syllogistic form. That would, Indeed, justly expose a man to the imputation of disgusting jiediuitry and tediousness. JJut, in f-wt, he who never uses an expir;ssion horrowed fioio the Aristotelic logic, may yet, unohservcd, he availing hiiriself, in the most important manner of its use, hy bringing dehnitions, divisions, and arguments, to the test of itu rules.
" In the mere application of it to the examining of an argument which we dcslro to refute, — the logician will be able to bring the argument in his own mind to syllo-
208 ELEMENTS OF THE PHILOSOPHY
real-ly the case, one might have expected that the advo- cates who have undertaken its defence (considering how much their pride was interested in the controversy) would have given us some better specimens of its prac- tical utility, in defending it against the unscientific at- tacks of Bacon and of Locke. It is, however, not a little remarkable, that, in every argument which they have attempted in its favor, they have not only been worsted by those very antagonists whom they accuse of ignorance, but fairly driven from the field of battle.*
gistic form. — He will then have before his view every constituent part of the argu- ment ; some of which may have been wholly suppressed by his antagonist, and others disguised by ambiguity and declamation. — He know.^ every point in which it is subject to examination. — He perceives immediately, by the rules of his art, wheth- er the premises may be acknowledged, and the conclusion denied, for want of a vis consequenticB. — If not, he knows where to look for a weakness. — He turns to each of the premises, and considers whether they are false, dubious, or equivocal : and is thus prepared and directed to expose every weak point in the argument with clear- ness, precision, and method ; and this to those who perhaps are wholly ignorant of the aids by which the speaker is thus enabled to carry conviction with his dis- course."— Commentary on the Compendium of Logic, used in the University of Dublin. Dublin, 180-5.
* In most of the defences of the school logic which I have seen, the chief weapon employed has been that kind of argument which, in scholastic phraseology, is called the Argumentum ad Hominem ; an argument in the use of which much regard to consistency is seldom to be expected. — In one sentence, accordingly, Bacon and Locke are accused of having never read Aristotle ; and, in the next, of having bor- rowed from Aristotle the most valuable part of their v/ritings.
With respect to I^ocke, it has been triumphantly observed, that his acquaintance with Aristotle's logic must have been superficial, as he has, in one of his objections, manifestly confounded particular with singular propositions. (Commentary on the Dubhn Compendium.) The criticism, 1 have no doubt, is just ; but does it, there- fore, follow, that a greater familiarity with the technical niceties of an art which he despised, would have rendered this profound thinker more capable of forming a just estimate of its scope and spirit, or of its efficacy in aiding the human understanding ? Somewhat of the same description are the attempts which have been repeatedly made to discredit the strictures of Dr. Keid, by appealing to his own acknowledg- ment, that there ims^ht possibly be some parts of the Analytics and Topics which he had never read. The passage in which this acknowledgment is made, is so charac- teristical of the modesty and candor of the writer, that I am tempted to annex it to this note ; — more especially, as I am persuaded, that, with many readers, it will have the effect of confirming, rather than of shaking, their confidence in the general cor- rectness and fidelity of his researches.
" In attempting to give some account of the Analytics and of the Topics of Aris- totle, ingenuity requires me to confess, that though I have often purposed to read the whole with care, and to understand what is intelligible, yet my courage and patience always failed before I had done. Why should I throw away so much time and pain- ful attention upon a thing of. so little real use ? If I had Hved in those ages when the knowledge of Aristotle's Organon entitled a man to the highest rank in philoso- phy, ambition might have induced me to employ upon it some years of painful study ; and less, I conceive, would not be sufhcient. Such reflections as these always got the better of my resolution, when the iiist ardor began to cool. All I can say is, that I have read some parts of the books with cave, some slightly, and some perhaps not at all. I have glanced over the whole often, and when any thing attracted my at- tention, have dipped into it till my appetite was satisfied. Of all reading, it is the most dry and the most painful, employing an infinite labor of demonstration, about things of the most abstract nature, delivered in a laconic style, and often, I think,
OF THE HUMAN MIND. 209
It has, indeed, been asserted by an ingenious and learned writer, that " he has never met with a person unacquainted with logic, who could state and maintain his argument with facility, clearness, and precision ; — that he has seen a man of ^he acutest mind puzzled by the argument of his antagonist ; sensible, perhaps, that it was inconclusive, but wholly unable to expose the fal- lacy which rendered it so : while a logician, of perhaps very inferior talents, would be able at once" to discern and to mark it." *
I do not deny that there may be some foundation for this statement. The part of Aristotle's Organon which seems, in the design, to be the most practically useful (although it is certainly very imperfect in the execution) is the book of Sophisms ; a book which still supphes a very convenient phraseology for marking concisely some of the principal fallacies which are apt to impose on the understanding in the heat of a viva voce dispute. f Whether it affords any aid in detecting or discerning these fallacies, may perhaps be doubted. But it is certainly an acquisition, and an acquisition of no contemptible value, to have always at hand a set of technical terms, by which we can point out to our hearers, without cir- cumlocution or discussion, the vulnerable parts of our antagonist's reasoning. That nothing useful is to be learned from Aristotle's logic I am far from thinking ; but I beheve that all which is useful in it might be redu- ced into a very narrow compass ; and 1 am decidedly of opinion, that wherever it becomes a serious and fa- vorite object of study, it is infinitely more likely to do harm than good. Indeed, I cannot help considering it
with affected obscurity ; and all to prove general propositions, whicli, when applied to particular instances, appear self-evident." Chap. III. sect. 1.
* Mr. Walker, author of the Coininentary on the Dublin Compendiuin of Logic.
t Such phrases, for example, as, 1. Fallacia accidentis. 2. A dictcT secundum quid, ad dictum simpliciter. 3. Jib ignorantia elenchi. 4. Anon causa pro causd. 5. Fallacia consequsntis. 6. Petltio principii. 7. Fallacia plurium interroga- tionum, S)'c.
I have mentioned those fallacies alone which are called by logicians Fallaci^B extra, dictionctn ; for as to those which are called Fallacies in dictione (such as the Fallacia cequivocationis, Fallacia amphibolia., Fallacia accenttis vel Pro- 7iu7iciaiionis, Fallacia a figurd dictionis, 4'c.) they are too contemptible to be deserving of any notice. — For some remarks on this last class of fallacies, See Note (IVi.)
VOL. IT. 27
210 ELEMENTS OF THE PHILOSOPHY
as strongly symptomatic of some unsoundness in a man's judgment, when I find him disposed (after all that has been said by Bacon and Locke) to magnify its impor- tance either as an inventive or as an argumentative Organ. Nor does this opinion rest upon theory alone. It is confirmed by all that I have observed, (if, after the example of the author last quoted, I may presume to mention the results of my own observations,) with re- spect to the intellectual characters of the most expert dialecticians whom I have happened to know. Among these, I can with great truth say, that although 1 recol- lect several possessed of much learning, subtlety, and ingenuity, I can name none who have extended by their discoveries the boundaries of science ; or on whose good sense I should conceive that much rehance was to be placed in the conduct of important affairs.
Some very high authorities, I must, at the same time, confess, may be quoted on the opposite side of the question ; among others, that of Leibnitz, unquestiona- bly one of the first names in modern philosophy. But, on this point, the mind of Leibnitz was not altogether unwarped ; for he appears to have early contracted a partiaHty, not only for scholastic learning, but for the projects of som^e of the schoolmen, to reduce, by means of technical aids, the exercise of the discursive faculty to a sort of mechanical operation ; — a partiality which could not fail to be cherished by that strong bias towards synthetical reasoning from abstract maxims, which char- acterizes all his philosophical speculations. It must be remembered too, that he lived at a period, when logical address was still regarded in Germany as an indispensa- ble accomplishment to all whose taste led them to the cultivation of letters or of science. Nor was this an accomplishment of easy acquisition ; requiring, as it must have done, for its attainment, a long course of laborious study, and, for its successful display, a more than ordi- nary vshare of acuteness, promptitude, and invention. To all which it may be added, that while it remained in vogue, it must have been peculiarly flattering to the vanity and self-love of the possessor ; securing to him, in every contest with the comparatively unskilful, an in-
OF THE HUMAN MIND. 211
fallible triumph. These considerations (combined with that attachment to the study of jurispradence which he retained through life) may, I think, go far to account for the disposition which Leibnitz sometimes shows to mag- nify a httle too much the value of this art. It is, be- sides, extremely worthy of remark, with respect to this eminent man, within what narrow hmi^s he circumscribes the province of the school logic, notwithstanding the favorable terms in which he occasionally speaks of it. The following passage in one of his letters is particularly deserving of attention, as it confines the utihty of syllo- gism to those controversies alone which are carried on in writing, and contains an explicit acknowledgment, that, in extemporaneous discussions, the use of it is equally nugatory and impracticable.
" I have myself experienced the great utility of the forms of logic in bringing controversies to an end ; and wonder how it has happened, that they should have been so often applied to disputes where no issue was to be expected, while their real use has been altogether over- looked. In an argument which is carried on viva voce, it is scarcely possible that the forms should continue to be rigorously observed ; not only on account of the tediousness of the process, but chiefly from the-difficulty of retaining distinctly in the memory all the different links of a long chain. Accordingly, it commonly hap- pens, that after one prosyllogism, the disputants betake themselves to a freer mode of conference. But if, in a controversy carried on in writing, the legitimate forms were strictly observed, it would neither be difficult nor disagreeable, by a mutual exchange of syllogisms and answers, to keep up the contest,* till either the point to be proved was completely estabhshed, or the disputant had nothing farther to allege in support of it. For the introduction, however, of this into practice, man}^ rules remain to be prescribed ; the greater part of which are to be collected from the practice of lawyers." f
* The words in the -original arc — " non ine;ratum nee ilifficile foret, mittendo remittendoque syllojTismos et respoiisiones tanuliu reciprocare strram, donee vel confeetuin sit quod probanduin crat, vel nihil ultia habeat quod afferat argumenta- tor."
t Leibnitz. Op. Tom. VI. p. 72. Edit. Dutens.
212 ELEMET^TS OF THE PHILOSOPHY
This concession, from so consummate a judge, I con- sider as of great consequence in the present argument. For my own part, if I were called on to plead the cause of the school logic, I should certainly choose to defend, as the more tenable of the two posts, that which Leib- nitz has voluntarily abandoned. Much might, I think, on this ground be plausibly alleged in its favor, in conse- quence of its obvious tendency to cultivate that inval- uable talent to a disputant, which Aristotle has so significantly expressed by the word d^^^tvoia ;* — a talent of vv^hich the utihty cannot be so forcibly pictured, as in the lively and graphical description given by John- son, of the inconveniences with which the want of it is attended.
" There are men whose powers operate only at leisure and in retirement, and whose intellectual vigor deserts them in conversation ; whom merriment confuses, and objection disconcerts ; whose bashfulness restrains their exertion, and suffers them not to speak till the time of speaking is past ; or whose attention to their own char- acter makes them unwilling to utter at hazard what has not been considered and cannot be recalled." f
The tendency, however, of scholastic disputations to cure these defects, it must not be forgotten, belongs to them only in common with all other habits of extempo- raneous debate ; and the question still recurs, Whether it would not be wiser to look for the remedy, in exercises more analogous to the real business of life ?
After having said so much in disparagement of the art of syllogizing, I feel it incumbent on me to add, that I would not be understood to represent a general ac- quaintance with it as an attainm^ent of no value, even in these times. The technical language connected with it is now so incorporated with all the higher departments
* Aristotle's definition of a,yx'^oi» turns upon one only of the many advantages which presence of mind bestows, in the manaoement of a viva voce dispute. "HS* ayx'i^oiK 'iffriv ilffro^toi Ti; It a.ffKi'ff-TM ^^ovc^ rou i^'iirov. (Sagacitarf est bona quajdam medii conjectatio brevissiiuo tempore.) Analyt. Post. Lib. i. cap. 34. I use the word, upon this occasion, in that extensive and obvious sense which its etymology suggests, and in which the corresponding Latin ])hrase is employed by Quinctilian. " In alter- catione opus est imprimis ingenio veloci ac mobili, animo prcesenti et acri. Non enim cogitandum, sed dicendum statim est." Quinct. Lib. vi. cap. 4.
t Life of Dryden.
OF THE HUMAN MIND. 213
of learning, that, independently of any consideration of its practical applications, some knowledge of its peculiar phraseology may be regarded as an indispensable prep- aration both for scientific and for literary pursuits.* To the philosopher, it must ever remain a subject of specu- lation peculiarly interesting, as one of the most singular facts in the history of the Human Understanding. The ingenuity and subtlety of the invention, and the compre- hensive reach of thought displayed in the systematical execution of so vast a design, form a proud and imper- ishable monument to the powers of Aristotle's mind, and leave us only to regret, that they were wasted upon objects of so little utilit}^ In no point of view, how^ev- er, does this extraordinary man appear to rise so far above the ordinary level of the species, as when we consider the dominion which he exercised, during so long a succession of ages, over the opinions of the most civihzed nations. Of this dominion the basis was chiefly laid in the syllogistic theory, and in the preparatory books on the Categories and on Interpretation ; a part of his works to which he was more indebted for his au- thority in the schools than to all the rest put together. Is it extravagant to conjecture, that Aristotle himself foresaw this ; and that, knowing how prone the learned are to admire what they do not comprehend, and to pride themselves on the possession of a mystical jargon, unin- telligible to the multitude, he resolved to adapt himself to their taste in those treatises which were destined to serve, in the first instance, as the foundation of his fame ?
* It was with grout pleasure I read the concluding paragraph of the introduction prefixed to a Coiiipend of Logic, sanctioned b}^ so learned a body as the University of Dublin.
" Utrum hjECce ars per se revera aliquera praestet usum, quidam dubitavere. Qiio- niam vcro in Authorum insigniorum scripiis, seepe occurrant termini Logici, hos ter- minos explicates habere, ideoqiie et ipsius artis partes pra^cipuas, omnino necessarium vidctur. H;cc itaque in scqucnti coinpendio eliicere est i)ropositum."
(Artis Logico? Compendium. In usum Juventutis Collegii Dubliniensis.)
The arrangement of tliis department of academical study, proposed by M. Prevost, of Geneva, seems to be very judiciously and happily imagined.
" Dialecticam, qua) ]ingu;c [ihilosophica) usum tradit, seorsim docere : et logicam, quae ralionis analysin instituit, ab onuii de verbis disputatione sejungere visum est.
" Logicam autemin trcs partes dividimus ; dc veritate, de errore, de methodo : ut haec mentis medicina, ad instarmediciucc corporis, exhibcat ordine statum naturalem, raorbos, curationcm."
See the preface to a short but masterly tract De Probabilitatc, printed at Geneva, in 1794.
214 ELEMENTS OF THE PHILOSOPHY
If such was really his idea, the event has shown hovv soundly he judged of human nature, in this grand exper- iment upon its w^eakness and ductility.*
That Aristoic's works have of late fallen into general neglect, is a common subject of complaint among his idolaters. It would be nearer the truth to say, that the number of Aristode's rational and enhghtened admirers was never so great as at the present moment. In the same proportion in which his logic has lost its credit, his ethics, his politics, his poetics, his rhetoric, and his natu- ral history, have risen in the pubhc estim.ation. No sim- ilar triumph of genius is recorded in the annals of phi- losophy : — To subjugate, for so m^any centuries, the minds of men, by furnishing employment (unproductive as it was) to their intellectual faculties, at a time when the low state of experimental knowledge did not supply more substantial materials for their reasonings ; — and af- terwards, when, at the distance of two thousand years, the light of true science began to dawn, to contribute so large a share to its growing splendor.
In the course of the foregoing animadversions on the syllogistic theory, I have proceeded on the supposition, that the whole glory of the invention belongs to Aristo- tle. It is proper, however, before dismissing the sub- ject, to take some notice of the doubts which have been
* The following historical sketch from Ludovicus Vives may serve to show, that the foregoing supposition is not altogether gratuitous. "A temporibus Platonis et Aristoteiis usque ad Alexandrum Aphrodisa3um, qui vixit Severo et ejus filiis Principi- bus, Aristoteles nominabatur magis, quam vel legebatur a doctis vel intelligebatur. Primus ille aggressus eum enarrare, et adjuvit studia multorum et ad alia in eo Philo- sopho quajrenda excitavit. Mansit tamen crebrior in manibus hominum et notior Plato, usque ad schojas in Gallia et Italia publice constitutas, id est, quamdiu Graeca et Latina lingua viguerunt. Postea vero quam theatrica) cceperunt esse disciplinse, omnisque earum fructus existimatus est, posse disputando fucum facere, et os obtu- lare, et pulverem ob oculos jacere, idque imperitissima peritia, et nominibus ad lubi- tum confictjs, accomodatiores ad rem visi sunt libri logici Aristoteiis et physici, relic- tis permultis. prceclaris ejus operibus : Platone vero, et quod ab eis non intellegere- tur, quamvis multo minus Aristoteles, et quod artificium videretur docere, ne nomin- ato quidem ; non quod minorera aut ineruditiorem putem Platone Aristotelem, sed quod ferenduin non est, Piatonem saactissimum philosophum prajteriri, et Aristote- lem ita legi, ut meliore rejectd parte, qua; retinetur id cogatw loqui, quod ipsiju- bent." Ludovic. Vives de Civ. Dei, L. viii. c. 10.
A remark similar to this is made by Bayle. " Ce qui doit etonner le plus les hora- mes sages, c'est quo lesprofesseurs se soient si furieusement entetez des hypotheses philosophiques d'vVristote. Si Ton avoit eu cette prevention pour sa poistique, et pour sa rlietorique, il y auroit moins de sujet de s'etonner ; mais, on s'est entete du plus foible de ses ouvreges, je veux dire, de sa logique et de sa physique." — (Bayle, Art. Jlristote.)
OF THE HUMAN MIND. 215
suggested upon this head, in consequence of the Hghts recently thrown on the remains of ancient science still existing in the East. Father Pons, a Jesuit missionary, was (I believe) the first person who communicated to the learned of Europe, the very interesting fact, that the use of the syllogism is, at this day, familiarly known to the Bramins of India ; * but this information does not seem to have attracted much attention in England, till it was corroborated by the indisputable testimony of Sir Wilham Jones, in his third discourse to the Asiatic So- ciety.f " It will be sufficient," he observes, "in this dissertation to assume, what might be proved beyond controversy, that we now hve among the adorers of those very deities who were worshipped under different names in old Greece and Italy, and among the profes- sors of those philosophical tenets, which the Ionic and Attic writers illustrated with all the beauties of their molodious language. On one hand we see the trident of Neptune, the eagle of Jupiter, the satyrs of Bacchus, the bow of Cupid, and the chariot of the Sun ; on the other, we hear the cymbals of Rhea, the songs of the Muses, and the pastoral tales of Apollo Nomius. In more retired scenes, in groves, and in seminaries of learning, we may perceive the Brahmans and the Ser- manes mentioned by Clemens, disputing in the forms of logic, or discoursing on the vanity of human enjoyments, on the immortahty of the soul, her emanation from the eternal mind, her debasement, wanderings, and final union with her source. The six philosophical schools, whose principles are explained in the Dersana Sastra, comprise all the metaphysics of the old academy, the Stoa and the Lyceum ; nor is it possible to read the Vedanta, or the many fine compositions in illustration of it, without believing that Pythagoras and Plato derived their sublime theories from the same source with the sages of India." J
* Lctties Eflifiaritcs et Curieuscs, Tome XXVI. (old edition.)— Tome XIV. edit, of 1781. The letter is dated 1740.
t Delivered in 178S.
j Works of Sir 'William Jones, Vol. I. p. 28.
In the same discourse, we are informed, that " the Hindoos have niunerons woiks on grammar, logic, rhetoric, music, which are extant and accessible." An examina-
216 ELEMENTS OF THE PHILOSOPHY
In a subsequent discourse, the same author mentions " a tradition, which prevailed, according to the well- informed author of the Dabistdn, in the Panjdb, and in several Persian provinces, that, among other Indian cu- riosities, which Callisthenes transmitted to his uncle, was a technical system of logic, which the Brahmans had communicated to the inquisitive Greek, and which the Mohammedan writer supposes to have been the ground- work of the famous Aristotehan method. If this be true," continues Sir W. Jones, — and none will dispute the justness of his remark, " it is one of the most inter- esting facts that I have met with in Asia." *
Of the soundness of the opinion concerning the ori- gin of the Greek philosophy, to which these quotations give the sanction of an authority so truly respectable, our stock of facts is as yet too scanty to enable us to form a competent judgment. Som.emay perhaps think, that the knowledge of the Aristotelian logic which ex- ists in India, may be sufficiently accounted for by the Mohammedan conquests ; and by the veneration in which Aristotle was held, from a very early period, by the followers of the prophet. f On the other hand, it
tion of these is certainly an object of literary curiosity, highly deserving of farther attention.
* Eleventh discourse, delivered in 1794.
•( " La philosophie Peripatetique s'est tellement etablie par tout, qu'on n'en lit plus d'autre par toutes les universitez Chretiennes. Celles meines, qui sont con- traintes de reqevoir les impostures de Mahomet, n'enscignent les sciences que con- formement aux principes du Lycee, auxquels lis s'attachent si fort, qu'Averioes, Al- farabius, Albumassar, et assez d'autres philosophes Arabes se sont souvent eloignes des sentiments de leur prophete, pour ne pas contredire ceux d'Aristote, que les Turcs ont en leur idiome Turquesque et en Arabe, comme Belon le rapporte." — La Motte le Vayer ; quoted by Bayle, Art. Aristote.
" L'Auteur, dont j'emprunte ces paroles, dit dans un autre volume, que, selon la relation d'Olearius, les Perses ont toutes les oeuvres d'Aristote, expliquees par beau- coup de comnientaires Arabes. ' Bergeron (dit il) remarque, dans son Traite des Tartares, qu'ils possedent les livres d'Aristote, traduits en leur langue, enseignant, avec autant de soumission qu'on pent faire ici, sa doctrine a Samarcand, universite du Grand Mogol, et a present ville capitale du Rcyaume d'Usbec.' "
In the 8th volume of the Asiatic Re;>earches, there is a paper by Dr. Balfour, con- taining some curious extracts (accompanied with an English version) from a Peisian translation of an Arabic 'r realise, entitled (he " Essence of Logic." In tbe intro- duction to these extracts, Dr. Balfour mentions it as an indisputable fact, that " the system of logic, generally ascribed to Aristotle, constitutes, at this time, the logic of all the nations of Asia who profess the Mahojnetan faith ; " and it seems to have been with a view of rendering this fact still more palpable to common readers, that the author has taken tVie tiouble to translate, through the medium of the Per- sian, the Arabic original ; from vvhicli language the knowledge of Aristotle's logic, possessed by the orientals, is supposed to have been derived.
OF THE HUMAN MIND. 217
must be acknowledged, that this part of Aristotle's work contains some intrinsic evidence of aid borrowed from a more ancient school. Besides that imposing appear- ance which it exhibits of systematical completeness in its innumerable details ; and which we can scarcely suppose that it could have received from the original inventor of the art, there is a want of harmony or unity in some of its fundamental principles, which seems to betray a com- bination of different and of discordant theories. I al- lude more particularly to the view which it gives of the nature of science and of demonstration, compared with Aristotle's well-known opinions concerning the natural progress of the mind in the acquisition of knowledge. That the author of the Organon was fully aware of an incongruity so obvious, there can be Uttle doubt ; and it was not improbably with a view to disguise or to conceal it, that he was induced to avoid, as much as possible, every reference to examples ; and to adopt that abstract and symbolical language which might divert the atten- tion from the inanity of his demonstrations, by occupy- ing it in a perpetual effort to unriddle the terms in which they are expressed.
Nor does there seem to be any thing in these sugges- tions (which I hazard with much diffidence) inconsist- ent with Aristotle's own statement, in the concluding chapter of the book of Sophisms. This chapter has in- deed (as far as I know) been universally understood as advancing a claim to the whole art of syllogism ; * but I must acknowledge, that it appears to me to admit of a very fair construction, without supposing the claim to comprehend all the doctrines delivered in the books of Analytics. In support of this idea, it may be remarked, that while Aristotle strongly contrasts the dialectical art, as taught in the preceding treatise, with the art of dis-
* " The conclusion of this treatise," the book of Sophisms, " out!;ht not to be overlooked : it manifestly relates, not to the present treatise only, but also to the whole Analytics and Topics of the author." — Reid's Analysis, &,c. Chap. v. Sect, iii.
If I were satisfied that this observation is just, I should think that nothing short of the most irresistible evidence could be reasonably opposed to the direct assertion of Aristotle. It is quite iriconccival)lc, that he should have wilfully concealed or mis- represented the truth, at a period when there could not fail to be many philosopher? in Greece, both able and willing to expose the decepliou.
VOL II. 28
218 ELEMENTS OF THE PHILOSOPHY
putation as previously practised in Greece, he does not make the shghtest reference to the distinction between demonstrative and dialectical syllogisms, or to those doc- trines with respect to demonstration and science, which accord so ill with the general spirit of his philosophy. It does not seem, therefore, to be a very mireasonable supposition, that to these doctrines (with which, for many reasons, he might judge it expedient to incorporate his own inventions and innovations) he only gave that systematical and technical form, which, by its pecuhar phraseology and other imposing appendages, was calcu- lated at once to veil their imperfections, and to gratify the vanity of those who should make them objects of study. It is surely not impossible, that the syllogistic theory may have existed as a subject of abstract specu- lation, long before any attempt was made to introduce the syllogism into the schools as a weapon of controver- sy, or to prescribe rules for the skilful and scientific management of 2i-vivd voce dispute.
It is true, that Aristotle's language, upon this occa- sion, is somewhat loose and equivocal ; but it must be remembered, that it was addressed to his contempora- ries, who were perfectly acquainted with the real extent of his merits as an inventor ; and to whom, accordingly, it was not necessary to state his pretensions in terms more definite and explicit.
I shall only add, that this conjecture (supposing it for a moment to be sanctioned by the judgment of the learn- ed) would still leave Aristode in complete possession of by far the most ingenious and practical part of the scho- lastic logic ;* while, at the same time, — should future
• This was plainly the opinion of Cicero : " In hacaite," he observes, speaking of the dialectical art, as it was cultivated by the Stoics, — " in hac arte, si 7nodo est heec ars, nullum est prajceptum quomodo vernm inveniatur, sed tantum est quomodo ju- dicetur." — And in a few sentences after, " Quare istam artem totam dimittamus, quae in excogitandis argumentis muta nimium est, in judicandis nimium loquax." (De Orat. Lib. ii. 86, 87.) The first sentence is literally applicable to the doctrine of syllogism considered theoretically : the second contrasts the inutility of this doctrine with the importance of such subjects as are treated of in Aristotle's Topics.
Whether Cicero and Quinctilian did not overrate the advantages to be derived from the study of the Loci as an organ of invention is a question altogether foreign to our present inquiries. That it was admirably adapted for those argumentative and rhetorical displays which were so highly valued in ancient times, tliere can be no doubt, after what these great masters of oratory have written on the subject ; but it does not follow, that, in the present state of society, it would reward the labors of
OF THE HUMAN P^IND. 219
researches verify the suspicions of Sir William Jones and others, that the first rudiments of the art were im- ported into Greece from the East, — it would contribute to vindicate his character against that charge of plagia- rism, and of unfairness tow^ards his predecessors, which has been admitted even by some who speak with the most unbounded reverence of his intellectual endow- ments.
From the logic of Aristotle, I now proceed to that of Lord. Bacon ; a logic which professes to guide us sys- tematically in investigating the lav/s of nature, and in ap- plying the knowledge thus acquired, to the enlargement of human power, and the augmentation of human hap- piness.
Of some of the fundamental rules by which this mode of philosophizing is more pecuharly distinguished, I in- tend to treat at considerable length ; — directing my at- tention chiefly to such questions as are connected with the theory of our intellectual faculties. In this point of view, the author has left much to be supplied by his suc- cessors ; the bent of his own genius having fortunatel}'' determined him rather to seize, by a sort of intuitive penetration, great practical results, than to indulge a comparatively sterile curiosity, by remounting to the first sources of experimental knowledge in the principles and laws of the human frame. It is to this humbler task that I propose to confine myself in the sequel. To fol- low him through the details of his Method, would be in- consistent with the nature of my present undertaking.
those who wish to cultivate either the eloquence of the bar, or that which leads to distinction in our popular assemblies.
220 ELEMENTS OF THE PHILOSOPHY
CHAPTER FOURTH.
OP THE METHOD OP INQUIRY POINTED OUT IN THE EXPERIMENTAL OR INDUCTIVE LOGIC,
SECTION I.
Mistakes of the Ancients concerning the proper object of Philosophy. — Ideas of Ba- con on the same subject. — Inductive Reasoning. — Analysis and Synthesis. — Es- sential difference between Legitimate and Hypothetical Theories.
I HAVE had occasion to observe more than once, in the course of the foregoing speculations, that the ob- jectof physical science is not to trace necessary con- nexions, but to ascertain constant conjunctions ; not to investigate the nature of those efficient causes on which the phenomena of the universe ultimately de- pend, but to examine with accuracy what the phenom- ena are, and what the general laws by which they are regulated.
In order to save repetitions, I here beg leave to refer to some observations on this subject in the first volume. I request more particularly the reader's attention to what I have said, in the second section of the first chap- ter, on the distinction between physical and efficient causes ; and on the origin of that bias of the imagina- tion which leads us to confound them under one com- mon name. That, when we see two events constantly conjoined as antecedent and consequent, our natural apprehensions dispose us to associate the idea of causa- tion or efficiency with the former, and to ascribe to it that power or energy by which the change was produ- ced, is a fact obvious and unquestionable ; and hence it is, that in all languages, the series of physical causes and eff"ects is metaphorically likened to a chain, the finks of which are supposed to be indissolubly and ne- cessarily connected. The shghtest reflection, at the same time, must satisfy us that these apprehensions are inconsistent, and even absurd ; our knowledge of phys-
OF THE HUMAN MIND. 221
ical events reaching no farther than to the laws which regulate their succession ; and the words poioer and energy expressing attributes not of Matter but of Mind. It is by a natural bias or association somewhat similar (as I have remarked in the section above-mentioned) that we connect our sensations of color, with the pri- mary quaUties of body.*
This idea of the object of physical science (which may be justly regarded as the ground-work of Bacon's JYovum Organon) differs essentially from that which was entertained by the ancients ; according to whom " Phi- losophy is the science of causes." If, indeed, by causes they had meant merely the constant forerunners or an- tecedents of events, the definition would have coincided nearly with the statement which I have given. But it is evident, that by causes they meant such antecedents as were necessarily connected with the effects, and from a knowledge of which the effects might be fore- seen and demonstrated : And it was owing to this confusion between the proper objects of physics and of metaphysics, that, neglecting the observation of facts exposed to the examination of their senses, they vainly attempted, by synthetical reasoning, to deduce as neces- sary consequences from their supposed causes, the phe- nomena and laws of nature. — " Causa ea est," says Cicero, " quae id efficit cujus est causa. Non sic causa intelligi debet, ut quod cuique antecedat, id ei causa sit ; sed quod cuique efficienter antecedat. — Itaque dicebat Carneades ne Apollinem quidem posse dicere futura, nisi ea, quorum causas natura ita contineret, ut ea fieri
* Were it not for this bias of the imagination to identify efficient with physical causes, the attention would be continually diverted from the necessary business of life, and the useful exercise of our faculties suspended, in a fruitless astonishment at that hidden machinery, over which nature has drawn an impenetrable veil. To prevent this inconvenient distraction of thought, a farther provision is made in that gradual and imperceptible process by which the changes in the state of the Universe are, in gene- ral accomplished. If an animal or a vegetable were brought into being before our eyes, in an instant of time, — the event would not be in itselt'morc wonderful than their slow growth to maturity from an embryo, or from a seed. But, on the former suppo- sition, there is no man who would not perceive and acknowledge the immediate agency of an intelligent cause ; whereas, according to the actual order of things, the effect steals so insensibly on the observation, that it excites little or no curiosity, ex- cepting in those who possess a sufficient degree of reflection to contrast the present state of the objects around them, with their first origin, and with the progressive stages of their existence.
222 ELEMENTS OF THE PHILOSOPHY
necesse esset. Causis enim efficientibus quamque rem cognitis, posse denique sciri quid fiiturum esset." *
From this disposition to confound efficient with phys- ical causes, may be traced the greater part of the theo- ries recorded in the history of philosophy. It is this which has given rise to the attempts, both in ancient and modern times, to account for all the phenomena of moving bodies by means of impulse ; f and it is this also which has suggested the simpler expedient of explaining them by the agency oi minds united with the particles of matter.J As the communication of motion by ap-
* De Fato, 48, 49. The language of Aristotle is equally explicit. 'jEmaiaa&ai 8e oiofisSa e'naarov anXag, alka fii) TovaocpiaTty.ov tqotioVjTov ttUTCc GVj.iSsCijy.og, orav ttjv t alxlav oiw^s&a yivaatcsiv, di 7jv to ngayfid ioTiv, OTt ixdi'ov alxltt taxi, xal fi7] ivds;^sxaL xovx' allcog i';(siv. " Scire autem putamus unamquamque rem simpliciter, non sophistico modo, id est, ex acci- denti, cum putamus causam cognoscere, propter quam res est, ejus rei causam esse, nee posse earn aliter se habere." — Analyt. Poster. Lib. i. cap. 2.
Nothing;, however, can place in so strong a light Aristotle's idea of the connexion between physical causes and effects, as the analogy, which he conceived it to bear to the connexion between the links of a mathematical chain of reasoning. Nor is this mode of speaking abandoned by his modern followers. " To deny a first cause," says Dr. Gillies, " is to deny all causation : to deny axioms is, for the same reason, to deny all demonstration." (Vol. L p. 108.) And in another passage, " We know a mathematical proposition, when we know the causes that make it true. In de- monstration, the premises are the causes of the conclusion, and therefore prior to it. We cannot, therefore, demonstrate things in a circle, supporting the premises by the conclusion ; because this would he to suppose, that the one proposition could be both prior and posterior to the other." (Ibid. p. 96.) (Can one mathematical theorem be said to be prior to another in any other sense, than in respect of the order in which they are first presented to our knowledge ?)
f See Philosophy of the Human Mind, Vol. 1. Chap. i. sect. 2.
With respect to the connexion between inpulse and motion, I have the'misfortune to differ from my very learned and highly respected friend M. Prevost of Geneva ; whose opinions on this point may be collected from the two following sentences. " La cause diff ere du simple signe precurseur, par sa force, ou son energie produc- tive.— L'impulsion est un phenomene si commun, sounds a des lois si bien dis- cutees, et si universelles, que toute cause qui s'y reduit semble former une classe eminente, et meriter seule le nom d\dgent." Essais de Philosophie, Tome II. pp. 174, 175.
I have read with great attention all that M. Prevost has so ingeniously urged in vindication of the theory of his illustrious countryman Le Sage ; but without expe- riencing that conviction which I have in general received from his reasonings. The arguments of Locke and Hume on the other side of the question appear to my judg- ment, the longer I reflect on them, the more irresistible ; not to mention the power- ful support which they derive from the subsequent speculations of Boscovich. See Locke's Essay, B, II. Chap. 2.3. § 28, 29, and Hume's Essay on JVecessary Con- nexion, Part I.
In employing the word misfortune, on this occasion, I have no wish to pay an un- meaning compliment ; but merely to express the painful diffidence which I always feel in my own conclusions, when they happen to be at variance with those of a writer equally distinguished by the depth and by the candor of his philosophical researches.
For some additional illustrations of M. Prevost's opinion on this subject, see Ap- pendix.
X To this last class of theories may also be referred the explanations of physical
or THE HUMAN MIND. 223
parent impulse, and our own power to produce motion by a volition of the mind, are two facts, of which, from our earliest infancy, we have every moment had experience ; we are apt to fancy that we understand perfectly the nexus by which cause and effect are here necessarily conjoined ; and it requires a good deal of reflection to satisfy us that, in both cases, we are as completely in the dark, as in our guesses concerning the ultimate cau- ses of magnetism or of gravitation. The dreams of the Pythagorean school, with respect to analogies or harmo- nies between the constitution of the universe, and the mathematical properties of figures and of numbers, were suggested by the same idea of necessary connexions existing among physical phenomena, analogous to those which link together the theorems of geometry or of arithmetic ; and by the same fruitless hope of penetrat- ing, by abstract and synthetical reasoning, into the mysterious processes of nature.
Beside this universal and irresistible bias of the imagi- nation, there were some pecuharities in the genius and scientific taste of Aristotle, which gave birth to various errors calculated to mislead his followers in their physi- cal inquiries. Among these errors may be mentioned, as one of the most important, the distinction of causes (introduced by him) into the efficient, the material, the formal, and the final ; — a distinction which, as Dr. Reid justly observes, amounts only (like many other of Aris- totle's) to an explanation of the different meanings of an ambiguous word ; and which, therefore, was fitter for a dictionary of the Greek language, than for a philosophical treatise.* Of the effect of this enumera- tion of causes in distracting the attention, some idea may be formed, when it is recollected, that, according to Aristotle, it is the business of the philosopher to rea- son demonstratively from all the four.f ^
The same predilection of Aristotle for logical or rath- er verbal subtilties, encouraged, for many ages, that
phenomena by such causes as sympathies, antipathies, Nature's honor of a void, &c. and other phrases borrowed by analogy from the attributes of animated beings.
* Analysis of Aristotle's Logic. Chap. ii. sect. 3.
t Nat. Auscult. Lib. ii. cap. 7.
224 ELEMENTS OF THE' PHILOSOPHY
passion for fanciful and frivolous distinctions, which is so adverse to the useful exercise of the intellectual powers. Of its tendency to check the progress of physical knowledge, the reader will be enabled to judge for him- self, by perusing the 16th and 17th chapters of Mr. Harris's Philosophical Arrangements ; which chapters contain a very elaborate and not inelegant view of what the author is pleased to call the ancient Theory of Mo- tion. A later writer of the same school has even gone so far as to assert, that it is such researches alone which merit the title of the Philosophy of Motion : and that the conclusions of Galileo and of Newton, amounting (as they unquestionably do) to nothing more than a classification and generalization of facts, deserve no higher an appellation than that of JYatural History*
In contrasting as I have now done, the spirit of Bacon's mode of philosophizing with that of the ancients, I do not mean to extol his own notions concerning the rela- tion of cause and effect in physics, as peculiarly correct and consistent. On the contrary, it seems to me evi- dent, that he was led to his logical conclusions, not by any metaphysical analysis of his ideas, but by a convic- tion founded on a review of the labors of his predeces- sors, that the plan of inquiry by which they had been guided must have been erroneous. If he had perceived as clearly as Barrow, Berkeley, Hume, and many others, have done since his time,f that there is not a single instance
* Ancient Metaphysics, passim. — The censure bestowed on Aristotle's Physics, by the authors of the French Treatise of Logic, entitled i'^ri de Penser, is judicious and discriminating. " Le principal defaut qu'on y pent trouver, n'est pas qu'elle soit fausse, mais c'est au contraire qu'elle est trop vraie, et qu'elle ne nous apprend que des choses qu'il est impossible d'ignorer."
t In alluding to the relation between cause and effect, Bacon sometimes indulges his fancy in adopting metaphorical and popular expressions. " Namque in limine Philosophic, cum secundae causae, tanquam sensibus proximse, ingerant se menti hu- manse, mensque ipsa in illis heereat, atque commoretur, oblivio primao causee obrepere possit. Sin quis ulterius pergat, causarumque dependentium seriem et concatena- tionem, atque opera providentiaj intueatur, tunc secundum poctarum mythologiam, facile creUct, su7nniunnaturalis catena; annulum pedi soVii. Jovis affigi." — De Aug. Scient. Lib. i. This is very nearly the language of Seneca. " Cum fatum nihil aliud sit quam series implexa causarum, ille est prima omnium causa ex qua ceeterse pen- dent."
In other instances, he speaks (and, in my opinion, much more philosopically) of the " opus quod operatur Deus a primordio usque ad fincm ; " a branch of knowl- edge which he cxpresly describes as placed beyond the examination of the human faculties. But this speculation, although the most interesting that can employ our tlioughts, has no immediate connexion with the logic of physical science. — See Note (N.)
OF THE HUMAN MIND. 225
in which we are able to trace a necessary connexion be- tween two successive events, or to explain in what man- ner the one follows from the other as an infalhble conse- quence, he would have been naturally led to state his prin- ciples in a form far more concise and methodical, and to lay aside much of that scholastic jargon by which his mean- ing is occasionally obscured. Notwithstanding, however, this vagueness and indistinctness in his language, his com- prehensive and penetrating understanding, enlightened by a discriminating survey of the fruitless inquiries of for- mer ages, enabled him to describe, in the strongest and happiest terms, the nature, the object, and the limits of philosophical investigation. The most valuable part of his works, at the same time, consists, perhaps, in his re- flections on the errors of his predecessors ; and on the various causes which have retarded the progress of the sciences and the improvement of the human mind. That he should have executed, with complete success, a system of logical precepts for the prosecution of experimental inquiries, at a period when these were, for the first time, beginning to engage the attention of the curious, was al- together impossible ; and yet in his attempt towards this undertaking, he has displayed a reach of thought and a justness of anticipation, which, when compared with the discoveries of the two succeeding centuries, seem fre- quently to partake of the nature of prophecy. " Prout Physicamajora indies incrementa capiet, et nova axiom- ata educet, eo mathematicae nova opera in multis indige- bit, et plures demum fient mathematicae mixtae." * Had he foreseen all the researches of the Newtonian school, his language could not have been more precise or more decided.
" Bacon," it has been observed by Mr. Hume, " was
* De Aug. Sclent. Lib. iii. Cap. vi.
By the word Axiom, Bacon means a general principle obtained by induction, from which we may safely proceed to reason synthetically. It is to be regretted, that he did not make choice of a less equivocal term, as Newton has plainly been misled by his example, in the very illogical application of this name to the laws of motion, and to those general /ac^s which serve as the basis of our reasonings in catoptrics and di- optrics. (See pp. 29, .30, of this volume.)
I shall take this opportunity to remark, that Newton had evidently studied Bacon's writings with care; and has followed them, (sometimes too implicitly,) in his logic- al phraseologj'. Of this remark various other proofs will occur afterwards.
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226 ELEMENTS OF THE PHILOSOPHY
ignorant of geometry ; and only pointed out at a dis- tance the road to true philosophy." — " As an author and philosopher," therefore, this historian pronounces him, " though very estimable^ yet inferior to his contempora- ry Galileo, perhaps even to Kepler." * The parallel is, by no means, happily imagined ; inasmuch as the indi- viduals whom it brings into contrast, directed their at- tention to pursuits essentially different, and v^^ere char- acterized by mental powers unsusceptible of comparison. As a geometer or astronomer. Bacon has certainly no claim whatever to distinction ; nor can it even be said, that, as an experimentalist, he has enriched science by one important discovery ; but, in just and enlarged con- ceptions of the proper aim of philosophical researches, and of the means of conducting them, how far does he rise above the level of his age ! Nothing, indeed, can place this in so strong a light, as the history of Kepler himself; unquestionably one of the most extraordinary persons who adorned that memorable period, but deep- ly infected, as his writings show, with prejudices bor- rowed from the most remote antiquity. The mysterious theories of the Pythagoreans which I formerly mention- ed, and which professed to find in the mathematical properties of figures and numbers, an explanation of the system of the universe, seem, from one of his earher publications, to have made a strong impression on his imagination ; f while at an after period of hfe he indulged
♦History of England. Appendix to tlie reign of James L
+ Mysterium Cosmographicum, de adrairabili proportione orbium coelestium de- que causis coelorum numeri, magnitudinis, motuumque periodicorum genuinis et propriis, demonstraium per quinque regularia corpora Geometrica, 1598. Kepler informs us, that he sent a copy of this book to Tycho Brahe ; the subject of whose answer he has had the candor to record. " Argumentum literarum Brahei hoc erat, ut suspensis speculationibus a priori descendentibus, animum potius ad observationes, quas simul offerebat, considerandas adjicerem, inque iis primo gradu facto, postea denium ad causas ascenderem." — To this excellent advice the subsequent discove- ries, which have immortalized the name of Kepler, may (in the opinion of Mr. Mac- laurin) be ascribed. Account ofJVtwtoii's Discoveries, Book \. Chap. iii.
An aphorism of Lord Bacon, concerning the relation which Mathematics bears to Natural Philosophy, exhibits a singular contrast to the aim and spirit of the Myste- rium Cosmographicum. " In secunda schola Platonis, Procli et aliorum, Natura- lis Philosophia infccta et corrupta fuit, per Mathcmaticam ; qum Philosophiam J\raturalem terminare, non generare aut procreare debet.'' (Nov. Org. Lib. i. Aphor. xcvi.) — The very slender knowledge of this science which Bacon probably possessed, renders it only the more wonderful, that he should have been so fortunate in seizing, or rather in divining, its genuine use aud application in physical re- searches.
OF THE HUMAJY MIND. 227
himself in a train of thinking about the causes of the planetary motions, approaching to the speculations of the late learned author of Ancient Metaphysics.
" Nego," says he, in his Commentaries on the planet Mars, " ullum motum perennem 7ion rectum a Deo con- ditum esse praesidio mentali destitutum. — Hujus motoris manifestum est duo fore munia ; alterum ut facultate pol- leat transvectandi corporis ; alterum ut scientia proeditus sit inveniendi circularem limitem per illam puram auram setheriam nullis hujusmodi regionibus distinctam." — In another part of his work, he seriously gives it as his opinion, that the minds of the planets must have a power of making constant observations on the sun's apparent diameter, that they may thereby be enabled so to regu- late their motions, as to describe areas proportional to the times. " Credibile est itaque, si qua facultate preediti sint 7notores illi observandae hujus diametri, earn tanto esse argutiorem quam sunt ocuh nostri, quanto opus ejus et perennis motio nostris turbulentis et confusis negotiis est constantior.
" An ergo binos singulis planetis tribues oculos Kep- lere ! Nequaquam. Neque est necesse. Neque enim ut moveri possint, pedes ipsis atque alse sunt tribuen-
From such extravagancies as these, how wide the transition to the first sentence of the Novum Organon !
The ignorance of geometry with which Mr. Hume reproaches Bacon, will not ap- pear surprising, when it is considered, that, sixty years after the time when he left Cambridge, mathematical studies were scarcely known in that University. For this fact we have the direct testimony of Dr. Wallis, (afterwards Astronomical Professor at Oxford,) who was admitted at Emanuel College, Cambridge, in 1632 ; and who informs us, that at that time, " Mathematics were scarce looked upon as Academical Studies, but rather Mechanical ; as the business of traders, merchants, seamen, car- penters, surveyors of land, and almanack-makers in London." — " Among more than two hundred Students in our College, I do not know of any two who had more than I, (if so much,) which was then but little ; and but very few in that whole Univer- sity. For the study of Mathematics was then more cultivated in London than in the Universities."
(See an Jlccount of so?ne passages in the Life ofJDr. Wallis, written by himself when he was upwards of eighty, and pubHshed by Hearne, in his edition of Lang- toft's Chronicle.)
The same writer, from whom this information is derived, lived to sec not only the institution of the Royal Society of London, hut the illustration which the University of Cambridge derived from the names of Barrow and of Newton ; and even survived, for seventeen years, the publication of Newton's Principia. — That Lord Bacon's writings contributed, more than any other single cause, to give this sudden impulse to science in England, it is impossible to doubt.
226 elements of the philosophy
" Homo Nature minister et interpres tantum fa- cit et intelligit quantum de nature ordine re vel mente observaverit, nec amplius scit aut po- TEST."
In calling man the interpreter of Nature, Bacon had plainly the same idea of the object of physics, which I at- tempted to convey, when I said, that what are commonly called the causes of phenomena, are only their establish- ed antecedents or signs ; and the same analogy which this expression suggests to the fancy, has been enlarged upon at considerable length, by the inventive and philo- sophical Bishop of Cloyne, as the best illustration which he could give of the doctrine in question. It would be difficult, indeed, to select another equally apposite and luminous ; and not less difficult to find an author equally qualified to avail himself of its aid. I shall make no apology, therefore, for borrowing his words.
" There is a certain analogy, constancy, and uniformi- ty in the phenomena or appearances of nature, which are a foundation for general rules ; and these are a grammar for the understanding of nature, or that series of effects in the visible world, whereby we are enabled to foresee what will come to pass in the natural course of things. Plotinus observes, in his third Ennead, that the art of presaging is, in some sort, the reading of natu- ral letters denoting order ; and that so far forth as anal- ogy obtains in the universe, there may be vaticination. And in reality, he that foretells the motions of the plan- ets, or the effects of medicines, or the results of chemical or mechanical experiments, may be said to do it by natural vaticination.
** We know a thing when we understand it, and we understand it when we can interpret or tell what it sig- nifies. Strictly the sense knows nothing. We perceive, indeed, sounds by hearing, and characters by sight ; but we are not therefore said to understand them. After the same manner, the phenomena of nature are alike visible to all ; but all have not ahke learned the connex- ion of natural signs, or understand what they signify, or know how to vaticinate by them. There is no question, says Socrates in Themtcto, concerning that which is
OF THE HUMAJV MIND. 229
agreeable to each person, but concerning what will in time to come be agreeable, of which all men are not equally judges. He that foreknoweth what will be, in every kind, is the wisest. According to Socrates, you and the cook may judge of a dish on the table equally well ; but while the dish is making, the cook can better foretell what will ensue from this or that manner of com- posing it. Nor is this manner of reasoning confined only to morals or politics, but extends also to natural science.
" As the natural connexion of signs with the things signified is regular and constant, it forms a sort of ration- al discourse, and is therefore the immediate effect of an intelligent cause." *
The same language with respect to the office and use of philosophy has been adopted by Reid, and at a much earher period by Hobbes ; and it was evidently by a similar train of thinking (as I already hinted) that Bacon was led to call philosophy the interpretation of nature.
According to the doctrine now stated, the highest, or rather the only proper object of Physics, is to ascertain those estabhshed conjunctions of successive events, which constitute the order of the Universe ; to record the phenomena which it exhibits to our observations, or which it discloses to our experiments ; and to refer these phenomena to their general laws. While we are apt to fancy, therefore, (agreeably to popular conceptions and language,) that we are investigating efficient causes, we are, in reality, only generalizing eff'ects ; and when we advance from discovery to discovery, we do nothing more than resolve our former conclusions into others still more comprehensive. It was thus that Galileo and TorricelH proceeded in proving that all terrestrial bodies gravitate towards the earth ; and that the apparent levity of some of them is merely owing to the greater gravity of the atmosphere. In establishing this important con- clusion, they only generalized the law of gravity, by
* Siris : or a Chainof Philosophical Reflections and Inquiries concerning the Vir- tues of Tar- Water. §§ 252, 253, 254.
230 ELEMEJfTS OF THE PHILOSOPHY
reconciling with it a variety of seeming exceptions ; but they threw no light whatever on that mysterious power, in consequence of which all these phenomena take place. In like manner, when Newton showed that the same law of gravity extends to the celestial spaces ; and that the power by which the moon and planets are re- tained in their orbits, is precisely similar in its effects to that which is manifested in the fall of a stone, — he left the efficient cause of gravity as much in the dark as ever, and only generalized still farther the conclusions of his predecessors. It was, indeed, the most astonishing and subhme discovery which occurs in the history of science ; a discovery not of less consequence in Natural Religion than in Natural Philosophy, — and which at once demon- strated (in direct contradiction to all the ancient sys- tems) that the phenomena exhibited by the heavenly bodies, are regulated by the same laws which fall under our observation on the surface of this globe. Still, how- ever, it was not the discovery of an efficient cause, but only the generalization of a fact.*
From what has been said, it is sufficiently evident, that the ultimate object which the philosopher aims at in his researches, is precisely the same with that which every man of plain understanding, however uneducated, has in view, when he remarks the events which fall under his observation, in order to obtain rules for the future regulation of his conduct. The more knowledge of this kind we acquire, the better can we accommo- date our conduct to the estabhshed course of things ;
* " The laws of attraction and repulsion are to be regarded as laws of motion, and these only as rules or methods observed in the production of natural effects, the effi- cient and final causes whereof are not of mechanical consideration. Certainly if the explaining a phenomenon be to assign its proper efficient and final cause, it should seem the mechanical philosophers never explained any thing ; their jirovince being only to discover the laws of nature ; that is, the general rules and methods of motion ; and to account for particular phenomena, by reducing them under, or showing their conformity to, such general rules." — Berkeley's Siris.
" The words attraction and repulsion may, in compliance with custom, be used where, accurately speaking, motion alone is meant." — " Attraction cannot produce, and in that sense account for, the phenomena ; being itself one of the phenomena produced and to bo accounted for." — Ibid.
For some very important as well as refined observations on the respective provinces of physics and of metaphysics in the theory of motion, see a Tract by Dr. Berkeley, first published at London in 172L The title is De Motu ; sive de MotlU principio et naturd, ct de causd communicationis Motuum.
OF THE HUMAN MIND. 231
and the more are we enabled to avail ourselves of natural agents as instruments for accomplishing our purposes. It is with truth, therefore, that Bacon so often repeats, that " every accession which Man gains to his knowl- edge is also an accession to his power ; and extends the limits of his empire over the world which he inhab- its."
The knowledge of the philosopher differs from that information which is the fruit of common experience, not in kind, but in degree. The latter is, in general, confined to such facts as present themselves spontane- ously to the eye : and so beautifully is the order of na- ture adapted to our wants and necessities, that while those laws in which we are most deeply interested are obtruded on our notice from our earliest infancy, others are more or less removed from the immediate examina- tion of our senses, to stimulate curiosity, and to present a reward to industry. That a heavy body, when unsup- ported, will fall downwards ; that a painful sensation would be felt, if the skin were punctured or lacerated ; that life might be destroyed by plunging into a river, or by throwing one's self headlong from a precipice, are facts as well known to the savage as to the philosopher, and of which the ignorance would be equally fatal to both. For acquiring this, and other information of the same sort, httle else is requisite than the use of our per- ceptive organs : And, accordingly, it is familiar to every man, long before the period that, in his maturer years, falls under the retrospect of memory.
For acquiring a knowledge of facts more recondite, observation and experiment must be employed ; * and,
• To these Condorcet adds calculation. " Bacon," he observes, " has revealed the true method of studj'ing nature, by employing the three instruments with which she has furnished us for the discovery of her secrets, — observation, experiment, and calculation." — (Tableau Historique des Progrts de V Esprit Humain.) In this enumeration, it appears to me that there is a great defect, in point of logical distinct- ness. Calculation is certainly not an instrument of discovery at all analogous to ex- periment and observation : it can accomplish nothing in the study of nature, till they have supplied the materials ; and is, indeed, only one of the many arts by which \ve are enabled to give a greater degree of accuracy to their results. The use of optical glasses ; of the thermometer and barometer ; of time-pieces ; and of all the various instruments of practical geometry, might, with equal propriety, have been added to the list.
The advantages, at the same time, which Natural Philosophy has derived, in mod- ern times, from the arithmetical precision thus given to scientific details, must be al-
232 ELEMEJVTS OF THE PHILOSOPHY
accordingly, the use of these media forms one of the characteristical circumstances by which the studies of the philosopher are distinguished from the experience of the multitude. How much the stock of his informa- tion must thereby be enlarged is sufficiently manifest. By habits of scientific attention, his accuracy as an ob- server is improved ; and a precision is given to his judg- ment, essentially different from the vagueness of ordinary perception : by a combination of his own observations with those made by others, he arrives at many conclu- sions unknown to those who are prevented, by the ne- cessary avocations of human life, from indulging the impulse of a speculative curiosity ; while the experi- ments which his ingenuity devises, enable him to place nature in situations in which she never presents herself spontaneously to view, and to extort from her secrets over which she draws a veil to the eyes of others.*
lowed to be immense ; and they would be well entitled to an ample illustration in a system of inductive logic. To those who may wish to prosecute the subject in this view, I would beg leave to susigest the word jnensuration as equally precise and more comprehensive, than the word calculation, as employed by Condorcet.
* These primary and essential organs of accurate information, {observation and ex- periment,) which furnish the basis to the whole superstructure of physical science, are very clearly and concisely described by Boscovich, in one of his notes on Stay's poem,i)e Systemate Mundi. " Observationes fiunt spectando id quod natura per se ipsam sponte exhibet : hujusmodi sunt observationes pertinentes ad astronomiam et historiam naturalem. Experimeiifa fiunt ponendo naturam in eas circumstantias, in quibus debeat agere et nobis ostendere id quod quEerimus, quod pertinet ad physicam experimentalem. Porro et ferro et igni utimur, ac dissolvimus per vim compagem corporum, potissimum in chemia, et naturam quodammodo velut torquentes cogimus revelare sua secreta."
I have elsewhere remarked, that the physical discoveries of the moderns have been chiefly owing to the skilful contrivance and conduct of experiments ; and that this method of interrogating nature was, in a great measure, unknown to the ancients. {Philosophical Essays, 4to. p. xxxv.) Even Aristotle himself is acknowledged, by one of his most devoted admirers, to have confined himself chiefly to observation ; and is, on this very ground, proudly contrasted with the empirical experimentalists of the present times. " Aristotle," says Dr. Gillies, " was contented with catching na- ture in the fact, without attempting, after the modern fashion, to put her to tlie tor- ture ; and in rejecting experiments operose, toilsome, or painful, either to their objects or their authors, he was justified by the habits of thinking, almost universally preva- lent in his age and country. Educated in free and martial republics, careless of wealth, because uncorrupted by luxury, the whole tribe of ancient Philosophers, dedicated themselves to agreeable only and liberal pursuits, with too proud a disdain of arts merely useful or lucrative. They ranked with the first class of citizens ; and, as such, were not to be lightly subjected to unwholesome or disgusting employ- ments. To bend over a furnace, iniialing noxious steams, to torture animals, or to touch dead bodies, appeared to them operations not more misbecoming their hu- manity, than unsuitable to their dignity. For such discoveries as the heating and mixing of bodies offers to inquisitive curiosity, the naturalists of Greece trusted to slaves and mercenary mechanics, whose poverty or avarice tempted them to work in metals and minerals ; and to produce, by unwearied labor, those colored and
OF THE HtlMAIi MIND. 233
But the observations and experiments of the philoso- pher are commonly only a step towards a farther end. This end is, firsts to resolve particular facts into other facts more simple and comprehensive ; and, secondly, to apply these general facts (or, as they are usually called, these laws of nature) to a synthetical explanation of particular phenomena. These two processes of the mind, together with that judicious employment of ob- servation and experiment which they presuppose, ex- haust the whole business of philosophical investigation ; and the great object of the rules of philosophizing is, to show in what manner they ought to be conducted.
I. For the more complete illustration of this funda- mental doctrine, it is necessary for me to recur to what has been already stated with respect to our igno- rance of efficient causes. As we can, in no instance, perceive the link by which two successive events are connected, so as to deduce by any reasoning a priori, the one from the other as a consequence or effect, it follows, that when we see an event take place which has been preceded by a combination of different circum- stances, it is impossible for human sagacity to ascertain
sculptured ornaments, those s^n^^j rings, cups, and vases, and other admired but fiivolous elegancies, of which (in tire opinion of good judges of ait) our boasted chemistry <-annot produce the materials; noi', were the materials at hand, supply us with instruments fit to shape. The woik-shops of tradesmen ihen revealed those mysteries which are now sought for in colleges and laboratoiies ; and useful knowl- edge, perhaps, was not the less likely to be advanced, while the arts were confined to artists only ; nor facts the more likely to be perverted, in order to support favorite theories, before the empiiic had yet assumed the name, and usurped the fundi uis, of X\\e^\\Woso\}hex.^'-~Translation of Aristotle^ s Ethics and PoUlics,'Wo\. I. p. 161, 2d Ed.
In another passage, we are told by the same author, that "(he learning of Greece properly terminates in the Stagiritc, by whom it was finall)' embodied into one great work ; a work rather impaired than improved by the labors of succeeding ages." .' — Ibid. p. X. of the Preface.
Notwithstanding the length of this note, I must beg leave to add to it a short ex- tract fom one of the aphorisms of Lord Bacon. — " Of the cr(7f//u. lor guiding our judgment among so many different and discoulanf school-;, there is iione more to be relied on, than that which is exliiiiited by their /)u//s ,• lor the fruits of any specula- tive docliine, or the inventions which it has really produced, are, as it were, sponsors or vouchers for the truths which it contains. Now, it is well known, that from the philosophy of the Greeks, with its numerous derivative schools, hardly one cxperi- nienial discovery can be collected which has any tendency to aid or to meliorate the condition of man, or which is entitled to rank with the acknowledged piinciples of genuine science." — " Wherefore, a-; in religion, faith is proved by its works, so in philo-iopliy. it wore to he wished, that those theoiies should be accounted vain, which, when tried by theii- fiuils, are barren ; — much more those, which, instead of grapes and olives, have produced only tho tliorns and thistles of controversy." — J\''ov. Or". Lib. i. Aph. Ixiii.
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234 ELEMENTS OF THE PHILOSOPHY
whether the effect is connected with all the circumstan- ces, or only with a part of them ; and (on the latter supposition) which of the circumstances is essential to the result, and which are merely accidental accessories or concomitants. The only way, in such a case, of coming at the truth, is to repeat over the experiment again and again, leaving out all the different circumstan- ces successively, and observing with what particular combinations of them the effect is conjoined. If there be no possibility of making this separation, and if, at the same time, we wish to obtain the same result, the only method of ensuring success is to combine together a,ll the various circumstances which were united in our for- mer trials. It is on this principle, that I have attempted, in a former chapter of this work, to account for the superstitious observances which always accompany the practice of medicine among rude nations. These ^are commonly ascribed to the influence of imagination, and the low state of reason in the earlier periods of society ; but the truth is, that they are the necessary and unavoida- ble consequences of a limited experience, and are to be corrected, not by mere force of intellect, but by a more enlarged acquaintance with the established order of nature.*
Observations perfectly similar to those which I made with respect to medicine, are applicable to all the other branches of philosophy. Wherever an interesting change is preceded by a combination of different cir- cumstances, it is of importance to vary our experiments in such a manner as to distinguish what is essential from what is accessory ; and when we have carried the de- composition as far as we can, we are entitled to consid- er this simplest combination of indispensable conditions, as the physical cause of the event.
When, by thus comparing a number of cases, agree- ing in some circumstances, but differing in others, and all attended with the same result, a philosopher connects, as a general law of nature, the event with its physical cause, he is said to proceed according to the method of
* Elements of (lie Philosophy of (he Human Mind, Vol. L Chap. v. Part 11. Sect. i.
OF THE HUMAN MIND. 235
induction. This, at least, appears to me to be the idea which, in general, Bacon himself annexes to the phrase ; * although I will not venture to affirm, that he has always employed it with uniform precision. I acknowledge, also, that it is often used by very accurate writers, to denote the whole of that system of rules, of which the process just mentioned forms the most essential and characteristical part.
The same word induction is employed by mathema- ticians in a sense not altogether different. In that gen- eral ybrww/a (for instance) known by the name of the Binomial Theorem, having found that it corresponds with the table of powers raised from a Binomial root, as far as it is carried by actual multiplication, we have no scruple to conclude, that it holds universally. Such a proof of a mathematical theorem is called a proof by induction ; — a mode of speaking obviously suggested by the previous apphcation of this term to our inferences concerning the laws of nature. There is, at the same time, notwithstanding the obvious analogy between the two cases, one very essential circumstance by which they are discriminated; — that, in mathematical induction, we are led to our conclusion (as I shall afterwards en- deavour to show) by a process of thought, which, although not conformable to the rules of legitimate de- monstration, involves, nevertheless, a logical inference of the understanding with respect to an universal truth or theorem ; whereas, in drawing a general physical conclusion from particular facts, we are guided merely by our instinctive expectation of the continuance of the laws of nature ; an expectation which, implying liide, if any, exercise of the reasoning powers, operates alike on the philosopher and on the savage.
To this behef in the permanent uniformity of physi- cal laws, Dr. Reid long ago gave the name of the induc- tive principle. " It is from the force of this principle," he observed, " that we immediately assent to that axiom upon which all our knowledge of nature is buili, That
* " Inrhictio, qufo ad inventioncm ct demonstiationein scientiarum et aitiuin ciit utilis, naturain scpaiaic debet, per rejectiories et exclusiones debitas," &c. &c. — Nov. Org. Lib. i. Aph. cv.
236 ELEMENTS OF THE PHILOSOPHY
effects of the same kind must have the same cause. For effects and causes, in the operations of nature, mean nothing but signs, and the things signified by them. We perceive no proper causality or efficiency in any natural cause ; but only a connexion estabhshed by the course of nature betv^^een it and what is called its ef- fects." *
A late celebrated writer, more distinguished by the singular variety and versatility of his talents, than by the depth or soundness of his understanding, was pleas- ed to consider Reid's inductive principle as a fit subject of ridicule ; asserting that the phenomenon in question was easily explicable by the common principles of expe- rience, and the association of ideas. " Though no man," says he, " has had any experience of what is future, every man has had experience of what urns future. "f Of the shallowness of this solution philosophers are, I believe, now very generally convinced ; but even if the case were otherwise, the fact remarked by Reid would be equally endded to the attention of logicians as the basis of all physical science, nor would it be easy to distinguish it by a name less hable to objection than that which he has selected.
In all Bacon's logical rules, the authority of this law of belief is virtually recognised, although it is no where formally stated in his writings; and although the doc- trines connected with it do not seem to be easily recon- cileable with some of his occasional expressions. It is, indeed, only of late that natural philosophers have been fully aware of its importance as the ground-work of the inductive logic ; the earlier writers under whose review it fell having been led to consider it chiefly by its sup- posed subserviency to their metaphysical or to their theological speculations. Dr. Reid and M. Turgot were, so far as I know, the first who recognised its existence as an original and ultimate law of the understanding ; — the source of all that experimental knowledge which we
• Inquiry into the Human Mind, Chap. vi. Sect. 24.
•f Priestley's Examination of Reid, B(;attic, and Oswald, p. 85. Some very judi- cious and decisive stiicturcs on this theory of Priestley may be found in Dr. Camp- bell's PhiloBophy of Rhetoric. See note at the end of the sixth Chapter of Book i.
OF THE HUMAN MINB. 237
begin to acquire from the moment of our birth, as well as of those more recondite discoveries which are dignified by the name of science. It is but justice to Mr. Hume to acknowledge that his Treatise of Human Nature fur- nished to Dr. Reid all the premises from which his con- clusions were drawn ; and that he is therefore fairly en- titled to the honor of having reduced logicians to the alternative of either acquiescing in his sceptical inferen- ces, or of acknowledging the authority of some in- stinctive principles of behef, overlooked in Locke's Analysis.*
H. There is another circumstance which frequently adds to the difficulty of tracing the laws of nature ; and which imposes on the philosopher, while carrying on the process of induction, the necessity of following a still more refined logic than has been hitherto describ- ed.— When a uniformity is observed in a number of dif- ferent events, the curiosity is roused by the coincidence, and is sometimes led insensibly to a general conclusion. In a few other cases, a multiplicity of events, which appear to common observers to be altogether anomalous, are found, upon a more accurate and continued exami- nation of them, to be subjected to a regular law.f The cycles by which the ancients predicted eclipses of the sun and moon ; the two laws inferred by Kepler from the observations of Tycho Brahe ; the law of refraction inferred by Snellius from the tables of Kircher and Scheiner, are instances of very comprehensive and most important rules obtained by the mere examination and comparison of particulars. Such purely empirical dis- coveries, however, are confined almost entirely to optics and astronomy, in which the physical laws combined together are comparatively few, and are insulated from the influence of those incalculable accidents which, in general, disturb the regularity of terrestrial phenomena. In by far the greater number of instances, the appear- ances of nature depend on a variety of different laws, all of which are often combined together in producing one single event : And wherever such a combination
• Note (0.) t Philosophy of the Human Mindj Vol. I. Chap. vi. Sect. it.
238 ELEMENTS OF THE PHILOSOPHY
happens, although each law may take place with the most complete uniformity, it is likely that nothing but confusion will strike the mere observer. A collection of such results, therefore, would not advance us one step in the knowledge of nature ; nor would it enable us to anticipate the issue of one new experiment. In cases of this description, before we can avail ourselves of our past experience, we must employ our reaoning powers in comparing a variety of instances together, in order to discover, by a sort of analysis or decompo- sition, the simple laws which are concerned in the phe- nomenon under consideration ; — after which we may proceed safely, in determining a priori what the result will be of any hypothetical combination of them, wheth- er total or partial.*
These observations have led us to the same conclu- sion with that which forms the great outline of Bacon's plan of philosophizing ; and which Newton has so suc- cessfully exemphfied in his inquiries concerning gravita- tion and the properties of light. While they point out, too, the respective provinces and uses of the analytic and the synthetic methods, they illustrate the etymologi- cal propriety of the names by which, in the Newtonian School, they are contradistinguished from each other.
In fact, the meaning of the words analysis and synthe- sis, when applied to the two opposite modes of investi- gation in physics, is extremely analogous to their use in the practice of chemistry. The chief difference lies in this, that in the former case, they refer to the logical processes of the understanding in the study of physical laws ; in the latter to the operative processes of the laboratory in the examination of material substances.
* " Itaque naturae facienda est prorsus solutio et separatio ; non per ignem certe, 66(1 per menteiii, tanqiiam ionem divinurn." Nov. Oigan. Lib. II. Aplior. xvi. The remainder of the aphoiism is equally worthy of attention ; in reading- which, how- ever, as well as the rest of Bacon's philosophical works, 1 must request, for a reason afterwards to be mentioned, that the woid Law may be substituted (or i''«'OT, wher- ever it may occur. — An attention to this circumstance will be found of much use in studying the JYorum Organon.
A similar idea, under other metaphorical disguises, often occurs in Bacon. Con- Bidering the circumstances in vvliich he wrote, logical precision was altogether im- possible ; yet it is astonishing with what force he conveys the spirit of the soundest philosophy of the eighteenlli century. "Nequeenim in piano via sita est, aed ascen- dendo et descendendo ; ascendendo primo ad axiomata, descendendo ad opera." Nov. Org. Lib. L Aphor. ciii.
V
OF THE HUMAN MIND. 239
If the foregoing remarks are well founded, they lead to the correction of an oversight which occurs in the ingenious and elegant sketch of the History of Astron- omy, lately pubhshed among the posthumous works of Mr. Smith ; and which seems calculated to keep out of view, if not entirely to explode, that essential distinction which I have been endeavouring to estabhsh, between the inductive logic of Bacon's followers, and the hypo- thetical theories of their predecessors.
" Philosophy," says Mr. Smith, " is the science of the connecting principles of nature. Nature, after the larg- est experience that common observation can acquire, seems to abound with events which appear solitary and incoherent with all that go before them : which, there- fore, disturb the easy movement of the imagination ; which make its ideas succeed each other, if one may say so, by irregular starts and sallies ; and which thus tend, in some measure, to introduce a confusion, and distraction, and giddiness of mind. Philosophy, by re- presenting the invisible chains which bind together all these disjointed objects, endeavours to introduce order into this chaos of jarring and discordant appearances ; to allay this tumult of the imagination ; and to restore it, when it surveys the great revolutions of the universe, to that tone of tranquillity and composure, which is both most agreeable in itself, and most suitable to its nature. Philosophy, therefore, may be regarded as one of those arts which address themselves to the imagination, by rendering the theatre of nature a more coherent, and, therefore, a more magnificent spectacle, than otherwise it would have appeared to be."
That this is one of the objects of philosophy, and one of the advantages resulting from it, I very readily admit. But, surely, it is not the leading object of that plan of inductive investigation which was recommended by Ba- con, and which has been so skilfully pursued by New- ton. Of all philosophical systems, indeed, hypothetical or legitimate, it must be allowed, that to a certain de- gree, they both please the imagination and assist the memory, by introducing order and arrangement among facts, which had the appearance, before, of being alto-
240 ELEMENTS OF THE PHILOSOPHY
gether unconnected and isolated. But it is the peculiar and exclusive prerogative of a system fairly obtained by the method of induction, that, while it enables us to ar- range facts already known, it furnishes the means of as- certaining, by synthetic reasoning, those which we have no access to examine by direct observation. The differ- ence, besides, among hypothetical theories, is merely a difference of degree, arising from the greater or less in- genuity of their authors ; whereas legitimate theories are distinguished from all others radically and essentially ; and, accordingly, while the former are liable to perpet- ual vicissitudes, the latter are as permanent as the laws which regulate the order of the universe.
Mr. Smith himself has been led, by this view of the object of philosophy, into expressions concerning the Newtonian discoveries, which seem to intimate, that, although he thought them far superior, in point of ingen- uity, to any thing the world had seen before, yet that he did not consider them as so completely exclusive of a still happier system in time to come, as the Newtonians are apt to imagine. " The system of Newton," he ob- serves, "now prevails over all opposition, and has ad- vanced to the acquisition of the most universal empire that was ever estabhshed in philosophy. His principles, it must be acknowledged, have a degree of firmness and solidity that we should in vain look for in any other sys- tem. The most sceptical cannot avoid feeling this. They not only connect together most perfectly all the phenomena of the heavens which had been observed before his time ; but those also which the persevering industry and more perfect instruments of later astrono- mers have made known to us, have been either easily and immediately explained by the application of his principles, or have been explained in consequence of more laborious and accurate calculations from these principles, than had been instituted before. And even we, while we have been endeavouring to represent all philosophical systems as mere inventions of the imagina- tion, to connect together the otherwise disjointed and discordant phenomena of nature, have insensibly been drawn in to make use of language expressing the con-
OF THE HUMAN MIND. 241
necting principles of this one, as if they were the real chains which nature makes use of, to bind together her several operations."
If the view which I have given of Lord Bacon's plan of investigation be just, it will follow, That the Newtoni- an theory of gravitation can, in no respect whatever, ad- mit of a comparison with those systems which are, in the slightest degree, the offspring of imagination ; inas- much as the principle employed to explain the phenom- ena is not a hypothesis, but a general fact established by induction ; for which fact we have the very same evi- dence as for the various particulars comprehended under it. The Newtonian theory of gravitation, therefore, and every other theory which rests on a similar basis, is as little hable to be supplanted by the labors of future ages, as the mathematical conclusions of Euchd and Ar- chimedes. The doctrines which it involves may be de- livered in different, and perhaps less exceptionable forms ; but, till the order of the universe shall be regu- lated by new physical laws, their substance must for ev- er remain essentiall}^ the same. On the chains, indeed, which nature makes use of to hind together her several operations, Newton has thrown no light whatever ; nor was it the aim of his researches to do so. The subjects of his reasonings were not occult connexions, but par- ticular phenomena, and general laws ; both of them pos- sessing all the evidence which can belong to facts ascer- tained by observation and experiment. From the one or the other of these all his inferences, whether analyti- cal or synthetical, are deduced : Nor is a single hypoth- esis involved in his data, excepting the authority of that Law of Behef which is tacitly and necessarily assumed in all our physical conclusions, — The stability of the or- der of nature.
VOL. II. 31
242 ELEMENTS OF THE PHILOSOPHY
SECTION II.
Continuation of the Subject. — The Induction of Aristotle compared witla that of
Bacon.
In this section I intend to offer a few slight remarks upon an assertion which has been hazarded with some confidence in various late publications, that the method of investigation, so much extolled by the admirers of Lord Bacon, was not unknown to Aristotle. — It is thus very strongly stated by the ingenious author of a me- moir in the Asiatic Researches.*
" From some of the extracts contained in this paper, it will appear, 1st, That the mode of reasoning by i/if/wc- tion, illustrated and improved by the great Lord Veru- 1am in his Organum JYovum, and generally considered as the cause of the rapid progress of science in later times, wsiS perfectly known to Aristotle, and was distinct- ly delineated by him, as a method of investigation that leads to certainty or truth : and 2dly, That Aristotle was likewise perfectly acquainted, not merely with the form of induction, but with the proper materials to be employed in carrying it on — facts and experiments. We are therefore led to conclude, that all the blame of confining the human mind for so long a time in chains, by the force of syllogism, cannot be fairly imputed to Aristode ; nor all the merit of enlarging it, and setting it free, ascribed to Lord Verulam."
The memoir from which this passage is copied, con- sists of extracts translated (through the medium of the Persian) from an Arabic treatise entitled the Essence of Logic. When it was first presented to the Asiatic Soci- ety, the author informs us, that he was altogether igno- rant of the coincidence of his own conclusions with those of Dr. Gillies ; and he seems to have received much satisfaction from the subsequent perusal of the proofs alleged in support of their common opinion by that learn- ed writer. " From the perusal of this wonderful hook" Dr. GilUes's exposition of the Ethics and Politics of
* Asiatic Researches, Vol. Vlll. p. 89, 90. London Edition.
OF THE HUMAN MIND. 243
Aristotle, " I have now the satisfaction to discover, that the conjectures I had been led to draw from these scan- ty materials, are completely confirmed by the opinion of an author, who is probably better qualified than any pre- ceding commentator on Aristotle's works, to decide on this subject." *
It is observed by Bailly, in his History of Astronomy, that, although frequent mention is made of attraction in the writings of the ancients, we must not therefore " conclude that they had any precise or just idea of that law into which Newton has resolved the phenomena of the planetary revolutions. To their conceptions, this word presented the notion of an occult sympathy be- tween different objects ; and if any of them extended it from the descent of terrestrial bodies to explain the manner in which the moon was retained in her orbit, it was only an exhibition upon a larger scale of the popu- lar error." f The same author has remarked, on a dif- ferent occasion, that, in order to judge of the philoso- phical ideas entertained at a particular period, it would be necessary to possess the dictionary of the age, exhi- biting the various shades of meaning derived from fash- ion or from tradition. " The import of words," he adds, " changes with the times : their signification enlarging with the progress of knowledge. Languages are every moment perishing in detail from the variations introdu- ced by custom : they grow old like those that speak them, and, like them, gradually alter their features and their form." J
If this observation be just, with respect to the attraction of the ancients, when compared with the attraction of Newton, it will be found to apply with still greater force to the induction of Aristotle,§ considered in contrast with the induction of Bacon.
It is well known to those who are at all conversant with Bacon's writings, that, although he borrowed many expressions from the scholastic phraseology then in
♦ Asiatic Researches, Vol. VIII. p. 89, 90. London Edition. f Hist, de i'Astronomie Modcrnc, Tome II, p. 555, 556. X Ibid. p. 184. § '^recyuyn. Translated Inductio by Cicero.
244 ELEMENTS OF THE PHILOSOPHY
vogue, he has, in general, not only employed them in new acceptations, consonant to the general spirit of his own logic, but has, by definitions or explanations, endeavour- ed to guard his readers against the mistakes to which they might be exposed, from a want of attention to the innovations thus introduced in the use of consecrated terms. How far he judged wisely in adopting this plan, (which has certainly much injured his style in point of perspicuity,) I do not presume to decide ; I wish only to state the fact : — his motives may be judged of from his own words.
"Nobis vero ex altera parte (quibus, quantum cala- mo valemus, inter Vetera et nova in Uteris fosdus et commercium contrahere, cordi est) decretum manet, antiquitatem comitari usque ad aras ; atque vocabula antiqua retinere, quanquam sensum eorum et definitiones saepius immutemus ; secundum moderatum ilium et lau- datum, in Civihbus, novandi modum, quo, rerum statu novato, verborum tamen solennia durent ; quod notat Tacitus ; eadem magistratuum vocabiila.^^ *
Of these double significations, so common in Bacon's phraseology, a remarkable instance occurs in the use which he makes of the scholastic \YOYd forms. In one passage, he approves of the opinion of Plato, that the investigation of forms is the proper object of science; adding, however, that this is not true of the fonns which Plato had in view, but of a different sort of forms, more suited to the grasp of our faculties.! In another pas- sage, he observes, that when he employs the word forms, in speaking of natural philosophy, he is always to
* De Aug. Scient. Lib. iii. cap. iv.
The necessity under which the anti-Aiistotclians found themselves, in the earUer part of the 17th century, of disguising their attack on the prevailing tenets, is strongly illustrated in a letter from Des Cartes to Regius. " Pourquoi rejettez-vous publique- ment les qualites reelles et les formes substantielles, si cheres aux scholastiques ? J'ai declare, que je ne pretendois pas les nicr, mais que je n'en avois pas besoin pour expliquer mes pensees."
f " Manifestura est, Platonem, virum suhlimis ingenii (quique veluti ex rupe excelsa omnia circumspiciebat) in sua de ideis doctrina, ybrmas esse venim scientice objectum, vidisse ; utcunquc sententiaa hujus verissiina; fructum ^m\scnt,f<)r7nas pcnitus a ma- teria abstractas, non in materia determinatas, contcmplando et prcnsando. Quod si diligenter, serio, ct sincere, ad actionem, et usuin, et oculos convertamus ; non diffi- cile erit disquirere,et nolitiam assequi, qua3 sint iWsi for nice, qunrum cognitio res hu- manas meiis modis locupletare et beare possit." — Be Augment. Scient. Lib. iii. Cap. iv.
OF THE HUMA]>r MIND. 245
be understood as meaning the laws of nature.* Wheth- er so accurate a reasoner as Locke would have admitted Bacon's general apology for so glaring an abuse of words y may perhaps be doubted : but, after comparing the two foregoing sentences, would Locke (notwithstanding his ignorance of the syllogistic art) have inferred, that Ba- con's opinion of the proper object of science was the same with that of Plato 1 The attempt to identify Bacon's induction with the induction of Aristode, is (as I trust will immediately appear) infinitely more extravagant. It is like confounding the Christian Graces with the Graces of Heathen Mythology.
The passages in which Bacon has been at pains to guard against the possibility of such a mistake are so numerous, that it is surprising how any person, who had ever turned over the pages of the Novum Organon, should have been so unlucky as not to have lighted upon some one of them. The two following will suffice for my present purpose.
" In constituendo autem axiomate, forma inductionis aha quam adhuc in usu fuit, excogitanda est. Inductio enim quae procedit per enumerationem simplicem res puerilis est, et precario concludit. At inductio, quae ad inventionem et demonstrationem scientiarum et artium erit utilis, naturam se parare debet, per rejectiones et exclusiones debitas ; ac deinde post negativas tot quot sufficiunt, super affirmativas concludere ; quod adhuc factum non est, nee tentatum certe, nisi tantummodo a Platone, qui ad excutiendas definitiones et ideas, hac certe forma inductionis aliquatenus utitur. Verum ad hujus inductionis, sive demonstrationis, instructionem bonam et legitimam, quamplurima adhibenda sunt, quae adhuc nullius mortalium cogitationem subiere ; adeo ut in ea major sit consumenda opera, quam adhuc consump- ta est in syllogismo. Atque in hac certe inductione, spes maxima sita est."f
* " Nos quum de formis loquimur, nil aliud intelligimus, quam leges illas, quae naturam aliquam simplicem ordinant et constituunt; ut calorem, lumen, pondus, in omnimoda materia et subjecto susceptibili. Itaque eadcm res est forma calidi, aut forma luminis, et lex calidi, sivelex lurainis," — JVou. Org. Lib. ii. Aph. xvii.
t Nov. Org. Lib. i. Aph. cv.
246 ELEMENTS OF THE PHILOSOPHY
■" Cogitavit et illud — Restare inductionem tanquam
ultimum et unicum rebus subsidium et perfugium. Verum et hujus nomen tantummodo notum esse ; vim et usum homines hactenus latuisse." *
That I may not, however, be accused of resting my judgment entirely upon evidence derived from Bacon's writings, it may be proper to consider more particularly to what the induction of Aristotle really amounted, and in what respects it coincided with that to which Bacon has extended the same name.
" Our behef," says Aristotle in one passage, " is, in every instance, founded either on syllogism or induc- tion." To which observation he adds, in the course of the same chapter, that " induction is an inference drawn from all the particulars which it comprehends." f It is manifest, that upon this occasion, Aristotle speaks of that induction which Bacon, in one of the extracts quoted above, describes as proceeding by simple enumeration ; and which he, therefore, pronounces to be " a puerile employment of the mind, and a mode of reasoning lead- ing to uncertain conclusions." In confirmation of Ba- con's remark, it is sufficient to mention, by way of illus- tration, a single example ; which example, to prevent cavils, I shall borrow from one of the highest logical au- thorities,— Dr. WaUis of Oxford.
" In an inference from induction," says this learned writer, "if the enumeration be complete, the evidence will be equal to that of a perfect syllogism ; as if a person should argue, that all the planets (the Sun excepted) borrow their light from the Sun, by proving this sepa- rately, of Saturn, Jupiter, Mars, Venus, Mercury, and the Moon. It is, in fact, a syllogism in Darapti, of which this is the form :
" Saturn, Jupiter, Mars, Venus, Mercury, and the Moon, each hor- roio their light from the Sun :
* Cogitata et Visa. The short tract to which Bacon has prefixed this title, con- tains a summary of what he seems to have considered as the leading tenets of his philosophical works. It is one of the most highly finished of all his pieces, and is marked throughout with an impressive brevity and solemnity, which commands and concentrates the attention. Nor does it aflect to disguise that consciousness of in- tellectual force, which might he expected from a man destined to fix a new era in the history of human reason. — Franciscu.'? Baconus sic cooitavit, &c. &c.
t First Analytics, Chap, xxiii. Vol. I. p, 126. Edit. Du Val.
OF THE HUMAN MIND. 247
" But this enumeration comprehends all the Planets, the Sun ex- cepted: " Therefore all the Planets, (the Sun excepted,) horrmo their light from the Sun.'^*
If the object of Wallis had been to expose the puer- ility and the precariousness of such an argument, he could not possibly have selected a happier illustration. The induction of Aristode, when considered in this light, is indeed a fit companion for his syllogism ; inasmuch as neither can possibly advance us a single step in the acquisition of new knowledge. How different from both is the induction of Bacon, which, instead of carry- ing the mind round in the same circle of words, leads it from the past to the/ii^wre, from the known to the un- knoimi 1 f
Dr. Wallis afterwards very justly remarks, " that in- ductions of this sort are of frequent use in mathematical demonstrations ; in which, after enumerating all the pos- sible cases, it is proved, that the proposition in question is true of each of these considered separately ; and the general conclusion is thence drawn, that the theorem holds universally. Thus, if it were shown, that, in all
* Institutio Logica, Lib. iii. Cap. 15. The reasoning employed by Wallis to show that the above is a legitimate syllogism in Darapti, affords a specimen of the facility with which a logical conjuror can transform the same argument into the most different shapes. " Siquis objiciat, hunc non esse legitimum in Barapti syllogismum, eo quod conclusionem habeatuniversalem; dicendum erit, hanc universalem (qualis qualis est) esseuniversalem collectivarn ; quae singularis est. Estque vox omiiishic loci (quae dici solet) pars Categorematica ; ufpote pars termini minoris (ut ex minori proposi- tione liquet) qui hie est (non PlanetcB sed) omnes Planetm (excepto sole) seu tota collectio reliquorum (excepto sole) Planetarum, quae collectio unica est ; adeoque conclusio singularis. Quas quidem (ut singulares aliae) quamvis sit propositio Uni- versalis, vi materiaj ; non tamen talis est ut non possit esse conclusio in tertia figura. Quippe in tertia figura, quoties minor terminus, seu praedicatum minoris propositionis (adeoque subjectum conclusionis) est quid singulare, necesse est ut conclusio ea sit (vi materia, non formae) ejusmodi universalis."
In justice to Dr. Wallis, it is proper to subjoin to these quotations, a short extract from the dedication prefixed to this treatise. — " Exempla retineo, quae apud logicos trita sunt ; ex philosophia quam vocant Veterem et Peripateticam petita : quia logicain liic trado, et quidem Peripateticam ; non naturalein philosophiam. Adeoque, de quatuor elementis ; de telluris quiete in universi medio ; de gravium motu deorsum, leviumque sursum ; de septenario planetarum numero, aliisque ; sic loquor, ut loqui Solent Peripatetici."
f " In aite judicandi (ut etiam vulgo receptum est) aut per Inductionem, aut per Syllogismum concluditur. At quatenus ad judicium, quod tit per inductionem, nihil est, quod nos detinere debeat : uno siquidem eodemque mentis opere illud quod qnce- ritur, et invenitur et judicatur. — At inductionis formam vitiosam prorsus valere jubemud ; legitimam ad Novum Organum remittimus." — De Aug. Scient. Lib. v. Cap. iv.
248 ELEMENTS OF THE PHILOSOPHY
right-angled triangles, the three angles are equal to two right angles, and that the same thing is true in all acute- angled, and also in all obtuse-angled triangles ; it would necessarily follow, that in every triangle the three angles are equal to two right angles ; these three cases mani- festly exhausting all the possible varieties of which the hypothesis is susceptible."
My chief motive for introducing this last passage, was to correct an idea, which, it is not impossible, may have contributed to mislead some of Walhs's readers. As the professed design of the treatise in question, was to ex- pound the logic of Aristotle, agreeably to the views of its original author ; and as all its examples and illustra- tions assume as truths the Peripatetic tenets, it was not unnatural to refer to the same venerated source, the few incidental reflections with which Wallis has enrich- ed his work. Of this number is the foregoing remark, which differs so very widely from Aristode's account of mathematical induction, that I was anxious to bring the two opinions into immediate contrast. The following is a faithful translation from Aristotle's own words :
" If any person were to show, by particular demon- strations, that every triangle, separately considered, the equilateral, the scalene, and the isosceles, has its three angles equal to two right angles, he would not, therefore, know that the three angles of a triangle are equal to two right angles, except after a sophistical manner. Nor would he know this as an universal property of a trian- gle, although, besides these, no other triangle can be conceived to exist ; for he does not know that it belongs to it qua triangle : Nor that it belongs to every triangle, except in regard to number ; his knowledge not extend- ing to it as a property of the genus, although it is impos- sible that there should be an individual which that genus does not include." *
* Jia tovTO Otis' ixv rig dsl^j] xad^ sxaaxov to xglyoivov anodsi^si ^ f.iioc tJ hiqa, on 8vo ogdaq s^Sk t'y.Kaiov, to laonlevqov xioqlq, xal to axalrjvov, Kul TO iaoaziXig' ovnca olds to tqI/oivov ou 8vo oQ&cclg iaov, si (iri tov ao-
Poster. Lib. i. Cap. v.
OF THE HUMAN MIJTD. 249
For what reason Aristotle should have thought of ap- plying, to such an induction as this the epithet sophisticaly it is difficult to conjecture. That it is more tedious, and therefore less elegant, than a general demonstration of the same theorem, is undoubtedly true ; but it is not on that account the less logical, nor, in point of form, the less rigorously geometrical. It is, indeed, precisely on the same footing with the proof of every mathematical proposition which has not yet been pushed to the utmost possible limit of generalization.
It is somewhat curious, that this hypothetical exam- ple of Aristotle is recorded as a historical fact by Pro- clus, in his commentary on Euclid. " One person, we are told," I quote the words of Mr. Maclaurin, " dis- covered, that the three angles of an equilateral triangle are equal to two right angles ; another went farther, and showed the same thing of those that have two sides equal, and are called isosceles triangles : and it was a third that found that the theorem was general, and extended to triangles of all sorts. In like manner, when the science was farther advanced, and they came to treat of the con- ic secUons, the plane of the section was always supposed perpendicular to the side of the cone ; the parabola was the only section that was considered in the right-angled cone, the ellipse in the acute-angled cone, and the hy- perbola in the obtuse-angled. From these three sorts of cones, the figures of the sections had their names for a considerable time, till, at length, Apollonius showed that they might all be cut out of any one cone, and, by this discovery merited in those days the appellation of the Great Geometrician." *
It would appear, therefore, that, in mathematics, an inductive inference may not only be demonstratively certain, but that it is a natural, and sometimes perhaps a necessary step in the generalization of our knowledge. And yet it is of one of the most unexceptionable induc-
I have rendered the last clause according to the best of my judgment ; but, incase of any misapprehension on my p-.irt, 1 hn.ve transcribed the author's words. It may be proper to mention, that tliis iihistration is not produced by Aiislotle as an instance of induction ; but it obviously fails under his own definition of it, and is accordingly considered in that light by Dr. WaJlis.
• Account of Sir Isaac Newton's Phil. Discoveriei, Book i. Chap. v.
VOL. II. 32
250 ELEMENTS OF THE PHIJLO SOPHY
tive conclusions in this science (the only science in which it is easy to conceive an enumeration which ex- cludes the possibihty of any addition) that Aristotle has spoken, — as a conclusion resting on sophistical evi- dence.
So much with respect to Aristode's induction, on the supposition that the enumeration is complete.
In cases where the enumeration is imperfect, Dr. Wal- lis afterwards observes, "That our conclusion can only amount to aprobabihty or to a conjecture ; and is always liable to be overturned by an instance to the contrary." He observes also, " That this sort of reasoning is the principal instrument of investigation in what is now call- ed experimental philosophy ; in which, by observing and examining particulars, we arrive at the knowledge of universal truths." * All this is clearly and correctly ex- pressed ; but it must not be forgotten, that it is the lan- guage of a writer trained in the schools of Bacon and of Newton.
Even, however, the induction here described by Dr. Wallis, falls greatly short of the m.ethod of philosophiz- ing pointed out in the JYovum Organon. It coincides exactly with those empirical inferences from mere ex- perience, of which Bacon entertained such slender hopes for the advancement of science. " Reseat expe- rientiamera; quae si occurrat, casus ; si quaesita sit, ex- perimentum nominatur. Hoc autem experientiae genus nihil aliud est, quam mera palpatio, quali homines noctu utuntur, omnia pertentando, si forte in rectam viam incidere detur ; quibus multo satius et consuldus foret, diem prsestolari aut lumen accendere, deinceps viam inire. At contra, verus experientiae ordo primo llimen accendit, deinde per lumen iter demonstrat, incipiendo ab experientia ordinata et digesta, et minime praeposte- ra aut erratica, atque ex ea educendo axiomata, atque ex axiomatibus constitutis rursus experimenta nova, quum nee verbum divinum in rerum massam absque or- dine operatum sit." f
* Institutio I,op,ica. — Soe tlie Chapter De Induciione et Exemplo. t IS'ov. Org. Aph. Ixxxii.
or THE HLTMAIV MIND. 251
It is a common mistake, in the logical phraseology of the present times, to confound the words experience and induction as convertible terms.* There is, indeed, be- tween them a very close affinity ; inasmuch as it is on experience alone that every legitimate induction must be raised. The process of induction therefore presup- poses that of experience ; but according to Bacon's views, the process of experience does by no means im- ply any idea of induction. Of this method Bacon has repeatedly said, that it proceeds " by means of rejec- tions and exclusions" (that is, to adopt the phraseology of the Newtonians, in the way of analysis) to separate or decompose nature ; so as to arrive at those axioms or general laws, from which we may infer (in the way of synthesis) other particulars formerly unknown to us, ami perhaps placed beyond the reach of our direct ex- amination, f ' But enough, and more than enough, has been already said to enable my readers to judge, how far the assertion is correct, that the induction of Bacon was Vv^ell known to Aristotle. Whether it be yet loell known to all his com- mentators, is a different question ; with the discussion of which I do not think it necessary to interrupt any longer the progress of my work.
* " Let it always be remembered, that tbe autlior who first tavioht this dortrine (that the true art of reasoning is iiofhing but a language accuralcli/ drfined and sliilfully arranged,) had previously endeavoured lo prove, (hat all our notions, as well as the signs by which they are expressed, originate in perceptions of sense ; and that the principles on which languages are first constructed, as well as every step in their progress to i)erfcction, all ultimately depend on inductions from observation ; in one word, on experience merely.''^ — Aristotle's Ethics and Politics hy GJillies, Vol. I. pp. 94, 95.
In tiie latter of these pages, I observe the following sentence, which is of itself suf- ficient to show what notion the Aristotelians still annex to the word under considera- tion. " Every kind ot reasoning is carried on cither by syllogism or by induction ; the former pioving to us, that a particular pioposition is true, because it is deducihie from a general one, already known to us; and the latter demonstrating a general truth, be- cause it holds in all particular cases."
It is obvious, that this species of induction never can be of the slightest U'se in the study of nature, where the phenomena which it is our aim to classify under their general laws, are, in respect of number, if not infinite, at least incalculable and in- comprehensible hy our faculties.
f Nov. Org. Aph. cv. ciii.
252 ELEMENTS OF THE ]^HILOS0FHT
SECTION III.
Of the Import of the Words Analysis and Synthesis, in the Language of Modern
Philosophy.
As the words analysis and synthesis are now become of constant and necessary use in all the different depart- ments of knowledge ; and as there is reason to suspect, that they are often employed without due attention to the various modifications of their import, which must be the consequence of this variety in their apphcation, — it may be proper, before proceeding farther, to illustrate, by a few examples, their true logical meaning in those branches of science, to which I have the most frequent occasions to refer in the course of these inquiries. I begin wdth some remarks on their primary signification in that science, from which they have been transferred by the moderns to Physics, to Chemistry, and to the Philosophy of the Human Mind,
I.
Preliminary Observations on the Analysis and Synthesis of the Greek Geometricians.
It appears from a very interesting relic of an ancient writer,* that, among the Greek geometricians, two dif- ferent sorts of analysis were employed as aids or guides to the inventive powers ; the one adapted to the solution of problems ; the other to the demonstration of theo- rems. Of the former of these, many beautiful exemph- fications have been long in the hands of mathematical students ; and of the latter, (which has drawn much less attention in modern times,) a satisfactory idea may be formed from a series of propositions published at Ed- inburgh about fifty years ago.f I do not, however, know
• Preface to the seventh book of the Mathematical CoUeclions of Pappus Alexan- drinus. An extract from the Latin version of it by Dr. Halley may be found in Note (P.) _
t Propositiones Geometricse More Veterum Demonstrataj. Auctore Matthceo Stew- art, S. T. P. MatheseoH in Academia Edinensi Professore, 1763.
OF THE HUMAN MIND. 253
that any person has yet turned his thoughts to an exam- ination of the deep and subtle logic displayed in these analytical investigations ; although it is a subject well worth the study of those who delight in tracing the steps by which the mind proceeds in pursuit of scientific dis- coveries. This desideratum it is not my present purpose to make any attempt to supply ; but only to convey such general notions as may prevent my readers from falhng into the common error of confounding the analysis and synthesis of the Greek Geometry, with the analysis and synthesis of the Inductive Philosophy.
In the arrangement of the following hints, I shall con- sider, in the first place, the nature and use of analysis in investigating the demonstration of theorems. For such an appUcation of it, various occasions must be constant- ly presenting themselves to every geometer ; — when engaged, for example, in the search of more elegant modes of demonstrating propositions previously brought to hght; or in ascertaining the truth of dubious theorems, which, from analogy, or other accidental circumstances, possess a degree of verisimihtude sufficient to rouse the curiosity.
In order to make myself intelligible to those who are acquainted only with that form of reasoning which is used by Euclid, it is necessary to remind them, that the enunciation of every mathematical proposition consists of two parts. In the first place, certain suppositions are made, and secondly, a certain consequence is affirm- ed to follow from these suppositions. In all the demon- strations which are to be found in Euclid's Elements, (with the exception of the small number of indirect de- monstradons,) the particulars involved in the hypotheti- cal part of the enunciation are assumed as the principles of our reasoning ; and from these principles a series or chain of consequences is, link by link, deduced, till we at last arrive at the conclusion which the enunciation of the proposition asserted as a truth. A demonstration of this kind is called a Synthetical demonstration.
Suppose now, that I arrange the steps of my reason- ing in the reverse order ; that I assume hypothetically the truth of the proposition which I wish to demon-
^54 ELEMENTS OF THE PHILOSOPHY
strate, and proceed to deduce from this assumption, as a principle, the different consequences to which it leads. If, in this deduction, I arrive at a consequence which I already know to be true, I conclude with confidence, that the principle from which it was deduced is hkewise true. But if, on the other hand, I arrive at a conse- quence which I know to be false, I conclude, that the principle or assumption on which my reasoning has pro- ceeded is false also. — Such a demonstration of the truth or falsity of a proposition is called an Analytical de- monstration.
According to these definitions of Analysis and Syn- thesis, those demonstrations in Euclid which prove a proposition to be true, by showing, that the contrary supposition leads to some absurd inference, are, proper- ly speaking, analytical processes of reasoning. In eve- ry case, the conclusiveness of an analytical proof rests on this general maxim. That truth is always consistent with itself; that a supposition which leads, by a concat- enation of mathematical deductions, to a consequence which is true, must itself be true ; and that which ne- cessarily involves a consequence which is absurd or im- possible, must itself be false.
It is evident, that, when we are demonstrating a prop- osition with a view to convince another of its truth, the synthetic form of reasoning is the more natural and pleasing of the two ; as it leads the understanding di- rectly from known truths to such as are unknown. When a proposition, however, is doubtful, and we wish to satisfy our own minds with respect to it ; or when we wish to discover a new method of demonstrating a theo- rem previously ascertained to be true ; it will be found (as I already hinted) far more convenient to conduct the investigation analytically. The justness of this remark is universally acknowledged by all who have ever exer- cised their ingenuity in mathematical inquiries ; and must be obvious to every one who has the curiosity to make the experiment. It is not, however, so easy to point out the principle on which this remarkable differ- ence between these two opposite intellectual processes depends. The suggestions which I am now to offer ap-
OF THE HUMAN MIND. 255
pear to myself to touch upon the most essential circum- stance ; but I am perfectly aware that they by no means amount to a complete solution of the difficulty.
Let it be supposed, then, either that a new demonstra- tion is required of an old theorem ; or, that a new and doubtful theorem is proposed as a subject of examina-, tion. In what manner shall I set to work, in order to. discover the necessary media of proof? From the hy-; pothetical part of the enunciation, it is probable, thafa great variety of different consequences may be immedi- ately deducible ; from each of which consequences a series of other consequences will follow : At the same time, it is possible, that only one or two of these trains of reasoning may lead the way to the truth which I wish to demonstrate. By what rule am I to be guided in se- lecting the line of deduction which I am here to pursue ? The only expedient which seems to present itself, is merely tentative or experimental ; to assume successive- ly all the different proximate consequences as the first link of the chain, and to follow out the deduction from each of them, till I, at last, find myself conducted to the truth which I am anxious to reach. According to this suppo- sition, I merely grope my way in the dark, without rule or method : the object I am in quest of may, after all my labor, elude my search ; and even, if I should be so for- tunate as to attain it, my success affords me no lights whatever to guide me in future on a similar occasion.
Suppose now that I reverse this order, and prosecute the investigation analytically ; assuming (agreeably to the explanation already given) the proposition to be true, and attempting, from this supposition, to deduce some acknowledged truth as a necessary consequence. I have here one fixed point from which I am to set out ; or, in other words, one specific principle or datum from which all my consequences are to be deduced ; while it is perfectly immaterial in what particular conclusion my deduction terminates, provided this conclusion be pre- viously known to be true. Instead, therefore, of being limited, as before, to one conclusion exclusivelij, and left in a state of uncertainty where to begin the investigation, I have one single supposition marked out to me, from
256 ELEMENTS OF THE PHILOSOPHY
which my departure must necessarily be taken ; while, at the same time, the path which I follow, may terminate with equal advantage in a variety of different conclu- sions. In the former case, the procedure of the under- standing bears some analogy to that of a foreign spy, landed in a remote corner of this island, and left to ex- plore, by his own sagacity, the road to London. In the latter case, it may be compared to that of an inhabitant of the metropohs, who wished to effect an escape, by any one of our sea-ports, to the continent. It is scarce- ly necessary to add, that as this fugitive, — should he hap- pen after reaching the coast, to alter his intentions, — would easily retrace the way to his own home ; so the geometer, when he has once obtained a conclusion in manifest harmony with the known principles of his science, has only to return upon his own steps (c(Bca re- gens jilo vestigia) in order to convert his analysis into a direct synthetical proof.
A palpable and familiar illustration (at least in some of the most essential points) of the relation in which the two methods now described stand to each other, is presented to us by the operation of unloosing a difficult knot, in order to ascertain the exact process by which it was formed. The illustration appears to me to be the more apposite, that I have no doubt it was this very anal- ogy, which suggested to the Greek geometers the meta- phorical expressions of analysis and of solution, which they have transmitted to the philosophical language of modern times.
Suppose a knot, of a very artificial construction, to be put into my hands as an exercise for my ingenuity, and that I was required to investigate a rule, which others, as well as myself, might be able to follow in practice, for making knots of the same sort. If I were to proceed in this attempt, according to the spirit of a geometrical synthesis, I should have to try, one after another, all the various experiments which my fancy could devise, till I had, at last, hit upon the particular knot I was anxious to tie. Such a process, however, would evidently be so completely tentative, and its final success would, after all, be so extremely doubtful, that common sense could
• OF THE HUMAN MIND. 257
not fail to suggest immediately the idea, of tracing the knot through all the various comphcations of its progress, by cautiously undoing or imknitiing each successive turn of the thread in a retrograde order, from the last to the first. After gaining this first step, were all the former complications restored again, by an inverse repetidon of the same operations v^^hich I had performed in undoing them, an infallible rule would be obtained for solving the problem originally proposed ; and, at the same time, some address or dexterit}^, in the practice of the general meth- od, probably gained, which would encourage me to un- dertake, upon future occasions, still m.ore arduous tasks of a similar description. The parallel between this ob- vious suggestion of reason, and the refined logic of the Greek analysis, undoubtedly fails in several particulars ; but both proceed so much on the same cardinal principle, as to account sufficiently for a transference of the same expressions from the one to the other. That this trans- ference has actually taken place in the instance now un- der consideration, the literal and primidve import of the words dvd and Xvai?, affords as strong presumptive evi- dence as can well be expected in any etymological spec- ulation.
In applying the method of analysis to geometrical pro- blems, the investigation begins by supposing the problem to be solved ; after which, a chain of consequences is deduced from this supposition, terminating at last in a conclusion, which either resolves into another problem, previously knov/n to be within the reach of our resourc- es ; or which involves an operation known to be im- practicable. In the former case, all that remains to be done, is to refer to the construction of the problem in which the analysis terminates ; and then, by reversing our steps, to demonstrate synthetically, that thi^ con- struction fulfils all the conditions of the problem in ques- tion. If it should appear, in the course of the compo- sition, that in certain cases the problem is possible, and in others not, the specification of these different cases (called by the Greek geometers the dtoptc^ttos or deter- mination) becomes an indispensable requisite towards a complete solution.
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258 ELEMENTS OF THE PHILOSOPHY
The utility of the ancient analysis in facilitating the solution of problems, is still more manifest than in facili- tating the demonstration of theorems ; and, in all proba- bility, was perceived by mathematicians at an earlier period. The steps by Avhich it proceeds in quest of the thing sought, are faithfully copied (as might be easily shown) from that natural logic which a sagacious mind would employ in similar circumstances ; and are, in fact, but a scientific apphcation of certain rules of method, collected from the successful investigations of men who were guided merely by the light of common sense. The same observation may be applied to the analytical processes of the algebraical art.
In order to increase, as far as the state of mathemati- cal science then permitted, the powers of their analysis, the ancients, as appears from Pappus, wrote thirty-three different treatises, (known among mathematicians by the name of totzos dvaXvo^isvos,) of which number there are twenty-four books, whereof Pappus has particularly described the subjects and the contents. In what man- ner some of these were instrumental in accomplishing their purpose, has been fully explained by different modern writers ; particularly by the late very learned Dr. Simson of Glasgow. Of Euchd's Data, (for exam- ple,) the first in order of those enumerated by Pappus, he observes, that, " it is of the most general and neces- sary use in the solution of problems of every kind ; and that whoever tries to investigate the solutions of prob- lems geometrically, will soon find this to be true ; for the analysis of a problem requires, that consequences be drawn from the things that are given, until the thing that is sought be shown to be giveti also. Now, supposing that the Data were not extant, these consequences must, in every particular instance, be found out and demon- strated from the things given in the enunciation of the problem ; whereas the possession of this elementary book supersedes the necessity of any thing more than a reference to the propositions which it contains." *
* Letter from Dr. Simson to George Lewis Scott, Esq. published by Dr. Traill. Sec his Account of Dr. Simson's Life and Writings, page 118.
i
OF THE HUMAN MIND. 259
With respect to some of the other books mentioned by Pappus it is remarked by Dr. Simson's biographer, that " they relate to general problems of frequent recur- rence in geometrical investigations : and that their use was for the more immediate resolution of any proposed geometrical problem, which could be easily reduced to a particular case of any one of them.. By such a reduc- tion the problem was considered as fully resolved ; be- cause it was then necessary only to apply the analysis, composition, and determination of that case of the gen- eral problem, to this particular problem which it was shown to comprehend."*
From these quotations it manifestly appears, that the greater part of what was formerly said of the utility of analysis in investigating the demonstration of theorem.s, is applicable, mutatis mutandis, to its employment in the solution of problems. It appears farther, that one great aim of the subsidiary books, comprehended under the title of TOTtog dvalvo^svos was to multiply the number of such conclusions as might secure to the geometer a legitimate synthetical demonstration, by returning back- wards, step by step, from a known or elementary con- struction. The obvious effect of this was, at once to abridge the analytical process, and to enlarge its resour- ces ; on a principle somewhat analogous to the increas- ed facilities which a fugitive from Great Britain would gain, in consequence of the multiplication of our sea- ports. .
Notwithstanding, however, the immense aids afforded to the geometer by the ancient analysis, it must not be imagined that it altogether supersedes the necessity of ingenuity and invention. It diminishes, indeed, to a wonderful degree, the number of his tentative experi- ments, and of the paths by which he might go astray ; f but (not to mention the prospective address which it sup- poses, in preparing the way for the subsequent investi-
* Ibid. pp. 159,^ 160.
t " Nihil a vera, et genuina analysi magls distat, nihil magis abhonct, (|iiam tentan- di methodus ; banc enim amoverc ct ccrtissima via ad quaesituin perducerc, praeci- puus est analyseos finis."
Extract from a MS. of Dr. Simson, published by Dr. Traill. See his Account, &c. p. 127.
260 ELEMENTS OF THE PHILOSOPHY
gation, by a suitable construction of the diagram) it leaves much to be supphed at every step, by sagacity and practical skill ; nor does the knowledge of it till disciplined and perfected by long habit, fall under the description of that 5i^Va/,iis avalvrim] which is justly represented by an old Greek writer,* as an acquisition of greater value than the most extensive acquaintance with particular mathematical truths.
According to the opinion of a modern geometer and philosopher of the first eminence, the genius thus dis- played in conducting the approaches to a preconceived mathematical conclusion, is of a far higher order than that which is evinced by the discovery of new theorems. " Longe sublimioris ingenii est," says Galileo, " aheni Problematis enodatio, aut ostensio Theorematis, quam novi cujuspiam inventio : hsc quippe fortunee in incer- tum vagantibus obviaplerumque esse solet ; totavero ilia, quanta est, studiosissimam attentae mentis, in unum ali- quem scopum collimantis, ratiocinationem exposcit."f Of the justness of this observation, on the whole, I have no doubt ; and have only to add to it, by way of com- ment, that it is chiefly while engaged in the steady pur- suit of a particular object, that those discoveries which are commonly considered as entirely accidental, are most likely to present themselves to the geometer. It is the methodical inquirer alone who is entitled to expect such fortunate occurrences as Galileo speaks of ; and wher- ever invention appear^ as a characteristical quality of the mind, we may be assured, that something more than chance has contributed to its success. On this occa- sion, the fine and deep reflection of Fontenelle will be found to apply with peculiar force : " Ceshasards ne sont que pour ceux guijouent hien.''^
* See the preface of Maiiniis to Euclid's Data. In the piefoce to the 7th book of Pappus, the same idea is expressed by the phiase luvafm zv^tnxri.
•f Not having the works of Galileo at hand, I quote this passage on the authority of Guido Giandi, who has introduced it in the preface to liis demonstration of Huy- gen's Theorems concerning the Logarithmic Line. — Vid. Hugenii Opera Rcliqua, Tom. I. p. 43.
OF THE HUMAN MIND. 261
II.
Critical Remarks on the vague Use, among Modern Writers, of the Terms Analysis
and Synthesis.
The foregoing observations on the Analysis and Syn- thesis of the Greek Geometers may, at first sight, appear somewhat out of place, in a disquivsilion concerning the principles and rules of the Inductive Logic. As it was, however, from the Mathematical Sciences, that these words were confessedly borrowed by the experimental inquirers of the Newtonian School, an attempt to illus- trate their original technical import seemed to form a necessary introduction to the strictures w^hich I am about to offer, on the loose and inconsistent applications of them, so frequent in the logical phraseology of the pres- ent times.
Sir Isaac Newton himself has, in one of his Queries fairly brought into comparison the Mathematical and the Physical Jlnalysis, as if the word, in both cases, convey- ed the same idea. " Jls in Mathematics, so in JYatural Philosophy, the investigation of difficult things, by the method of Analysis, ought ever to precede the method of Composition. This analysis consists in making experi- ments and observations, and in drawing conclusions from them by induction, and admitting of no objections against the conclusions, but such as are taken from ex- periments, or other certain truths. For hypotheses are not to be regarded in experimental philosophy. And al- though the arguing from experiments and observations by induction be no demonstration of general conclu- sions ; yet it is the best way of arguing which the na- ture of things admits of, and may be looked upon as so much the stronger, by how much the induction is more general. And if no exception occur from phenomena, the conclusion may be pronounced generally. But if, at any time afterwards, any exception shall occur from experiments ; it may then begin to be pronounced, with such exceptions as occur. By this way of analysis we may proceed from compounds to ingredients ; and from motions to the forces producing them ; and, in general,
262 ELEMENTS OF THE PHILOSOPHY
from effects to their causes ; and from particular causes to more general ones, till the argument end in the most general. This is the method of analysis. And the syn- thesis consists in assuming the causes discovered, and established as principles, and by them explaining the phenomena proceeding from them, and proving the ex- planations." *
It is to the first sentence of this extract (which has been repeated over and over by subsequent writers) that I would more particularly request the attention of my readers. Mr. Maclaurin, one of the most illustrious of Newton's followers, has not only sanctioned it by tran- scribing it in the words of the author, but has endeavour- ed to illustrate and enforce the observation which it con- tains. "It is evident, that as in Mathematics, so in Natural Philosophy, the investigation of difficult things by the method of analysis ought ever to precede the method of composition, or the synthesis. For, in any other way, we can never be sure that we assume the principles which really obtain in nature ; and that our system, after we have composed it with great labor, is not mere dream or illusion." f The very reason here stated by Mr. Maclaurin, one should have thought, might have convinced him, that the parallel between the two kinds of analysis was not strictly correct : inasmuch as this reason ought, according to the logical interpretation of his words, to be applicable to the one science as well as to the other, instead of exclusively applying (as is obviously the case) to inquiries in Natural Philosophy.
After the explanation which has been already given of geometrical and also of physical analysis, it is almost superfluous to remark, that there is litde, if any thing, in which they resemble each other, excepting this, that both of them are methods of investigation and discov- ery ; and that both happen to be called by the same name. This name is, indeed, from its literal or etymo- logical import, very happily significant of the notions conveyed by it in both instances ; but, notwithstanding
* See the concluding paragraphs of Newton's Optics, t Account of Newton's Discoveries.
OF THE HUMAN MIND. 263
this accidental coincidence, the wide and essential dif- ference between the subjects to which the two kinds of analysis are apphed, must render it extremely evident, that the analogy of the rules which are adapted to the one can be of no use in illustrating those which are suited to the other.
Nor is this all : The meaning conveyed by the word analysis, in Physics, in Chemistry, and in the Philoso- phy of the Human Mind, is radically different from that which was annexed to it by the Greek Geometers, or which ever has been annexed to it, by any class of mod- ern Mathematicians. In all the former sciences, it naturally suggests the idea of a decomposition of what is complex into its constituent elements. It is defined by Johnson, " a separation of a compound body into the several parts of which it consists." — He afterwards mentions, as another signification of the same word, " a solution of any thing whether corporeal or mental, to its first elements ; as of a sentence to the single words ; of a compound word to the particles and words which form it ; of a tune to single notes ; of an argument to single propositions." In the following sentence, quoted by the same author from Glanville, the word analysis seems to be used in a sense precisely coincident with what I have said of its import, when apphed to the Ba- conian method of investigation. " We cannot know any thing of nature but by an analysis of its true initial causes." *
In the Greek geometry, on the other hand, the same word evidently had its chief reference to the retrograde direction of this method, when compared with the natu- ral order of didactic demonstration. Tijv Toiavn^v scpodov (says Pappus) avdXv6iv xocXovftav, olov avdnaXiv Xv6lv ;
* By the true initial causes of a phenomenon, Glanville means (as mightbe easily shown by a comparison with other parts of his works) the simple laws from the com- bination of which it 7-csults, and from a previous knowledge of which, it might have been synthetically deduced as a consequence.
That Bacon, when he speaks of those separations of nature, by means of com- parisons, exclusions, and rejections, which form essential steps in the inductive process, had a view to the analytical operations of the chemical laboratory, appears sufficiently from the following words, before quoted : " Itaque naturre facienda est prorsus solutio et separatio ; non per ignem ccrte, sed per mentem, tanquam ignem divinum."
264 ELEMENTS OF THE PHILOSOPHY
a passage which Halley thus translates : hie processus Analysis vocatur, quasi dicas, inversa solutio. That this is the primitive and genuine import of the preposition avd, is very generally admitted by Grammarians ; and it accords, in the present instance, so happily with the sense of the context, as to throw a new and strong light on the justness of their opinion,*
In farther proof of what I have here stated with re- spect to the double meaning of the words analysis and synthesis, as employed in physics and in mathematics, it may not be superfluous to add the following considera- tions. In mathematical analysis, we always set out from a hypothetical assumption, and our object is to arrive at some known truth, or some datum, by reasoning synthet- ically from which we may afterwards return, on our own footsteps, to the point where our investigation began. In all such cases, the synthesis is infallibly obtained by reversing the analytical process ; and as both of them have in view the demonstration of the same theorem, or the solution of the same problem, they form, in reaUty, but different parts of one and the same investigation. But in natural philosophy, a synthesis which merely re- versed the analysis would be absurd. On the contrary, our analysis necessarily sets out from known facts ; and after it has conducted us to a general principle, the synthetical reasoning which follows, consists always of an application of this principle to phenomena different from those comprehended in the original induction. >
In some cases, the natural philosopher uses the word analysis, where it is probable that a Greek geometer would have used the word synthesis. Thus, in astron- omy, when we attempt from the known phenomena to establish the truth of the Copernican system, we are
* The force of this preposition, in its primitive sense, may perhaps, without any false refinement, he traced more or less palpably, in every instance to which the word analysis is with any propriety applied. In what Johnson calls (for example) " the separation of a compound body into the several parts of which it consists," — we pro- ceed on the supposition, that these parts have previously been combined, or put to- gether, so as to make up the oggrc^nte whole, submitted to the examination of the chemist ; and, consequently, that the analytic process follows an inverted or retro- grade direction, in respect of that in which the compound is conceived to have been originally formed. — A similar remark will be found to apply (mutatis mulandis) to otiier cases, however apparently different.
OF THE HUMA]^ MII^D. 265;
said to proceed analytically. But the analogy of ancient geometry would apply this word to a process directly the reverse ; a process which, assuming the system as true, should reason from it to the known phenomena : after which, if the process could be so reversed as to prove that this system, and this system alone, is consistent with these facts, it would bear some analogy to a geometrical synthesis.
These observations had occurred to me, long before I bad remarked, that the celebrated Dr. Hooke (guided also by what he conceived to be the analogy of the Greek geometry) uses the words analysis and synthesis in physics, precisely in the contrary acceptations to those assigned to them in the definitions of Sir Isaac New- ton. " The methods," he observes, " of attaining a knowledge in nature may be two ; either the analytic or the synthetic. The first is the proceeding from the causes to the effects. The second, from the effects to the causes. The former is the more difficult, and sup- poses the thing to be already done and known, which is the thing sought and to be found out. This begins from the highest, most general, and unversal principles or causes of things, and branches itself out into the more particular and subordinate. The second is the more proper for experimental inquiry, which from a true in- formation of the effect by a due process, finds out the immediate cause thereof, and so proceeds gradually to higher and more remote causes and powers effective, founding its steps upon the lowest and more immediate conclusions." *
* Hooke's Posthumous Works, p. 330.
As this volume is now become extremely rare, I shall transcribe the paragraph which immediately follows the above quotation.
"An inquisition by the former (or analytic) method, is resembled fitly enough by the example of an architect, who hath a full comprehension of what he designs to do, and acts accordingly : But the latter (or synthetic) is more properly resembieil to that of a husbandman or gardener, who prepares his ground, and sows his seed, and diligently cherishes the growing vegetable, supplying it continually with fitting mois- ture, food, and shelter, — observing and cherishing its continual progression, till it comes to its perfect ripeness and maturitj', and yields him the fruit of his labor. Nor is it to be expected, that a production of such perfection as this is designed, should be brought to its coiu])lcte ripeness in an instant ; but as all the works of na- ture, if it be na'iurally proceeded with, it must have its due time to acquire its due form and full maturity, by gradual growth and a natural progression ; not but that the other method is also of excellent and necessary use, and will very often facilitate and
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266 ELEMENTS OF THE PHILOSOPHY
That Hooke was led into this mode of speaking by the phraseology of the ancient mathematicians, may, I think, be safely inferred from the following very sagacious and fortunate conjecture with respect to the nature of their analytical investigations, which occurs in a different part of the same volume. I do not know that any thing ap- proaching to it is to be found in the works of any other EngUsh author prior to Dr. Halley.
" What ways the ancients had for finding out these mediums, or means of performing the thing required, we are much in the dark ; nor do any of them show the way, or so much as relate that they had such a one : Yet 'tis believed they were not ignorant of some kind of algebra, by which they had a certain way to help themselves in their inquiries, though that we now use be much confined and limited to a few media. But I do rather conceive, that they had another kind of analytics, which went backwards through almost all the same steps by which their demonstrations went forwards, though of this we have no certain account, their writings being altogether silent on that particular. However, that such a way is practicable, I may hereafter, upon some other occasion, show by some examples ; whereby it will plainly appear, how much more useful it is for the finding out the ways for the solution of problems than that which is now generally known and practised by species."*^ *
hasten the progress. An instance of which kind I designed, some years since, to have given this honorable society, in some of my lectures upon the motions and in- fluences of the celestial bodies, if it had been then fit ; but 1 understand, the same thing will now be shortly done by Mr. Newton, in a Treatise of his, now in the press : But that will not he the only instance of that kind which I design to produce, for that I have diverse instances of the like nature, wherein, from a hypothesis being supposed, on a premeditated design, all the phenomena of the subject will be a pri- ori foretold, and the eifects naturally follow, as proceeding from a cause so and so qualified and limited. And, in truth, the synthetic way, by experiments and observations, will be very slow, if it be not often assisted by the analytic, which proves of excellent use, even though it proceed by a false position ; for that the discovery of a negative is one way of restraining and limiting an affirmative."
Change the places of the words analytic and synthetic in this last sentence ; and the remark coincides exactly with what Boscovich, Hartley, Le Sage, and many other authors, have advanced in favor of synthetical explanations from hypothetical theo- ries. I shall have occasion afterwards to offer some additiomal suggestions in support of their opinion, and to point out the limitations which it seems to require.
* Hookc's Post. Works, p. 68.
Of the illustrations here promised by Hooke of the utility of the analytical method in geometrical investigations, no traces, as far as I have observed, occur in his writ-
OF THE HUMAN MIND. 267
The foregoing remarks, although rather of a critical than of a philosophical nature, may, I hope, be of some use in giving a little more precision to our notions on this important subject. They are introduced here, not with the most distant view to any alteration in our es- tabUshed language, (which, in the present instance, ap- pears to me to be not only unexceptionable, but very happily significant of its true logical import,) but merely to illustrate the occasional influence of words over the most powerful understandings ; and the vagueness of the reasonings into which they may insensibly be be- trayed, by a careless employment of indefinite and am- biguous terms.
If the task were not ungrateful it would be easy to produce numerous examples of this from writers of the highest and most deserved reputation in the present times. I must not, however, pass over in silence the name of Condillac, who has certainly contributed, more than any other individual, to the prevalence of the logi- cal errors now under consideration. " I know well," says he on one occasion, " that it is customary to dis- tinguish different kinds of analysis ; the logical analysis, the metaphysical, and the mathematical ; but there is, in fact, only 07ie analysis ; and it is the same in all the sci- ences." * On another occasion, after quoting from the logic of Port Royal a passage in which it is said " That analysis and synthesis differ from each other, only as the road we follow in ascending from the valley to the moun- tain, differs from the road by which we descend from the mountain into the valley," — Condillac proceeds thus : " From this comparison, all I learn is, That the two methods are contrary to one another, and conse- quently, that if the one be good, the other must be bad. In truth we cannot proceed otherwise than from the known to the unknow^n. Now, if the thing unknown be upon the mountain, it will never be found by descending
ings. And it would appear from the following note by the editor, on the passage last quoted, that nothing important on the subject had been discovered among his papers.
" I do not any where find, that this was ever done by Dr. Hookc, and leave the usefulness tlierefore to be considered by the learned."
* La Logique, Seconde Partie, Chap. vii.
268 ELEMENTS OF THE PHILOSOPHY
into the valley; and if it be in the valley, it will not be found by ascending the mountain. There cannot, there- fore, be two contrary roads by which it is to be reached. Such opinions," Condillac adds, " do not deserve a more serious criticism."*
To this very extraordinary argument, it is unnecessary to offer any reply, after the observations already made on the analysis and synthesis of the Greek geometers. In the application of these two opposite methods to their respective functions, the theoretical reasoning of Con- dillac is contradicted by the universal experience of mathematicians, both ancient and modern; and is, in- deed, so palpably absurd, as to carry along with it its own refutation, to the conviction of every person capa- ble of comprehending the terms of the question. Nor w^ould it be found more conclusive or more intelHgible, if applied to the analysis and synthesis of natural phi- losophers ; or indeed to these words, in any of the vari- ous acceptations in which they have ever hitherto been understood. As it is affirmed, however, by Condillac, that " there neither is, nor can be, more than one analy- sis," a refutation of his reasoning, drawn from any par- ticular science, is, upon his own principle, not less con- clusive, than if founded on a detailed examination of the whole circle of human knowledge. I shall content my- self, therefore, on the present occasion, with a reference to the mathematical illustrations contained in the former part of this section.
With regard to the notion annexed to this word by Condillac himself, I am not certain if, after all that he has writen in explanation of it, I have perfectly seized his meaning. " To analyze," he tells us, in the begin- ning of his Logic, " is nothing more than to observe in a successive order the qualities of an object with the view of giving them in the mind that simultaneous order in which they co-exist." f In illustration of this defini- tion, he proceeds to remark. That " although with a single glance of the eye a person may discover a multi- tude of objects in an open champaign which he has pre-
* La Logiqiic, Secondc Paitie, Chap. vi. I La Logi()uc, Premiere Piirtic Chap, ii.
OF THE HUMAN MIND. 269
viously surveyed with attention, yet that the prospect is never more distinct, than when it is circumscribed with- in narrow bounds, and only a small number of objects is taken in at once. We always discern with accuracy but a part of what we see."
" The case," he continues, " is similar with the intel- lectual eye. I have, at the same moment, present to it, a great number of the familiar objects of my knowledge. I see the whole group, but am unable to mark the dis- criminating qualities of individuals. To comprehend with distinctness all that offers itself simultaneously to my view, it is necessary that I should, in the first place, decompose the mass ; — in a manner analogous to that in which a curious observer would proceed in decom- posing, by successive steps, the co-existent parts of a landscape. — It is necessary for me, in other words, to analyze my thoughts." *
The same author afterwards endeavours still farther to unfold his notion of analysis, by comparing it to the natural procedure of the mind in the examination of a machine. " If I wish," says he, " to understand a ma- chine, I decompose it, in order to study separately each of its parts. As soon as I have an exact idea of them all, and am in a condition to replace them as they were formerly, I have a perfect conception of the machine, having both decomposed and recomposed it." f
In all this, I must confess, there seems to me to be much, both of vagueness and of confusion. In the two first quotations, the word anahjsis is employed to denote nothing more than that separation into parts, which is necessary to bring a very extensive or a very complica- ted subject within the grasp of our faculties ; — a descrip- tion, certainly, which conveys but a very partial and imperfect conception of that analysis which is represent- ed as the great organ of invention in all the sciences and arts.J In the example of the machine, Condillac's
• Ibid. In this last paragraph, I have introduced one or two additional clauses which seemed to me necessary for convej-ine; clearly the author's idea. Those who take the trouble to compare it with the original, will be satisfied, that, in venturing on these slight interpolations, I had no wish to misrepresent his opinion.
t Ibid. Chap. iii.
X " Ce qu'on nomme mithode (Tinvention, n'est autre chose que I'analyse. Cost
®70 ELEMENTS OF THE PHILOSOPHY
language is somewhat more precise and unequivocal ; but when examined with attention, will be found to pre- sent an illustration equally foreign to his purpose. This is the more surprising, as the instance here appealed to might have been expected to suggest a juster idea of the method in question, than that which resolves into a literal rfe-composition and re-composition of the thing to be analyzed. That a man may be able to execute both of these manual operations on a machine, without ac- quiring any clear comprehension of the manner in which it performs its work, must appear manifest on the slight- est reflection ; nor is it less indisputable, that another person, without disengaging a single wheel, may gain by a process purely intellectual, a complete knowledge of the whole contrivance. Indeed, I apprehend, that it is in this way alone that the theory of any comphcated machine can be studied ; for it is not the parts, separate- ly considered, but the due combination of these parts, which constitutes the mechanism.* An observer, ac- cordingly, of common sagacity, is here guided by the logic of nature, to a species of analysis, bearing as much resemblance to those of mathematicians and of natural philosophers, as the very different nature of the cases admits of. Instead of allowing his eye to wander at large over the perplexing mazes of such a labyrinth, he begins by remarking the ultimate effect ; and thence proceeds to trace backwards, step by step, the series of intermediate movements by which it is connected with the vis motrix. In doing so, there is undoubtedly a sort of mental decomposition of the machine, inasmuch as all its parts are successively considered in detail ; but it is not this decomposition which constitutes the analysis. It is the methodical retrogradation from the mechanical effect to the mechanical power.f
elle qui a fait toutes les d^couvertes ; c'est par elle que nous retrouverons tout co qui a ^te trouv^." Ibid.
* If on any occasion, a literal decomposition of a machine should be found necessa- ry, it can only be to obtain a view of some of its parts, wliich in their combined state are concealed from observation.
f That tliis circumstance of retrogradation or inversion, figured more than any other in the imagination of Pappus, as the characteristical feature of geometrical analysis, appears indisputably from a clause already quoted from the preface to his 7th Book ; — T«i/ 'rotaurtiv %<fohov iviXuatv KuXov/ttv, eiov atdraXiv xiatv. To say, thoro-
OF THE HUMAN MIND. 271
The passages in Condillac to which these criticisms refer, are all selected from his treatise on Logic, writ- ten purposely to establish his favorite doctrine wath respect to the influence of language upon thought. The paradoxical conclusions into which he himself has been led by an unwarrantable use of the words analysis and synthesis, is one of the most remarkable instances which the history of modern literature furnishes of the truth of his general principle.
Nor does this observation apply merely to the pro- ductions of his more advanced years. In early hfe, he distinguished himself by an ingenious work, in which he professed to trace analytically the history of our sensa- tions and perceptions ; and yet it has been very justly remarked of late, that all the reasonings contained in it are purely synthetical. A very eminent mathematician of the present times has even gone so far as to mention it " as a model of geometrical synthesis." * He would, I apprehend, have expressed his idea more correctly, if, instead of the epithet geometrical, he had employed, on this occasion, logical or metaphysical ; in both of which sciences, as was formerly observed, the analytical and synthetical methods bear a much closer analogy to the • experimental inductions of chemistry and of physics, than to the abstract and hypothetical investigations of the geometer.
The abuses of language which have been now under our review will appear the less wonderful, when it is considered that mathematicians themselves do not always speak of analysis and synthesis with their char- acteristical precision of expression ; the former Avord being frequently employed to denote the modern calcu- lus, and the latter, the pure geometry of the ancients.
fore, as many writers have done, that the analysis of a geometrical problem consists in decomposing or resolving it in such a manner as may lead to the discovery of the composition or synthesis, — is at once to speak vaguely, and to keep out of view the cardinal principle on which the utility of the method hinges. There is, indeed, one species of decomposition exemplified in the Greek geometry ; — that which has for its object to distinguish all the various cases of a general problem ; but tliis part of the investigation was so far from being included by the ancients in their idea of analysis, that they bestowed upon it an appropriate name of its own ; — the three requisites to a complete solution being (according to Pappus) ivaXwira/, xo) ^uv^titui,
* M. Lacroix. See the Introduction to his Elements of Geometry.
272 ELEMENTS OF THE PHILOSOPHY
This phraseology, although it has been repeatedly cen- sured by foreign writers, whose opinions might have been expected to have some weight, still continues to prevail very generally upon the Continent. The learn- ed and judicious author of the History of Mathematics complained of it more than fifty years ago ; remarking the impropriety " of calling by the name of the synthetic method, that which employs no algebraical calculus, and which addresses itself to the mind and to the eyes, by means of diagrams, and of reasonings expressed at full , length in ordinary language. It would be more exact," he observes farther, "to call it the method of the ancients, which (as is now universally known) virtually supposes, in all its synthetical demonstrations, the previous use of analysis. As to the algebraical calculus, it is only an abridged manner of expressing a process of mathemat- ical reasoning ; — which process may, according to cir- cumstances, be either analytical or synthetical. Of the latter, an elementary example occurs in the algebraical demonstrations given by some editors of Euchd, of the propositions in his second Book." *
This misapphcation of the words analysis and synthe- sis, is not, indeed, attended with any serious inconven- iences, similar to the errors occasioned by the loose • phraseology of Condillac. It was surely better, however, that mathematicians should cease to give it the sanction of their authority, as it has an obvious tendency, — ^beside the injustice which it involves to the inestimable remains of Greek geometry, — to suggest a totally erroneous theory, with respect to the real grounds of the unrival- led and transcendant powers possessed by the modern calculus, when applied to the more complicated research- es of physics.f
• Histoiie des Mathematiques, par Montucla, Tome Premier, pp. 175, 176.
t In the ingenious and profound work of M. De Gerando, entitled, JDes Signes et de VArt de Penser, consideres dans leur rapports mutuels, there is a very valuable chapter on the Analysis and Synthesis of metaphysicians and of geometers. (See Vol. IV. p. 172.) The view of the subject which I have taken in the foregoing section, has but little in common with that given by this excellent philosopher ; but in one or two instances, where we have both touched upon the same points, (particularly in the strictures upon the logic of Condillac,) there is a general coincidence between our criticisms, which adds much to my confidence in my own conclusions.
OF THE HUMAN MIND. 273
SECTION IV.
THE CONSIDERATION OF THE INDUCTIVE LOGIC RESUMED.
I. •
Additional Remarks on the distinction between Experience and Analogy. — Of the grounds afforded by the latter for Scientific Inference and Conjecture.
In the same mannner in which our external senses are struck with that resemblance between different individ- uals which gives rise to a common appellation, our superior faculties of observation and reasoning, enable us to trace those more distant and refined simiUtudes which lead us to comprehend different species under one common genus. Here, too, the principles of our nature, already pointed out, dispose us to extend our conclusions from what is familiar to what is comparative- ly unknown ; and to reason from species to species, as from individual to individual. In both instances, the logical process of thought is nearly, if not exactly, the same ; but the common use of language has established a verbal distinction between them ; our most correct writers being accustomed (as far as I have been able to observe) to refer the evidence of our conclusions, in the one case, to experience, and in the other to analogy. The truth is, that the difference between these two de- nominations of evidence, when they are accurately analyzed, appears manifestly to be a difference, not in kijidy but merely in degree; the discriminative peculiari- ties of individuals invahdating the inference, as far as it rests on experience solely, as much as the characteristic- al circumstances which draw the line between different species and different genera.^'
* In these observations on the import of the word analogy, as employed in philoso- phical discussions, it gives me great pleasure to find that I have struck nearly into the same train of thinking with M. Prevost. I allude more particularly to the following passage in his Essais de Philosophie.
" Le mot Analogie, dans I'origine, n'cxprime que la resscmblance. Mais I'usage I'applique a une resscmblance eloignee : d'ou vient que les conclusions analogiques sont souvcnt hasardecs, et ont besoin d'etre deduites avec ait. Toutes les fois done
VOL. II. 35
274 ELEMENTS OF THE PHILOSOPHY
This difference in point of degree (it must at the same time be remembered) leads, where it is great, to impor- tant consequences. In proportion as the resemblance between two cases diminishes in the palpable marks which they exhibit to our senses, our inferences from the one to the other are made with less and less confidence ; and, therefore, it is perfectly right, that we should rea- son with more caution from species to species, than from individual to individual of the same kind. In what fol- lows, accordingly, I shall avail myself of the received distinction between the words experience and analogy ; a distinction which I have hitherto endeavoured to keep out of view, till I should have an opportunity of explain- ing the precise notion which I annex to it. It would, in truth, be a distinction of important use in our reasonings, if the common arrangements, instead of originating, as they have often done, in ignorance or caprice, had been really the result of an accurate observation and compar- ison of particulars. With all the imperfections of these arrangements, however, a judicious inquirer will pay so much regard to prevailing habits of thinking, as to dis- tinguish very scrupulously what common language refers to experience from what it refers to analogy, till he has satisfied himself, by a dihgent examination, that the dis- tinction has, in the instance before him, no foundation in truth. On the other hand, as mankind are much more disposed to confound things which ought to be distin-
que, dans nos raisonnemens, nous portons des jugeraens sercblables sur des objets qui n'ont qu'une ressemblance eloignee, nous laisonnons analogiquement. La res- semblance prochaine est celle qui fonde la premiere generalisation, celle qu'on nom- me I'esp^ce. On nomme eloignee la ressemblance qui fonde les generalisations superieures, c'est-a-dire, le genre et ses divers degres. Mais cette definition n'est pas rigoureusementsuivie.
" Quoiqu'il en soit, on concjoit des cas, entre lesquels la ressemblance est si parfaite, qu'il ne s'y trouve aucune difference sensible, si ce n'est celle du terns et du lieu. Et il est des cas dans lesquels on appcr(;oit beaucoup de ressemblance, mais ou I'on decouvre aussi quelques differences independantes de la diversite du temps etdulieu. Lorsque nous ferons un jugement general, fonde sur la premiere espece de ressem- blance, nous dlrons que nous usons de la methode d'induclion. Lorsque la seconde espece de ressemblance autorisera nos raisonnemens, nous dirons que c'est de la methode d'analogie que nous faisons usage. On dit ordinairemcnt que la methode d'induclion conclut du particulier au general, et que la methode d'analogie conclut du semblablc au semblable. Si I'on analyse ces definitions, on vena que nous n'avons fait autre chose que leur donner de la precision." {Essais de Philosophie, Tom. n. p. 202.)
Sec also the remarks on Induction and Analogy in the four following articles of M. Prdvost's work.
OF THE HUMAN MIND. 275
guished, than to distinguish things which are exactly or nearly similar, he will be doubly cautious in concluding, that all the knowledge which common language ascribes to experience is equally solid ; or that all the conjectures which it places to the account of analogy are equally suspicious.
A different idea of the nature of analogy has been given by some writers of note ; and it cannot be denied, that, in certain instances, it seems to apply still better than that proposed above. The two accounts, however, if accurately analyzed, would be found to approach much more nearly, than they appear to do at first sight ; or rather, I am inclined to think, that the one might be re- solved into the other, without much straining or over refinement. But this is a question chiefly of speculative curiosity, as the general remarks which I have now to offer, will be found to hold with respect to analogy, con- sidered as a ground of philosophical reasoning, in what- ever manner the word is defined ; provided only it be understood to express some sort of correspondence or affinity between two subjects, which serves, as a princi- ple of association or of arrangement, to unite them to- gether in the mind.
According to Dr. Johnson, (to whose definition I allude more particularly at present,) analogy properly means " a resemblance between things with regard to some circumstances or effects ; as when learning is said to enlighten the mind ; — that is, to be to the mind what light is to the eye, by enabling it to discover that which was hidden before." The statement is expressed with a precision and justness not always to be found in the definitions of this author ; and it agrees very nearly with the notion of analogy adopted by Dr. Ferguson, — that " things which have no resemblance to each other may nevertheless be analogous ; analogy consisting in a resemblance or correspondence of relations." * As an illustration of this. Dr. Ferguson mentions the analogy between the fin of a fisli and the wing of a bird ; the fin bearing the same relation to the water, which the
Principles of Moral and Political Science. Vol. I. p. 107.
276 ELEaiENTS OF THE PHILOSOPHY
wing does to the air. This definition is more particu- larly luminous, when applied to the analogies which are the foundation of the rhetorical figures of metaphor and allusion ; and it apphes also very happily to those which the fancy delights to trace between the material and the intellectual worlds ; and which (as I have re- peatedly observed) are so apt to warp the judgment in speculating concerning the phenomena of the human mind.
The pleasure which the fancy receives from the con- templation of such correspondences, real or supposed, obviously presupposes a certain disparity or contrast in the natures of the two subjects compared ; and, there- fore, analogy forms an associating principle, specifically different from resemblance, into which Mr. Hume's theo- ry would lead us to resolve it. An additional proof of this is furnished by the following consideration, That a resemblance of objects or events is perceived by sense^ and, accordingly, has some efi"ect even on the lower ani- mals ; a correspondence (or, as it is frequently called, a resemblance) of relations, is not the object of sense, but of intellect, and, consequently, the perception of it imphes the exercise of reason.
Notwithstanding, however, the radical distinction be- tween the notions expressed by the words resemblance and analogy, they may often approach- very nearly to each other in their meaning ; and cases may even be conceived, in which they exactly agree. In proof of this, it is sufficient to remark, that in objects, the parts of which respectively exhibit that correspondence which is usually distinguished by the epithet analogous, this correspondence always deviates, less or more, from an exact conformity or identity ; insomuch, that it some- times requires a good deal of consideration to trace in detail the parallel circumstances, under the disguises which they borrow from their diversified combinations. An obvious instance of this occurs when we attempt to compare the bones and joints in the leg and foot of a man with those in the leg and foot of a horse. Were the correspondence in all the relations perfectly exact, the resemblance between the two objects would be manifest
OF THE HUMAN MIJVD. 277
even to sense ; in the very same manner that, in geome- try, the similitude of two triangles is a necessary conse- quence of a precise correspondence in the i-elations of their homologous sides.*
This last observation may serve, in some measure, to justify an assertion which was already hazarded, — That the two definitions of analogy formerly mentioned, are very nearly allied to each other ; — inasmuch as it shows by a more careful analysis than has commonly been ap- phed to this subject, that the sensible dissimilitude be- tween things of different species arises chiefly from the want of a palpable conformity in the relations of their constituent parts. Conceive that more remote corres- pondence which reason or fancy traces between the parts of the one and the parts of the other, gradually to approach nearer and nearer to the same standard ; and it is evident, that, in the course of the approximation, you will arrive at that degree of manifest resemblance, which will bring them under the same generic name ; till at last, by continuing this process of the imagination, the one will become a correct picture or image of the other, not only in its great outlines, but in its minutest details.
From this view of the subject, too, as well as from the former, it appears, how vague and ill defined the meta- physical hmits are which separate the evidence of analogy from that of experience ; and how much room is left for the operation of good sense, and of habits of scientific research, in appreciating the justness of that authority which, in particular instances, the popular forms of speech may assign to either.
The illustrations which I have to ofi'er of this last re- mark, in so far as it relates to experience, may, I think, be introduced more usefully afterwards ; but the vague conceptions which are generally annexed to the word analogy, together with the prevailing prejudices against it, as a ground of philosophical reasoning, render it proper for me, before proceeding any farther, to attempt the correction of some popular mistakes connected with the use of this obnoxious term.
* See Note (Q.)
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It is not necessary for the purposes which I have at present in view, to investigate very curiously the princi- ples, which, in the first instance, dispose the mind to indulge in analogical conjectures from the known to the unknown. It is sufficient to observe, that this dis- position, so far from being checked, receives additional encouragement from habits of philosophical study ; — the natural tendency of these habits being only to guide it into the right path and to teach it to proceed cautiously, according to certain general rules, warranted by experi- ence.
The encouragement which philosophical pursuits give to this natural disposition, arises chiefly from the innu- merable proofs they afford of that systematical unity and harmony of design which are every where conspic- uous in the universe. On this unity of design is found- ed the most soHd argument which the light of reason supphes for the unity of God ; but the knowledge of the general fact on which that argument proceeds is not confined to the student of theology. It forces itself irresistibly on the thoughts of all who are famiharly con- versant with the phenomena, either of the material or of the moral world ; and is recognised as a principle of rea- soning, even by those who pay httle or no attention to its most sublime and important application.
It is well known to all who have the slightest ac- quaintance with the history of medicine, that the ana- tomical knowledge of the ancients was derived almost entirely from analogical conjectures, founded on the dissection of the lower animals ; * and that, in conse-
* " If we read the works of Hippocrates with impartiality, and apply his accounts of the parts to what we now know of the human body, we must allow his descrip- tions to he imperfect, incorrect, sometimes extravagant, and often unintelligible, that of the bones only excepted. He seems to have studied these with more suc- cess than the other parts, and tells us, that he had an opportunity of seeing a human skeleton."
" Erasistratus and Herophilus, two distinguished anatomists at Alexandria, were probably the first who were authorized to dissect human bodies. Their voluminous works are all lost : but they are quoted by Galen, almost in every page." . . .
" What Galen principally wanted was opportunities of dissecting human bodies, for his subject was most commonly some quadruped, wliose structure was supposed to come nearest to the human."
" About the year 1.540, the great Vesalius appeared. He was equally laborious in reading the ancients, and in dissecting bodies ; and in making the comparison, he could not but see, that many of Galen's descriptions were erroneous. — The spirit of
OF THE HUMAN MIND. 279
queiice of this, many misrepresentations of facts, and many erroneous theories, (blended however, with various important truths,) were transmitted to the physiologists of modern Europe. What is the legitimate inference to be deduced from these premises ? Not, surely, that analogy is an organ of no use in the study of nature ; but that, although it may furnish a rational ground of conjecture and inquiry, it ought not to be received as direct evidence, where the fact itself lies open to exam- ination ; and that the conclusions to which it leads ought, in every case, to be distrusted, in proportion as the sub- jects compared depart from an exact coincidence in all their circumstances.
As our knowledge of nature enlarges, we gradually learn to combine the presumptions arising from analogy, with other general principles by which they are limited and corrected. In comparing, for example, the anatomy of different tribes of animals, we invariably find, that the differences in their structure have a reference to their way of life, and to the habits for which they are destin- ed ; so that, from knowing the latter, we might be able, on some occasions, to frame conjectures a priori con- cerning the former. It is thus, that the form of the teeth, together with the length and capacity of the in- testines, vary in different species, according to the qual- ity of of the food on which the animal is to subsist. Similar remarks have been made on the different situa- tion and disposition of the mammcE, according as the animal is uniparous, or produces many at a birth ; on the structure and direction of the external ear, according as the animal is rapacious, or depends for security on his speed ; — on the mechanism of the pupil of the eye, ac- cording as the animal has to search for his food by day or by night, — and on various other organs in the bodily
opposition and emulation was presently roused, and many of his contemporaries endeavoured to defend Galen at the expense of Vesalius. In their disputes they made their appeals to the liunian body ; and thus in a few years our art was greatly improved. And Vesalius being detected in the very fault which he condemns in Galen, to wit, describing from the dissections of brutes, and not of the human body, it exposed so fully tha^ blunder of the older anatomists, that, in succeeding times, there has been little reason for such complaint.''
Introductory Lectures, delivered by Dr. William Hunter, to his last course of anat- omy, (London, 1784,) pp. 13, 19, 25, 40.
280 ELEMENTS OF THE PHILOSOPHY
economy, when compared with the functions which they are intended to perform. If, without attending to cir- cumstances of this sort, a person should reason confi- dently from the anatomy of one species to that of anoth- er, it cannot be justly said, that analogy is a deceitful guide, but that he does not know how to apply analogy to its proper purpose. In truth, the very consideration which gives to the argument from analogy its chief force, points here manifestly to the necessity of some modifi- cation of the original conclusion, suited to the diversity of the case to which it is to be applied.
It is remarked by Cuvier, that " a canine tooth, adapt- ed to tear flesh, was never found combined in the same animal with a hoof, fit for supporting the weight of the body, but totally useless as a weapon to a beast of prey." — " Hence," he observes, " the rule that every hoofed animal is herbivorous ; — and hence (as corollaries from this general principle) the maxims, that a hoofed foot indicates grinding teeth with flat surfaces, a long ahmentary canal, a large stomach, and often more stom- achs than one, with many other similar consequences.
" The laws which regulate the relations between dif- ferent systems of organs," continues this very ingenious and sound philosopher, " have the same influence on the difl"erent parts of the same system, and connect to- gether its diff'erent modifications, by the same necessary principles. In the alimentary system, especially, where the parts are large and numerous, these rules have their most striking applications. The form of the teeth, the length, the convolutions, the dilatations of the ahmentary canal, the number and abundance of the gastric hquors, are in the most exact adaptation to one another, and have similar fixed relations to the chemical composition, to the soUd aggregation, and to the solubihty of the ahment ; insomuch that, from seeing one of the parts by itself, an experienced observer could form conclu- sions tolerably accurate, with respect to the confor- mation of the other parts of the same system, and might even hazard more than random conjectures with respect to the organs of other functions.
" The same harmony subsists among the different parts
OF THE HUMAN MIND. 281
of the system of organs of motion. As all the parts of this system act mutually, and are acted upon, especially when the whole body of the animal is in motion, the forms of all the different parts are strictly related. There is hardly a bone that can vary in its surfaces, in its cur- vatures, in its protuberances, without corresponding va- riations- in other bones ; and in this way, a skilful natu- ralist, from the appearance of a single bone, will be often able to conclude to a certain extent, with respect to the form of the v/hole skeleton to which it belonged.
"These laws of co-existence," Cuvier adds, "which have just been indicated, are deduced by reasoning from our knowledge of the reciprocal influence of the functions and of the uses of the different organs of the body. Having confirmed them by observation, we are en- abled, in other circumstances, to follow a contrary route ; and, when we discover constant relations of form between particular organs, we may safely conclude, that they exercise some action upon one another ; and we may thus be frequently led to form just conjectures with re- spect to their uses. — It is, indeed, chiefly from the atten- tive study of these relations, and from the discovery of relations which have hitherto escaped our notice, that physiology has reason to hope for the extension of her limits ; and, accordingly, the comparative anatomy of animals is to her one of the most fruitful sources of val- uable discovery." *
The general result of these excellent observations is, that the improvement of physiology is to be expected chiefly from lights furnished by analogy ; but that, in order to follow this guide with safety, a cautious and re- fined logic is still more necessary than in conducting those reasonings which rest on the direct evidence of experience. When the ancient anatomists, without any examination of the facts within their reach, or any con- sideration of the peculiar functions likely to be connect- ed with man's erect form and rational faculties, drew in- ferences concerning his internal frame, merely from the
* See the Introduction to the Lerons d'Anatomie comparee de G. Cuvier. The ahove translation is taken from a very interesting tract, entitled, An Introduction to the Study of the Animal Economy. (Edinburgh, 1801.)
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282 ELEMENTS OF THE PHILOSOPHY
structure of the quadrupeds ; the errors into which they fell, — so far from affording any solid argument against the use of analogy when judiciously employed, — have only pointed out to their successors the necessity of a more discriminating and enhghtened apphcation of it in future ; and have ultimately led to the discovery of those comprehensive Laws of the Animal Economy, which, by reconciling apparent anomalies with the con- sistency and harmony of one grand design, open, at eve- ry successive ?tep of our progress, more enlarged and pleasing views of the beneficent wisdom of nature.
This speculation might be carried farther, by extend- ing it to the various analogies which exist between the Animal and the Vegetable kingdoms, contrasted with those characteristical pecuharities by which they are re- spectively adapted to the purposes for which they are destined. It is, however, of more consequence, on the present occasion, to turn our attention to the analogies observable among many of the physical processes by which different effects are accomphshed, or different phenomena produced, in the system of inanimate and unorganized matter. Of the existence of such analo- gies, a satisfactory proof may be derived, from the ac- knowledged tendency of philosophical habits and scien- tific pursuits, to familiarize the mind with the order of nature, and to improve its penetration in anticipating fu- ture discoveries. A man conversant with physics and chemistry is much more likely than a stranger to these studies to form probable conjectures concerning those laws of nature which still remain to be examined. There is a certain character or style (if I may use the expreS' sion) in the operations of Divine Wisdom ; — something which every where announces, amidst an infinite variety of detail, an inimitable unity and harmony of design ; and in the perception of which jjhilosophical sagacity and genius seem chiefly to consist. It is this which bestows a value so inestimable on the Queries of Newton.*
* How very deeply Newton's mind was impressed with those ideas of analogy which I have hero ventured to ascribe to him, appears from his own words. " Have not the same particles of bodies certain powers, virtues, or forces, by which they act at a distance, not only upon the rays of light for reflecting, refrticting, and inflecting
OF THE HUMAN MIND. 283
This view of the numberless analogies displayed in that part of the universe which falls under our immedi- ate notice, becomes more particularly impressive, when it is considered, that the same unity of design may be distinctly traced, as far as the physical researches of as- tronomers have extended. In the knowledge of this fact, we possess important moral Ughts, for which we are entirely indebted to the Newtonian school ; the univer- sal creed of antiquity having assumed as a principle, that the celestial phenomena are, in their nature and laws, essentially difierent from the terrestrial. The Persian Magi, indeed, are said to have laid down, as one of their maxims, — avf-iTtadrj elvat id avco rots ycaTa ; — but that no maxim could stand in more direct opposition to the tenets of the Grecian philosophers, appears sufficiently from the general strain of their physical and astronomi- cal theories. The modern discoveries have shovvn, with demonstrative evidence, how widely, in this fundamental assumption, these philosophers erred from the truth ; and, indeed, it was a conjecture a priori^ originating in some degree of scepticism with respect to it, that led the way to the doctrine of gravitation. Every subse- quent step which has been gained in astronomical sci- ence has tended more and more to illustrate the sagaci- ty of those views by which Newton was guided to this fortunate anticipation of the truth ; as well as to con- firm, upon a scale which continually grows in its magni- tude, the justness of that magnificent conception of uni- form design, which emboldened him to connect the physics of the Earth with the hitherto unexplored mys- teries of the Heavens.
Instructive and interesting, however, as these physi- cal speculations may be, it is still more pleasing to trace
them, but also upon one anollicr, for pioducina; a great i)art of the phenomena of na- ture ? For it is well known that bodies act one upon another, by the attractions of gravity, magnetism, and electricity ; and these instances show the tenor and course of nature, and make it not improbable but that there maij be more attractive pow- ers than these. For nature is very consonant and conformable to herself." See the 31st Query, at tlic end of his Optics,
In a subsequent part of tiiis (Jurry he recurs to the same principle. " .\nd thus J\\itu7'e loill be very conformable to herself and very simple ; perforniinc,- all the great motions of the licavenly bodies by the attraction of gravity, wiiich intercedes those bodies ; and almost all the small ones of their particles, some other atti-active and repelling powers, which intercede the particles."
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the uniformity of design which is displayed in the econ- omy of sensitive beings ; to compare the arts of human Ufe with the instincts of the brutes, and the instincts of the different tribes of brutes with each other ; and to re- mark, amidst the astonishing variety of means which are employed to accompHsh the same ends, a certain analo- gy characterize them all ; — or to observe, in the minds of different individuals of our own species, the workings of the same affections and passions, manifesting, among men of every age and of every country, the kindred fea- tures of humanity. It is this which gives the great charm to what we call Jfature in epic and dramatic com- position,— when the poet speaks a language " to which every heart is an echo," and which, amidst the manifold effects of education and fashion, in modifying and dis- guising the principles of our constitution, reminds all the various classes of readers or of spectators, of the exist- ence of those moral ties which unite them to each other, and to their common parent.*
Nor is it only in the material and moral worlds, when considered as separate and independent systems, that this unity of design is perceptible. They mutually bear to each other numberless relations^ which are more par- ticularly remarkable, when we consider both, in their combined tendencies with respect to human happiness and improvement. There is also a more general analo- gy, which these two grand departments of nature exhib- it, in the laiDs by which their phenomena are regulated, and a consequent analogy between the methods of in- vestigation peculiarly applicable to each. I have already repeatedly taken notice of the erroneous conclusions to which we are hable, when we reason directly from the one to the other ; or substitute the fanciful analogies between them, which language occasionally suggests, as a philosophical explanation of the phenomena of either. But it does not follow from this, that there is no analogy between the rules of inquiry, according to which they are to be studied. On the contrary, it is from the prin- ciples of inductive philosophizing, which are applicable
* Outlines of Moral Philosojiliy, pp. 198, 199, 3d. Edit.
OF THE HUMAN MIND. 285
to both in common, that we infer the necessity of resting our conclusions in each, upon its own appropriate phe- nomena.
I shall only add, to what has been now stated on the head of analogy, that the numberless references and de- pendencies betv/een the material and the moral worlds, exhibited within the narrow sphere of our observation on this globe, encourage, and even authorize us to con- clude, that they both form parts of one and the same plan ; — a conclusion congenial to the best and noblest principles of our nature, and which all the discoveries of genuine science unite in confirming. Nothing, indeed, could be more inconsistent with that irresistible disposi- tion which prompts every philosophical inquirer to argue from the known to the unknown, than to suppose that, while ail the different bodies which compose the materi- al universe are manifestly related to each other, as parts of a connected ivhole, the moral events which happen on our planet are quite insulated ; and that the rational be- ings who inhabit it, and for whom we may reasonably presume it was brought into existence, have no relation whatever to other intelligent and moral natures. The presumption unquestionably is, that there is one great 77ioral system, corresponding to the material system : and that the connexions which we at present trace so dis- tinctly among the sensible objects composing the one, are exhibited as so many intimations of some vast scheme, comprehending all the intelligent beings who compose the other. In this argument, as well as in numberless others, which analogy suggests in favor of our future prospects, the evidence is precisely of the same sort with that which first encouraged Newton to extend his physiccJ speculations beyond the hmits of the Earth. The sole difference is, that he had an opportu- nity of verifying the results of his conjectures by an ap- peal to sensible facts : but this accidental circumstance (although it certainly aff"ords peculiar satisfaction and conviction to the astronomer's mind) does not affect the grounds on which the conjecture was originally formed, and only furnishes an experimental proof of the justness of the principles on which it proceeded. Were it not.
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however, for the palpable confirmation thus obtained of the Theory of Gravity, it would be difficult to vindicate against the charge of presumption, the mathematical ac- curacy with which the Newtonians pretend to compute the motions, distances, and magnitudes of worlds, ap- parently so far removed beyond the examination of our faculties.*
The foregoing observations have a close connexion with some reasonings hereafter to be offered in defence of the doctrine of final causes. They also throw addi- tional light on what was remarked in a former chapter concerning the unity of truth : — a most important fact in the theory of the human mind, and a fact which must strike every candid inquirer with increasing evidence, in proportion to the progress v/hich he makes in the mter- pretation of Jfature. Hence the effect of philosophical habits in animating the curiosity, and in guiding the in- ventive powers ; and hence the growing confidence which they inspire in the ever-consistent and harmonious conclusions of inductive science. It is chiefly (as Ba- con has observed) from partial and desultory researches that scepticism arises ; not only as such researches sug- gest doubts which a more enlarged acquaintance with
* " I know no author," says Dr. Reid, " who has made a more just and a more happy use of analogical reasoning, than Bishop Butler, in his Analogy of Religion, Natural and Revealed, to the Constitution and Course of Nature. In that excellent work, the author does not ground any of the truths of religion upon Analogy, as their proper evidence. He only makes use of Analogy to answer objections against them. When objections are made against the truths of religion, which may be made with equal strength against what we know to be true in the course of nature, such objections can have no weight." — Essays on the Intell. Powers, p. 54.
To the same purpose itis observed by Dr. Campbell, that " analogical evidence is generally more successful in silencing objections than in evincing truth. Though it rarely refutes, it frequently repels refutation ; like those weapons which, though they cannot kill the enemy, will ward his blows." — Pkil. of Rhet. Vol. I. p. 145.
This estimate of the force of analogical reasoning, considered as a weapon of con- troversy, is discriminating and judicious. The occasion on which the logician wields it to the best advantage is, undoubtedly, in repelling the objections of an adversary. But after the foregoing observations, I may be permitted to express my doubts, whether both of these ingenious writers have not somewhat underrated the import- ance of analogy as a medium of proof, and as a source of new information. — I ac- knowledge, at the same time, that between the positive and the negative applications of this species of evidence, there is an essential dlflt'erence. When employed to re- fute an objection, it may often furnish an argument irresistibly and unanswerably con- vincing : when employed as a medium of i)roof, it can never authorize more tiian a probable conjecture, inviting and encouraging farther examination. In some instan- ces, however, the probability resulting fmiu a concurrence of did'ercnt analogies may rise so higli, as to proeluce anelfcct on the belief scarcely distinjjuishable Irom moral ceitahily.
OF THE HUMAN MIND. 287
the universe would dispel, but as they withdraw the at- tention from those comprehensive views which combine into a symmetrical fabric — all whose parts mutually lend to each other support and stabihty — the most remote, and seemingly the most unconnected discoveries. " Ete- nim symmetria scientics, singulis scilicet partibiis se invicem sustinentibics, est, et esse debet, vera atque expedita ra- tio refellendi objectiones minorum gentium : Contra, si singula axiomata, tanquam baculos fascis seorsim extra- has, facile erit ea infirmare, et pro libito, aut flectere, aut frangere. JNTum non in aula spatiosa consultius foret, unum accendere cereum, aut lychnuchum suspendere, variis luminibus instructum, quo omnia simul perlustren- tur, quam in singulos angulos quaquaversus exiguam cir- cumferre lucernam 7 " *
II.
Use and Abuse of Hypotheses in Philosophical Inquiries. — Difference between Gra- tuitous Hypotheses, and those which are suppported by Presumptions suggested by Analogy. — Indirect Evidence which a Hypothesis may derive from its agree- ment with the Phenomena. — Cautions against extending some of these Conclu- sions to the Philosophy of the Human Mind.
As some of the reasonings in the former part of this Section may, at first sight, appear more favorable to the use of Hypotheses than is consistent with the severe rules of the Inductive Logic, it may not be superfluous to guard against any such misapprehensions of my mean- ing, by subjoining a few miscellaneous remarks and il- lustrations.
The indiscriminate zeal against hypotheses, so gener- ally avowed at present by the professed followers of Ba- con has been much encouraged by the strong and deci- ded terms in which, on various occasions, they are repro- bated by Newton.f But the language of this great man, when he happens to touch upon logical questions, must
* De Augment. Scient. Lib. i.
I " Hypotheses non fingo. Quicquid enim ex phcnoracnis non dedncitur hypothe- sis vocanda est, ct hypotheses, seu metaphysical, sen physicie, scu qualitatum occul- tarum, scu niechanic;n, in philosophiri, cxperimentali locum non habcnt." Sec the general Scholium at tlic end of the Principia.
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not always be too literally interpreted. It must be qual- ified and limited, so as to accord with the exemplifica- tions which he himself has given of his general rules. Of the truth of this remark, the passages now alluded to afibrd a satisfactory proof ; for, while they are ex- pressed in the most unconditional and absolute terms, so many exceptions to them occur in his own writings, as to authorize the conclusion, that he expected his read- ers would of themselves be able to supply the obvious and necessary comments. It is probable that, in these passages, he had more particularly in his eye the Vorti- ces of Des Cartes.
" The votaries of hypotheses," says Dr. Reid, " have often been challenged to show one useful discovery in the works of nature that was ever made in that way." * In reply to this challenge, it is sufficient, on the present occasion, to mention the theory of Gravitation, and the Copernican system. f Of the former we have the testi- mony of Dr. Pemberton, that it took its first rise from a conjecture or hypothesis suggested by analogy ; nor, in- deed, could it be considered in any other light, till that period in Newton's life, wdien, by a calculation founded on the accurate measurement of the earth by Picard, he evinced the coincidence between the law which regu- lates the fall of heavy bodies, and the power which re- tains the Moon in her orbit. The Copernican system, however, furnishes a case still stronger, and still more directly applicable to our purpose ; inasmuch as the only evidence which the author was able to ofier in its favor, was the advantage which it possessed over every other hypothesis, in explaining, with simplicity and beauty, all the phenomena of the heavens. In the mind of Co- pernicus, therefore, this system was nothing more than a hypothesis ; — but it was a hypothesis conformable to
* Essays on the Intellectual Powers of Man, p. 88, 4to Edit. In another part of the same volume, the following assertion occurs. " Of all the discoveries that have been made concerning the inward structure of the human body, never one was made by conjecture. — The same tiling may be said, with justice, of every other part of the works of God, wherein any real discovery has been made. Such discoveries have always been made by patient observation, by accurate experiments, or by conclusions drawn by strict reasoning from observations and experiments ; and such discoveries have always tended to refute, but not to confirm, the theories and hypotheses which ingenious men had invented." Ibid. p. 49.
t See Note (R.)
OF THE HUMAN MIND. ^9
the universal analogy of nature, always accomplishing her ends by the simplest means. " C'est pour la simpli- cite,^'' says Bailly, " que Copernic replacale soleil au cen- tre du monde ; c'est pour elle que Kepler va detruire tons les epicycles que Copernic avoit laisses subsister : peu de principes, de grands moyens en petit nombre, des phenomenes infinis et varies, voila le tableau de I'univers." *
According to this view of the subject, the confidence which we repose in Analogy rests ultimately on the ev- idence of Experience ; and hence, an additional argu- ment in favor of the former method of investigation, when caudously followed ; as well as an additional proof of the imperceptible shades by which Experience and Analogy run into each other.
Nor is the utility of hypothetical theories confined to those cases in which they have been confirmed by sub- sequent researches : it may be equally great, where they have completely disappointed the expectations of their
t Histoiie de T Astionomie Moderne, Tome II. p. 2.
From this anticipation of simplicity in the laws of nature, (a logical jirinciple not less universally recognised among ancient than among modern philosophcis,) Bailly has drawn an argument in support of his favorite hypothesis concerning the origin of the sciences. His words are these : " La simplicite n'est pas essenticliement un principe, un axiome, c'est lo resultat des travaux ; ce n'est pas une idee de I'enfance du monde, elle appartient a la maturite des hommes; c'est la plusgrande des verites que I'observation constante arrache a I'illusion des effets : cene peutetre qu'un resto de la science piiinilive. Lorsque chez un peu]ile, possesseur d'une mythologie com- pliquee,et qui n'a d'autre physique que ces fables, les philosoplies, voulaiil reduire la nature a un seul principe, annonceront que I'eau est la source de toutes choses, ou le feu I'agent universe], nous dirons a ces phiiosophes : Vous parlez une langue qui n'est pas la votrc ; vous avez saisi par un instinct pliilosophique ces verites au-des- sus de votre siecle, de votre nation, et de vous-memes ; c'est la sagesse des anciena qui vous a ete transmise par tradition," &c. &c. Sec. — Ibid. p. 4.
To the general remark which introduces this passage I readily subscribe. The con- fidence with which philosophers anticipate the simplicity of Nature's laws is unques- tionably the result of experience, and of experience alone ; and implies a far more extensive knowledge of her operations than can be expected from the uninformed multitude. The inference, however, deduced from this, by the ingenious and elo- quent, but sometimes too fanciful historian, is not a little precipitate. The passion for excessive simplification, so remarkably exemplified in the physical systems of the Greeks, seems to be sufficiently accounted for by their scanty stock of facts, combin- ed with that aml)ition to explain every tiling from the smallest possilije number of data, which, in all ages of the world, has been one of the most common infiruiilies of genius. On the other hand, the principle in question, when stated in the form of a proposilion, is of so abstract and metaphysical a nature, that it is hiiihiy improba- ble it should have survived the shock of revolutions which had proved fatal to the memory of particular discoveries. The arts, it has been frequently observed, are more easily transmitted by mere tradition, from one generation to another, than the speculative .sciences ; and, for a similar reason, physical .'systems are far less likely to sink into oblivion, than abstract maxims, which have no immediate reference lo "ob- jects of sense, or to the ordinary concerns of life.
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authors. Nothing, I think, can be juster than Hartley's remark, that " any hypothesis which possesses a sufficient degree of plausibihty to account for a number of facts, helps us to digest these facts in proper order, to bring new ones to hght, and to make experimenta crucis for the sake of future inquirers," * Indeed, it has probably been in this way that most discoveries have been made j for although a knowledge of facts must be prior to the formation of a legitimate theory ; yet a hypothetical theory is generally the best guide to the knowledge of connected and of useful facts.
The first conception of a hypothetical theory, it must always be remembered, (if the theory possesses any plausibility whatever) presupposes a general acquaint- ance with the phenomena which it aims to account for ; and it is by reasoning synthetically from the hypothesis, and comparing the deductions with observation and experiment, that the cautious inquirer, is gradually led, either to correct it in such a manner as to reconcile it w^ith facts, or finally to abandon it as an unfounded con- jecture. Even in this latter case, an approach is made to the truth in the way of exclusion; while, at the same time, an accession is gained to that class of associated and kindred phenomena which it is his object to trace to their parent stock. f
In thus apologizing for the use of hypotheses, I only repeat in a different form the precepts of Bacon, and the comments of some of his most enlightened followers. "The prejudice against hypotheses which many people entertain," says the late Dr. Gregory, " is founded on the equivocal signification of a word. It is commonly confounded with theory ; — but a hypothesis properly means the supposition of a principle, of whose existence there is no proof from experience, but which may be
* Observations on Man, Cliap. i. Piop. v.
f " llliul inteiiiTi moneinus ; lit nemo animo concidat, atit quasi confundatuv, si ex- perimenta, quibtis inciimbit, expectationi sua; non rcspondeant. Eteniin quod succe- dit, niagis cornplace ; at quod non succedit, sajpcnutnero non minus informat. At- que illud semper in animo tenendum, experimenta lucifera etiam adhuc magis, quani fructifera ambi^nda esse. Atque dc literata experientid li;pc dicta sint ; quaj sa-
tacitas potius est, et odoratio qutsdam venatica, quam scientia." De Augm. Sclent, ib V. Cap, ii.
OF THE HUMAI^ MIND. 291
rendered more or less probable by facts which are nei- ther numerous enough nor adequate to infer its exist- ence. When such hypotheses are proposed in the modest and diffident manner that becomes mere suppo- sitions or conjectures, they are not only harmless, but even necessary for establishing a just theory. They are the first rudiments or anticipation of Principles. With- out these, there could not be useful observation, nor experiment, nor arrangement, because there could be no motive or principle in the mind to form them. Hypoth- eses then only become dangerous and censurable, when they are imposed on us for just principles ; because, in that case, they put a stop to further inquiry, by leading the mind to acquiesce in principles which may as prob- ably be ill as well founded." *
Another eminent writer has apologized very ingenious- ly, and I think very philosophically, for the hypotheses and conjectures which are occasionally to be found in his own works. The author I mean is Dr. Stephen Hales, who, in the preface to the second volume of his Vegetable Statics, has expressed himself thus :
" In natural philosophy we cannot depend on any mere speculations of the mind ; we can only reason with any tolerable certainty from proper data, such as arise from the united testimony of many good and cred- ible experiments.
" Yet it seems not unreasonable on the other hand, though not far to indulge, to carry our reasonings alitde farther than the plain evidence of experiment will war- rant ; for since at the uttermost boundaries of those things which we clearly know, a kind of twilight is cast on the adjoining borders of Terra Incognita, it seems reasonable, in some degree, to indulge conjecture there ; otherwise we should m.ake but very slow advances, either by experiments or reasoning. For new experiments and discoveries usually owe their first rise only to lucky guess- es and probable conjectures ; and even disappointments in these conjectures often lead to the things sought for."
To these quotations I shall add two short extracts
•Lectures on the Duties and the Qualifications of r Physician.
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from Dr. Hooke, (the contemporary, or rather the pre- decessor of Newton,) whose acute and original remarks on this subject reflect the greater credit on his talents, that they were published at a period, when the learned body of which he Vv^as so illustrious an ornament, seem plainly to have been more disposed to follow the letter of some detached sentences, than to imbibe the general spirit of Bacon's logic.
" There may be use of method in the collecting of materials as well as in the employment of them ; for there ought to be some end and aim ; some predesign- ed module and theory; some purpose in our experiments. And though this Society have hitherto seemed to avoid and prohibit preconceived theories and deductions from particular and seemingly accidental experiments ; yet I humbly conceive, that such, if knowingly and judiciously made, are mattters of the greatest importance ; as giv- ing a characteristic of the aim, use, and signification thereof; and without which many, and possibly the most considerable particulars, are passed over without regard and observation." *
"Where the data on which our ratiocinations are founded are uncertain and only conjectural, the conclu- sions or deductions therefrom can at best be no other thaa probable, but still they become more and more probable, as the consequences deduced from them appear, upon examinations by trials and designed observations, to be confirmed by fact or effect. So that the effect is that which consummates the demonstration of the invention ; and the theory is only an assistant to direct such an in- quisition as may procure the demonstration of its exist- ence or non-existence. "f
As an illustration of this last remark, Hooke mentions his anticipation of Jupiter's motion upon his axis, long before he was able, by means of a good telescope, to ascertain the fact. A much more remarkable instance, however, of his philosophical sagacity, occurs in his anticipation of that theory of the planetary motions,
• Hooke's Poslhumous Works, p. 280.
t Ibid, p. 537. For another extract from the same work, see Note (S.)
OF THE HUMAN MIND. 293
which, soon after, was to present itself, with increased and at length demonstrative evidence, to a still more in- ventive and powerful mind. This conjecture (which I shall state in his own words) affords, of itself, a decisive reply to the undistinguishing censures which have so often been bestowed on the presumptuous vanity of at- tempting, by means of hypotheses, to penetrate into the secrets of nature.
" I will explain," says Hooke, in a communication to the Royal Society in 1666, "a system of the world very different from any yet received. It is founded on the three following positions.
" 1. That all the heavenly bodies have not only a gravitation of their parts to their own proper centre, but that they also mutually attract each other within their spheres of action.
" 2. That all bodies having a simple motion, will con- tinue to move in a straight line, unless continually de- flected from it by some extraneous force, causing them to describe a circle, an ellipse, or some other curve.
" 3. That this attraction is so much the greater as the bodies are nearer. As to the proportion in which those forces diminish by an increase of distance, I own I have not discovered it, although I have made some experi- ments to this purpose. I leave this to others, who have time and knowledge sufhcient for the task."
The argument in favor of Hypotheses might be push- ed much farther, by considering the tentative or hypo- thetical steps by which the most cautious philosophers are often under the necessity of proceeding, in conduct- ing inquiries strictly experimental. These cannot be better described than in the words of Boscovich, the slightest of whose logical hints are entided to pecuhar attention. — " In some instances, observations and experi- ments at once reveal to us all that we wish to know. In other cases, we avail ourselves of the aid of hypothe- ses ; — by which loord, however, is to he understood, not fictions altogether arbitrary, but suppositions conformable to experience or to analogy. By means of these, we are enabled to supply the defects of our data, and to con- jecture or divine the path to truth ; always ready to
294 ELEMENTS OF THE PHILOSOPHY
abandon our hypothesis, when found to involve, conse- quences inconsistent with fact. And indeed, in most cases, I conceive this to^be the method best adapted to physics ; a science in which the procedure of the inquir- er may be compared to that of a person attempting to decipher a letter written in a secret character ; and in which legitimate theories are generally the slow result of disappointed essays, and of errors which have led the way to their own detection." *
Nor is it solely by the erroneous results of his own hy- potheses, that the philosopher is assisted in the investi- gation of truth. Similar lights are often to be collected from the errors of his predecessors ; and hence it is, that accurate histories of the different sciences may justly be ranked among the most effectual means of accelerating their future advancemement. It was from a review of the endless and hopeless wanderings of preceding inquirers, that Bacon inferred the necessity
* De Solis ac Lunae Defectibus. Lond. 1760, pp. 211, 212. For the continuation of the above passage, see Note (T.)
Many remarks to the same purpose may be found in Bacon. The following happen at present to occur to my memory:
" Deo (formarum inditori et opifici) et fortasse angelis competit, formas per affir- mationem immediate nosse, atque ab initio contemplationis. Sed certe supra homi- nem est ; cui tantum conceditur, procedere primo per negativas, et postremo loco
desinere in affi-rmativas, post omnimodain exclusionem Post rejec-
iionemet exclusionem debitis modis factam, secundo loco (tanquam in fundo) mane- bit (abeuntibus in fumum opinionibus volatilibus) forma affirmativa, solida, et vera. Atque hoc brevi dictu est, sed per multas ambages ad hoc pervenitur." — JVow. Org. Lib. II. Aphor. XV. XVI. _ '
" Prudens interrogatio, quasi dimidium scientia?. Idcirco quo amplior et certior fuerit anticipatio nostra; eo magis directa et compendiosa erit investigatio." — De ^ug. Scient. Lib. V. Cap. 3.
" Vaga experientia et se tantum sequens mera palpatio est, et homines potius stupe- facit, quam informat." — JVov. Org. Lib. I. Aphor. C.
The reader who wishes to prosecute farther this speculation concerning the use of hypotheses, may consult with advantage three short but interesting memoirs upon Method, by the late M. Le Sage of Geneva, which M. Prevost has annexed as a sup- plement to his Essais de Philosophie. That I may not be supposed, however, to acquiesce in all this author's views, 1 shall mention two strong objections to which some of them appear to me to be liable.
1. In treating of the method of Hypothesis, Le Sage uniformly contrasts it with that of Analogy, as if the two were radically distinct, and even opposite in their spirit ; whereas it seems evident, that some perception of analogy must have given birth to every hypothesis which possesses asuiiicient degree of plausibility to deserve farther examination.
2. In applying the rules of mathematical Method to Physics, he makes f^xr too little allowance for the essential difTcrence between the two sciences. This is more par- ticularly remarkable in his observations on the aid to be derived, in investigating the laws of nature, from the method of Exclusions, — so happily employed by Frenicle de Bessy (a Frencii mathematician of the 17th century) in the solution of some very difficult problems relating to numbers. — See Note (U.)
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of avoiding every beaten tract ; and it was this which encouraged him, — with a confidence in his own powers amply justified by the event — to explore and to open a new path to the mysteries of nature : Inveniam viam, aut faciam. In this respect, the maturity of reason in the species is analogous to that in the individual ; not the consequence of any sudden or accidental cause, but the fruit of reiterated disappointments correcting the mis- takes of youth and inexperience. " There is no sub- ject," says Fontenelle, " on which men ever come to form a reasonable opinion, till they have once exhausted all the absurd views which it is possible to take of it. What follies," he adds, " should we not be repeating at this day, if we had not been anticipated in so many of them by the ancient philosophers ! " Those systems, therefore, which are false, are by no means to be re- garded as altogether useless. That of Ptolemy (for ex- ample) as Bailly has well observed, is founded on a prejudice so natural and so unavoidable, that it may be considered as a necessary step in the progress of astro- nomical science ; and if it had not been proposed in ancient times, it would infallibly have preceded, among the moderns, the system of Copernicus, and retarded the period of its discovery.
In what I have hitherto said in defence of the method of Hypothesis, I have confined myself entirely to its utility as an organ of investigation ; taking all along for granted, that, till the principle assumed has been fairly inferred as a law of nature, from undoubted facts, none of the explanations which it affords are to be admitted as legitimate theories. Some of the advocates for this method have however gone much farther ; asserting, that if a hypothesis be sufficient to account for all the phenomena in question, no other proof of its conformity to truth is necessary. " Supposing," says Dr. Hartley, " the existence of the (kther to be destitute of all direct evidence, still, if it serves to explain and account for a great variety of phenomena, it will, by this means, have an indirect argument in its favor. Thus, we admit the key of a cipher to be a true one, when it explains ^the cipher completely ; and the decipherer judges himself
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to approach to the true key, in proportion as he advan- ces in the explanation of the cipher ; and this without any direct evidence at all."* On another occasion, he observes, that " Philosophy is the art of deciphering the mysteries of nature ; and that every theory which can explain all the phenomena, has the same evidence in its favor, that it is possible the key of a cipher can have from its explaining that cipher." f
The same very ingenious and plausible reasoning is urged by Le Sage in one of his posthumous fragments ; J and, long before the publication of Hardey's work, it had struck Gravesande so strongly, that, in his Ititroduc- tio ad Philosophiam, he has subjoined to his chapter on the Use of Hypotheses, another on the Art of Decipher- ing. Of the merit of the latter it is no slight proof, that D'Alembert has inserted the substance of it in one of the articles of the Encyclopedie.^
In reply to Hartley's comparison between the business of the philosopher and that of the decipherer, Dr. Reid observes, that " to find the key requires an understand- ing equal or superior to that which made the cipher. This instance, therefore," he adds, " will then be in point, when he who attempts to decipher the works of nature by a hypothesis, has an understanding equal or superior to that which made them." ||
This argument is not stated with the author's usual correctness in point of logic ; inasmuch as the first proposition contrasts the sagacity of the decipherer with that of the contriver of the cipher ; and the second, Avith that of the author of the composition deciphered. Nor
* Observations on Man, Vol. L pp. 15, 16. (4th Edit.)
•j- Ibid. p. 350. The section from which this quotation is taken (entitled " Of Prop- ositions and the nature of Assent,") contains very ingenious and just observations, blended with others strongly marked with the author's peculiar turn of thinking. Among these last maybe mentioned his Theory of Mathematical Evidence, coinciding exactly with that which has since been proposed by Dr. Beddoes. Compare Hartley with pp. 130, and 131, of this volume.
X " N'admettonsnous pas pour vraift, la clef d'une lettre ecrite en chiffres, ou celle d'une logogryphe ; quand cettc clef s'applique exactement a tous les caiacteres dont il faut rendre raison .' " Opuscules do G. L. Le Sage, relatifs a. la Methode. See M. Prevosf s Essais de Philosophie.
§ Article Dechiffrer. See Also D'AIernbert's CEuvres Posthuraes. Tome H. p. 177. — Grdvesande's Logic was published in 1736.
II Essays on the Intell. Powers, p. 88.
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is this all. The argument proceeds on the supposition, that, if the task of the scientific inquirer be compared to that of the decipherer, the views of the author of nature may, with equal propriety, be compared to those of the inventor of the cipher. It is impossible to imagine that this was Hartley's idea. The object of true phi- losophy is, in no case presumptuously to divine an alpha- bet of secret characters or ciphers, purposely employed by infinite Wisdom to conceal its operations ; but, by the diligent study of facts and analogies legible to all, to dis- cover the key which infinite Wisdom has itself prepared for the interpretation of its own laws. In other words, its object is, to concentrate and to cast on the unknown parts of the universe, the hghts which are reflected from those which are known.
In this instance, as well as in others, where Reid reprobates hypotheses, his reasoning uniformily takes for granted, that they are wholly arbitrary and gratuitous. " If a thousand of the greatest wits," says he, " that ever the world produced, were, without any previous knowl- edge in anatomy, to sit down and contrive how% and by what internal organs, the various functions of the human body are carried on — how the blood is made to circulate, and the limbs to move — they would not, in a thousand years, hit upon any thing like the truth." f Nothing can be juster than this remark ; but does it authorize the conclusion, that, to an experienced and skilful anatomist, conjectures founded on analogy, and on the considerar tion of uses, are of no avail as media of discovery ? The logical inference, indeed, from Dr. Reid's own statement, is not against anatomical conjectures in general, but against the anatomical conjectures of those who are ig- norant of anatomy.
The same reply may be made to the following asser- tion of D'Alembert ; another writer, who, in my opinion, has, on various occasions, spoken much too hghtly of analogical conjectures. " It may be safely affirmed, that a mere theorist (un physicien cle cabinet) who, by means of reasonings and calculations, should attempt to divine
* Essays on the Intell. Powers, p. 49.
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the phenomena of nature, and who should afterwards compare his anticipations with facts, would be astonished to find how wide of the truth almost all of them had been."* If this observation be confined to those sys- tem-builders, who, without any knowledge of facts, have presumed to form conclusions a priori concerning the universe, its truth is so obvious and indisputable, that it was hardly worth the while of this profound philosopher so formally to announce it. If extended to such men as Copernicus, Kepler, and Newton, and to the illustrious train who have issued from the Newtonian school, it is contradicted by numberless examples, of which D'Alem- bert could not fail to be perfectly aware. f
The sagacity which guides the Philosopher in conjec- turing the laws of nature has, in its metaphysical origin, a very near affinity to that acquired perception of human character, which is possessed by Men of the World. The conclusions of one individual with respect to the springs of action in the breast of another, can never, on the most favorable supposition, amount to more than to a Hypothesis supported by strong analogies ; yet how different is the value of the Hypothesis, according to the intellectual habits of him by whom it is formed ! What more absurd and presumptuous than the theories of the cloistered schoolman concerning the moral or the politi- cal phenomena of active life ! What more interesting and instructive than the slightest characteristical sketches from the hand of a Sully or of a Clarendon !
To these suggestions in vindication of hypotheses it may be added, that some of the reasonings which, with propriety, were urged against them a century ago, have already, in consequence of the rapid progress of knowl- edge, lost much of their force. It is very justly remark- ed by M. Prevost, that " at a period when science has advanced so far as to have accumulated an immense treasure of facts, the danger of hypotheses is less, and
* Melanges de Litteratuie, &c. Tome V. § 6. (entitled Eclaircissement sur ce qui a et6 dit, &.C. dc I'art do conjcctuicr.)
I Accordingly, in another part of tlie same article, he has said : " L'analogie, c'est- a-dire, la ressenihlance plus ou iiioins i^rande des faits, le rapport plus ou moins sen- sible qu'ils ont entr'eux, est I'unique regie des physiciens, soit pour expliquer les faits couaus, soit pour en decouvrir de nouveaux."
OF THE HUMAN MIND. 299
their advantages greater, than in times of comparative ignorance." For this he assigns three reasons. " 1. The multitude of facts restrains Imagination, by presenting, in every direction, obstacles to her v^anderings ; and by overturning her frail edifices. 2. In proportion as facts multiply, the memory stands in greater need of the aid of connecting or associating principles.* 3. The chance of discovering interesting and luminous relations among the objects of our knowledge increases with the growing number of the objects compared." f — The con- siderations already stated suggest a 4th reason in con- firmation of the same general proposition : — That, by the extension of human knowledge, the scale upon which the Analogies of nature may be studied, is so augmented as to strike the most heedless eye ; while, by its diffu- sion, the perception of these analogies (so essential an element in the composition of inventive genius) is in- sensibly communicated to all who enjoy the advantages of a liberal education. Justly, therefore, might Bacon say, " Certo sciant homines, artes inveniendi solidas et ve- ras adolescere et incrementa sumere cum ipsis inventis."
But although I do not think that Reid has been suc- cessful in his attempt to refute Hartley's argument, I am far from considering that argument as sound or conclu- sive. My chief objections to it are the two following.
1. The cases compared are by no means parallel. In that of the cipher, we have all the facts before us ; and, if the key explains them, we may be certain, that nothing can directly contradict the justness of our in- terpretation. In our physical researches, on the other hand, we are admitted to see only a few detached sen- tences extracted from a volume, of the size of which we are entirely ignorant. No hypothesis, therefore, how numerous soever the facts may be with which it tallies, can completely exclude the possibihty of exceptions or limitations hitherto undiscovered.
It must, at the same time, be granted, that the proba- bility of a hypothesis increases in proportion to the
* With respect to the utility of hypothetical theories, as adminicles to the natural powers of memory, see the foraier volume of tliis work, Chap. vi. Sections 3 and 4. t See Note (X.)
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number of phenomena for which it accounts, and to the simplicity of the theory by which it explains them ; — and that, in some instances, this probabihty may amount to a moral certainty. The most remarkable example of this which occurs in the history of science is, undoubt- edly, the Gopernican system. I before observed, that at the period when it was first proposed, it was nothing more than a hypothesis ; and that its only proof rested on its conformity, in point of simplicity, to the general economy of the Universe. " When Copernicus," says Mr. Maclaurin, " considered the form, disposition, and motions of the system, as they were then represented after Ptolemy, he found the whole void of order, sym- metry, and proportion ; like a piece," as he expresses himself, " made up of parts copied from different origi- nals, which, not fitting each other, should rather repre- sent a monster than a man. He therefore perused the writings of the ancient philosophers, to see whether any more rational account had ever been proposed of the motions of the Heavens. The first hint he had was from Cicero, who tells us, in his Academical Questions, that Nicetas, a Syracusian, had taught that the earth turns round on its axis, which made the whole heavens ap- pear to a spectator on the earth to turn round it daily. Afterwards, from Plutarch he found that Philolaus, the Pythagorean, had taught that the earth moved annually round the sun. He immediately perceived, that, by al- lowing these two motions, all the perplexity, disorder, and confusion he had complained of in the celestial mo- tions, vanished ; and that, instead of these, a simple regular disposition of the orbits, and a harmony of the motions appeared, worthy of the great Author of the world." *
Of the truth of this hypothesis, the discoveries of the last century have afforded many new proofs of a direct and even demonstrative nature ; and jQt, it m.ay be fair-
* Account of Newton's Philosophical Discoveries, p. 45. (2d Edit.) This presumptive argument, as it presented itself to the mind of Copernicus, is thus stated by Bailly : " Lcs hommcs sentent que la nature est simple ; les stations et les retrogradalions dcs planetes offroient des apparences bizarrcs ; le princi^e, qui les ramenoit a une marchc simple, et naturellc, ne pouvoit ctre quhme veriti." Hist, de I'Astron. Mod. Tom. L p. 35L
OF THE HUMAN MIND. 301
ly questioned, whether to Copernicus and Gahleo, the analogical reasoning stated in the preceding quotation, did not, of itself, appear so conclusive, as to supersede the necessity of any farther evidence. The ecclesiastic- al persecutions which the latter encountered in defence of his supposed heresy, sufficiently evinces the faith which he reposed in his astronomical creed.
It is, however, extremely worthy of remark, with re- spect to the Copernican system, that it affords no illustra- tion whatever of the justness of Hartley's logical maxim. The Ptolemaic system was not demonstrably incon- sistent with any phenomena known in the sixteenth century : and, consequently, the presumption for the new hypothesis did not arise from its exclusive coinci- dence with the facts, but from the simphcity and beauty which it possessed as a theory. The inference to be deduced from it is, therefore, not in favour of hypoth- eses in general, but of hypotheses sanctioned by anal-
The fortunate hypothesis of a Ring encircling the body of Saturn, by which Huygens accounted, in a manner equally simple and satisfactory, for a set of ap- pearances which, for forty years, had puzzled all the astronomers of Europe, bears, in all its" circumstances, a closer resemblance than any other instance I know of, to the key of a cipher. Of its truth it is impossible for the most sceptical mind to entertain any doubt, when it is considered, that it not only enabled Huygens to ex- plain all the known phenomena, but to predict those which were afterwards to be observed. This instance, accordingly, has had much stress laid upon it by differ- ent writers, particularly by Gravesande and Le Sage.* I must own, I am somewhat doubtful, if the discovery of a key to so limited and insulated a class of optical facts, authorizes any valid argument for the employment of mere hypotheses, to decipher the complicated phenome- na resulting from the general laws of nature. It is, in-
* Gravesande, Intiod. ad Philosoph. §§ 979, 985. Opuscules do Le Sage, Pre- mier Memoire, § 25. Tlie latter writer mentions the theory in question, as a hy- pothesis which received no countenance whatever from the analogy of any preced- ing astronomical discovery.
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deed, an example most ingeniously and happily selected : but would not perhaps have been so often resorted to, if it had been easy to find others of a similar description.
2. The chief objection, however, to Hartley's compar- ison of the theorist to the decipherer is, that there are few, if any, physical hypotheses, which afford the only way of explaining the phenomena to which they are ap- plied ; and therefore, admitting them to be perfectly consistent with all the known facts, they leave us in the same state of uncertainty, in which the decipherer would find himself, if he should discover a variety of keys to the same cipher. Descartes acknowledges, that the same effect might, upon the principles of his philosophy, admit of manifold explanations ; and that nothing per- plexed him more than to know which he ought to adopt in preference to the others. " The powers of nature," says he, " I must confess, are so ample, that no sooner do I observe any particular effect, than I immediately perceive that it may be deduced from my principles, in a variety of different ways ; and nothing, in general, ap- pears to me more difficult, than to ascertain by which of these processes it is really produced." * The same re- mark may (with a very few exceptions) be extended to every hypotheti'cal theory which is unsupported by any collateral probabilities arising from experience or analo- gy ; and it sufficiently shows, how infinitely inferior such theories are, in point ofevidence, to the conclusions obtained by the art of the decipherer. The principles, indeed, on which this last art proceeds, may be safely pronounced to be nearly infalhble.
In these strictures upon Hartley, I have endeavoured to do as much justice as possible to his general argument, by keeping entirely out of sight the particular purpose which it was intended to serve. By confining too much his attention to this. Dr. Reid has been led to carry, far- ther than was necessary or reasonable, an indiscriminate
* Dissertatio de Methodo. In the sentence immediately following, Descartes mentions the general rule which he followed, when such an embarrassment occurred. " Hinc aliter me cxtricare non possum, quam si rursus aliqua experimenta quaeram ; quse talia sint, ut eorum idem non sit futurus eventus, si hoc modo quam si ilJo expli- cetur." The rule is excellent ; and it is only to be regretted, that so few exemplifi- cations of it are to be found in his writings.
OF THE HUMAN MIND. 303
zeal against every speculation to which the epithet hy- pothetical can, in any degree, be apphed. He has been also led to overlook the essential distinction between hy- pothetical inferences from one department of the Mate- rial World to another, and hypothetical inferences from the Material World to the Intellectual. It was with the view of apologizing for inferences of the latter descrip- tion, that Hartley advanced the logical principle which gave occasion to the foregoing discussion ; and, there- fore, I apprehend, the proper answer to his argument is this : — Granting your principle to be true in all its ex- tent, it furnishes no apology whatever for the Theory of Vibrations. If the science of mind admit of any illus- tration from the aid of hypotheses, it must be from such hypotheses alone as are consonant to the analogy of its own phenomena. To assume, as a fact, the existence of analogies between these phenomena and those of mat- ter, is to sanction that very prejudice which it is the great object of the inductive science of mind to eradicate.
I have repeatedly had occasion, in some of my former publications, to observe, that the names of almost all our mental powers and operations are borrowed from sensible images. Of this number are intuition ; the dis- cursive faculty ; attention ; reflection ; conception ; im- agination ; apprehension ; comprehension ; abstraction ; invention ; capacity ; penetration ; acuteness. The case is precisely similar with the following terms and phrases, relative to a different class of mental phenom- ena ; — inclination ; aversion ; deliberation ; pondering ; weighing the motives of our actions ; yielding to that motive which is the strongest ; — expressions (it may be remarked in passing) which, when employed, without a very careful analysis of their import, in the discussion concerning the liberty of the will, gratuitously prejudge the very point in dispute ; and give the semblance of demonstration, to what is, in fact, only a series of iden- tical propositions, or a sophistical circle of words.*
* " Notliin;);," says Berkeley, " seems more to have contributed towards engaging men in controversies and mistakes witli regard to the nature and operations of the mind, than the being used to speak of those things in terms borrowed from sensible ideas. For example, the will is termed the motion of the soul. This infuses a be-
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That to the apprehensions of uneducated men such metaphorical or analogical expressions should present the images and the things typified, inseparably combined and blended together, is not wonderful ; but it is the busi- ness of the philosopher to conquer these casual asso- ciations, and, by varying his metaphors, when he cannot completely lay them aside, to accustom himself to view the phenomena of thought in that naked and undisguis- ed state in which they unveil themselves to the powers of consciousness and reflection. To have recourse, therefore, to the analogies suggested by popular lan- guage, for the purpose of explaining the operations of the mind, instead of advancing knowledge, is to confirm and to extend the influence of vulgar errors.
After having said so much in vindication of analogical conjectures as steps towards physical discoveries, I thought it right to caution my readers against supposing, that what I have stated admits of any apphcation to analogical theories of the human mind. Upon this head, however, I must not enlarge farther at present. In treating of the inductive logic, I have studiously confin- ed my illustrations to those branches of knowledge in which it has already been exemplified with indisputable success ; avoiding, for obvious reasons, any reference to sciences in which its utility still remains to be ascer- tained.
Supplemental Observations on the words Induction and Analogy, as used in
Mathematics.
Before dismissing the subjects of induction and analogy, considered as methods of reasoning in Physics, it remains for me to take some slight notice of the use occasionally made of the same terms in pure Mathemat- ics. Although, in consequence of the very different na-
lief, that the mind of man is as a ball in motion, impelled and determined by the ob- jects of sense, as necessarily as that is by the stroke of a racket." — Principles of Human Knowled're.
OF THE HUMAN MIXD. 305
tures of these sciences, the induction and analogy of the one cannot fail to differ widely from the induction and analogy of the other, yet, from the general history of language, it may be safely presumed, that this applica- tion to both of a common phraseology, has been sug- gested by certain supposed points of coincidence be- tween the two cases thus brought into immediate com- parison.*
It has been hitherto, with a very few if any excep- tions, the universal doctrine of modern as well as of an- cient logicians, that " no mathematical proposition can be proved by induction." To this opinion Dr. Reid has given his sanction in the strongest terms ; observing, that " although in a thousand cases, it should be found by experience, that the area of a plane triangle is equal to the rectangle under the base and half the altitude, this would not prove that it must be so in all cases, and cannot be otherwise, which is what the mathematician affirms." f
That some limitation of this general assertion is ne- cessary, appears plainly from the well-known fact, that induction is a species of evidence on which the most scrupulous reasoners are accustomed, in their mathe- matical inquiries, to rely with implicit confidence ; and which, although it may not of itself demonstrate that the theorems derived from it are necessarily true, is yet abundantly sufficient to satisfy any reasonable mind that they hold universally. It was by induction (for exam- ple) that Newton discovered the algebraical /ormi^/a by which we are enabled to determine any power whatev- er, raised fi^om a binomial root, without performing the progressive multiphcations. The formula expresses a relation between the exponents and the co-efhcients of the different terms, which is found to hold in all cases, as far as the table of powers is carried by actual calcu- lation ; — from which Newton inferred, that if this table
* I have already observed (see p. 235 of this volume) that mathematicians fre- quently avail themselves of that sort of iiuluctinn wliicli Bacon describes "' as pro- ceedinaj by simple enumeration." The induction, of which I am now to treat, has very little in common with the other, and bears a much closer resemblance to that recommended in the Novum Organon.
t Essays on the Intell. Powers, p. 615, 4to. edit.
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were to be continued in infinitum, the same formula would correspond equally with every successive power. There is no reason to suppose that he ever attempted to prove the theorem in any other way ; and yet, there cannot be a doubt, that he was as firmly satisfied of its being universally true, as if he had examined all the dif- ferent demonstrations of it which have since been given.* Numberless other illustrations of the same thing might be borrowed, both from arithmetic and geometry. f
Into what principles, it may be asked, is the validity of such a proof in mathematics ultimately resolvable ? — To me it appears to take for granted certain general logical maxims ; and to imply a secret process of legiti- mate and conclusive reasoning, though not conducted agreeably to the rules of mathematical demonstration, nor perhaps formally expressed in words. Thus in the instance mentioned by Dr. Reid, I shall suppose, that I have first ascertained experimentally the truth of the proposition in the case of an equilateral triangle ; and
* " The truth of this theorem was long; known only by tiial in particular cases, and by induction from analogy ; nor does it appear that even Newton himself ever attempted any direct proof of it." (Hutton's Mathematical Dictionary, Art. Bino- mial Theorem.) For some interesting information with respect to the history of this discovery, see the very learned Introduction prefixed by Dr. Hutton to his edition of Sherwin's Mathematical Tables ; and the second volume (p. 165) of the Scriptores Logarithmici edited by Mr. Baron Maseres.
I In the Jlrithmetica Infinitorum of I)r. V/allis, considerable use is made of the Method of Induction. " A I'aide d'une induction habilement menagee," saysMon- tucla, " et du fil de I'analogie dont il sijut toujours s'alder avec succes, il soumita la geometric une multitude d'objets qui lui avoient echappe jusqu'alors." (Hist, des Mathem. Tome II. p. 299.) This innovation in the established forms of mathe- matical reasoning gave offence to some of his contemporaries ; in particular, to M. de Fermat, one of the most distinguished geometers of the seventeenth century. The ground of his objection, however, (it is worthy of notice,) was not any doubt of the conclusions obtained by Wallis ; but because he thought that their (ruth might have been established by a more legitimate and elegant process. " Sa fa9on de demontrer, qui est fondee sur induction plutot que sur un raisonnement a la mode d'Archimede, fera quelque peine aux novices, qui veulent des syllogismcs demonstra- tifs depuis le commencement jusqu'a la fin. Ce n'est pas que je ne I'approuve, mais toutes ses piopositions pouvant etre demontrees vid ordinarid, legitimd, et Jlrchi- OTe£Z^<i, en beaucoup moins de paroles, que n'en conlient sonlivre,je ne stjai pas pourquoi il a prefere cette maniere a I'ancienne, qui est plus convainquante et plus elegante, ainsi que j'espere lui faire voir a nion premier loisir." Lettre de M. de Fer- mat a M. le Cliev. Kenelme Digby. (See Format's Varia Opera Mathematica,^. 191.) For Wallis's reply to these strictures, see his Algebra, Cap. Ixxix ; and his C&mmercium Epistolicum.
In the Opuscules cf M. Le Sage, I find the following sentence quoted from a work of La Place, which I have not had an opportunity ot seeing. The judgment of so great a master, on a logical question relative to his own studies, is of peculiar value. " La methode d'induction, quoique excellente pour decouvrir des verites generates, ne doit pas dispenser de les demontrer avec rigueur." — Lemons donnees aux Ecoles JVormales, Prem. Vol. p. 380.
OF THE HUMAN MIND. 307
that I afterwards find it to hold in all the other kinds of triangles, whether isosceles or scalene, right-angled, ob- tuse-angled, or acute-angled. It is impossible for me not to perceive, that this property, having no connexion with any of the particular circumstances, which discrim- inate different triangles from each other, must arise from something common to all triangles, and must therefore be a universal jj^operty of that figure. In hke manner, in the binomial theorem, if the formula correspond with the table of powers in a variety of particular instances, (which instances agree in no other respect, but in being powers raised from the same binomial root,) w^e must conclude — and, I apprehend that our conclusion is per- fectly warranted by the soundest logic, — that it is this common property which renders the theorem true in all these cases, and consequently, that it mtist necessarily hold in every other. Whether, on the supposition that we had never had any previous experience of demon- strative evidence, we should have been led, by the mere inductive process, to form the idea of necessary truths may perhaps be questioned ; but the slightest acquaint- ance with mathematics is sufficient to produce the most complete conviction, that whatever is universally true in that science, must be true of necessity ; and, therefore, that a universal, and a necessary truth, are, in the lan- guage of mathematicians, synonymous expressions. If this view of the matter be just, the evidence afforded by mathematical induction must be allowed to differ radically from that of physical ; the latter resolving ulti- mately into our instinctive expectation of the laws of na- ture, and consequently, never amounting to that demon- strative certainty, which excludes the possibility of anomalous exceptions.
I have been led into this train of thinking by a remark which La Place appears to me to have stated in terms much too unqualified ; — " Que la marche de Newton, dans la decouverte de la gravitation universelle, a ete exactement la meme, que dans celle de la formule du bi- nome." When it is recollected, that, in the one case, Newton's conclusion related to a contingent, and in the other to a necessary truth, it seems difficult to conceive,
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how the logical procedure which conducted him to both should have been exactly the same. In one of his que- ries, he has (in perfect conformity to the principles of Bacon's logic) admitted the possibility, that " God may vary the laws of nature, and make worlds of several sorts, in several parts of the universe." " At least," he adds, " I see nothing of contradiction in all this." * Would JN^ewton have expressed himself ^'ith equal scep- ticism concerning the universality of his binomial theo- rem ; or admitted the possibihty of a single exception to it, in the indefinite progress of actual involution 1 In short, did there exist the shghtest shade of difference between the degree of his assent to this inductive result, and that extorted from him by a demonstration of Eu- cHd 1
Although, therefore, the mathematician, as well as the natural philosopher, may, without any blame able latitude of expression, be said to reason by induction, when he draws an inference from the known to the unknown, yet it seems indisputable, that, in all such cases, he rests his conclusions on grounds essentially distinct from those which form the basis of experimental science.
The word analogy, too, as well as induction, is common to physics and to pure mathematics. It is thus we speak of the analogy running through the general properties of the different conic sections, with no less propriety than of the analogy running through the anatomical structure of different tribes of animals. In some instan- ces, these mathematical analogies are collected by a species of induction; in others, they are inferred as consequences from more general truths, in which they are included as particular cases. Thus, in the curves which have just been mentioned, while we content our- selves (as many elementary writers have done) f with deducing their properties from mechanical descriptions on a plane, we rise experimentally from a comparison of the propositions which have been separately demon- strated with respect to each curve, to more comprehen-
* Query 31. f L'Hospital, Simson, &c.
OF THE HUMAN MIND. 309
sive theorems, applicable to all of them ; whereas, when we begin with considering them in their common origin, we have it in our power to trace from the source, both their generic properties, and their specific peculiarities. The satisfaction arising from this last view of the sub- ject can be conceived by those alone who have experien- ced it ; although I am somewhat doubtful whether it be not felt in the greatest degree by such as, after having risen from the contemplation of particular truths to oth- er truths more general, have been at last conducted to some commanding station, where the mutual connexions and affinities of the whole system are brought, at once, under the range of the eye. Even, however, before we have reached this vantage-ground, the contemplation of the analogy, considered merely as a fact, is pleasing to the mind ; partly, from the mysterious wonder it ex- cites, and partly from the convenient generalization of knowledge it affords. To the experienced mathematician this pleasure is farther enhanced, by the assurance which the analogy conveys, of the existence of yet undiscov- ered theorems, far more extensive and luminous than those which have led him by a process so indirect, so tedious, and comparatively so unsatisfactory, to his gen- eral conclusions.
In this last respect, the pleasure derived from analogy in mathematics, resolves into the same principle with that which seems to have the chief share in rendering the analogies among the different departments of nature so interesting a subject of speculation. In both cases, a powerful and agreeable stimulus is applied to the curios- ity, by the encouragement given to the exercise of the inventive faculties, and by the hope of future discovery, which is awakened and cherished. As the analogous properties (for instance) of the conic sections, point to some general theorems of which they are corollaries ; so the analogy between the phenomena of Electricity and those of Galvanism irresistibly suggests a confident, though vague, anticipation of some general physical law comprehending the phenomena of both, but differently modified in its sensible results by a diversity of circum-
310 ELEMENTS OF THE PHILOSOPHY
stances.* Indeed, it is by no means impossible, that the pleasure we receive even from those analogies which are the foundation of poetical metaphor and simile, may be found resolvable, in part, into the satisfaction connected with the supposed discovery of truth or the supposed ac- quisition of knowledge : the faculty of imagination giv- ing to these illusions a momentary ascendant over the sober conclusions of experience : and gratifying the un- derstanding with a flattering consciousness of its own force, or at least with a consolatory forgetfulness of its own weakness.
SECTION V.
Of certain misapplications of the words Experiencea. nd Induction in the Phraseology of Modern Science. — Illustrationsj from Medicine and from Political Economy.
In the first section of this Chapter, I endeavoured to point out the characteristical peculiarities by which the Inductive Philosophy of the Newtonians is distinguished from the hypothetical systems of their predecessors ; and which entitle us to indulge hopes with respect to the permanent stability of their doctrines, which might be regarded as chimerical, if, in anticipating the future history of science, we were to be guided merely by the analogy of its revolution in the ages that are past.
In order, however to do complete justice to this ar- gument, as well as to prevent an undue extension of the foregoing conclusions, it is necessary to guard the read- er against a vague application of the appropriate terms of inductive science to inquiries which have not been rigorously conducted according to the rules of the in- ductive logic. From a want of attention to this consid- eration, there is a danger, on the one hand, of lending to sophistry or to ignorance the authority of those illus- trious names whose steps they profess to follow^ ; and, on the other, of bringing discredit on that method of investigation, of which the language and other technical arrangements have been thus perverted.
* Sec Note (Y.)
OF THE HUMAN MIJ^D. 311
Among the distinguishing features of the new logic, when considered in contrast with that of the schoolmen, the most prominent is the regard which it professes to pay to experience, as the only solid foundation of human knowledge. It may be worth while, therefore, to con- sider, how far the notion commonly annexed to this word is definite and precise ; and whether there may not sometimes be a possibility of its being employed in a sense more general and loose, than the authors who are looked up to as the great models of inductive inves- tigation understood it to convey. *"
In the course of the abstract speculations contained in the preceding section, I have remarked, that although the difference between the two sorts of evidence which are commonly referred to the separate heads of experi-
* As the reflections which follow are entirely of a practical nature, I shall express myself (as far as is consistent witli a due regard to precision) agreeably to the modes of speaking in common use ; without affecting a scrupulous attention to some spec- ulative distinctions, which, however curious and interesting, when considered in connexion with the Theory of the Mind, do not lead to any logical conclusions of essential importance in the conduct^ of the Understanding. In such sciences for example, as Astronomy, Natural^Philosophy, and Chemistry, which rest upon phe- nomena open to the scrutiny of every inquirer, it would obviously be puerile in the extreme to attempt drawing the line between facts which have been ascertained by our own personal observation, and those whicli we have implicitly adopted upon our faith in the universal consent of the scientific world. The evidence, in both cases, may be equally irresistible ; and sometimes the most cautious reasoners may justly be disposed to consider that of testimony as the least fallible of the two.
I3y far the greater part, indeed, of what is commonly called experimental knowl- edge, will be found, when traced to its origin, to resolve entirely into our confidence in the judgment and the veracity of our fellow-creatures; nor (in the sciences al- ready mentioiicd) has this identification of the evidence of testimony with that of experience, the slightest tendency to affect the legitimacy of our inductive conclu- sions.
In some other branches of knowledge, (more particularly in those political doc- trines which assume as incontrovertible data the details of ancient history,) the authority of testimony is, for obvious reasons, much more questionable ; and to dig- nify it in these, with the imposing character of experience, is to strengthen one of the chief bulwarks of popular prejudices. This view of the subject, however, al- though well entitled to the attention of the logician, has no immediate connexion with my present argument; and accordingly I shall make no scruple, in the sequel, to comprehend under the name of experience, the grounds of our assent to rdl the facts on which our reasonings proceed, provided only that the certainty of these facts be, on either supposition, equally indisputable.
The logical errors which it is the aim of this section to correct, turn upon a still more dangerous latitude in the use of this word ; in consequence of which, the au- thority of experience conies insensibly to be extended to innumerable opinions rest- ing solely on supposed analogies ; while, not unfrequently, the language of Bacon is quoted in bar of any theoretical argument on the other side of the question.
1 have added this note, partly to obviate some criticisms, to which my own phra- seology may, at first sight, appear liable ; and partly to point out the connexion be- tween the following discussion, and some of the foregoing speculations.
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ence and of analogy, be rather a difference in degree than in kind, yet that it is useful to keep these terms in view, in order to mark the contrast betvy een cases which are separated from each other by a very wide and pal- pable interval ; more especially to mark the difference between an argument from individual to individual of the same species, and an argument from species to spe- cies of the same genus. As this distinction, however, when accurately examined, turns out to be of a more vague and popular nature than at first sight appears, it is not surprising that instances should occasionally present themselves, in which it is difficult to say, of the evidence before us, to which of these descriptions it ought to be referred. Nor does this doubt lead merely to a ques- tion concerning phraseology : it produces a hesitation which must have some effect even on the judgment of a philosopher ; the maxims to which we have been ac- customed, in the course of our early studies, leading us to magnify the evidence of experience as the sole test of truth ; and to depreciate that of analogy, as one of the most fertile sources of error. As these maxims proceed on the supposition, that the respective provin- ces of both are very precisely defined, it is evident, that admitting them to be perfectly just in themselves, much danger may still be conceivable from their inju- dicious apphcation. I shall endeavour to illustrate this remark by some familiar instances ; which, I trust, will be sufficient to recommend it to the farther considera- tion of future logicians. To treat of the subject with that minuteness of detail which is suited to its impor- tance, is incompatible with the subordinate place which belongs to it in my general design.
It is observed by Dr. Reid,* that, " in medicine, phy- sicians must, for the most part, be directed in their pre- scriptions by analogy. The constitution of one human body is so like to that of another, that it is reasonable to think, that what is the cause of health or sickness to one, may have the same effect on another. And this," he adds, " is generally found true, though not without some exceptions."
Essays on the Intellect. Powers, p. 63.
OF THE HUMAN MIND. 313
I am doubtful if this observation be justified by the common use of language ; which, as far as I am able to judge, uniformly refers the evidence on which a cau- tious physician proceeds, not to analogy but to experi- ence. The German monk, who (according to the popu- lar tradition) having observed the salutary effects of antimony upon some of the lower animals, ventured to prescribe the use of it to his own fraternity, might be justly said to reason analogically ; inasmuch as his ex- perience related to one species, and his inference to another. But if, after having thus poisoned all the monks of his own convent, he had persevered in recom- mending the same mineral to the monks of another, the example of our most correct writers would have author- ized us to say, (how far justly is a different question,) that he proceeded in direct opposition to the evidence of experience.
In offering this slight criticism on Dr. Reid, I would be very far from being understood to say, that the com- mon phraseology is more unexceptionable than his. I would only remark, that his phraseology on this occasion is almost pecuhar to himself; and that the prevailing opin- ions, both of philosophers and of the multitude, incHne them to rank the grounds of our reasoning in the medi- cal art, at a much higher point in the scale of evidence, than what is marked by the word analogy. Indeed, I should be glad to know% if there be any one branch of human knowledge, in which men are, in general, more disposed to boast of the lights of experience, than in the practice of medicine.
It would perhaps, have been better for the w^orld, if the general habits of thinking and of speaking, had, in this instance, been more agreeable than they seem to be in fact, to Dr. Reid's ideas ;— or at least, if some quali- fying epithet had been invariably added to the w^ord experience, to show with how very great latitude it is to be understood, when applied to the evidence on which the physician proceeds in the exercise of his art. The truth is, that, even on the most favorable supposition, this evidence, so far as it rests on experience, is weak- ened or destroyed by the uncertain conditions of every
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new case to which his former results are to be applied ; and that, without a pecuhar sagacity and discrimination in marking, not only the resembling, but the character- istical features of disorders, classed under the same technical name, his practice cannot, with propriety, be said to be guided by any one rational principle of decis- ion, but merely by blind and random conjecture. The more successfully this sagacity and discrimination are ex- ercised, the more nearly does the evidence of medical practice approach to that of experience ; but, in every instance, without exception, so immense is the distance between them, as to render the meaning of the word experience, when applied to medicine, essentially differ- ent from its import in those sciences where it is possible for us, in all cases, by due attention to the circumstances of an experiment, to predict its result with an almost infallible certainty.*
Notwithstanding this very obvious consideration, it has become fashionable among a certain class of medical practitioners, since the lustre thrown on the inductive logic of Bacon by the discoveries of Newton and the researches of Boyle, to number their art with the other branches of experimental philosophy ; and to speak of the difference between the empiric and the scientific physician, as if it were exactly analogous to that between the cautious experimenter and the hypothetical theorist in physics. Experience, (we are told,) and experience alone, must be our guide in medicine, as in all the other departments of physical knowledge : — Nor is any inno- vation, however rational, proposed in the estabhshed rou-
* " L'art (le conjecturer en Medecine ne sauroit consister dans une suite de raison- neinens appuyes sur vin vain systenie. Cast uniquement l'art de comparer une ma- ladie qu'on doit guerir, avec les maladies semblables qu'on a deja connues par son experience ou par celle des autres. Get art consiste meme quelquefois a appercevoir un rapport entre des maladies qui paroissent n'en point avoir, comme aussi des difle- rences essentielles, quoique fugitives, entre celles qui paroissent se ressembler le plus. Plus on aura rassemble de faits, plus on sera en etat de conjecturer heureusement ; suppose neanmoins qu'on ait d'ailleurs cette justesse d'esprit que la nature seule pent donner.
"Ain=i le nieilleur medecin n'est pas (comme le prejuge le suppose) celui qui accumule en aveuti;le et en courant beaucoup de pratique, mais celui qui ne fait que des observations l)ien approfondies, et qui joint a ces observations le nombre beau- coup plus grand des observations faites dans tous les siecles par des hommes aniines du nieme esprit quo lui. Ces observations sont la veritable ear/7ertence du medecin." D'Jllcmbert, Edaircissemens sur les Elemens de Philosophie, § vi.
OF THE HUMAN MIND. 315
tine of practice, but an accumulation of alleged cases is immediately brought forward as an experimental proof of the dangers which it threatens.
It was a frequent and favorite remark of the late Dr. Cullen, — that there are more false facts current in the world than false theories ; and a similar observation oc- curs more than once, in the JVovum Organon. " Men of learning," says Bacon in one passage, " are too often led, from indolence or creduhty, to avail themselves of mere rumors or whispers of experience, as confirmations, and sometimes as the very ground-work of their philoso- phy ; ascribing to them the same authority as if they rested on legitimate testimony. Like to a government which should regulate its measures, not by the official information received from its own accredited ambassa- dors, but by the gossipings of newsmongers in the streets. Such in truth, is the manner in which the interests of philosophy, as far as experience is concerned, have been hitherto administered. Nothing is to be found which has been duly investigated ; nothing which has been verified by a careful examination of proofs ; nothing which has been reduced to the standard of number, weight, or measure." *
This very important aphorism deserves the serious attention of those who, while they are perpetually de- claiming against the uncertainty and fallacy of systems, are themselves employed in amassing a chaos of insulated particulars, which they admit upon the slenderest evi- dence. Such men, sensible of their own incapacity for scientific investigation, have often a mahcious pleasure in destroying the fabrics of their predecessors ; or, if they should be actuated by less unworthy motives, they may yet feel a certain gratification to their vanity, in as- tonishing the world with anomalous and unlooked-for phenomena ; — a weakness which results not less natu- rally from ignorance and folly, than a bias to premature generalization from the consciousness of genius. — Both of these weaknesses are undoubtedly adverse to the progress of science ; but, in the actual state of human
*Nov. Org. Lib. I. Aph. xcviii.
316 ELEMENTS OF THE PHILOSOPHY
knowledge, the former is perhaps the more dangerous of the two.
In the practice of medicine, (to which topic I wish to confine myself more particularly at present,) there are a variety of other circumstances, which, abstracting from any suspicion of bad faith in those on whose testimony the credibihty of facts depends, have a tendency to vitiate the most candid accounts of what is commonly dignified with the title of experience. So deeply rooted in the constitution of the mind is that disposition on which philosophy is grafted, that the simplest narrative of the most iUiterate observer involves more or less of hypothesis ; nay, in general, it will be found, that, in proportion to his ignorance, the greater is the number of conjectural principles involved in his statements.
A village -apothecary (and, if possible, in a still greater degree, an experienced nurse) is seldom able to de- scribe the plainest case, without employing a phraseolo- gy of which every word is a theory ; whereas a simple and genuine specification of the phenomena which mark a particular disease ; — a specification unsophisticated by fancy, or by preconceived opinions, may be regarded as unequivocal evidence of a mind trained by long and successful study to the most diflficult of all arts, that of the faithful interpretation of nature.
Independently, however, of all these circumstances, which tend so powerfully to vitiate the data whence the physician has to reason ; and supposing his assumed facts to be stated, not only with the most scrupulous re- gard to truth, but with the most jealous exclusion of theoretical expressions, still the evidence upon which he proceeds is, at best, conjectural and dubious, when com- pared with what is required in chemistry or in mechan- ics. It is seldom, if ever, possible, that the description of any medical case can include all the circumstances with which the result was connected ; and, therefore, how true soever the facts described may be, yet when the conclusion to which they lead comes to be apphed as a general rule in practice, it is not only a rule rashly drawn from one single experiment, but a rule transferred from a case imperfectly known, to another of which we
OF THE HUMAN MIND. 317
are equally ignorant. Here, too, it will be found, that the evidence of experience is incomparably less in favor of the empiric, than of the cautious theorist ; or rather, that it is by cautious theory alone, that experience can be rendered of any value. Nothing, indeed, can be more absurd than to contrast, as is commonly done, ex- perience vi^ith theory, as if they stood in opposition to each other. Without theory, (or, in other words, with- out general principles, inferred from a sagacious com- parison of a variety of phenomena,) experience is a bhnd and useless guide ; while, on the other hand, a legitimate theory (and t?ie same observation may be ex- tended to hypothetical theories, supported by numerous analogies) necessarily presupposes a knowledge of con- nected and well ascertained facts, more comprehensive, by far, than any mere empiric is likely to possess. When a scientific practitioner, accordingly, quits the empirical routine of his profession, in quest of a higher and more commanding ground, he does not proceed on the supposition that it is possible to supersede the ne- cessity of experience by the most accurate reasonings a priori ; but, distrusting conclusions which rest on the observation of this or that individual, he is anxious, by combining those of an immense multitude, to separate accidental conjunctions from estabhshed connexions, and to ascertain those laws of the human frame which rest on the universal experience of mankind. The idea of following nature in the treatment of diseases ; — an idea which, I believe, prevails more and more in the practice of every physician, in proportion as his views are en- larged by science, is founded, not on hypothesis, but on one of the most general laws yet known with respect to the animal economy ; and it imphes an acknowledge- ment, not only of the vanity of abstract theories, but of the limited province of human art.*
* " Gaudet corpus vi prorsus mirabili, qua contra morbos se tucatur ; multos arceat ; multos jam inchoatos quain optime et citissime solvat ; aliosque, suo niodo, ad felicem exitum len(iu-i perducat.
" Ha3c Autocratcia,vis JVatura medicatrix, vocatur ; medici^, philosophis, notis- sima, et jure celeberrima. Hrec sola ad multos morbos sanandos suflicit, in omnibus fere prodest : Quia ct medicamenta, sua natura optima, tantuin solummodo prosunt.
318 ELEMENTS OF THE PHILOSOPHY
These slight remarks are sufficient to show, how vague and indeterminate the notion is, which is commonly an- nexed to the word experience by the most zealous advo- cates for its paramount authority in medicine. They seem farther to show, that the question between them and their adversaries amounts to little more than a dis- pute about the comparative advantages of an experience guided by penetration and judgment, or of an experi- ence which is to supersede all exercise of our rational faculties ; of an experience accurate, various, and dis- criminating, or of one which is gross and undistinguish- ing, like the perceptions of the lower animals.
Another department of knowledge in which constant appeals are made to experience^ is the science o^ politics ; and, in this science also, I apprehend, as well as in the former, that word is used with a far greater degree of latitude than is generally suspected. Indeed, most of the remarks which have been already offered on the one subject, may be extended (mutatis mutandis) to the other. I shall confine my attention, therefore, in what foUoAvs, to one or two pecuharities by which politics is specifically and exclusively characterized as an object of study ; and which seem to remove the species of evi- dence it admits of, to a still greater distance than that of medicine itself, from what the word experience naturally suggests to a careless inquirer.
The science of politics may be divided into two parts ; the first having for its object the theory of gov- ernment ; the second, the general principles of legisla- tion. That I may not lose myself in too wide a field, I shall, on the present occasion, wave all consideration of the former ; and, for the sake of still greater pre- cision, shall restrict my remarks to those branches of the latter, which are comprehended under the general title of Political Economy ; — a phrase, however, which I wish to be here understood in its most extensive mean- ing.*
quantum hujus vires insitas excitent, dirigant, gubernent. Medicina enim neque agit in cadaver, neque repugnante natura aliquid proficit."
Conspectus Mediciute Theoreticae. Auctore Jacobo Gregory, M. D. §§. 59, 60. (Edin. 1782.)
* See Note (Z.)
OF THE HUMAN MIKD. Si 9
They who have turned their attention, during the last century, to inquiries connected with population, national wealth, and other collateral subjects, maybe divided into two classes ; to the one of which we may, for the sake of distinction, give the title of political arithmeticians, or statistical collectors ; to the other, that of political econo- mists, or political philosophers. The former are general- ly supposed to have the evidence of experience in their favor, and seldom fail to arrogate to themselves exclu- sively, the merit of treading closely in the footsteps of Bacon. In comparison with them, the latter are consid- ered as httle better than visionaries, or, at least, as enti- tled to no credit whatever, when their conclusions are at variance with the details of statistics.
In opposition to this prevaiUng prejudice, it may, with confidence, be asserted, that, in so far as either of these branches of knowledge has any real value, it must rest on a basis of well ascertained facts ; and that the differ- ence between them consists only in the different nature of the facts with which they are respectively conversant. The facts accumulated by the statistical collector are merely particular results, which other men have seldom an opportunity of verifying or of disproving : and which, to those who consider them in an insulated state, can never afford any important information. The facts which the political philosopher professes to investigate are exposed to the examination of all mankind ; and while they enable him, hke the general laws of physics, to ascertain numberless particulars by synthetic rea- soning, they furnish the means of estimating the credi- biUty of evidence resting on the testimony of individual observers.
It is acknowledged by Mr. Smith, with respect to him- self, that he had " no great faith in political arithmetic ;" * and I agree with him so far as to think, that litde, if any, regard is due to a particular phenomenon, when stated as an objection to a conclusion resting on the general laws which regulate the course of human affairs. Even ad- mitting the phenomenon in question to have been accu-
• Wealth of Nations, Vol. H. p. 310. 9th Edit.
320 fiLEMEI«-TS OF THE PHILOSOPHY
rately observed, and faithfully described, it is yet possi- ble that we may be imperfectly acquaint&d with that combination of circumstances whereby the effect is mod- ified ; and that, if these circumstances were fully be- fore us, this apparent exception would turn out an addi- tional illustration of the very truth which it w^as brought to invahdate.
If these observations be just, instead of appealing to pohtical arithmetic as a check on the conclusions of po- litical economy, it would often be more reasonable to have recourse to pohtical economy as a check on the extravagancies of political arithmetic. Nor will this as- sertion appear paradoxical to those who consider, that the object of the political arithmetician is too frequently to record apparent exceptions to rules sanctioned by the general experience of mankind ; and, consequently, that in cases where there is an obvious or a demonstrative incompatibility between the alleged exception and the general principle, the fair logical inference is not against the truth of the latter, but against the possibility of the former.
It has long been an established opinion among the most judicious and enhghtened philosophers, — that as the desire of bettering our condition appears equally from a careful review of the motives which habitually influence our own conduct, and from a general survey of the history of our species, to be the master-spring of human industry, the labor of slaves never can be so productive as that of freemen. Not many years have elapsed, since it was customary to stigmatize this reasoning as visionary and metaphysical ; and to oppose to it that species of evi- dence to which we were often reminded that all theories must bend ; — the evidence of experimental calculations, furnished by intelligent and credible observers on the other side of the Atlantic. An accurate examination of the fact has shown how wide of the truth these calcula- tions were ; — but, independently of any such detection of their fallacy, might it not have been justly affirmed, that the argument from experience was decidedly against their credibihty ; — the facts appealed to resting solely upon the good sense and good faith of individual witness-
OF THE HUMAN MIND. 321
es ; while the opposite argument, drawn from the prin- ciples of the human frame, was supported by the united voice of all nations and ages ?
If we examine the leading principles which run through Mr. Smith's Inquiry into the Nature and Causes of the Wealth of Nations, we shall find, that all of them are general facts or general results, analogous to that which has been just mentioned. Of this kind, for in- stance, are the following propositions, — from which a very large proportion of his characteristical doctrines follow, as necessary and almost manifest corollaries : That what we call the Political Order, is much less the effect of human contrivance than is commonly imagined : — That every man is a better judge of his own interest than any legislator can be for him ; and that this regard to private interest (or, in other words, this desire of bettering our condition) may be safely trusted to as a principle of action universal among men in its opera- tion ; — a principle stronger, indeed, in some than in oth- ers, but constant in its habitual influence upon all : — That, where the rights of individuals are completely pro- tected by the magistrate, there is a strong tendency in human affairs, arising from what we are apt to consider as the selfish passions of our nature, to a progressive and rapid improvement in the state of society : — That this tendency to improvement in human affairs is often so very powerful, as to correct the inconveniences threatened by the errors of the statesman : — And that, therefore, the reasonable presumption is in favor of eve- ry measure which is calculated to afford to its fartljer developement, a scope still freer than what it at present enjoys ; or, which amounts very nearly to the same thing, in favor of as great a liberty in the employment of industry, of capital, and of talents, as is consistent with the security of property, and of the other rights of our fellows-citizens. — The premises, it is perfectly obvi- ous, from which these conclusions are deduced, are nei- ther hypothetical assumptions, nor metaphysical abstrac- tions. They are practical maxims of good sense, ap- proved by the experience of men in all ages of the world ; and of which, if we wish for any additional
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confirmations, we have only to retire within our own bo- soms, or to open our eyes on what is passing around us. From these considerations it would appear, that in pohtics, as well as in many of the other sciences, the loudest advocates for experience are the least entitled to appeal to its authority in favor of their dogmas ; and that the charge of a presumptuous confidence in human wisdom and foresight, which they are perpetually urging against pohtical philosophers, may, with far greater jus- tice, be retorted on themselves. An additional illustra- tion of this is presented by the strikingly contrasted ef- fects of statistical and of philosophical studies on the in- tellectual habits in general ; — the former invariably en- couraging a predilection for restraints and checks, and all the other technical combinations of an antiquated and scholastic policy ; — the latter, by inspiring, on the one hand, a distrust of the human powers, when they attempt to embrace in detail, interests at once so com- plicated and so momentous ; and, on the other, a reli- gious attention to the designs of Nature, as displayed in the general laws which regulate her economy ; — leading, no less irresistibly, to a gradual and progressive simpli- fication of the pohtical mechanism. It is, indeed^ the never-failing result of all sound philosophy, to humble, more and more, the pride of science before that Wisdom which is infinite and divine ; — whereas, the farther back we carry our researches into those ages, the institutions of which have been credulously regarded as monuments of the superiority of unsophisticated good sense, over the false refinements of modern arrogance, we are the more struck with the numberless insults offered to the most obvious suggestions of nature and of reason. We may remark this, not only in the moral depravity of rude tribes, but in the universal disposition which they discov- er to disfigure and distort the bodies of their infants ; — in one case, new-modelling the form of the eye-hds ; — in a second, lengthening the ears ; — in a third, checking the growth of the feet ; — 'in a fourth, by mechanical pres- sures applied to the head, attacking the seat of thought and intelligence. To allow the human form to attain, in perfection, its fair proportions, is one of the latest im-
OF THE HUMAN MIND. 323
provements of civilized society ; and the case is per- fectly analogous in those sciences which have for their object to assist nature in the cure of diseases ; in the developement and improvement of the intellectual fac- ulties ; in the correction of bad morals ; and in the res ulations of political economy.
&
SECTION VI.
or THE SPECULATION CONCERNING FINAL CAUSES.
I.
Opinion of Lord Bacon on the Subject.— Final Causes rejected by Descartes, and by the majority of French Philosophers. — Recognised as legitimate Objects of re- search by Newton. — Tacitly acknowledged by all as a useful logical Guide, even in Sciences which have no immediate relation to Theoloi^y.
The study of Final Causes may be considered in two different points of view ; first, as subservient to the evi- dences of natural rehgion ; and, secondly, as a guide and auxiliary in the investigation of physical laws. Of these views it is the latter alone which is immediately connected with the principles of the inductive logic ; and it is to this, accordingly, that I shall chiefly direct my attention in the following observations. I shall not, how- ever, adhere so scrupulously to a strict arrangement, as to avoid all reference to the former, where the train of my reflections may naturally lead to it. The truth is, that the two speculations will, on examination, be found much more nearly alUed, than might at first sight be ap- prehended.
I before observed, that the phrase Fined Cause was first introduced by Aristotle ; and that the extension thus given to the notion of causation contributed powerfully to divert the inquiries of his followers from the proper objects of physical science. In reading the strictures of Bacon on this mode of philosophizing, it is necessa- ry always to bear in mind, that they have a particular reference to the theories of the schoolmen ; and, if they should sometimes appear to be expressed in terms too
324 ELEMENTS OF THE PHILOSOPHY
unqualified, due allowances ought to be made for the undistinguishmg zeal of a reformer, in attacking preju- dices consecrated by long and undisturbed prescription. " Causarum finalium inquisitio sterilis est, et tanquam virgo Deo consecrata, nihil parit.'' Had a similar remark occurred in any philosophical work of the eighteenth century, it might, perhaps, have been fairly suspected to savour of the school of Epicurus ; although, even in such a case, the quaintness and levity of the conceit would probably have inclined a cautious and candid reader to interpret the author's meaning with an indul- gent latitude. On the present occasion, however, Ba- con is his own best commentator ; and I shall therefore quote, in a faithful, though abridged translation, the pre- paratory passage by which this allusion is introduced.
" The second part of metaphysics is the investigation of final causes ; which I object to, not as a speculation which ought to be neglected, but as one which has, in general, been very improperly regarded as a branch of physics. If this were merely a fault of arrangement, I should not be disposed to lay great stress upon it ; for arrangement is useful chiefly as a help to perspicuity, and does not affect the substantial matter of science : But, in this instance, a disregard of method has occasion- ed the most fatal consequences to philosophy ; inas- much as the consideration of final causes in physics has supplanted and banished the study of physical causes ; the fancy amusing itself with illusory explanations deriv- ed from the former, and misleading the curiosity from a steady prosecution of the latter," After illustrating this remark by various examples, Bacon adds : " I would not, however, be understood, by these observations, to insinuate, that the final causes just mentioned may not be founded in truth, and, in a metaphysical view, ex- tremely worthy of attention ; but only, that when such disquisitions invade and overrun the appropriate province of physics, they are likely to lay waste and ruin that de- partment of knowledge." The passage concludes with these words : " And so much concerning metaphysics ; the part of which relating to final causes, I do not deny, has been often enlarged upon in physical, as well as in
OF THE HUMAN MIND. 325
metaphysical treatises. But while, in the latter of these it is treated of with propriety, in the former, it is alto- gether misplaced ; and that, not merely because it vio- lates the rules of a logical order, but because it operates as a powerful obstacle to the progress of inductive science." *
The epigrammatic maxim which gave occasion to these extracts has, I beheve, been oftener quoted (particular- ly by French writers) than any other sentence in Ba- con's works ; and as it has in general been stated, with- out any reference to the context, in the form of a de- tached aphorism, it has been commonly "supposed to convey a meaning widely different from what appears to have been annexed to it by the author. The remarks with which he has prefaced it, and which I have here submitted to the consideration of my readers, sufficiently show, not only that he meant his proposition to be re- stricted to the abuse of final causes in the physics of Aristotle, but that he was anxious to guard against the possibility of any misapprehension or misrepresentation of his opinion. A further proof of this is afforded by the censure which, in the same paragraph, he bestows on Aristotle, for " substituting Nature, instead of God, as the fountain of final causes ; and for treating of them rather as subservient to logic than to theology."
A similar observation may be made on another sen- tence in Bacon, in the interpretation of which a very learned writer, Dr. Cudworth, seems to have altogether lost sight of his usual candor. " Incredibile est quantum agmen idolorum philosophiae immiserit, naturalium ope- rationum ad similitudinem actionum humanarum reduc- tio." " If," says Cudworth, '" the Advancer of Learning here speaks of those who unskilfully attribute their own properties to inanimate bodies, (as when they say, that matter desires forms as the female does the male, and that heavy bodies descend down by appetite towards the centre, that they may rest therein,) there is nothing to be reprehended in the passage. But, if his meaning be extended further to take away all final causes from the
* Dc Augm. Scient. Lib. III. Cap. iv. v. See Note (AA.)
326 ELEMENTS OF THE PHILOSOPHY
things of nature, then is it the very spirit of atheism and infidehty. It is no idol of the cave or den, (to use that affected language,) that is, no prejudice or fallacy im- posed on ourselves, from the attributing our own ani- malish properties to things without us, to think that the frame and system of this whole world was contrived by a perfect understanding and mind."
It is difficult to conceive that any person who had read Bacon's works, and who, at the same time, was ac- quainted with the theories which it was their great ob- ject to explode, could, for a moment, have hesitated about rejecting the latter interpretation as altogether absurd ; and yet the splenetic tone which marks the conclusion of Cudworth's strictures, plainly shows, that he had a decided leaning to it, in preference to the former.* The comment does no honor to his liberality ; and, on the most favorable supposition, must be imputed to a superstitious reverence for the remains of Grecian wisdom, accompanied with a corresponding dread of the unknown dangers to be apprehended from philosophical innovations. Little was he aware, that, in turning the attention of men from the history of opinions and sys- tems, to the observation and study of nature, Bacon was laying the foundation of a bulwark against atheism, more stable and impregnable than the united labors of the ancients were able to rear ; — a bulwark which derives additional strength from every new accession to the stock of human knowledge.!
* Even the ybrmer interpretation is not agreeable (as appears manifestly from the context) to Bacon's idea. The prejudices which he has here more particularly in view, are those which take their rise from a bias in the mind to imagine a greater equality and uniformity in nature than really exists. As an instance of this, he men- tions the universal assumption among the ancient astronomers, that all the celestial motions are performed in orbits perfectly circular; — an assumption, which, a few years before Bacon wrote, had been completely disproved by Kepler. To this he adds some other examples from physics and chemistry ; after which he introduces the general reflection animadverted on by Cudworth. — The whole passage concludes with these words. " Tanta est harmoniae discrepantia inter spiritum hominis est spiritum mundi."
The criticism may appear minute ; but I cannot forbear to mention, as a proof of the carelessness with which Cudworth had read Bacon, that the prejudice supposed by the former to belong to the class of idola speciis, is expressly quoted by the lat- ter, as an example of the idola tribiis. — (See the 5th Book de Augment. Scient. Chap, iv.)
t " Extabit eximiura Newtoni opus adversus Atheorum impetus raunitissimum prse- sldium." Cotesii Praef. in Edit. Secund. Princip.
In the above vindication of Bacon, I have abstained from any appeal to the instan-
or THE HUMAN MIND. 327
Whether Bacon's contempt for the Final Causes of the AristoteUans has not carried him to an extreme in recommending the total exclusion of them from physics, is a very different question ; and a question of much im- portance in the theory of the inductive logic. My own opinion is, that his views on this point, if considered as apphcable to the present state of experimental science, are extremely limited and erroneous. Perhaps, at the time when he wrote, such an exclusion may have ap- peared necessary, as the only effectual antidote against the errors which then infected every branch of philoso- phy ; but granting this to be true, no good reason can be given for continuing the same language, at a period when the proper object of physics is too well under- stood, to render it possible for the investigation of final causes to lead astray the most fanciful theorist. What harm can be apprehended from remarking those proofs of design which fall under the view of the physical in- quirer in the course of his studies 7 Or, if it should be thought foreign to his province to speak of design, he may, at least, be permitted to remark what ends are re- ally accomplished by particular means ; and what advan- tages result from the general laws by which the phenom- ena of nature are regulated. In doing this he only states a fact ; and if it be illogical to go farther, he may leave the inference to the moralist or the divine.
In consequence, however, of the vague and common-
ces in which he has himself forcibly and eloquently expressed the same sentiments here ascribed to him ; because I conceive that an author's real opinions are to be most indisputably judged of from the general spirit and tendency of his writings. The following passage, however, is too precious a document to be omitted on the present occasion. It is, indeed, one of the most hackneyed quotations in our language ; but it forms, on that very account, the most striking constrast to the voluminous and now neglected erudition displayed by Cudworth in defence of the same argument.
" I had rather believe all the fables in the Legend, and the Talmud, and the Alco- ran, than that this universal frame is without a mind ! It is true that a little philoso- phy inclineth man's mind to atheism ; but depth in pbilosopby bringcth men's minds about to religion ; for while the mind of man looketh upon second causes scattered, it may sometimes rest in them and go no farther; but when it beholdeth the chain of them confederate and linked together, it must needs tly to Providence and Deitj' ; nay, even that school which is most accused of atheism, doth most demonstrate reli- gion ; that is, the school of Leucippus, and Democritus, and Epicurus ; for it is a thousand times more credil)le, that four mutable elements and one imnuitable fifth essence, duly and eternally placed, need no God, than that an army of infinite small portions, or seeds unplaced, should have produced this order and beauty witliout a di- vine marshal." Bacon's Essai^s.
328 ELEMENTS OF THE PHILOSOPHY
place declamation against final causes, sanctioned (as has been absurdly supposed) by those detached expres- sions of Bacon, which have suggested the foregoing reflections, it has, for many years past, become fashion- able to omit the consideration of them entirely, as incon- sistent with the acknowledged rules of sound philoso- phizing ; — a caution (it may be remarked by the way) which is most scrupulously observed by those writers who are the most forward to censure every apparent anoma- ly or disorder in the economy of the universe. The effect of this has been to divest the study of nature of its most attractive charms ; and to sacrifice to a false idea of logical rigor, all the moral impressions and pleasures which physical knowledge is fitted to yield.*
Nor is it merely in a moral view, that the consideration of uses is interesting. There are some parts of nature in which it is necessary to complete the physical theo- ry ; nay, there are instances, in v/hich it has proved a powerful and perhaps indispensable, organ of physical discovery. That Bacon should not have been aware of this, will not appear surprising, when it is recollected, that the chief facts which justify the observation have been brought to hght since his time.
Of these /ac^s, the most remarkable are furnished by th,e science of anatomy. To understand the structure of an animal body, it is necessary not only to examine the conformation, of the parts, but to consider their func- tions ; or, in other words, to> consider their ends and uses: nor, indeed, does the most accurate knowledge of the former, till perfected by the discovery of the latter, afford satisfaction to an inquisitive and scientific mind. Every anatomist, accordingly, whatever his m'etaphysi-
* " If a traveller," says the great Mr. Boyle, " being in some ill-inhabited eastern country, should come to a large and fair building, such as one of the most stately of those they call caravanzeras, though he would esteem and be delighted with the magnificence of the structure, and the commodiousness of the apartments, yet sup- posing it to have been erected but for the honor or the pleasure of the founder, he would commend so stately a fabric, without thanking him for it ; but, if he were satis- fied that this commodious building was designed by the founder as a receptacle for passengers, who were freely to have the use of the many conveniences the apart- ments afforded, he would then think himself obliged, not only to praise the magnifi- cence, but with gratitude to acknowledge the bounty and the philanthropy of so^ mu- nificent a benefactor." — BoyWs Works, Vol. IV. p. 517. Folio edition.
OF THE HUMAN MIND. 329
cal creed may be, proceeds, in his researches, upon the maxim, that no organ exists without its appropriate des- tination ; and although he may often fail in his attempts to ascertain what this destination is, he never carries his scepticism so far, as, for a moment, to doubt of the gene- ral principle. I am inclined to think, that it is in this way the most important steps in physiology have been gain- ed ; the curiosity being constantly kept alive by some new problem in the animal machine ; and, at the same time, checked in its wanderings, by an irresistible con- viction, that nothing is made in vain. The memorable account given by Mr. Boyle of the circumstances which led to the discovery of the circulation of the blood, is but one of the many testimonies which might be quoted in confirmation of this opinion.
" I remember, that when I asked our famous Harvey, in the only discourse I had with him, (which was but a little while before he died,) what were the things which induced him to think of a circulation of the blood ? he answered me, that when he took notice, that the valves in the veins of so many parts of the body were so placed, that they gave free passage to the blood towards the heart, but opposed the passage of the venal blood the contrary way, he was invited to think, that so provident a cause as nature had not placed so many valves with- out design ; and no design seemed more probable, than that, since the blood could not well, because of the in- terposing valves, be sent by the veins to the limbs, it should be sent through the arteries, and return through the veins whose valves did not oppose its course that way." *
* Boyle's Works, Vol. IV. p. 5.S9 Folio ed. See Outlines of Moral Philosophy, p. 185. (Edin. 1793.)
The reasoning here ascribed to Harvey seems now so very natural and obvious, that some have been disposed to question his claim to the high rank commonly as- signed to him among the improvers of science. The late Dr. William Hunter has said that after the discovery of the valves in the veins, which Harvey learned, while in Italy, from his master Fabricius ab Aquapcndente, the remaining step might easily have been made by any person of common abilities. " This discovery," he observes, " set Harvey to work upon the use of tlie heart and vascular system in animals : and in the course of some years, he was so happy as to discover, and to prove beyond all possibility of doubt, the circulation of the blood." He afterwards expresses his astonishment that this discovery should have been left for Harvey ; adding, that " Providence meant to reserve it for him, and would not let men see what was be-
voL. II. 42
330 ELEMENTS OF THE PHILOSOPHY
This perception of design and contrivance is more peculiarly impressive, when we contemplate those in- stances in the animal economy, in which the same effect is produced, in different combinations of circumstances, by different means : — when we compare, for example, the circulation of the blood in the foetus, with that in the body of the animal after it is born. On such an occa- sion, how is it possible to withhold the assent from the ingenious reflection of Baxter ! " Art and means are designedly multiphed, that we might not take it for the effects of chance ; and, in some cases, the method itself is different, that we might see it is not the effect of surd necessity." *
fore them, nor understand what they read." — Hunter's Introductory Lectures, p. 42 et seq.
Whatever opinion be formed on this point, Dr. Hunter's remarks are valuable, as an additional proof of the regard paid by anatomists to Final Causes, in the study of physiology.
See also Haller, Elem. Physiolog. Tom. I. p. 204.
* Inquiry into the Nature of the Human Soul, Vol. L p. 136. (3d Ed.)
The following passage from an old English divine may be of use for the farther illustration of this argument. I quote it vtrith the greater confidence, as 1 find that the most eminent and original physiologist of the present age (M. Cuvier) has been led, by his enlightened researches concerning the laws of the animal economy, into a train of thinking strikingly similar.
" Man is always mending and altering his works ; but nature observes the same tenor, because her works are so perfect, that there is no place for amendments, no- thing that can be reprehended. The most sagacious men in so many ages have not been able to find any flaw in these divinely contrived and formed machines ; no blot or error in this great volume of the world, as if any thing had been an imperfect essay at the first ; nothing that can be altered for the better ; nothing but if it were altered would be marred. This couid not have been, had man's body been the work of chance, and not counsel and providence. Why should there be constantly the same parts ? Why should they retain constantly the same places ? Nothing fo con- trary as constancy and chance. Should I see a man throw the same number a thou- sand times together upon but three dice, could you persuade me that this were acci- dental, and that there was no necessary cause for it .'' How much more incredible then is it, that constancy in such a variety, such a multiplicity of parts, should be the result of chance ? Neither yet can these works be the effects of Necessity or Fate, for then there would be the same constancy observed in the smaller as well as in the larger parts and vessels ; whereas there we see nature doth, as it were, sport itself, the minute ramifications of all the vessels, veins, arteries, and nerves, infinitely varying in individuals of the same species, so that they are not in any two alike." — Ray's Wisdom of God in the Creation.
" Nature," says Cuvier, " while confining herself strictly within those limits which the conditions necessary for existence prescribed to her, has yielded to her spontane- ous fecundity wherever these conditions did not limit her operations ; and without ever passing beyond the small number of combinations, that can be realized in the essential modifications of the important organs, she seems to ha.ve given full scope to her fancy, in filling up the subordinate parts. With respect to these, it is not in- quired, whether an individual form, whether a particular arrangement be necessary; it seems often not to have been aked, whether it be even useful, in order to reduce it to practice ; it is sufficient that it be possible, that it destroy not the harmony of the whole. Accordingly, as we recede from the principal organs, and approach to those of less importance, the varieties in structure and appearance become more
OF THE HUMAN MIND. 331
The study of comparative anatomy leads, at every step, so directly and so manifestly to the same conclu- sion, that even those physiologists who had nothing in view but the advancement of their own science, unani- mously agree in recommending the dissection of animals of different kinds, as the most effectual of all helps for as- certaining the functions of the various organs in the human frame ; — tacitly assuming as an incontrovertible truth, that, in proportion to the variety of means by which the same effect is accompUshed, the presumption increases, that this effect was an end in the contemplation of the artist. " The intention of nature," says one author, " in the formation of the different parts, can no where be so well learned as from comparative anatomy ; that is, if we would understand physiology, and reason on the func- tions of the animal economy, we must see how the same end is brought about in other species. — We must con- template the part or organ in different anim.als ; its shape, position, and connexion with the other parts ; and observe Avhat thence arises. If we find one com- mon EFFECT constantly produced, though in a very dif- ferent way, we may safely conclude that this is the use or function of the part. — This reasoning can never be- tray us, if we are but sure of the facts." *
The celebrated Albinus expresses himself to the same purpose in his preface to Harvey's Exercitatio de Motu Cordis. " Incidenda autem animalia, quibus par- tes illae quarum actiones quasrimus easdem atque homini sunt, aut certe similes iis ; ex quibus sine metu erroris judicare de ilhs hominis Uceat. Quin et reliqua, si mo- do ahquam habeant ad hominem similitudinem, idonea sunt ad aliquod suppeditandum."
If Bacon had lived to read such testimonies as these in favor of the investigation of Final Causes ; or had witnessed the discoveries to which it has led in the
numerous ; and when we arrive at the surface of tlie hody, where the parts the least essential, and whose injuries are the least momentous, are neccssaiily placed, the number of varieties is so great, that the conjoined labors of naturali-its have not yet been able to give us an adequate idea of them." Legons d'Anatoinie Com- parce.
* Letter by an anonymous correspondent, prefixed to Monro's Comparative Anat- omy. Londonj 1744.
332 ELEMENTS OF THE PHILOSOPHY
study of the animal economy, he would, I doubt not, have readily admitted, that it was not altogether uninter- esting and unprofitable, even to the physical inquirer. Such, however, is the influence of an illustrious name, that, in direct opposition to the evidence of historical facts, the assertion of the complete sterility of all these speculations is, to the present day, repeated, with undi- minished confidence, by writers of unquestionable learn- ing and talents. In one of the most noted physiological works which have lately appeared on the Continent, Bacon's apophthegm is cited more than once withunquali- ified approbation ; although the author candidly owns, that it is difficult jfor the most reserved philosopher al- ways to keep it steadily in view, in the course of his inquiries.*
The prejudice against final causes, so generally avow- ed by the most eminent philosophers of France, during the eighteenth century, was first introduced into that country by Descartes. It must not, however, be im- agined, that, in the mind of this great man, it arose from any bias towards atheism. On the contrary, he him.self tells us, that his objection to the research of uses or ends, was founded entirely on the presumptuous confidence which it seemed to argue in the powers of human rea- son ; as if it were conceivable that the hmited faculties of man could penetrate into the counsels of Divine wisdom. Of the existence of God he conceived that a demonstrative proof was afforded by the idea we are able to form of a Being infinitely perfect, and necessari- ly existing ; and it has, with some probability, been con- jectured, that it was his partiality to this new argument of his own, which led him to reject the reasonings of his predecessors in support of the same conclusion, f
* " Je regarde, avec le grand Bacon, la Philosophie des causes finales comme ste- rile : inais il est bien difficile a, I'homme le plus reserve, de n'y avoir jamais recouvs dans ses explications." — Rapports du Physique et du Moral de V Homme. Par M. leSenateur Cabanis. Tom I. p. 352. Paris, 1S05.
f " Nullas unquam rationes circa res naturales a fine, quam Deus aut natura in iis faciendis sibi proposuit, desumemus ; quia non tantum debemus nobis arrogare, ut ejus consiliorum participes nos esse putemus." Princip. Piirs. I. § 28. " Dum base perpendo attentius, occurrit primo non mihi esse mirandum si quajdam a Deo fiant quorum rationes non intcUigam ; nee de ejus existcntia ideo esse dubilandum, quod forte (juaidam alia esse expcriar quje quare, vel quomodo ab illo facta sint non
OF THE HUMAN MIND. 333
To this objection of Descartes, an elaborate, and, in my opinion, a most satisfactory reply, is to be found in the works of Mr. Boyle. The principal scope of his essay may be collected from the following short extract :
" Suppose that a countryman, being in a clear day brought into the garden of some famous mathematician, should see there one of those curious gnomatic instru- ments, that show at once the place of the sun in the zodiac, his declination from the equator, tHe day of the month, the length of the day, &,c. &c. It would indeed be presumption in him, being unacquainted both with the mathematical disciplines, and the several intentions of the artist, to pretend or think himself able to discov- er all the ends for which so curious and elaborate a piece was framed : but when he sees it furnished with a stile, with horary lines and numbers, and in short with all the requisites of a sun-dial, and manifestly perceives the shadow to mark from time to time the hour of the day, it would be no more a presumption than an error in him to conclude, that (whatever other uses the instrument was fit or was designed for) it is a sun-dial, that was meant to show the hour of the day." *
With this opinion of Boyle that of Newton so entirely coincided, that (according to Maclaurin) he thought the consideration of final causes essential to true philosophy ; and was accustomed to congratulate himself on the ef- fect of his writings in reviving an attention to them, af- ter the attempt of Descartes to discard them from
comprehendo ; cum enim jam sciam naturam meam esse valde infinnam et limita- tam, Dei autem naturam esse iminensam, incomprehensibilem, infinitam, ex hoc satis etiam scio innumerabilia ilium posse quorum causas ignorem ; atqiie ob hanc unicani rationem totiim illud causarum genus quod a fine peti solet in rebus physicis nullam usum habere existimo ; non enim absque tcraeritate me puto posse investigarc fines Dei." Meditatio Quarta.
See Note (BB.)
* In the same Essay, Mr. Boyle has ofTcied some very judicious stricture on'the abuses to which the research of final causes is liable, when incautiously and pre- sumptuously pursued. An abstract of these, accompanied with a few illustrations from later writers, might form an interesting chapter in a treatise of inductive logic.
The subject has been since prosecuted with considerable ingenuity by Le Sage of Geneva, who has even attempted (and not altogether without success) to lay down logical rules for the investigation of ends. To this sludj^ which he was anx- ious to form into a separate science, he gave the very ill chosen name of Trlcologie ; a name, if I am not mistaken, first suggested by Wollius. — For some valuable frag- ments of his intended work with respect to it, see the Account of his Life and Wri- tings by his friend M. Pievost. (Geneva, 1805.)
334 ELEMENTS OF THE PHILOSOPHY
physics. On this occasion, Maclaurin has remarked, " that of all sort of causes, final causes are the most clearly placed in our view ; — and that it is difficult to comprehend, why it should be thought arrogant to at- tend to the design and contrivance that is so evidently displayed in nature, and obvious to all men ; — to main- tain, for instance, that the eye was made for seeing, though we may not be able either to account mechanic- ally for the refraction of light in its coats, or to explain how the ima,ge is propagated from the retina to the mind." * — It is Newton's own language, however, which alone can do justice to his sentiments on the present subject.
" The main business of natural philosophy is to argue from phenomena, without feigning hypotheses, and to deduce causes from effects till we come to the very first cause, which certainly is not mechanical ; and not only to unfold the mechanism of the world, but chiefly to re- solve these and such like questions : Whence is it that JYature does nothing in vain; and ivhence arises all that order and beauty lohich we see in the world 1 — How came the bodies of animals to be contrived with so much art, and for what ends loere there several parts ? Was the eye contrived without skill in optics, and the ear without knowledge of sounds ? " *
In multiplying these quotations, I am well aware that authorities are not arguments ; but when a prejudice to which authority alone has given currency is to be combated, what other refutation is likely to be effec- tual?
After all, it were to be wished that the scholastic phrase ^«a/ cause could, without affectation, be dropped from our philosophical vocabulary ; and some more un- exceptionable mode of speaking substituted instead of it. In this elementary work, I have not presumed to lay aside entirely a form of expression consecrated in the writings of Newton, and of his most eminent follow- ers ; but I am fully sensible of its impropriety, and am
* Account of Newton's Philosophical Discoveries, Book I. Chap. H. t Newton's Optics, Query 28.
OF THE HUMAN MIKD. 335
not without hopes that I may contribute something to encourage the gradual disuse of it, by the indiscriminate employment of the words ends and uses to convey the same idea. Little more perhaps than the general adop- tion of one or other of these terms is necessary, to bring candid and reflecting minds to a uniformity of language as well as of sentiment on the point in question.
It was before observed, Avith respect to anatomists, that all of them, without exception, w^hether professedly friendly or hostile to the inquisition of final causes, con- cur in availing themselves of its guidance in their phys- iological researches. A similar remark w^ill be found to apply to other classes of scientific inquirers. Whatever their speculative opinions may be, the moment their cu- riosity is fairly engaged in the pursuit of truth, either physical or moral, they involuntarily, and often perhaps unconsciously, submit their understandings to a logic borrowed neither from the schools of Aristotle nor of Bacon. The ethical system (for example) of those an- cient philosophers who held that Virtue consists in fol- lowing Nature, not only involves a recognition of final causes, but represents the study of them, in as far as re- gards the ends and destination of our own being, as the greatbusiness and duty of life.* The system, too, of those physicians who profess to follow Nature in the treat- ment of diseases, by watching and aiding her medicative powers, assumes the same doctrine as its fundamental principle. A still more remarkable illustration, howev- er, of the influence which this species of evidence has over the belief, even when W' e are the least aware of its connexion with metaphysical conclusions, occurs in the history of the French Economical System. Of the comprehensive and elevated views which at first suggest- ed it, the title of Physiocratie, by which it Avas early distinguished, aff'ords a strong presumptive proof; and the same thing is more fully demonstrated, by the fre-
* " Discitc, O miseri, ct causas cognoscito rerum, Quid suinus, cl qiiidnam victuri gignimur."
Persics.
I^yoj Si Tt ^ovlofxai' naxa^iad-iiv xtjv <pvaiv, kuI tcixjuj imaO-ui.
Epictet,
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qiient recurrence made in it to the physical and moral laws of Nature, as the unerring standard which the legislator should keep in view in all his positive institu- tions.* I do not speak at present of the justness of these opinions. I wish only to remark, that, in the state- ment of them given by their original authors, it is taken for granted as a truth self-evident and indisputable, not merely that benevolent design is manifested in all the physical and moral arrangements connected with this globe, but that the study of these arrangements is indis- pensably necessary to lay a sohd foundation for poUtical science.
The same principles appear to have led Mr. Smith into that train of thinking which gave birth to his inqui- ries concerning National Wealth. " Man," he observes in one of his oldest manuscripts now extant, " is gene- rally considered by statesmen and projectors as the ma- terials of a sort of political mechanics. Projectors disturb Nature in the course of her operations in human affairs ; and it requires no more than to let her alone, and give her fair play in the pursuit of her own de- signs."— And in another passage : " Little else is requi- site to carry a state to the highest degree of opulence from the lowest barbarism, but peace, easy taxes, and a tolerable administration of justice ; all the rest being brought about by the natural course of things. All governments which thwart this natural course ; which force things into another channel ; or which endeavour to arrest the progress of society at a particular point, are unnatural, and to support themselves are obhged to be oppressive and tyrannical." f Various other passages of a similar import might be quoted, both from his Wealth of Nations, and from his Theory of Moral Sentiments.
This doctrine of Smith and Quesnay, which tends to
* " Ces loix forraent ensemble ce qu'on appelle la loi naturelle. Tous les hom- ines et toutes les puissances humaines doivent etre soumis a ces loix souveraines, institutccs par I'etrc supreme : clles sent immuables et irrefragables, et les meilleures loix possibles ; et par consequent, la base du governement Ic plus parfait, ctla regie fondamentale dc toutes les loix positives ; car les loix positives ne sent que des loix de manutention relatives a I'ordre naturel evidemment lo plus avantageux au genre huroain." — Quksnay.
t Biographical Memoirs of Smith, Robertson, and Reid, p. 100.
OF THE HUMAN MIND. 337
simplify the theory of legislation, by exploding the poli- cy of those complicated checks and restraints which swell the municipal codes of most nations, has now, I beheve, become the prevailing creed of thinking men all over Europe ; and, as commonly happens to prevail- ing creeds, has been pushed by many of its partisans far beyond the views and intentions of its original au- thors. Such too is the effect of fashion, on the one hand, and of obnoxious phrases on the other, that it has found some of its most zealous abettors and propagators among writers who would, without a moment's hesitation have rejected, as puerile and superstitious, any refer- ence to final causes in a philosophical discussion.
II.
Danger of confounding Final with Physical Causes in the Philosophy of the Human
Mind.
Having said so much upon the research of Final Causes in Physics, properly so called, I shall subjoin a few remarks on its apphcation to the Philosophy of the Human Mind ; — a science in which the just rules of in- vestigation are as yet far from being generally under- stood. Of this no stronger proof can be produced, than the confusion between final and efficient causes, which perpetually recurs in the writings of our latest and most eminent morahsts. The same confusion, as I have already observed, prevailed in the physical reason- ings of the Aristotelians ; but since the time of Bacon, has been so completely corrected, that, in the wildest theories of modern naturalists, hardly a vestige of it is to be traced.
To the logical error just mentioned it is owing, that so many false accounts have been given of the princi- ples of human conduct or of the motives by which men are stimulated to action. When the general laws of our internal frame are attentively examined, they will be found to have for their object the happiness and im- provement both of the individual and of society. This
VOL II. 43
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is their Final Cause, or the end for which we may pre- sume they were destined by our Maker. But, in such cases, it seldom happens, that, while Man is obeying the active impulses of his nature, he has any idea of the ulti- mate ends which he is promoting ; or is able to calculate the remote effects of the movements which he impress- es on the httle wheels around him. These active im- pulses, therefore, may, in one sense, be considered as the efficient causes of his conduct ; inasmuch as they are the means employed to determine him to particular pursuits and habits ; and as they operate (in the first instance, at least) without any reflection on his part on the purposes to which they are subservient. Philoso- phers, however, have in every age been extremely apt to conclude, when they had discovered the salutary tendency of any active principle, that it was from a sense or foreknowledge of this tendency that the prin- ciple derived its origin. Hence have arisen the theo- ries which attempt to account for all our actions from self-love ; and also those which would resolve the whole of morahty, either into political views of general expe- diency, or into an enlightened regard to our own best interests.
I do not know of any author who has been so com- pletely aware of this common error as Mr. Smith. In examining the principles connected with our moral constitution, he always treats separately of their final causes, and of the mechanism (as he calls it) by which nature accomplishes the effect ; and he has even been at pains to point out to his successors the great impor- tance of attending to the distinction between these two speculations. — " In every part of the universe, we ob- serve means adjusted with the nicest artifice to the ends which they are intended to produce ; and in the mechan- ism of a plant or animal body, admire how every thing is contrived for advancing the two great purposes of na- ture, the support of the individual, and the propagation of the species. But in these, and in all such objects, we still distinguish the efficient from the final cause of their several motions and organizations. The digestion of the food, the circulation of the blood, and the secretion
OF THE HUMAN MIND. 339
of the several juices which are drawn from it, are ope- rations all of them necessary for the great pm-poses of animal life ; yet we never endeavour to account for them from those purposes as from their efficient causes, nor imagine that the blood circulates, or the food di- gests of its own accord, and with a view or intention to the purposes of circulation or digestion. The w^ieels of the watch are all admirably adapted to the end for which it was made, the pointing of the hour. All their various motions conspire in the nicest manner to produce this effect. If they were endowed with a desire and inten- tion to produce it, they could not do it better. Yet we never ascribe any such intention or desire to them, but to the watch-maker, and we know that they are put in- to motion by a spring, which intends the effect it produ- ces as little as they do. But though, in accounting for the operations of bodies, we never fail to distinguish, in this manner, the efficient from the final cause, in ac- counting for those of the mind, we are apt to confound these two different things with one another. When, by natural principles, we are led to advance those ends which a refined and enhghtened reason would recom- mend to us, we are very apt to impute to that reason, as to their efficient cause, the sentiments and actions by which we advance those ends, and to imagine that to be the wisdom of Man, which, in reality, is the wisdom of God. Upon a superficial view, this cause seems suffi- cient to produce the effects which are ascribed to it ; and the system of Human Nature seems to be more simple and agreeable, when all its different operations are, in this manner, deduced from a single principle." *
These remarks apply with peculiar force to a theory of morals which has made much noise in our own times ; — a theory which resolves the obligation of all the differ- ent virtues into a sense of their utilitij. At the time when Mr. Smith wrote, it had been recently brought in- to fashion by the ingenious and refined disquisitions of Mr. Hume ; and there can be Httle doubt, that the fore- going strictures were meant by the author as an indirect refutation of his friend's doctrines.
* Theory of Moral Sentiments, Vol. I. p. 21G, et seq. 6th edit.
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The same theory (which is of a very ancient date*) has been since revived by Mr. Godwin, and by the late excellent Dr. Paley. Widely as these two writers differ in the source whence they derive their rule of conduct, and the sanctions by which they enforce its observance, they are perfectly agreed about its paramount authority over every other principle of action. " Whatever is ex- pedient" says Dr. Paley, " is right. It is the utility of any moral rule alone which constitutes the obligation of it. ||
. . . . But then, it must be expedient on the whole, at the long run, in all its effects collateral and re- mote, as well as those which are immediate and direct ; as it is obvious, that, in computing consequences, it makes no difference in what way, or at what distance they ensue." | — Mr. Godwin has no where expressed himself, on this fundamental question of practical ethics, in terms more decided and unquahfied.
The observations quoted from Mr. Smith on the prone- ness of the mind, in moral speculations, to confound to- gether efficient and final causes, furnish a key to the chief difficulty by which the patrons of this specious but very dangerous system have been misled.
Among the quahties connected with the different vir- tues, there is none more striking than their beneficial influence on social happiness ; and accordingly, moral- ists of all descriptions when employed in enforcing par- ticular duties, such as justice, veracity, temperance, and the various charities of private life, never fail to enlarge on the numerous blessings which follow in their train. The same observadon may be apphed to self-interest ; inasmuch, as the most effectual way of promoting it is
* " Ipsa utilitas, justi prope mater et asqui." — Horat. Sat. Lib. I. 3.
f Principles of Moral and Political Philosophy, Vol. I. p. 70. 5th edit.
X Ibid. p. 78.
In another part of his work, Dr. Paley explicitly asserts, that every moral rule is liable to be superseded in particular cases on the ground of expediency. " Moral philosophy cannot pronounce that any rule of morality is so rigid as to bond to no exceptions ; nor, on the other hand, can she comprise these exceptions within any previous description. She confesses, that the obligation of every law depends upon its ultimate utility ; that this utility having a finite and determinate value, situations may be feigned, and consequently may possibly arise, in which the general tendency is outweighed by the enormity of the particular mischief; and of course, where ulti- mate utility renders it as much an act of duty to break the rule, as it is on other oc- casions to observe it." — Vol. II. p. 411.
OF THE HUMAN MIND. 341
universally acknowledged to be by a strict and hab itual regard to the obligations of morality. — In consequence of this unity of design, which is not less conspicuous in the moral than in the natural world, it is easy for a phi- losopher to give a plausible explanation of all our duties from one principle ; because the general tendency of all of them is to determine us to the same course of life. It does not, however, follow from this, that it is from such a comprehensive survey of the consequences of uman conduct, that our ideas of right and wrong are derived ; or that we are entitled, in particular cases, to form rules of action to ourselves, drawn from specula- tive conclusions concerning the final causes of our moral constitution. If it be true (as some theologians have presumed to assert) that benevolence is the sole princi- ple of action in the Deity, we must suppose that the duties of veracity and justice were enjoined by him, 7iot on account of their intrinsic rectitude, but of their utih- ty : but still, with respect to man, these are sacred and indispensable laws — lavv^s which he never transgresses without incurring the penalties of self-condemnation and remorse : And indeed if, without the guidance of any internal monitor, he were left to infer the duties incum- bent on him from a calculation and comparison of remote effects, we may venture to affirm, that there w^ould not be enough of virtue left in the world to hold society to- gether.
To those who have been accustomed to reflect on the general analogy of the human constitution, and on the admirable adaptation of its various parts to that scene in which we are destined to act, this last consideration will, independently of any examination of the fact, sug- gest a very strong presumption a priori against the doc- trine to which the foregoing remarks relate. For is it at all consonant with the other arrangements, so wisely cal- culated for human happiness, to suppose that the con- duct of such a fallible and short-sighted creature as ]\Ian, would be left to be regulated by no other principle than the private opinion of each individual concerning the expediency of his own actions ? or, in other words, by the conjectures which he might form on the good or evil
342 ELEMENTS OF THE PHILOSOPHY
resulting on the whole from an endless train of future contingencies 7 Were this the case, the opinions of mankind, with respect to the rules of morality, would be as various as their judgments about the probable is- sue of the most doubtful and difficult determinations in politics. Numberless cases might be fancied, in which a person would not only c/aim merit but actually j^ossess it, in consequence of actions which are generally regarded with indignation and abhorrence ; for, unless we admit such duties as justice, veracity, and gratitude, to be im- mediately and imperatively sanctioned by the authority of reason and of conscience, it follows as a necessary inference, that we are hound to violate them, whenever by doing so we have a prospect of advancing any of the essential interests of society ; or (which amounts to the same thing) that a good end'is sufficient to sanctify what- ever means may appear to us to be necessary for its ac- comphshment. Even men of the soundest and most penetrating understandings might frequently be led to the perpetration of enormities, if they had no other hght to guide them but what they derived from their own uncertain anticipations of futurity. And when we consider how small the number of such men is, in com- parison of those whose judgments are perverted by the prejudices of education and their own selfish passions, , it is easy to see what a scene of anarchy the world would become. Of this, indeed, we have too melancholy an experimental proof, in the history of those individuals, who have, in practice, adopted the rule of general expe- diency as their whole code of morahty ; — a rule which the most execrable scourges of the human race have, in all ages, professed to follow, and of which they have uniformly availed themselves, as an apology for their de- viations from the ordinary maxims of right and wrong.
Fortunately for mankind, the peace of society is not thus entrusted to accident, the great rules of a virtuous conduct being confessedly of such a nature as to be ob- vious to every sincere and well-disposed mind. And it is in a peculiar degree striking, that, while the theory of ethics involves some of the most abstruse questions which have ever employed the human faculties, the moral
OF THE HUMAN MIND. 343
judgments and moral feelings of the most distant ages and nations, with respect to all the most essential duties of hfe, are one and the same.*
Of this theory of utihty, so strongly recommended to some by the powerful genius of Hume, and to others by the well-merited popularity of Paley, the most satisfac- tory of all refutations is to be found in the work of Mr. Godwin. It is unnecessary to inquire how far the prac- tical lessons he has inculcated are logically inferred from his fundamental principle ; for although I apprehend much might be objected to these, even on his own hy- pothesis, yet, if such be the conclusions to which, in the judgment of so acute a reasoner, it appeared to lead with demonstrative evidence, nothing farther is requisite to il- lustrate the practical tendency of a system, which, ab- solving men from the obligations imposed on them with so commanding an authority by the moral constitution of human nature, abandons every individual to the guid- ance of his own narrow views concerning the complica- ted interests of political society. f
One very obvious consideration seems to have entire- ly escaped the notice of this, as well as of many other late inquirers : That, in ethical researches, not less than in those which relate to the material universe, the busi-
* " Si quid rectissimum sit, quccrimus ; perspicuura est. Si quid maxime expedi- at ; obscurum. Sin ii sumus, qui piofecto esse debemus, ut nihil arbitremur expe- dire, nisi quod rectum honestumque sit ; non potest esse dubiuni, quid i'aciendum nobis sit." — Cic. Ep. adFani. IV. 2.
t It is remarkable that Mr. Hume, by far the ablest advocate for the theory in ques- tion, has indirectly acknowledged its inconsistence with some of the most important facts which it professes to explain. " Though the heart" he observes in the 5th section of his Inquiry concerning Morals, " takes not part entirely with those gen- eral notions, nor regulates all its love and hatred by the universal abstract differences of vice and virtue, without regard to self, and the persons with whom we are more intimately connected : yet have these moral diflTerences a considerable influence, and being sufficient, at least for discourse, serve all the purposes in company, on tlie thea- tre, and in the schools." — On this passage, the following very curious note is to be found at the end of the volume ; a note (by the way) which deserves (o be added to the other proofs already given of the irresistible iniluence which the doctrine of final causes occasionally exercises over the most sceptical minds. " It is wisely or- dained by nature that private connexions should commonly prevail over universal views and considerations ; otherwise our affections ami actions would be dissipated and lost, for want of a jiropcr limited object." — Does not this remark imply an ac- knowledgment, J^irst, That the jirinciple of general expediency (the so/e principle of virtuous conduct, according to Mr. Hume, in our most important transactions with our fellow-creatures) would not contribute to the happiness of society, if men should co??i??io/i/i/ act upon it ; and. Secondly, That some provision is made in our moral constitution, (hat we shall, in fact, be influenced by other motives in discharging the olficeg of private life ?
344 ELEMENTS OF THE PHILOSOPHY
ness of the philosopher is hmited to the analytical in- vestigation of general laws from the observed phenome- na ; and that if, in any instance, his conclusions should be found inconsistent with acknowledged facts, the for- mer must necessarily be corrected or modified by the latter. On such occasions, the ultimate appeal must be always made to the moral sentiments and emotions of the human race. The representations, for example, which we read with so much delight, in those poets, of whatever age and country, who have most successfully touched the human heart : — of the heroical sacrifices made to gratitude, to parental duty, to filial piety, to con- jugal aff'ection ; — are not amenable to the authority of any ethical theory, but are the most authentic records of the phenomena which it is the object of such theories to generalize. The sentiment of Publius Syrus ; Omne dixeris maledictum, quum ingratum hommem dixeris — speaks a language which accords with every feeling of an unperverted mind ; — it speaks the language of Nature, which it is the province of the moralist, not to criticize, but to hsten to with reverence. By employing our rea- son to interpret and to obey this, and the other moral suggestions of the heart, we may trust with confidence, that we take the most eff'ectual means in our power to augment the sum of human happiness ; — but the discov- ery of this connexion between virtue and utility is the slow result of extensive and philosophical combinations ; and it would soon cease to have a foundation in truth, if men were to substitute their own conceptions of expe- diency, instead of those rules of action which are inspir- ed by the wisdom of God.*
It must not be concluded from the foregoing observa- tions, that, even in ethical inquiries, the consideration of final causes is to be rejected. On the contrary, Mr. Smith himself, whose logical precepts on this subject I have now been endeavouring to illustrate and enforce, has frequently indulged his curiosity in speculations about uses or advantages; and seems plainly to have considered them as important objects of philosophical
See Note (CC.)
OF THE HUMAN MIND. 345
study, not less than efficient causes. The only caution to be observed is, that the one may not be confounded with the other.
Between these two different researches, however, there is, both in physics and ethics, a very intimate con- nexion. In various cases, the consideration of final causes has led to the discovery of some general law of nature ; and in almost every case, the discovery of a general law clearly points out some wise and beneficent purposes to which it is subservient. Indeed it is chiefly the prospect of such applications which renders the in^ vestigation of general laws interesting to the mind.*
•SeeNqte (DD.)
VOL. II. 44
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CONCLUSION OF PART SECOND.
In the foregoing chapters of this Second Part, I have endeavoured to turn the attention of my readers to va- rious important questions relating to the Human Under- standing ; aiming, in the first place, to correct some fundamental errors in the theories commonly received with respect to the powers of intuition and of reason- ing ; and, secondly, to illustrate some doctrines connect- ed with the ground-work of the inductive logic, which have been either overlooked, or misapprehended by the generahty of preceding writers. The bulk to which the volume has already extended, renders it impossible for me now to attempt a detailed recapitulation of its con- tents : — Nor do I much regret the necessity of this omission, having endeavoured, in every instance, as far as I could, to enable the intelligent reader to trace the thread of my discussions.
In a work professedly elementary, the frequent refer- ences made to the opinions of others may, at first sight, appear out of place ; and it may not unnaturally be thought, that I have too often indulged in critical strict- ures, where I ought to have confined myself to a didac- tic exposition of first principles. To this objection I have only to reply, that my aim is not to supplant any of the estabhshed branches of academical study ; but, by inviting and encouraging the young philosopher, when his academical career is closed, to review, with atten- tention and candor, his past acquisitions, to put him in the way of supplying what is defective in the present systems of education. I have accordingly entitled my book Elements — not of Logic or of Pneumatology, but — of the Philosophy of the Human Mind ; a study which, according to my idea of it, presupposes a general ac- quaintance with the particular departments of literature and of science, but to which I do not know that any ele- mentary introduction has yet been attempted. It is a study, indeed, whereof little more perhaps than the ele-
OF THE HUMAN MIND. 347
ments can be communicated by the mind of one individ- ual to that of another.
In proof of this, it is sufficient here to hint, (for I must not at present enlarge on so extensive a topic,) that a knowledge of the general laws which regulate the intellectual phenomena is, to the logical student, of little practical value, but as a preparation for the study of himself. In this respect, the anatomy of the mind dif- fers essentially from that of the body ; the structure of the former (whatever collateral aids may be derived from observing the varieties of genius in our fellow- creatures) being accessible to those alone who can re- tire into the deepest recesses of their own internal frame ; and even to these presenting, along with the generic attributes of the race, many of the specific pe- culiarities of the individual. On this subject every wri- ter, whose speculations are at all worthy of notice, must draw his chief materials from within ; and it is only by comparing the conclusions of different writers, and sub- jecting all of them to the test of our personal experience, that we can hope to separate the essential principles of the human constitution from the unsuspected effects of education and of temperament ; * or to apply with ad- vantage, to our particular circumstances, the combined results of our reading and of our reflections. The con- stant appeal which in such inquiries, the reader is thus forced to make to his own consciousness and to his own judgment, has a powerful tendency to form a habit, not more essential to the success of his metaphysical re- searches, than of all his other speculative pursuits.
Nearly connected with this habit, is a propensity to weigh and to ascertain the exact import of words ; one of the nicest and most difficult of all analytical process- es ; and that upon which more stress has been justly laid by our best modern logicians, than upon any other organ for the investigation of truth. For the culture of
* I use the word temperament, in this instance, as synonymous with the idiosyn- crasy of medical authors ; a term which I thought miirht have savoured of affcctaiion if applied to the mind ; although authorities for such an einployineiit of it arc not wanting among old English writers. One exam])lc, directly in point, is quoted by Johnson from Glanvillc. " The uaderstauding also hath its idiosyncrasies, as well as other faculties."
348 ELEMENTS OF THE PHILOSOPHY
this propensity, no science is so peculiarly calculated to prepare the mind, as the study of its own operations. Here, the imperfections of words constitute the princi- pal obstacle to our progress ; nor is it possible to ad- vance a single step, without struggling against the associations imposed by the illusions of metaphorical terms, and of analogical theories. Abstracting, there- fore, from its various practical applications, and consid- ering it merely as a gymnastic exercise to the reasoning powers, this study seems pointed out by nature, as the best of all schools for inuring the understanding to a cautious and skilful employment of language as the in- strument of thought.
The two first chapters of this volume relate to logical questions, on which the established opinions appear to me to present stumbhng-blocks at the very threshold of the science* In treating of these, I have canvassed with freedom, but, I hope, with due respect, the doc- trines of some illustrious moderns, whom I am proud to acknowledge as my masters ; of those more particularly, whose works are in the highest repute in our British Universities, and whose errors I was, on that account, the most soHcitous to rectify. For the space allotted to my criticisms on Condillac, no apology is necessary to those, who have the shghtest acquaintance with the present state of philosophy on the Continent, or who have remarked the growing popularity, in this Island, of (Some of his weakest and most exceptionable theories.—^ On various controverted points connected with the theo- ry of evidence, both demonstrative and experimental, I trust, with some confidence, that I shall be found to have thrown considerable light : in other instances, I have been forced to content myself with proposing my doubts ; leaving the task of solving them to future inquirers. To awaken a dormant spirit of discussion, by pointing out the imperfections of generally received systems, is at least one step gained towards the farther advancement of knowledge.
It is justly and philosopically remarked by Burke, that ^^ nothing tends more to the corruption of science than to Suffer it to stagnate. These waters must be troubled
OF THE HUMAN MIND. 349
before they can exert their virtues. A man who works beyond the surface of things, though he may be wrong himself, yet he clears the way for others, and may chance to make even his errors subservient to the cause of truth." *
The subsequent chapters, relative to the Baconian Logic, bear, all of them, more or less in their general scope, on the theory of the intellectual powers, and on the first principles of human knowledge. In this part of my work, the reader wull easily perceive, that I do not profess to dehver logical precepts ; but to concentrate, and to reflect back on the Philosophy of the Mind, whatever scattered lights I have been able to collect from the experimental researches to which that Philoso- phy has given birth. I have aimed, at the same time, (and I hope not altogether without success,) to give somewhat more of precision to the technical phraseology of the Baconian school, and of correctness to their meta- physical ideas.
Before concluding these speculations, it may not be improper to caution my readers against supposing, that when I speak of the Baconian school, or of the Baconi- an logic, I mean to ascribe entirely to the JYovum Orga- non the advances made in physical science, since the period of its pubhcation. The singular effects of this, and of the other inestimable writings of the same au- thor, in forwarding the subsequent progress of scientific discovery, certainly entitle his name, far more than that of any other individual, to be applied as a distinguishing epithet to the modern rules of philosophizing ; but (as I have elsewhere observed) " the genius and writings of Bacon himself were powerfully influenced by the cir- cumstances and character of his age : Nor can there be a doubt, that he only accelerated a revolution which was already prepared by many concurrent causes." f — My reasons for thinking so, which rest chiefly on historical retrospects, altogether foreign to my present design, I must delay stating, till another opportunity.
To this observation it is of still greater importance to
• Inquiry into the Sublime and Beautiful, Part I. Sect. xix. t Outlines of Moral Philosophy, first printed in 1793.
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add, that, in contrasting the spirit and the utility of the new logic with those of the old, I have no wish to see the former substituted, in our universities, in room of the latter. By a strange inversion in the order of instruc- tion, Logic, instead of occupying its natural place at the close of the academical course, has always been consid- ered as an introduction to the study of the sciences ; and has, accordingly, been obtruded on the uninformed minds of youth, at their first entrance into the schools. While the syllogistic art maintained its reputation, this inver- sion was probably attended with little practical incon- venience ; the trite and puerile examples commonly re- sorted to for the illustration of its rules, presupposing a very slender stock of scientific attainments ; but now, when the word logic is universally understood in a more extensive sense, as comprehending, along with an out- line of Aristotle's Organon, some account of the doc- trines of Bacon, of Locke, and of their successors, it seems indispensably necessary, that this branch of edu- cation should be delayed till the understanding has ac- quired a wider and more varied range of ideas, and till the power of reflection (the last of our faculties which nature unfolds) begins to solicit its appropriate nourish- ment. What notions can be annexed to such words as analysis, synthesis, induction, experience, analogy, hy- pothetical and legitimate theories, demonstrative and moral certainty, by those whose attention has hitherto been exclusively devoted to the pursuits of classical learning? A fluent command, indeed, of this technical phraseology may be easily communicated; but it would be difficult to devise a more eff"ectual expedient for mis- leading, at the very outset of life, the inexperienced and unassured judgment. The perusal of Bacon's writings, in particular, disfigured as they are by the frequent use of quaint and barbarous expressions, suited to the scholastic taste of his contemporaries, ought to be care- fully reserved for a riper age.*
* Haller mentions, in his Elements of Physiology, that he was forced to enter on the study of logic in the tenth year of his age. " Memini me annum natum deci- mum, quo avidus histoiiam et poesin devorassem, ad logicam, et ad Claubergia- NAM logicam ediscendam coactum fuisse, qua nihil poterat esse, pro hujusmodl homuncione, sterilius." (Tomus VIIL Pars Secunda, p. 24. Lausanne, 1778.)
OF THE HUMAN MIND. 351
In confirmation of this last remark, many additional arguments might be drawn from the peculiar circum- stances in which Bacon wrote. At the period when he entered on his literary career, various branches of physi- cal science were already beginning to exhibit the most favorable presages of future improvement ; strongly inviting his original and powerful mind to co-operate in the reformation of philosophy. The turn of his genius fortunately led him to employ himself chiefly in general suggestions for the advancement of learning ; and, leav- ing to others the task of inductive investigation, to aim rather at stating such rules as might direct and sytema- tize their exertions. In his own experimental research- es he was not very fortunate ; nor is much reliance to be placed on the facts recorded in his Histories. Per- haps the comprehensiveness of his views diminished his curiosity with respect to the particular objects of sci- ence ; or, perhaps he found the multiphcity of his en- gagements in active life, more consistent with specula- tions, in which the chief materials of his reasonings were to be drawn from his own reflections, than with inquiries which demanded an accurate observation of external phenomena, or a minute attention to experimental pro- cesses. In this respect, he has been compared to the Legislator of the Jews, who conducted his followers within sight of their destined inheritance ; and enjoyed in distant prospect, that promised land which he himself was not permitted to enter.*
It seems difficult to imap;ine any attempt more extravagant, than that of instructing a child, only ten years old, in the logic of the schools ; and yet, it is by no means a task so completely impracticable, as to convey to a pupil, altogether uninitiated in the Elements of Physics, a distinct idea of the object and rules of the Novum Organon.
The example of Mr. Smith, during the short time he held the Professorship of Logic, at Glasgow, is worthy of imitaliouin those universities which admit of similar deviations from old practices. For an account of his plan, see Biographical Memoirs of Smith, Robertson, and Reid, p. 12 ; where I have inserted a slight but masterly sketch of his academical labors, communicated to me by his pupil and friend, the late Mr. Millar.
* See Cowley's Ode, prefixed to Sprat's History of the Royal Society.
Nor does Bacon himself seem to have been at all disposed to overrate the value of his own contributions to Experimental Science. " In rebus quibuscunque difficilio- ribus," he has observed on one occasion, " non expectandum est ut (piis simul et serat et nietat ; sed pr;Hparatione ojius cst.ut per giadus maturescant." But the most remarkable passage of this sort, which I recollect in his writings, occurs towards tiie close of his great work, De ^ugmcntis Scientianun . — " Tandem igitur paululum respirantes, atque ad oa, quae praitervecti sumus, oculos reflectentes, hunc tractatum
352 ELEMENTS OF THE PHILOSOPHY
The effect of this prophetic imagination in clothing his ideas, to a greater degree than a severe logician may- approve, with the glowing colors of a poetical diction, was unavoidable. The wonder is, that his style is so seldom chargeable with vagueness and obscurity ; and that he has been able to bequeath to posterity so many cardinal and eternal truths, to which the progressive hght of science is every day adding anew accession of lustre. Of these truths, however, (invaluable in themselves as heads or texts, pregnant with thought) many, — to bor- row the expression of a Greek poet, — sound only to the intelligent; — while others present those confident but indefinite anticipations of intellectual regions yet undis- covered, which, though admirably calculated to keep alive and to nourish the ardor of the man of science, are more fitted to awaken the enthusiasm than to direct the studies of youth. Some of them, at the same time (and these I apprehend, cannot be too early impressed on the memory) are singularly adapted to enlarge and to ele- vate the conceptions ; exhibiting those magnificent views of knowledge, which, by identifying its progress with the enlargement of human power and of human happi- ness, ennoble the humblest exertions of literary industry, and annihilate, before the triumphs of genius, the most dazzHng objects of vulgar ambition. — A judicious selec- tion of such passages, and of some general and striking aphorisms from the Novum Organon, would form a use- ful manual for animating the academical tasks of the stu- dent ; and for gradually conducting him from the level of the subordinate sciences, to the vantage-ground of a higher philosophy.
Unwilling as I am to touch on a topic so hopeless as that of Academical Reform, I cannot dismiss this sub- ject, without remarking, as Sifact which, at some future period, will figure in hterary history, that two hundred years after the date of Bacon's philosophical works, the
nostrum noii absimilem esse censemus sonis illis et prseludiis, quae praetentant musici, dum fides ad inodulationem concinnant : Quae ipsa quidem auiibus ing;ratum quiddam et asperuni exhibent ; at in causa sunt, ut quae sequuntur omnia sint suaviora : Sic ni- miium nos in aniinum induximus, ut in cithava Musarum concinnanda, et ad harmo- niain vcrain redigenda, operam navaremus, quo ab aliis postea pulsentur chordee, mcliore digito, aut plectro." — Bacon.
OF THE HUMAN MIND. 353
antiquated routine of study, originally prescribed in times of scholastic barbarism and of popish superstition, should in so many Universities, be still suffered to stand in the way of improvements, recommended at once by the present state of the sciences, and by the order which nature follows in developing the intellectual facul- ties. On this subject, however, I forbear to enlarge. — Obstacles of which I am not aware may perhaps render any considerable innovations impracticable ; and, in the mean time, it would be vain to speculate on ideal pro- jects, while the prospect of realizing them is so dis- tant and uncertain.
VOL. 11. 45
NOTES
ILLUSTRATIONS.
NOTES AND ILLUSTRATIONS.
Note (A.) page 27.
Of the fault in Euclid's arrangement which I h.)ve here remarked, some of the ancient editors were plainly aware, as they removed the two theoreins in question from the class of axioms, and placed them, with at least an equal impropriety, in that of postulates. " In quibusdam codicibus," says Dr. Gregory, " Axiomata 10 et 11 inter postulata numerantur." — Euclidis quce supersunt omnia. Ex Kecens. Dav. Gregorii. Oxon. 1703. p. 3.
The 8ih Axiom too in Euclid's enumeration is evidently out of its proper place. Ka) ra \(pa^fji,'o^ovTa. sir' aXXyiXa. '^icra. aXXyiXoi; icrri : — thus translated by Dr. Simson : " Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another." This, in truth, is not an axiom, but a definition. It is the definition of geometrical equality ; the fundamental principle upon which the comparison of all geometrical magnitudes will be found ultimately to depend.
For some of these slight logical defects in the arrangement of Euclid's definitions and axioms, an ingenious, and, I think, a solid apology, has been offered by M. Pre- vost, in his Essais de Philosophic. According to this author, (if I rightly under- stand his meaning,) Euclid was himself fully aware of the objections to which this part of his work is liable : but found it impossible to obviate them, without incurring the still greater inconvenience of either departing from those modes of proof which he had resolved to employ exclusively in the composition of his Elements ; * or of revoltingithe student, at his first outset, by prolix and circuitous demonstrations of manifest and indisputable truths. I shall distinguish by Italics, in the following quotation, the clauses to which I wish more particularly to direct the attention of my readers.
" C'est done I'imperfection (peut-etre inevitable) de nos conceptions, qui a en- gage a faire entrer les axiomes pour quelque chose dans les principes des sciences de raisonnement pur. Et ils y font un double office. Les uns remplacent des defini- tions. Les autres remplacent des propositions susceptibles d'etre demontrees. J'en donnerai des exemples tires des Elemens d'Euclide.
"Les axiomes remplacent quelquefois des definitions fres faciles a faire comme celle du mot tout. (El. Ax. 9.) D' autres suppUent a certaines definitions difficiles et qu'on evite, comme celles de la ligne droite et de V angle.
" Quelques axiomes remplacent des theoremes. J'ignore si (dans les principes d'Euclide) I'axiome 11 peut-etre demontre (comme I'ont cru Proclus et tant d'au- tres anciens et modernes.) SHlpeut Vetre, cet axiome supplee a unc demonstra- tion probablement laborieuse.
" Puisque les axiomes ne font autre oflicc que supplser a des definitions et a des theoremes, on demandera peut-etre qu'on s'en passe. Observons 1. Qu'ils evitent souvcnt des longueurs inutile s. 2. Qu'ils tranchent les disputes a Vepoque mcme ou la science est imparfaite. 3. Que s'il est un itat, auquel la science puisse s'en passer (ce que je n'affirme point), il est dumoins sage, et 7n6me indispensable, de les emj)loyer, tant que quelque insuffisance, dans ce degrA de perfection oil Von tend, interdit un ordre absolument irrcprochable. Ajoutons 4. Que dans chaque science il y a ordinairement un principe qu'on pourroit appellcr dominant, et qui par cette raison seule (et independamment de celles que je viens d'alleguer) a paru devoir
*By intiodiioiiig, for example, the idea of j>fot!07i, whiclihe has studied to avoid, as nmcli as possible, in delivering the liicmouts of Plane Geometry.
358 NOTES AND ILLUSTRATIONS.
etre sorti, pour ainsi dire, du champ des definitions pour etre mis en vue sous forme d'axiome. Tel me paroit etre en geometric le principe de congruence contenu dans le 8 axiorae d'Euclide." — Essais de PMlosophie Tom. II. pp. 30, 31, 32.
These remarks go far in my opinion, towards a justification of Euclid for the lati- tude with which he has used the word axiom in his Elements. As in treating, however, of the fundamental laws of human belief, the utmost possible precision of lano-uage is indispensably necessaiy, I must beg leave once more to remind my read- ers^that, in denying Axioms to be the first principles of reasoning in mathematics, I restrict the meanino- of that word to such as are analogous to the first seven in Euclid's list. Locke, in what he has written on the subject, has plainly understood the word in the same limited sense.
Note (B.) page 49.
The prevalence in India of an opinion bearing some resemblance to the Berkeleian Theory may be urged as an objection to the reasoning in the text ; but the fact is, that this resemblance is much slighter than has been generally apprehended. (See Philosophical Essays, pp. 81, 82, et seq.) On this point the following passage from ■ Sir William Jones is decisive ; and the more so, as he himself has fallen into the common mistake of identifying the Hindu belief with the conclusions of Berkeley and Hume. ^ ^
" The fundamental tenet of the Vedanti school consisted, not in denying the existence of matter, that is, of solidity, impenetrability, and extended figure, (to deny which would be lunacy) but in correcting the popular notion of it, and in contending, that it has no essence independent of mental perception, that existence and perceptibility are convertible terms, that external appearances and sensations are illusory, and would vanish into nothing, if the divine energy, which alone sustains them, were suspended but for a moment ; * an opinion which Epicharmus and Plato seem to have adopted, and which has been maintained in the present century with great elegance, but with little public applause ; partly because it has been mis- understood, and partly because it has been misapplied by the false reasoning of some unpopular writers, who are said to have disbelieved in the moral attributes of God, whose omnipresence, wisdom, and goodness, are the basis of the Indian philosophy. I have not sufficient evidence on the subject to profess a belief in the doctrine of the Veddnta, which human reason alone could, perhaps, neither fully demonstrate, nor fully disprove ; but it is manifest, that nothing can be farther removed from impi- ety than a system wholly built on the purest devotion." — Works of Sir William Jones, Vol. I. pp. 165,166.
From these observations, (in some of which, I must be permitted to say, there is a good deal of indistinctness, and even of contradiction,) it may on the whole be in- ferred, 1. That in the tenets of the Vedanti school, however different from the first apprehensions of the unreflecting mind, there was nothing inconsistent with the fundamental laws of human belief, any more than in the doctrine of Copernicus con- cernino-the earth's motion. 2. That these tenets were rather articles of a theologi- cal creed, than of a philosophical system ; or at least, that the two were so blended together, as sufficiently to account for the hold which, independently of any refined reasoning, they had taken of the popular belief.
In this last conclusion I am strongly confirmed, by a letter which I had the pleas- ure of receiving, a few years ago, from my friend Sir James Mackintosh, then Re- corder of Bombay. His good nature will, I trust, pardon the liberty I take in men- tioning his name upon the present occasion, as I wish to add to the following veiy curious extract, the authority of so enlightened and philosophical an observer. Amidst the variety of his other important engagements, it is to be hoped that the re- sults of his literary researches and speculations, while in the East, will not be lost to the world.
" I had yesterday a conversation with a young Bramin of no great
learning, the son of the Pundit (or assessor for Hindu law) of my court. He told
*Sir William Jones here evidently confounds the system which represents the material universe as not only at first created, l)ut as every moment upheld by the agency of Divine Power, with that of Berkeley and Hume, which, <lcnying the distinction between primary and secondary qualities, assorts, that extension, figure, and impenetrability are not less inconceivable, witliout a. percipient mind, than our sensations of heat and colil, sounds and odors. According to both systems, it may undoubtedly be said, Diiit the material universe has no existence independent of miwrf ; but it ought not to bo overlooked, that in the one, this word refers to the Creator, and in the other, to the created percipient.
NOTES AND ILLUSTRATIONS. 359
me, that besides the myriads of gods whom their creed admits, there was one whom they know by the name of Brim, or the great one, without form or limits, whom bo created intellect could make any approach towards conceiving ; that, in reality, there were no trees, no houses, no land, no sea, but all without was Maia, or illusion, the act of Brim ; that whatever we saw or felt was only a dream, or, as he expressed it in his imperfect English, thinking in one's sleep, and that the reunion of the soul to Brim, from whom it originally sprung, was the awakening from the long sleep of finite existence. All this you have heard and read before as Hindu speculation. What struck me was, that speculations so refined and abstruse should, in a long course of ages, have fallen through so great a space as that which separates the gen- ius of their original inventor from the mind of this weak and unlettered man. The names of these inventors have perished ; but their ingenious and beautiful theories, blended with the most monstrous superstitions have descended to men very little exalted above the most ignorant populace, and are adopted by them as a sort of arti- cles of faith, without a suspicion of their philosophical origin, and without the pos- sibility of comprehending any part of the premises from which they were deduced. I intend to investigate a little the history of these opinions, for I am not altogether without apprehension, that we may all the while be mistaking the hyperbolical effu- sions of mystical piety, for the technical language of a philosophical system. Noth- ing is more usual, than for fervent devotion to dvFell so long and so warmly on the meanness and worthlessness of created things, and on the all-sufficiency of the Su- preme Being, that it slides insensibly from comparative to absolute language, and, in the eagerness of its zeal to magnify the Deity, seems to annihilate eveiy^ thing else. To distinguish between the very different import of the same words in the mouth of a mystic and of a sceptic, requires more philosophical discrimination than most of our Sanscrit investigators have hitherto shown."
Note (C.) page 57.
The private correspondence here alluded to, was between Mr. Hume and the late Sir Gilbert Elliott*; a gentleman who seems to have united, with his other well- known talents and accomplishments, a taste for abstract disquisitions, which rarely occurs in men of the world ; accompanied with that soundness and temperance of judgment which, in such researches, are so indispensably necessary to guard the mind against the illusions engendered by its own subtilty. In one of his letters (of which the original draft in his own hand-writing was communicated to me by the Earl of Minto) he expresses himself thus : *
. . . " I admit, that there is no writing or talking of any subject which is of importance enough to become the object of reasoning, without having recourse to some degree of subtilty and refinement. The only question is, where to stop, how far we can go, and why no farther ? To this question I should be extremely happy to receive a satisfactoiy answer. I can't tell if I shall rightly express what I have just now in my mind ; but I often imagine to myself, that I perceive within me a certain instinctive feeling, which shoves away at once all over subtile refinements, and tells me, with authority, that these air-built notions are inconsistent with hfe and experience, and by consequence cannot be true or solid. From this I am led to think, that the speculative principles of our nature ought to go hand in hand with the practical ones ; and, for my own part, when the former are so far pushed, as to leave the latter quite out of sight, I am always apt to suspect that we have trans- gressed our limits. If it should be asked, how far will these practical principles go .' I can only answer, that the former difficulty will recur, unless it be found, that there is something in the intellectual part of our nature, resembling the moral sentiment in the moral part of our nature, which determines this, as it were, instinctively. Very possibly, I have wrote nonsense : however, this notion first occurred to me at London, in conversation with a man of some depth of thinking ; and talking of it since to your friend Henry Home,f I found that he seemed to entertain some notions nearly of the same kind, and to have pushed them much farther."
The practical principles referred to in this extract, seem to me to correspond very nearly with what I have cMcd fundamental laws of belief, or first elements of hu- man reason ; and the something in the intellectual part of our nature, resem- bling the moral sentiment in the moral part of our nature, is plainly descriptive of
♦The letter is dated in 17.51. t Afterwards Lord Karnes,
360 NOTES AND ILLUSTRATIONS.
what Reid and others have since called common sense ; coinciding, too, in sub- stance with the philosophy of Lord Kames, who refers our belief of the existence of the Deity, and of various other primary truths, to particular senses, forming a constit- uent part of our intellectual frame. I do not take upon me to defend the forms of expression which Mr. Hume's very ingenious correspondent has employed to convey his ideas ; and which, it is probable, he did not think it necessary for him, in addres- sing a confidential friend, to weigh wiih critical exactness : but his doctrine must be allowed to approximate remarkably to those parts of the works of Reid, where he appeals from the paradoxical conclusions of metaphysicians, to _ the principles on which men are compelled, by the constitution of their nature, to judge and to act in the ordinary concerns of life ;— as well as to various appeals of the same kind, which occur in Lord Karnes's writings. My principal object, however, in introducing it here, was to show, that this doctrine was the natural result of the state of science at the period when Reid appeared ; and, consequently, that no argument against his orio-inality in adopting it can reasonably be founded on a coincidence between his views concerning it and those of any preceding author.
Of Mr. Hume's respect for the literary attainments of this correspondent, so strong a proof occurs in a letter, (dated Ninev>?ells, March 10, 1751,) that I am tempted to subjoin to the foregoing quotation the passage to which I allude.
" You would perceive, by the sample 1 have given you, that I make Cleanthes the hero of the dialogue. Whatever you can think of to strengthen that side of the ar- gument, will be most acceptable to me. Any propensity you imagine I have to the other side crept in upon me against my will ; and 'tis not long ago that I burned an old manuscript book, wrote before I was twenty, which contained, page after page, the gradual progress of my thoughts on that head. It began with an anxious search after arguments to confirm the common opinion : Doubts stole in, — dissipated, — re- turned,— were again dissipated, — returned again : And it was a perpetual struggle of a restless imagination against inchnation, perhaps against reason.
" I have often thought, that the best way of composing a dialogue would be, for two persons that are of different opinions about any question of importance, to write alternately the different parts of the discourse, and reply to each other. By this means that vujgar error would be avoided, of putting nothing but nonsense into the mouth of the adversary ; and, at the same time, a variety of character and gen- ius being upheld, would make the whole look more natural and unaffected. Had it been my good fortune to live near you, I should have taken upon me the character of Philo in the dialogue, which you '11 own I could have supported naturally enough : and you would not have been averse to that of Cleanthes."
In a postscript to this letter, Mr. Hume recurs to the same idea. " If you '11 be persuaded to assist me in supporting Cleanthes, I fancy you need not take the mat- ter any higher than Part 3. He allows, indeed, in Part 2d, that all our inference is founded on the similitude of the works of nature to the usual effects of mind : oth- erwise they must appear a mere chaos. The only difificulty is, why the other dissim- ilitudes do not weaken the argument : And, indeed, it would seem from experience and feeling, that they do not weaken it so much as we might reasonably expect. A theory to solve this would be very acceptable." *
Note<D.) page 62.
It would perhaps be difficult to mention another phrase in our language, which ad- mits of so great a variety of interpretations as common sense ; and to which, of con- sequence, it could have been equally dangerous to annex a new technical meaning in stating a controversial argument. Dr. Beattie has enumerated some of these in the beginning of his Essay, but he has by no means exhausted the subject : nor is his enumeration altogether unexceptionable in point of logical distinctness. On this point, however, I must allow my readers to judge for themselves. — See Essay on the Nature and Immutability of Truth, p. 37, et seq. 2d Edit.
The Latin i)hrase sensus communis has also been used with much latitude. In various passages of Cicero it may be perfectly translated by the English phrase com- mon sense ; and, in the same acceptation, it is often employed in jnodern latinity. Of this (not to mention other authorities) many examples occur in the Lectiones Math-
* From tho above quotations it appears, that Mr. Hume's posthumous work, entitled Dialogues con- corning Natural Religion, was projected, and, in part at least, executed, twenty-five years fi)foro liis death.
NOTES AND ILLUSTRATIONS. 361
ematiccB of Dr. Barrow ; a work not more distinguished by originality and depth of thouglit, than by a logical precision of expression. In one of these, he appeals to common sense, (sensus communis,) in proof of the circumference of the circle being less than the perimeter of the circumscribed square. — Lect. 1.
On other occasiona, the sensus comrnunis of classical vi^riters plainly means something widely different ; as in those noted lines of Juvenal, so ingeniously illus- trated by Lord Shaftesbury in his Essay on the Freedom of Wit and Humor.
" Haec satis ad juvenem, quem nobis fama superbum Tradit, et inflatum, plenumque A'^erone propinquo. Rai'us enim ferme sensus communis in ilia Fortuna."
" Some commentators," says Shaftesbury, " interpret this very differently from what is generally apprehended. They make this cotnmon sense of the poet, by a Greek derivation, to signify sense of public weal, and of the common interest ; love of the community or society, natural affection, humanity, obligingness, or that sort of civility which rises from a just sense of the common rights of mankind, and the nat- ural equality there is among those of the same species.
" And, indeed, if we consider the thing nicely, it must seem somewhat hard in the poet to have deny'd wit or ability to a court such as that of Rome, even under a Tiberius or a Nero. But for humanity or sense of public good, and the common interest of mankind, 't was no such deep satire to question whether this was properly the spirit of a court. 'T was difhcult to apprehend what Community subsisted among courtiers; or what Public among an absolute Prince and his slave-subjects. And for real society, there could be none between such as had no other sense than that of pri- vate good.
" Our poet, therefore, seems not so immoderate in his censure ; if we consider it is the heart, rather than the head, he takes to task : when reflecting on a court edu- cation, he thinks it unapt to raise any affection towards a country ; and looks upon young Princes and Lords as the young masters of the world ; who, being indidged in all their passions, and trained up in all manner of licentiousness, have that thorough contempt and disregard of Mankind, which Mankind in a manner deserves, where arbitrary power is permitted, and a tyranny adored."
While I entirely agree with the general scope of these observations, I am inclined to think, that the sensus cominunis of Juvenal might be still more precisely vemlev- eAhy sympathy ; understanding this word (in the appropriate acceptation annexed to it by Mr. Smith) as synonymous with that fellow-feeling which disposes a man, in the discharge of his social duties, to place himself in the situation of others, and to regulate his conduct accordingly. Upon this supposition, the reflection in question coincides nearly with one of Mr. Smith's own maxims, that " the great never look upon their inferiors as their fellow-creatures ; " ^ — a maxim which, although suffi- ciently founded in fact to justify the sarcasm of the satirical poet, must (it is to be hoped for the honor of human nature) be understood with consideiable limitations, when stated as a correct enunciation of philosophical truth.
It yet remains for me to take some notice of the sensus communis of the school- men ; an expression which is perfectly synonymous with the word concejjtion, as defined in the first volume of this work. It denotes the power whereby the mind is enabled to represent to itself any absent object of perception, or any sensation which it has formerly experienced, its seat was supposed to be that part of the brain (hence called the sensorium, or the sensoriiun commune) where the nerves from all the organs of perception terminate. Of the peculiar function allotted to it in the scale of our intellectual faculties, llie following account is given by Hobbes : " Some say the senses receive the species of things, and deliver them to the Common Sense; and the Common Sense delivers them over to the Fancy; and the Fancy to the Memory, and the Memory to the Judgment ; like handing of things from one to another, with many words making nothing understood." — Q/" JJfa/i, Part I. Chap. 2.
Sir John Davis, in his poem on the Immortality of the Soul, (published in the reign of Queen Elizabeth) gives the name oi common sense to the ))o\ver o( imagin- ation ; (Sec Sections XIX. and XX.) and the very same i)hraseology occurs, at a later period, in the Philosophy of Descartes : (see, in particular, his Second Med-
* Theory of Moral Sentimonts, Vol. I. p. 13f>, (Hh odit.
VOL. II. 46
362 NOTES AND ILLUSTRATIONS.
itation, where he uses Sensus Communis as synonymous with Potentia Itnagina- trix.) Both of these writers, as appears evidently from the context, understand by Imagination what I have called Conception. To the power now denoted by the word Imagination, Sir John Davis gives the name of Fantasy. Gassendi seems disposed to consider this use of the phrase Sensus Communis as an innovation of Descartes, (see his Objections to Descartes' Second Meditation, § 6.) but it had been previously adopted by various philosophical writers ; and, in the English schoolSj was at that time familiar to every ear.
The singular variety of acceptations of which this phrase is susceptible ; and the figure which, on different occasions, it has made in the history of philosophy, will, I trust, furnish a sufficient apology for the length as well for the miscellaneous nature of the foregoing remarks.*
Note (E.) page 72.
The Arithmetical Prodigy, alluded to in the text, is an American boy, (still, I be- lieve, in London,) of whose astonishing powers in performing, by a mental process, hitherto unexplained, the most difficult numerical operations, some accounts have lately appeared in various Uterary journals. When the sheet containing the refer- ence to this note was thrown off, I entertained the hope of having an opportunity, before reaching the end of the volume, to ascertain, by personal observation, some particulars with respect to him, which I thought might throw light on my conclu- sions concerning the faculty of Attention, in the former volume of this work. In this expectation, however, I have been disappointed ; and have, therefore, only to apologize for having inadvertently excited a curiosity which I am at present unable to gratify.
[Since the first edition of this volume was published, I have seen the boy here alluded to ; but for too short a time, and under too unfavorable circumstances, to be able to form any satisfactory conclusions concerning the nature of his arithmetical processes. Whatever opinion may be entertained on this point, every person who has witnessed his public exhibitions must allow, that his powers of Memory and of concentrated Attention, when contrasted v/ith his very tender years, and with the constitutional playfulness of his disposition, entitle him to a conspicuous place among the rare phenomena of the intellectual world. Nor can I forbear to add, that the general character of his own mind seems to be simple, amiable, and interesting. When further advanced in life, he may probably have it in his power to communi- cate some curious information with respect to the origin and history of his peculiar in- tellectual habits. In the mean time, I must decline, for obvious reasons, to say any thing farther on the subject.]
Note (F.) page 118.
*Ei» Tovrois h Iffof^s Wo7vig. " In mathematical quantities, equality is identity." — Arist. Met. x. c. 3.
This passage has furnished to Dr. Gillies (when treating of the theory of syllo- gisms,) the subject of the following comment, in which, if I do not greatly deceive myself, he has proceeded upon a total misapprehension of the scope of the original : " In mathematical quantities," Aristotle says, that, " equality is sameness," because e x'oyo; o rtjs -prguiTvn ovirias il; \ffTi. " The dcfrnition of any particular object denoted by the one is precisely the same with the definition of any particular object denoted by the other." — GiUies's Aristotle, Vol. I. p. 87.
In order to enable my readers to form a judgment of the correctness of this para- phrase, I must quote Aristotle's words, according to his own arrangement, which, in •his insfanr.p. happens to be directly contrary to that adopted by hir= interpreter. Et/ o\ av 0 Xoyo; i rn; ■TrpuT'/i; ohff'iac lis ^, o'ov oil 'iffai yga.f/.fjLo.i ivSi!a,t ai avrai, xai Tcc 7ffa Kcc) ra, Iffoyuvia Tirpdycuva., kocitoi vXum ' aXX' h Tovrm; h i<roTns horns. 11^6
* Tl has baen obsorved to me very lately by a learned and ingenious friend, that in one of the phrases which I have proposed to suljstitule for tiie common sense of Huffier and Kcid,I have been anticipated, two hundred years ago, by Hir Walter Raleigh. " Where natural reason hath built any thing so strong against itself, as tiie same reason can hardly assail it, much loss 1/atter it down ; the same, in every question of nature, and infinite power, may be approved for iifaiidamciital law of human knowl- ediTB." (Preface to Raleigh's History of the World.) Tho coinciilence in point of expression, is not a little curious ; but is much less wonderful than the coincidence of tho thought with tho soundeBt_ lo- gical conclusions of tiie eighteenth century. — Tlio very eloquent and philoiophical passage which iw- medifttely follows tlio above sentence, iv noi loss wortliy of attention.
NOTES AND ILLUSTRATIONS. 363
first clause of this passage is, from its conciseness, obscure ; but Aristotle's meaning, on the whole, seems to be this : — •" That all those magnitudes, which bear the same ratio to the same magnitude, though in fact they may form a multitude, yet, in a scientific view, they may be regarded as one ; the mathematical notion of equality being ultimately resolvable into that oi unity or identity." * It was probably to obviate any diflSculty that might have been suggested by diversities of figure, that Aristotle has confined his examples to equal straight lines, and to such quadrangles as are not only equal but similar.
Let us now consider the paraphrase of Dr. Gillies. " In mathematical quantities, equality is sameness, because the definition of any particular object denoted by the one, is precisely the same with the definition of any particular object denoted by the other." Are we to understand by this, that " to all things which are equal the same definition is applicable ;" or conversely, that " all things to which tiie same definition is applicable, are equal ? " On the former supposition, it would follow, that the same definition is applicable to a circle, and to a triangle having its base equal to the circumference, and its altitude to the radius. On the latter, that all circles are of the same magnitude ; all squares, and all equilateral triangles. — There is, indeed, one sense wherein those geometrical figures which are called by the same name, (all circles, for example,) may be identified in the mind of the logician; inasmuch as any theorem which is proved of one, must equally hold true of all the rest ; and the reason of this is assigned, with tolerable correctness, in the la>t clause of the sentence quoted from Dr. Gillies. But how this reason bears on the question with respect to the convertibility of the terms equality and sameness, I am at a loss to conjecture.
Note (G.) page 146.
In an Essay on Quantity, (by Dr. Reid) published in the Transactions of the Royal Society of London, for the year 1748, mathematics is very correctly defined to be " the doctrine of measure." — " The object of this science," the author observes, "is commonly said to be quantity ; in which case, quantity ought to be delined, ivhat may be measured. Those who have defined quantity to be whatever is capa- ble of more or less, have given too wide a notion of it, which has led some persons to apply mathematical reasoning to subjects that do not admit of it." f The appro- priate objects of this science are therefore such things alone as admit not only of being increased and diminished, but of being multiplied and divided. In other words, the common quality which characterizes ail of them is their mensurability.
In the same Essay, Dr. Reid has illustrated, with much ingenuity, a distinction (hinted at by Aristotle |) of quantity into proper and improper. " I call that," says he, " proper quantity, which is measured b}' its own kind ; or which, of its own nature is capable of being doubled or trebled, without taking in any quantity of a different kind as a measure of it. Thus a line is measuied by known lines, as inches, feet, or miles ; and the length of a foot being knov>m, there can be no question about the length of two feet, or of any part or multiple of a foot. This known length, by being multiplied or divided, is sufficient to give us a distinct idea of any length whatsoever.
" Improper quantity is that which cannot be measured by its own kind, but to which wc assign a measure in some proper quantity that is related to it. Thus veloci- ty of motion, when we consider it by itself, cannot be measured. We may perceive one body to move faster, another slower, but we can perceive no proportion or ratio between their velocities, without taking iu some quantity of another kind to measure them by. Having therefore observed, that by a greater velocity, a greater space is passed over in the same time, by a less velocity, a less space, and by an equal velocity, an equal space ; we hence learn to measure velocity, by the space passed over in a given time, and to reckon it to be in exact proportion to that • and
* Tas iTgoy ro ccvro rov eciirov 'ixovrct X'oyov, Itra aXAjiXa/y 'iffri, — Euc. JElem. Lib. V. Prop. ix.
t In this remark, Dr. Reid, as appears from the title of liis paper, had an eye to the abuse of math- emalicul laiiguu^'o by Dr. Hutclicson, who had recently carried it bo far as to exhibit algebraical for- mula;) for ascertaining the moral merit or demerit of particular actions. (See his Inquiry into tba Original of our Ideas of Beauty and Virtue.)
\Kv^iu; Se Xlofl-a raura \iyirxi f^ivcc, ra. Si aXXa, vrdvra Kara, fvfiSiSvxil • t'lf ruura ya^ a'TroQx'fravTif, xa) ra eXXos YLoea Xiyofitv. — Jlriit. Caieg. cap. vi. IT.
364 l^OTES AJVD ILLUSTRATIONS.
having once assigned this measure to it, we can then, and not till then, conceive one velocity exactly double, or triple, or in any proportion to another. We can then introduce it into mathematical reasoning, without danger of error or confusion ; and may use it as a measure of other improper quantities.
" All the proper quantities we know may, I think, be reduced to these four : exten- sion, duration, number, and proportion.
"Velocity, the quantity of motion, density, elasticity, the vis insita and impressa the various kinds of centripetal forces, and the different orders of fluxions, are all improper quantities ; which therefore ought not to be admitt€d into mathematical reasoning, without having a measure of them assigned.
" The measure of an improper quantity ought always to be included in the definition of it ; for it is the giving it a measure that makes it a proper subject of mathematical reasoning. If all mathematicians had considered this, as carefully as Sir Isaac Newton has done, some trouble had been saved both to ■ themselves and their readers. That great man, whose clear and comprehensive understanding appears even in his definitions, having frequent occasion to treat of such improper quantities, never fails to define them, so as to give a measure of them, either in proper quantities or such as had a known measure. See the definitions prefixed to his Principia."
With these important remarks I entirely agree, excepting only the enumeration here given of the different kinds of proper quantity, which is liable to obvious and insurmountable objections. It appears to me that, acccording to Reid's own definition, extension is the only proper quantity within the circle of our knowledge. Duration is manifestly not measured by duration, in the same manner as a line is measured by a line ; but by some regulated motion, as that of the hand of a clock, or of the shadow on a sun-dial. In this respect it is precisely on the same footing with velocities and forces, all of them being measured, in the last result, by extension. As to number and proportion, it might be easily shown, that neither of them fall under the definition of quantity, in any sense of that word. In proof of this asser- tion (which may, at first sight, seem soaewhat paradoxical) I have only to refer to the mathematical lectures of Dr Barrow, and to some very judicious observations introduced by Dr. Clarke in his controversy with Leibnitz. It is remarkable, that, at the period when this essay was written. Dr. Reid should have been unacquainted with the speculations of these illustrious men on the same subject ; but this detracts little from the merits of his memoir, which rest chiefly on the strictures it contains on the controversy between the Newtonians and Leibnitzians concerning the meas- ure of forces.
Note (H.) page 147.
The following view of the relation betvpeen the theorems of pure geometry and their practical applications, strikes me as singularly happy and luminous ; more especially the ingenious illustrations borrowed from the science of geometry itself
" Lps verites que la geometrie demontre sur I'etendue, sont des verites purement hypothetiques. Ces verites cependant n'en sont pas rnoins utiles, eu egard aux consequences pratiques qui en residtent. II est aise de le faire sentir par une com- paraison tiree de la geomet'.ie meme. On connoit dans cette science des lignes courbes qui doivent s'approcher continuellement d'une ligne droite, sans la rencon- trer jamais, et qui neanmoins, etant tracees sur !e papier, se confondent sensiblement avec cette ligne droite au bout d'un assez petit espace. II en est de meme des propositions de geometrie ; elles sont la limite intellectuelle des v6rites physiques, le terme dont celles-ci peuvent approcher aussi pres qu'on le desire, sans jamais y arriver exactement. Mais si les theoremes mathematiques n'ont pas rigoureusement lieu dans la nature, ils servent du moins a resoudre, avec une precision suffisante pour la pratique, les differentes questions qu'on peut se proposer sur I'etendue. Dans I'univers il n'y a point de cercle parfait ; mais plus un cerclo approchera de I'etre, plus il approchera des proprietes rigoureuses du cercle parfaite que la geometrie demontre ; et il peut en approcher a un degre suffisant pour notre usage. 11 en est de meme des autres figures dont la geometrie detaille les proprietes. Pourdemon- trer en toute rigueur, les verites relatives a la figure des corps, on est oblige de supposer dans cette figure une perfection arbitraire qui n'y sauroit etre. En elfet, si le cercle, par exernple, n'est pas suppose rigoureux, il faudra autant de theoremes diffcrcns sur le cercle qu'on imaginera de figures difierentes plus ou moins appro- thantes du cercle parfait ; et ces figures clles-mcmes pourront encore etre absolu-
NOTES AND ILLUSTRATIONS. 365
ment hypothetiques, et n'avoir point de modele existant dans la nature. Les lignes qu'on considere dans la geometric usuelle, ne sent ni parfaitement droits ni parfaite- ment courbes ; les surfaces ne sont ni parfaitement planes ni parfaitement curvilignes ; mais il est necessaire de les supposer telles, pour arriver a des verites fixes et deter- mineeSj dent on puisse fairs ensuite i'application plus ou moins exacts aux lignes et aux surfaces physiques." — D'Alembert, Elemens de Philosophic, Article Geom- etrie.
Note (I.) page 160.
From some expressions in this quotation, it would seem that the writer considered it as now established by mathematical demonstration, not only that a provision is made for maintaining the order and the stability of the solar system ; but that after certain periods, all the changes arising from the mutual actions of the planets, begin again to be repeated over in an invariable and eternal round ; or rather that all this is the result of the -/lecessaj^/ properties of matter and of motion. So completely unfounded is this assumption in point of fact, that the astronomical discovery in question affords not the slightest analogical presumption in favor of a moral cycle ; even on the supposition, that the actions of the human race, and the motions of the globe which they inhabit, were both equally subjected to the laws of mechanism.
I shall avail myself of this opportunity to remark further, that notwithstanding the lustre thrown by the result of La Grange's investigations on the metaphysical rea- soning of Leibnitz against the manus emendatrix of Newton, — this reasoning, when we consider the vagueness of the abstract principles on which it rests, can be regarded in no other light than as a fortunate conjecture on a subject where he had neither experience nor analogy for a guide. The following argument is not ill-stated by Voltaire ; and, in my opinion, is more plausible than any thing alleged a priori, on the other side of the question, by Leibnitz. " II est trop clair par I'experience que Dieu a fait des machines pour etre detruites. Nous sommes I'ouvrage de sa sagesse ; et nous perissons. Pourquoi n'en seroit-il pas de memo du monde ; Leib- nitz veut que ce monde soit parfait ; mais si Dieu ne I'a forme que pour durer un certain tems, sa perfection consiste alors a ne durer que jusqu'a I'instant fixe pour sa dissolution." Voltaire's Account of Mewtori's Philosophy.
For some excellent observations on these opposite conjectures of Leibnitz and of Newton, see Edinburgh Review, Vol. XIV. pp. 80, SI.
The quotation which gave occasion to the foregoing strictures induces me to add, before concluding this note, that when we speak of La Grange's Demonstration of the stability of the Solar System, it is by no means to be understood that he has proved, by mathematical reasoning, that this system never will, nor ever can come to an end. The amount of his truly sublime discovery is, that the system does not, as Newton imagined, contain within itself, like the workmanship of mortal hands, the elements of its own decay; and that, therefore, its final dissolution is to be look- ed for, not from the operation of physical causes subjected to the calculations of as- tronomers, but from the will of that Almighty Being, by whose fiat it was at first called into existence. That this stability is a necessary consequence of the general laws by which we find the system to be governed, may, indeed, be assumed as a demonstrated proposition ; but it must always be remembered, that this necessity is only hypothetical or conditional, being itself dependent on the continuance of laws which may at pleasure be altered or suspended.
The whole of the argument in the text, on the permanence or stability of the order of nature, is manifestly to be understood with similar restrictions. It relates, not to necessary but to probable truths ; not to conclusions syllogistically deduced from abstract principles, but to future contingences, which we are determined to expect by a fundamental Law of Belief, adapted to the present scene of our speculations and actions.
Note (K.) page 165.
" The power of designating an individual object by an appropriate articulation, is a necessary step in the formation of limguagc, but very far removed indeed (Vom its consummation. Without the use of general signs, the speech of man would differ little from that of brutes : and the transition to the general term from the iKiine of the individual, is a difficulty which remains still to be surmounted. Condillac, in- deed, proposes to show, how this transition may be made in the natural course of things. ' Un enfant appelle du noia d'arbre le premier arbrc que nous lui montrons.
366 NOTES AND ILLUSTRATIONS*
Un second arbre qu'il voit ensuite lui lappelle la meine idee ; il lui donne le meme noin : de meme a. un troiseme, a un quatrieme, et voila le mot d'ar&re, donne d'abord a un individu, qui deviant pour lui un nom de classe ou de genre, une idee abstraite qui comprend tons les arbres en general.' In like manner, Mr. Adam Smith, in his dissertation on the Origin of Languages, and Mr. Dugald Stewart, in his Elements of the Philosophy of the Human Mind, endeavour to explain this process, by representing those words which were originally used as the proper names of individ- uals, to be successively transferred to other individuals, until at length each of them became insensibly the common name of a multitude. This, however, is more ingen- ious than solid. The name given to an individual, being intended exclusively to designate that individual, it is a direct subversion of its very nature and design, to apply it to any other individual, known to be different from the former. The child, it is true, may give the name oi father to an individual like to the person it has beep taught to call by that name : but this is from mistake, not from design ; from a confusion of the two as the same person, and not from a perception of resemblance between them whilst known to be different. In truth, they whose thoughts are occupied solely about individual objects, must be the more careful to distinguish them from each other ; and accordingly, the child will most preremptorily retract the appellation oi father, so soon as the distinctness is observed.* The object with those whose terms or signs refer only to individuals, must naturally be to take care, that every such term or sign shall be applied to its appropriate individual, and to none else. Resemblance can produce no other effect, than to enforce a greater caution in the application of the particular names, and therefore has no natural tenden- cy to lead the mind to the use of general terms." (Discourses and Dissertations on the Scriptural Doctrines of Atonement and Sacrifice. By WilKam Magee, D. D. Sen- ior Fellow of Trinity College, and Professor of Mathematics in the University of Dublin. Vol. II. pp. 63, 64. 3d Edit.)
The observations in pp. 164, 165, &c. of this volume, (to which I must request the attention of my readers before they proceed to the following remarks,) appear to me to weaken considerably the force of this reasoning, as far as it applies to the sub- stance of the theory in question. With respect to Mr. Smith's illustration^ drawn from the accident of a child's calling a stranger by the name oi father, I readily acknowledge that it was unluckily chosen ; and I perfectly assent to the strictures bestowed on it by Dr. Magee. In consequence of the habitual intercourse which this domestic relation naturally keeps up between the parties, the mistake of the child (as Dr. Magee very properly calls it) must, of course, be immediately corrected ; and therefore the example is of no use whatever in confirming the conclusion it is brought to support. It is to be regretted that, upon this occasion, Mr. Smith should not only have appealed to a period of infancy, when the notions of similarity and of identity cannot fail to be sometimes one and the same ; but should have assumed as a general fact, an accidental occurrence, which, if it ever has happened, may be justly regarded as an exception to the usual history of the species. While yet on the breast, a child is able to distinguish, with the utmost quickness and accuracy, between the face of an acquaintance and that of a stranger ; and, when it is so far advanced as to begin to utter articulate sounds, any tendency to transfer or to gen- eralize the words mother or nurse seems scarcely conceivable. We are apt to sup- pose that the first attempts towards speech are coeval with the study of language ; whereas the fact manifestly is, that these attempts are only the consequences of the progress previously and silently made in the interpretation of words. Long before this time, many of the logical difficulties which appear so puzzling to the speculative grammarian have been completely surmounted. f
* These remarks have a particular reference to the following sentence in Mr. Smith's Dissertation : " A child that is just learning to speak calls every person who comes to the[house its impa or its mama ; and thus bestows upon the whole species those names which it had been taught to apply to two indi- viduals."
f The general fact with respect to children, assumed by Mr. Smith in the foregoing note, is stated still more strongly by Aristotle. Both of these philosophers have, I suspect, trusted more, in this instance, to theory than to observation. Kai ra TratVioc to fAv 'Tf^urov •^r^offayo^ivit "Xavras rovs Siv^pa;, KfaTi^a; • xa) f^nri^as, rag yvvaTxa; • vtrn^ov "Si 'hio^iZii rovrcav E««T£gav. " Ac pueri quoque primum omnes viros appellant palres, et umncs muliores, matres: postea vero discern- nunt horum utrum(|ue." — Arist. J^Tat. Jiusc. Lib. 1. Cap. i.
Tliis passage (which I do not recollect to have seen quoted by any former writer) does honor to Aristotle's acutencss. The /act, indeed, asserted in it, is more than questionable ; but, admitting the fact to be true, it must be owned that Aristotlo has viewed it in a juster light than Mr. Smith ; — not as an instance of any disposition to generalize proper names, but merely of unperfect and undistinguiah- ing perception.
NOTES AND ILLUSTRATIONS. 367
But although this particular example has been ill chosen, it does not therefore follow that the authoi's theory is altogether unfounded. Whoever has paid any at- tention to the phenomena of the infant mind, must be satisfied of its strong bias ia the first developement of the intellectual powers, to apply to similar objects a com- mon name, without ever thinking of confounding them together. Nor does this hold merely with respect to similar objects : it holds also (and at a surprisingly early pe- riod of life) with respect to sunilav relations. A child who has been accustomed to the constant attentions and caresses of its mother, when it sees another child in the arms of its nurse, will naturally and infallibly call the nurse the child's mother. In this instance, as in numberless others, its error arises from generalizing too hastily ; — the distinction between the meanings of the two relative words mother and nurse being too complex to be comprehended, fill the power of observafion begins to be exercised with some degree of attention and accuracy. This disposition, however, to transfer names from one thing to another, the diversity of which is obvious even to sense, certainly affords no inconsiderable an argument in favor of the opinion dispu- ted by Dr. Magee.
It is, indeed, wonderful, how readily children transfer or generalize the name of the maternal relation (that which of all others must necessarily impress their minds most strongly) not only in the case of their own species, but of the lower animals ; applying with little or no aid from instrucfion, the word mother to the hen, the sheep, or the cow, whom they see employed in nurturing and cherishing their young.
To myself I own, it appears, that the theory of Condillac and Smith on this point, is confirmed by every thing I have been able to observe of children. Even generic terms will be found on examination, if I be not much deceived, to be origin- ally understood by them merely as proper names ; insomuch that the notions annex- ed by an infant to the words denoting the different arficles of its nursery-furniture, or the little toys collected for its amusement, are, in its concepfions, as individually and exclusively appropriated as the names of its father, mother, or nurse. If this ob- servafion be well-founded, the same gradual conversion of proper names into appel- latives, which Mr. Smith supposes to have taken place in the formation of a lan- guage, is exemplified in the history of every infant while learning to interpret its mother tongue. The case is nearly the same with the peasant, who has never seen but one town, one lake, or one river. All of these appellatives are to his ear, pre- cisely equivalent to so many proper names.
" Quo te, Moeri, pedes ? An, quo via ducit, in Urbem ? "
That resemblance is one of our most powerful associating principles will not be disputed ; and that, even in the maturity of our reason, we have a natural disposi- tion to generalize the meaning of signs, in consequence of apprehended similarifies, both of things and of relations, is equally certain. Why then siiould it be appre- hended, that there is any peculiar mystery connected with this step in the commence- ment of the progress, when it seems to admit of an explanation so satisfactory, from a law of the human mind, exemplified daily in facts falling within the circle of our own experience ?
Note (L.) page 184.
" Aristotle's rules are illustrated, or rather, in my opinion, purposely darkened, by putting letters of the alphabet for the several terms." — Reid's Analysis of Aristotle's Logic.
On this remark the follo^ving criticism has been made by Dr. Gillies : " In the Fiist Analytics, Aristotle shows, what is that arrangement of terms in each proposition, and that arrangement of propositions in each syllogism, which consti- tutes a necessary connexion between the premises and the conclusion. When this connexion takes place, the syllogism is perfect in point of form ; and when the form is perfect, the conclusion necessarily follows from the premises, whatever be the sig- nification of the terms of which they are composed. These terms, therefore, he commonly expresses by tlic letters of the alphabet, for the purpose of showing that our assent to the conclusion results, not from comparing the things signified, but merely from considering the relation which the signs (whether words or letters) bear to each other. Those, therefore, totally misconceive the meaning of Aristotle's logic, who think that, by employing letters instead of words, he has darkened the subject; since the more abstract and general his signs are, they must be the better
368 NOTES AND ILLUSTRATIONS.
adapted to show, that the inference results from considering them alone, without at all regarding the things which they signify." *
With the doctrine stated in the beginning of this extract I entirely agree. It co- incides, indeed, remarkably with a passage in the former volume of this work, where I have shown, at some length, that our assent to the conclusion of a legitimate syllo- gism results not from comparing the things signified, but merely from considering the relations of the signs ; and, consequently, that letters of the alphabet might be sub- stituted instead of verbal terms, without impairing the force of the argument. The observation appears to myself of considerable importance, when connected with the fundamental question there discussed, concerning the use of language as an instru- ment of thought ; but, I own, I am at a loss to conceive how it should have been supposed to bear on the present subject. The only point at issue between Dr. Gillies and Dr. Reid is, whether the use of letters instead of words be, or be not, a useful expedient for facilitating the study of logic ; and upon this, I apprehend, there can scarcely exist a diversity of opinion. No instance, I will venture to affirm, ever oc- curred of any hesitation in the mind of the merest novice about the conclusiveness of a legitimate syllogism, when illustrated by an example ; but how difficult to ex- plain to a person altogether unaccustomed to scholastic abstractions, the import and cogency of those symbolical demonstrations by which Aristotle has attempted to for- tify the syllogistic theory !
The partiality of Dr. Gillies for this technical device has probably arisen, in part, from his supposing it to bear a much closer analogy than it does, in fact, to the alge- braical art. Another very learned writer has proceeded on the same idea, when he observes, that " it should recommend the study of logic to mathematicians, that, in order to make his demonstrations universal, Aristotle uses letters as universal char- acters, standing for all kinds of terms or propositions." f It would be an idle waste of words to show, how very slight this analogy is, and how totally inapplicable to the question before us ; amounting to little more than this, that, in both cases, the alphabet happens to be employed as a substitute for common language. An analogy much more in point, may be traced in the practice of designating by letters the differ- ent parties in a hypothetical law-suit ; — a practice attended with no inconvenience, where these symbols only supply the place of proper names ; but which would at once convert the simplest case into an aanigma, if they were to be employed (as they are by Aristotle) to denote, not merely individual existences, but the relations of general ideas.
While Dr. Gillies has thus exerted his ingenuity in defending the use made by Aristotle of letters instead of words, it is to be regretted, that he has said nothing about the motives which induced that philosopher, in disproving the illegitimate modes, to content himself with general references to such words as bonum, habitus, prudentia, upon which the student is left to his own judgment, in ringing the vari- ous changes necessary for the illustration of the theory. A more effectual contri- vance could not easily have been thought of, for perplexing a subject, level, in itself, to the meanest capacity. In this respect, it answers the intended purpose still bet- ter than his alphabetical ybnnwZ^.
Note (M.) page 209.
As instances of what are called by logicians /aZZaci^ in dictione, a modern writer mentions the mistakes which may arise from confounding " liber Bacchus, et liber a servitute ; liber codex, et liber cortex ; crevi a cerno, et crevi a cresco ; infractus paiticipium ab infringe, et infractus compositum ab in etfractus, sensu plane con- trario." He mentions also the danger of confounding the literal with the figurative sense of a word, as vulpes when applied to a quadruped, and to a man noted for cunning. — " Sic siquis arguat," he adds for the sake of illustration, " stella7nlatrare, quia Stella qucedam Cams dicitur, facile respondebitur captioso argumento, distin- guendo varios sensus ejusdem vocis, indeque ostendendo syllogismi quatuor terminos (si sensum spectes) ubi tres saltern sono comparent."
To exemplify the fallacia accentus, the same writer warns us against confounding hortus and ortus ; hara and ara ; malum adjectivum, and malum pro pomo ; cer-
* Analysis of Aristotle's Speculative Works, &c. by Dr. Gillies, Vol. I. p. 89. 2d Edit. From a note at tho foot of the page it appears, that the remarks just quoted from Keid gave occa- sion to the above strictures, t Ancient Methapbysics, Vol. III. p. 51 of the Preface.
NOTES AND ILLUSTRATIONS. 369
vus and servus ; concilium and consilium, &c. &c. The remedy against such falla- cies, he gravely tells us, is to distinguish the words thus identified, so as to show that the syllogism consists of mere than three terms. " Solvuntur distinguendo ea quse confunduntur, indeque monstrando pluralitatem terminorum." He acknowledges, however, that fallacies of this sort are not likely to impose on a skilful logician. " Sed crassiores sunt has fallacia; quam ut perito imponant."
I have purposely quoted these remarks, not from a mere schoolman, but from an author justly distinguished both by science and learning. Dr. Wallis of Oxford. Thev are taken, too, from a treatise written with the express view of adapting the logic commonly taught in our universities to the ordinary business of life ; having a formal dedication prefixed to it to the Ro3'al Society of London, then recently instituted. The subject is the same with that of the third Book of Locke's Essay, relating to the abuse of words ; and the interval between the two publications was only two years. Yet how immense the space by which they are separated in the history of the Hu- man Mind !
The concluding paragraph, however, of this very puerile chapter on sophisms, bears marks of a mind fitted for higher undertakings. I cannot deny myself the pleasure of transcribing it, and of pointing it out to those who may hereafter specu- late upon the theory of wit, as not unworthy of their attention.
" Interim hie monendum duco ; quod hse fallacies, utcunque justam argument! vim non habeant, apprime tamen commodae sunt ad id omne quod ingeniosuin vulgo dicimus : Ut sunt joci, facetiae, dicteria, scommata, sarcasmi, retorsiones lepidae, (wit, raillery, repartee.) Quippe hoc omne fundari solet in hujusmodi failaciarum aliqua. Nonnunquam allusio fit ad verborum sonos ; nunc ad ambiguam vocum significationem ; nunc ad dubiam syntaxin ; nunc proverbialiter dici solita accom- modantur sensu proprio, aut vice versa : nunc aliud aperte dicitur, aliud clam insinua- tur ; saltern oblique insinuatur, quod non erat directo dicendum ; nunc verba contra- lio sensu captantur, et retorquentur ; nunc verisimile insinuatur ut verum, saltem ut suspectum ; nunc de uno dicitur, quod, mutato nomine, de alio intellectum vellent ; nunc ironice laudando vituperant ; nunc objecta spicula respondendo declinantur, aut etiam (obliquata) alio diriguntur, forte sic ut auctorem feriant ; et fere semper ex ambiguo luditur. Queb quidem failaciarum formulae, si frigids sint crassfeque, riden- tur ; si subtiliores arrident ; si acutae, titillant ; si aculeataj, pungunt."
Note (N.) page 224.
In the first volume of these Elements, I have endeavoured to trace the origin of that bias of the imagination, which has led men, in all ages of the world, to consider physical causes and effects as a series of successive events necessarily connected to- gether, like the links of a metallic chain. (See Chap. i. Sect. 2.) So very strong is this bias, that, even in the present times, some of the most sagacious and cautious of Bacon's followers occasionally show a disposition to relapse into the figuiative language of the multitude. " The chaia of natural causes," says Dr. Reid, " has, not unfitly, been compared to a chain hanging down from heaven : A link that is discovered supports the links below it, but it must itself be supported ; and that which supports it must be supported, until we come to the first link, which is supported by the throne of the Almighty." Essays on the Intellectual Powers, ^.\\a. ^{o Ed. It is difficult to reconcile the approbation here bestowed on the above similitude, with the excellent and profound remarks on the relation of cause and eft'ect, which occur in other parts of Dr. Reid's works. See Essays on the Active Powers, p. 44. and pp. 286, 287, 288. 4to Edit.
Mr. Maclaurin,in the concluding chapter of his Account of Newton's Discoveries, has still more explicitly lent the sanction of his name to this idea of a chain of sec- ond causes. " As we cannot but conceive the universe as depending on the first cause and chief mover, whom it would be absurd, not to say impious, to exclude from acting in it ; so we have some hints of the manner in which he operates in na fure, from the laws which we find established in it. Though he is the source of all efficacy, yet we find that place is left for second causes, to act in subordination to him ; and mechanism has its share in carrying on the great scheme of nature. The establishing the equality of action and re-action, even in those powers which seem to surpass mechanism, and to be more immediately derived from him, seems to be an indication that those powers, while they derive their efficacy from him, are, however, in a certain degree circumscribed and regulated in their operations by mechanical principles ; and that they are not to be considered as mere immediate volitions of
VOL. II. 47
370 NOTES AND ILLUSTRATIONS.
his, (as they are often represented,) but rather as instruments made by him, to per- form the purposes for which he intended them. If, for example, the most noble phe- nomena in nature be produced by a rare elastic cetherial medium, as Sir Isaac Newton conjectured, the whole efficacy of this medium must be resolved into his power and will who is the supreme cause. This, however, does not hinder, but that the same medium may be subject to the like laws as other elastic fluids, in its actions and vi- brations ; and that, if its nature were better known to us, we might make c\irious and useful discoveries concerning its effects from these laws. It is easy to see, that this conjecture no way derogates from the government and influences of the Deity ; while it leaves us at liberty to pursue our inquiries concerning the nature and opera- tions of such a medium : Whereas they who hastily resolve these powers into immediate volitions of the Supreme Cause, without adm.itting any intermediate instruments, put an end to our inquiries at once ; and deprive us of what is prob- ably the most sublime part of philosophy, by representing it as imaginary and fic- titious."
On the merits of this passage, considered in relation to the evidences of natural re- ligion, I do not mean to offer any remarks here. Some acute strictures upon it in this point of view (but expressed with a most unbecoming and offensive petulance) may be found in the third volume of Baxter's Inquiry into the Human Soul. — It is with the logical proposition alone, stated in the concluding sentence, that we are con- cerned at present ; and this (although Baxter has passed it over without any animad- version) appears to me highly exceptionable ; proceeding on a very inaccurate, or rather totally erroneous conception of the object and aim of physical science. From the sequel of the section to which this note refers, (particularly from pages 228, 229, 230,) I trust it will appear, that, supposing all the phenomena of the universe to be produced by the iminediate volitions of the Supreme Cause, the business of natural philosophers would be precisely the same as upon the hypothesis adopted by Maclaurin ; the investigation of the necessary connexions linking together physical causes and effects, (if any such necessary connexions do exist,) being confessedly placed beyond the reach of our faculties ; and, of consequence, our most successful researches terminating in the discovery of some general law, or in the farther gene- ralization and simplification of laws already known. In this intellectual process there is no more reason to apprehend that any limit is fixed to our inquiries, than that the future progress of geometry should be stopped by the discovery of some one truth comprising the whole science in a single theorem.
Nor do I apprehend that the theory which excludes from the universe mechanism (strictly so called) tends, in the smallest degree, to detract from its beauty and gran- deur ; notwithstanding the popular and much admired argument of Mr. Boyle in support of this idea. " As it more recommends," he observes, " the skill of an en- gineer to contrive an elaborate engine, so as that there need nothing to reach his ends in it, but the contrivance of parts void of understanding ; than if it were necessary that, ever and anon, a discreet servant should be employed to concur notably to the operations of this or that part, or to hinder the engine from being out of order : so it more sets off the wisdom of God, in the fabric of the universe, that he can make so vast a machine perform all those many things which he designed it should, by the mere contrivance of brute-matter, managed by certain laws of motion, and upheld by his ordinary and general concourse ; than if he employed, from time to time, an intel- ligent overseer to regulate and control the motion of the parts." * — " What may be the opinion of others," says Lord Kames, after quoting the foregoing passage, " I cannot say ; but to me this argument is perfectly conclusive. Considering this uni- verse as a great machine, the workmanship of an intelligent cause, I cannot avoid thinking it the more complete, the less mending or interposition it requires. The per- fection of every piece of workmanship, human and divine, consists in its answering the designed purpose, without bestowing further labor upon it."t — To myself, I must confess, Mr. Boyle's argument appears altogether unworthy of its author. The avowed use of a machine is to save labor ; and therefore, the less frequently the in- terposition of the artist is necessary, the more completely does the machine accom- plish the purpose for which it was made. These ideas surely do not apply to the works of the Almighty. The multiplicity of his operations neither distract his at- tention, nor exhaust his power ; nor can we, without an obvious inconsistency in the
* tnrjuiry into the vulgar notion of Nature.
t Of tlifi Laws of Mui.ioii. Published in tlio First Volume of thoPiiysical and Literary Essays, read before the lOditihurgli PljiloBophioal Society, (17.54.)
NOTES AND ILLUSTRATIONS. 371
very terms of the proposition, suppose him reduced to the necessity of economizing, by means of mechanism, the resources of Omnipotence.*
My object in these observations (I think it proper once more to remind my readers) is not to prejudge the metaphysical ques'ion between Maclaurin and Baxter; but merely to establish the two following propositions. 1. That this question is alto- gether foreign to the principles which form the basis of the inductive logic ; these principles neither affirming nor denying the existence of necessary connexions be- tween physical causes and effects, but only asserting, that such connexions, if they do exist, are not objects of human knowledge. 2. That no presumption in favor of their existence is afforded by Mr. Boyle's similitude ; the reasoning founded on the supposed analogy between the universe and a machine, being manifestly inapplicable where the power as well as the skill of the Contriver is admitted to be infinite. — If the remarks offered on these points be well founded, they may serve, at the same time, to show, that the attempt made in the text to illustrate some abstract topics connected with the received Rules of Philosophizing was not altogether superfluous.
The metaphysical doctrine maintained by Baxter in opposition to Maclaurin, seems to coinci^^e nearly with Malebrauche's Theory of Occasional Causes, as well as with the theology of the old Orphic verses quoted in the 7th chapter of Aristotle's Treatise de Mundo. — A very striking resemblance is observable between these verses, and the Hymn to Narrayna or the Spirit of God, translated by Sir AVilliam Jones from the writings of ancient Hindu Poets, f
Note (0.) page 237.
Although Dr. Reid was plainly led into this train of thinking by Mr. Hume, the same doctrine with respect to the relation of cause and effect, (considered as the object of physical science,) is to be found in many English writers of a far earlier date. Of this assertion I have produced various proofs in my first Volume, from Hobbes, Barrow, Berkeley, and others, to whose speculations on this head Dr. Reid does not seem to have paid any attention. To these quotations I beg leave to add the following, from a book, of which the third edition was published in 1737.
" Here it is worth observing, that all the real true knowledge we have of nature is entirely experimental ; insomuch, that how strange soever the assertion seems, we may lay this down as the first fundamental unerring rule in physics, that it is not within the compass of human under standing, to assign a purely speculative reason for any one phenomenon in nature ; as why grass is green, or snow is white ; why fire burns, or cold congeals. By a speculative reason, I mean assigning an immedi- ate efficient cause a priori, together with the manner of its operation, for any effect whatsoever purely natural. We find, indeed, by observation and experience, that such and such effects are produced ; but when we attempt to think of the reason why, and the manner how the causes work those effects, then we are at a stand, and all our resoning is precarious, or at best but probable conjecture.
" If any man is surprised at this, let him instance, in some speculative reason he can give for any natural phenomenon ; and how plausible soever it appears to him at first, he will, upon weighing it thoroughly, find it at last resolved into nothing more than mere observation and experiment, and will perceive that these expressions generally used to describe the cause or manner of the productions of nature, do really signify nothing more than the effects." The Procedure, Extents, and Limits of Human Understanding. Ascribed to Dr. Peter Brown, Bisliop of Cork. (London, 1737. 3d Ed.)
For the following veiy curious extracts, (together with many others of a similar import, both from English and from foreign writers,) I am indebted to a learned cor-
* A comparison still more absurd than that of Mr. Boyle occurs in the 6tli Chapter of Aristotle's book dc Mundo ; where he represents it as unbecoming the dignity of the Supreme Being ctirovpyiTv a.'ira.vra,, — " to put his own hand to every thing ; " a supposition, according to him, " mucli more un- Builiibloto theUivino majesty, tlian to conceive ageat monarcii like Xer.xcs taking upon liiniselfthe ac- tual execution of all his own decrees."
f The same opinion is explicitly avowed by Dr. Clarke, a zealous partisan of the Experimental Phi- losophy, and one of the ablest logicians that the Newtonian School has hitherto produced. " Tha course of nature, truly and properly speaking, is nothing but the will o( God, proditciiig certain ef- fects in a continued, regular, constant, end unifom mann»r." — Clarkt's Worki, Vol. U. p. 698. Fol. «dit.
372 NOTES AND ILLUSTRATIONS.
respondent, William Dickson, LL. D., a gentleman well known by his able and meri- torious exertions for the abolition of the slave trade.
" Confidence of science is one great reason we miss it : for on this account pre- suming we have it every where, we seek it not where it is ; and, therefore, fall short of the object of our inquiry. Now, to give further check to dogmatical pretensions, and to discover the vanity of assuming ignorance, we '11 make a short inquiry, whether there be any such thing as science in the sense of its asserters. In their notion, then, it is the knowledge of things in their true, immediate, necessary causes : Upon this I '11 advance the following observations.
" 1. All knowledge of causes is deductive ; for we know none by simple intuition, but through the mediation of their effects. So that we cannot conclude any thing to be the cause of another, but from its continual accompanying it ; for the causality itself is insensible. But now to argue from a concomitancy to a causality is not infal- libly conclusive ; yea, in this way lies notorious delusion, &c. &c. &c.
" 2. We hold no demonstration in the notion of the dogmatist, but where the contrary is impossible : " &c. &c. (Scepsis Scientifica : or Confess't Ignorance the Way to Science ; in an Essay of the Vanity of Dogmatizing and Confident Opinion; with a Reply to the Exceptions of the learned Thomas Albius.* By Joseph Glan- vill, M. A. London, 1665. Dedicated to the Royal Society.)
" Causalities are first found out by concomitancy, as I intimated. And our expe- rience of the dependence of one, and independence of the other, shows which is the effect, and which the cause. Definitions cannot discover causalities, for they are formed after the causality is known. So that, in our author's instance, a man cannot know heat to be the atoms of fire, til! the concomitancy be known, and the efficien- cy first presumed. The question is, then, How heat is known to be the effect of fire ? Our author answers by its definition. But how came it to be so defined ? The answer must be, by the concomitancy and dependence, for there 's nothing else as- signable." (SCIR|- tuum nihil est ; or the Author's Defence of the Vanity of Dog- matizing against the Exceptions of the learned Thomas Albius, in his late SCIRI. London, 1665.) ....
" Inter causara proprie dictam et effectum oportet esse necessarium nexum ; adeo ut posita actione causae sequatur necessario effectus. Cum Deus vult ahquid efiicere id necessario eveniat oportet, &c. Quia autera ejusmodi nexus non cernitur inter causas creataset effectus, nonnulli causas secundas, seu creatas, sua vi agere nega- runt. Negant corpora a corporibus moveri, quod inter motum corporis, et motum eorum in quee incidit, nullus deprehendatur nexus, adeo ut moto corpore A, necesse sit moveri corpus B, cui colliditur. lidem quoque negant corpora a spiritibus move- ri, quia inter voluntatem spirituum et motum corporum nullam connexionem animad- vertunt, &c. Fatendum a nobis hujusmodi connexum nullum cerni, nee sequi ex eo quod, corpore moto, id, in quod incidit, movetur ; aut ex eo quod, mente volente, corpus agitatur, corpora etmentera esse veras motus causas. Fieri posset, ut occa- siones tantum essent, quibus positis, alia causa ageret. Verum uti, ex ejusmodi pos- sibilitate, non colligeris rem ita se habere ; ita ne eo quod non adsequeris aliquid, consequens est ut nihil sit ; nisi aliunde probaveris tibi esse earum rerum, de quibus agitur, adaequatam ideam, aut rem repugnare, &c. — Possunt inesse corporibus metis, et spiritibus, facultates ignotae, de quibus judicium nullum, aut negando aut affirman- do, ferre possumus. Itaque ex aequo peccant, qui affirmant inesse iiscerto facultates efiiciendorum quorundam, quae an ab iis fiant ignorant ; et qui negant quidquam inesse corporibus et spiritibus, nisi quod in iis perspicue norunt." — Joannis Cleiici Opera Philosophica. Amstel. 1698. Ontol. T. I. p. 376.
After this cloud of authorities (many of which are from books in very general cir- culation,) it is surprising that the following sentence should have escaped the pen of Dr. Beattie. " The sea has ebbed and flowed twice every day in time past ; therefore the sea will continue to ebb and flow twice every day in time to come, — is by no means a logical deduction of a conclusion from premises. — This remark was FIRST MADE BY Mr. Hume." — Essay on Truth, 2d. ed. p. 126.
It is evident, that this remark is only a particular application of the doctrine con-
* Or White,, a Romish priest, author of a treatise entitled, Sciri give Sceptices et Scepticorum a Jure Disputatioiiis Exclusio. (See Biog. Diction.)
NOTES AND ILLUSTRATIONS.
373
tainedin the above quotations ; as well as in the numerous extracts to the same pur- pose, collected in Note (C.) at the end of the first Volume of this Work. In one of these (from Hobbes) the very same observation is made ; and a sort of theory is proposed to explain how the mind is thus led to infer the future from the past ; — a theory which, however unsatisfactory for its avowed purpose, is yet sufficient to show, that the author was fully aware, that our expectation of the continuance of the laws of Nature was a fact not to be accounted for from the received principles of the scho- lastic philosophy.
Note (P.) page 252.
From the Preface of Pappus Alexandrinus to the Seventh Book'of his Mathemati- cal Collection. (See Halley's Version and Restitution of Apollonius Pergajus de Sectione Rationis et Spatii, p. xxviii.
. . . . " Resolutio est methodus, qua a qusesito quasi jam concesso per ea quas delude consequuntur, ad conclusionera aliquam, cujus ope Corapositio fiat, per- ducamur. In resolutione enim, quod quaeritur ut jam factum supponentes, ex quo antecedente hoc consequatur expendimus ; iterumque quodnam fuerit hujus antece- dens ; atque ita deinceps, usque dum in hunc modum regredientes, in aliquid jam cognitum locoque principii habitum incidamus. Atque hie processus Analysis voca- tur, quasi dicas, inversa solutio. E contrario autem in Compositione, cognitum illud, in Resolutione ultimo loco acquisitum, ut jam factum prsemittentes ; et quae ibi con- sequentia erant, hie ut antecedentia naturali ordine disponentes, atque inter se con- ferentes, tandem ad Constructionem quaesitiperveniraus. Hoc autem vocamus Syn- thesin. Duplex autem est Analyseos genus, vel enim est veri indagatrix, diciturque Theoretica ; vel propositi investigatrix, ac Problematica vocatur. In Theoretico au- tem genere, quod queeritur, revera ita se habere supponentes, ac delude per ea qu« consequuntur, quasi vera sint (ut sunt ex hypothesi) argumentantes ; ad evidentem aliquam conclusionem procedimus. Jam si conclusio ilia vera sit, vera quoque est propositio de qua quseritur ; ac demonstratio reciproce respondet^analysi. Si vero in falsam conclusionem incidamus, falsum quoque erit de quo quseritur.* In Prob- lematico vero genere, quod proponitur ut jam cognitum sistentes, per ea quEe exinde consequuntur tanquam vera, perducimur ad conclusionem aliquam : quod si conclu- sio ilia possibilis sit ac ij-oj/o-r^ quod Mathematici Datum appellant ; possibile quoque erit quod proponitur : et hie quoque demonstratio reciproce respondebit Analysi. Si vero incidamus in conclusionem impossibilem, erit etiam problema impossibile. Di- orismus autem sive determinatio est qua discernitur quibus conditionibus quotque mo- dis problema effici possit. Atque hajc de Resolutione et Compositione dicta sunto."
Note (Q.) page 277.
The following passage from Buffon, although strongly marked with the author's characteristical spirit of system, is yet, I presume, sufficiently correct in the outline, to justify me for giving it a place in this note, as an illustration of what I have said in the text on the insensible gradations which fix the limits between resemblance and analogy.
"Take the skeleton of a man ; incline the bones of the pelvis ; shorten those of the thighs, legs, and arms ; join the phalatiges of the fingers and toes ; lengthen the jaws by shortening tlie frontal bones ; and lastly, extend the spine of the back. This skeleton would no longer represent that of a man ; it would be the skeleton of a horse. For, by lengthening the back-bone and the jaws, the number of the ver- tebrae, ribs, and teeth, would be increased; and it is only by the numbers of these bones, and by the prolongation, contraction, and junction of others, that the skeleton of a horse diffijrs from that of a man. The ribs, which are essential to the figure of animals, are found equally in man, in quadrupeds, in birds, in fishes, and even in the turtle. The foot of the horse, so apparently different from the hand of a man, is composed of similar bones, and, at the extremity of each finger, we have the same small bone resembling the shoe of a horse which bounds the foot of that animal. Raise the skeletons of quadrupeds, from the ape kind to the mouse, upon their hind
* From the account given in tlie text of Theoretical Jinnlysis, it would seem to follow, that its ad- vantages, as a method of investigation, increase in proportion to the variety of demonstrations of which a tlieoiom admits ; and that, in tlie case of a theorem admitting of one demonstration alone the two methods would he exactly on a level. The justness of this conclusion will, I hclieve, t)e found to correspond with the experience of every person conversant with the processes of the Greek Geom- etry.
374 NOTES AND ILLUSTRATIONS.
legs, and compare them with the skeleton of a man ; the mind will be instantly struck with the uniformity of structure observed in the formation of the whole group. This uniformity is so constant, and the gradations from one species to another are so im- perceptible, that, to discover the marks of their discrimination, requires the most mi- nute attention. Even the bones of the tail will make but a slight impression on the observer. The tail is only a prolongation of the os coccygis or rump bone, which is short in man. The ouran outang and true apes have no tail, and in the baboon and several other quadrupeds its length is very inconsiderable. Thus, in the creation of animals, the Supreme Being seems to have employed only one great idea, and, at the same time, to have diversified it In every possible manner, that men might have an opportunity of admiring equally the magnificence of the execution and the sim- plicity of the design." — Smellie's Translation.
As a proof that the general conclusion in which the foregoing extract terminates, requires some important qualifications and restrictions, it is sufficient to subjoin a few remarks from a later writer, who, with the comprehensive views of Buffbn, has combined a far greater degree of caution and correctness in his scientific details.
" It has been supposed by certain naturalists, that all beings may he
placed in a series or scale, beginning with the most perfect, and terminating in the most simple, or in the one which possesses qualities the least numerous and most common, so that the mind, in passing along the scale from one being to another, shall be no where conscious of any chasm or interval, but proceed by gradations al- most insensible. In reality, while we confine our attention within certain limits, and especially while we consider the organs separately, and trace them through animals of the same class only, we find them proceed, in their degradation, in the most uni- form and regular manner, and often perceive a part, or vestige of a part, in animals where it is of no use, and where it seems to have been left by Nature, only that she might not transgress her genejal law of continuity.
" But, on the one hand, all the organs do not follow the same order in their degra- dation. This organ is at its highest state of perfection in one species of animals ; that organ is most perfect in a different species, so that, if the species are to be ar- ranged after each particular organ, there must be as many scales or series formed, as there are regulating organs assumed ; and in order to construct a general scale of perfection, applicable to all beings, there must be a calculation made of the effect resulting from each particular combination of organs, — a calculation which, it is needless to add, is hardly practicable.
" On the other hand, these slight shades of difference, these insensible gradations continue to be observed, only while we confine ourselves to the same combinations of leading organs ; only while we direct our attention to the same great central springs. Within these boundaries all animals appear to be formed on one common plan, which serves as the ground-work to all the lesser internal modifications ; but the instant we pass to animals where the leading combinations are different, the whole of the resemblance ceases at once, and we cannot but be conscious of the abruptness of the transition.
" Whatever separate arrangements may be suitable for the two great classes of an- imals, with and without vertebrae, it will be impossible to place at the end of the one series and at the commencement of the other, two animals sufficiently resembling, to form a proper bond of connection." — Introduction to Cuvier's Legons d'Anato- mie Comparee.
Note(R.) page 288,
Of fortunate conjectures or hypotheses concerning the laws of nature, many addi- tional examples might be produced from the scientific iiistory of the eighteenth cen- tury. Franklin's sagacious and confident anticipation of the identity of lightning and of electricity, is one of the most remarkable. The various analogies previously remarked between their respective phenomena, had become, at this period, so stri- ki; ^jto philosophers, that the decisive experiment necessary to complete the theory, was carried into execution, in the course of the same month, on both sides of the Atlantic. In the circumstantial details recorded of that made in America, there is something peculiarly interesting. I transcribe them in the words of Dr. Priestley, who assures us that he received them from the best authority.
" After Franklin had published his method of verifying his hypothesis concerning the sameness of electricity with the matter of lightning, he was waiting for the erection of a spire in Philadelphia to carry his views into execution ; not imagining that a pointed rod, of a moderate heigth, could answer the purpose ; when it occurred to
NOTES AND ILLUSTRATIONS. 375
him that, hy means of a common kite, he could have a readier and better access to the regions of thunder, than by any spire whatever. Preparing, therefore, a large silk handkerchief and two cross sticks of a proper length on which to extend it, he took the opportunity of the first approaching thunder-storm to take a walk into a field in which there was a shed convenient for his purpose. But dreading the ridicule which too commonly attends unsuccessful attempts in science, he communicated his intended experiment to nobody but his son, who assisted him in raising the kite.
" The kite being raised, a considerable time elapsed before there was any appear- ance of its being electrified. One very promising cloud had passed over it without any effect ; when at length, just as he was beginning to despair of his contrivance, he observed some loose threads of the hempen string to stand erect, and to avoid one another, just as if they had been suspended on a common conductor. Struck with this promising appearance, he immediately presented his knuckle to the key, and (let the reader judge of the exquisite pleasure he must have felt at that moment) the discovery was complete. He perceived a very evident electric spark. Others succeeded, even before the string was wet, so as to put the matter past all dispute ; and when the rain had wet the string, he collected electric fire very copiously. This happened in June, 1752, a month after the electricians in France had verified the same theory, but before he heard of any thing they had done." — Priestley'' s History of Electricity , pp. 180, 181, 4to. ed.
Note (S.) page 392.
" Natural knowledge may not unaptly be compared to a vegetable, whether plant or tree, which springs from a seed sowed in a soil proper, and adapted by a skilful gardener for that plant. For as the seed, by small fibrills or roots it shoots out, re- ceives from the soil or earth a nourishment proper and adapted for ascending into the body or stock, to make it grow in bulk and strength, to shoot upwards, and from thence to shoot forth branches, and from them leaves, thereby to draw and receive outoftheaira more refined, spirituous, and enlivening juice, which, descending back into the body or stock, increases its stature, bulk, circumference, and strength, by new encirclings, and thereby enables it to send forth more fibrills and greater roots, which afford greater and more plentiful supplies to the stock or trunk, and ena- bles that to exert and shoot forth more branchings and greater numbers of leaves ; which, repeating all the effects and operations by continued and constant circula- tions, at length bring the plant to its full stature and perfection :
" So natural knowledge doth receive its first informations from the supplies afforded by select and proper phenomena of nature conveyed by the senses; these improve the understanding, and enable it to raise some branching? out into conclusions, co- rollaries, and maxims ; these afford a nutritive and strengthening power to the un- derstanding, and enable it to put forth new roots of inquisiUon, trials, observations, and experiments, and thereby to draw new supplies of information : which further strengthening the understanding, enable it to exert and produce new deductions and new axioms : These circulate and descend downwards, increasing and strengthening the judgment, and thereby enable it to make more striking out of roots of inquiries and experiments, which cause the like effects as before, but more powerfully, and so by consent and continued circulations from phenomena to make deductions, and from deductions to inquire phenomena, it brings the understanding to a complete and per- fect comprehension of the matter at first proposed to be considered." — Hooke's Posthumous Works, p. 553.
Note (T.) page 294.
" Aliquando observationes et experimenta immediate nobis exhibent principia, qua? quajriinus ; sed aliquando etiam hypotheses in auxilium vocamus, non tamen penltus arbitrarias, sed conformes lis quto observantur, et qua; supplentcs immediata- rumobservationum defectum, viam invesligationi sternunt, tanquam divinantibus ; utsi ea, qua; ex ipsisdeducuntur, inveniamus re ipsa, eadem retineamus, et progredi- amur ad nova conscctaria ; secus vero, ipsas rcjiciamus. Et quidein pleruinque hanc esse arbitror mcthodum omnium aptissimam in physica, qua; sa;pissime est velut qiia;dam enucleatio cpistola; arcanis notis conscripta;, ubi per attentationem, et per er- rores etiam plurimos paulatirn et caute progrcdiendo, ad vcram ejus theoriam deveni- tur : cujus rei specimen admodum luculcntum cxhibui in mea dissertationc de lu- mine, agens do rectilinea luminis propagatione ; ac in Stayana; Philosophia; Tomo I. agens de gcneralibus proprietatibus corporum, et de vi inertiae in primis ; Tomo
376 NOTES AND ILLUSTRATIONS.
vero IL agens de totius Astronomiae constitutione." — Boscovich de Soils ac Lunee Defectibus.
In Sprat's History of the Royal Society, a similar idea occurs, illustrated by an image equally fanciful and apposite. " It is not to be questioned, but many inven- tions of great moment have been brought forth by authors, who began upon supposi- tions, which afterwards they found to be untrue. And it frequently happens to phi- losophers, as it did to Columbus ; who first believed the clouds that hovered about the Continent to be the firm land : But this mistake was happy ; for, by sailing to- wards them, he was led to what he sought ; so by prosecuting of mistaken causes, with a resolution of not giving over the pursuit, they have been guided to the truth itself."
[The work from which this passage is taken (it may be here remarked, by the way) affords complete evidence of the share which, in the judgment of the founders of the Royal Society, Bacon had in giving a beginning to experimental pursuits in England. See in particular, Section xvi.]
Note (U.) page 294.
With respect to the application of the method of exclusions to physics, an impor- tant logical remark is made by Newton, in one of his letters to Mr. Oldenburgh. Ob- vious and trivial as it may appear to some, it has been overlooked by various writers of great name ; and therefore I think proper to state it in Newton's own words.
*' In the meanwhile, give me leave. Sir, to insinuate, that I cannot think it effectu- al for determining truth, to examine the several ways by which phenomena may be explained, unless where there can be a perfect enumeration of all those ways. You know the proper method for inquiring after the properties of things, is to deduce them from experiments. And I told you, that the theory which I propounded (con- cerning light and colors) was evinced to me, not by inferring, it is thus, because it is not otherwise ; that is, not by deducing it only from a confutation of contrary sup- positions, but by deriving it from experiments concluding positively and directly. The way, therefore, to examine it, is, by considering whether the experiments which I propound, do prove those parts of the theory to which they are applied ; or by prose- cuting other experiments which the theory may suggest for its examination," &c. &c. Horsley's Edition of JVewton's Works, Vol. IV. p. 320.
Note (X.) page 299.
" If we consider the infantine state of our knowledge concerning vision, light, and colors, about a century ago, very great advancements will appear to have been made in this branch of science ; and yet a philosopher of the present age has more deside- rata, can start more difficulties and propose more new subjects of inquiry than even Alhazen or Lord Bacon. The reason is, that whenever a new property of any sub- stance is discovered, it appears to have connexions with other properties, and other things, of which we could have no idea at all before, and which are by this means but imperfectly announced to us. Indeed, eveiy doubt imphes some degree of knowledge ; and while nature is a field of such amazing, perhaps boundless extent, it may be expected that the more knowledge we gain, the more doubts and difficul- ties we shall have ; but still, since every advance in knowledge is a real and valuable acquisition to mankind, in consequence of its enabling us to apply the powers of nature to render our situation in life more happy, we have reason to rejoice at every new difficulty that is started, because it informs us that more knowledge, and more advantage are yet unattained, and should serve to quicken our diligence in the pur- suit of them. Every desideratum is an imperfect discovery." Priestley's History of Discoveries relating to Vision, Light, and Colors, p. 773. (Lond. 1772.)
Note (Y.) page 310.
For the analogies between Galvanism and Electricity, see Traiti Elementaire de Physique, far M. VAbbe Haiiy, § 717, — The passage concludes with the following remark, which may be regarded as an additional proof, that, even when analogical conjectures appear to depart the most widely from the evidence of expeiience, it is from experience that they derive their whole authority over the belief. " Partout le fluid electrique semble se multiplier par la diversite des phenomenes ; et il nous avait tenement accoutumes a ses metamorphoses, que la nouveaute nieme de la forme sous laquclle il s'offrait dans le Galvanisrae naissant, semblait etre une raison de plus pour le reconnaitre."
NOTES AND ILLUSTRATIONS. 377
Note (Z.) page 318.
In that branch of politics which relates to the theory of Government, one source of error) (not unfrequently overlooked by the advocates for experience) arises from the vagueness of the langii9ge in which political facts are necessarily stated by the most faithful and correct historians. No better instance of this can be produced than the terms, monarchy, aristocracy, and democracy commonly employed to distinguish different forms of Government from each other. These words, in their strict philo- sophical acceptation, obviously denote not actual but ideal constitutions, existing only in the imagination of the political theorist ; while, in more popular discourse, they are used to discriminate, according to their prevailing bias or spiiit, the various mixed establishments exemplified in the history of human affairs. Polybius, accord- ingly, with his usual discernment, expresses his doubts, under which of the three simple forms the constitution of Rome, at the period when he had an opportunity of studying it, ought to be classed. " When we contemplate," he observes, " the power of the Consuls, it seems to be a monarchy ; when we attend to the power of the Sen- ate, it seems to be an aristocracy ; when we attend to the power of the People, we are ready to pronounce it a democracy."*
It is easy to see how much this scantiness and want of precision in our political vocabulary, must contribute to mislead the judgments of those reasoners who do not analyze very accurately the notions annexed to their words ; and at the same time, what a purchase they afford to the sophistry of such writers as are disposed, iu de- clamations addressed to the multitude, to take an undue advantage of the ambiguities of language.
Another source of error which goes far to invalidate the authority of various po- litical maxims supposed to be fouded on experience, is the infinite multiplicity of the seemingly trifling and evanescent causes connected with local manners and habits, which, in their joint result, modify, and in some cases counteract so powerfully, the effects of written laws and of established forms. Of these causes no verbal descrip- tion can convey an adequate idea ; nor is it always possible, even for the most atten- tive and sagacious observer, when the facts are before his eyes, to appreciate all their force : — So difficult is it to seize the nicer shades which distinguish the meanings of corresponding terms in different languages ; and to enter, at j^ears of maturity, into those delicate and complex associations, which, in the mind of a well-educated na- tive, are identified with the indigenous feelings of national sympathy and taste.
Of the truth of this remark, a striking illustration presents itself in the mutual igno- rance of the French and English nations (separated from each other by a very nar- row channel, and, for centuries past, enjoying so many opportunities of the most familiar intercourse) with respect to the real import of the words and pluases marking the analogous gradations of rank in the two countries. The words gcntilhomme and gentle-man are both derived from the same etymological root : yet how imperfect a translation does the one afford of the other ! and how impossible to convey by a definition all that is implied in either ! Among French writers of no inconsiderable name, we meet with reasonings which plainly show, that they considered the rela- tive rank of the members of our two Houses of Parliament, as something similar to what is expressed in their own language by the words noble and roiurier ; — while others, puzzled with the inexplicable phenomena occasionally arising from the boundless field of ambition opened in this fortunate island to every species of indus- try and of enterprise, have been led to conclude, that birth has, among us, no other value than what it derives from the privileges secured by the constitution to our he-
* Tills observation of Polybius has been very unjustly censured by Grotius. " Sod neque Polybli hie utorauctoritate,qulad mixtum genus reipublicsrel'ert llomanara rempublicanijqua; lllo tempore, si non actioncs ipsas, sod jus agcndi rc-picimus, more t'liit popularis : Nam et sonatus auctorilas, quam ad optimatum rcgimon refort, et consulura ([uos quasi legcs fuisso vult, subdita erat populo. Idem do alioruiii pulitica scrlbentlum scnlcntiis dictum volo, ijui magis cxtcrnam spccicm ot quotidianam ad- niiiiistiatiiinciii, fjuam jus ipsum summi imperii spectarc congruens ducunt suo lustituto." — (Do Jure Bolll ac I'aL-is, Lib. I. Cap. 3.) In reply to this criticism, it is sufficient to remark, that Polybius is not here speaking of the t/tcory of the Roman constitution, (about which there could be no diversity of opinion,) but of what common observers are so apt to overlook, — the actual state of that constitution, modified as it was by time, and chance, and experience. — Among the numerous commentators on Gro- tius, 1 recollect one only (llciiry do Coccoii) who lias viewed this question in its proper liglit. " Auctor inter ins, qui circa formas imperii falluutur, etiani Polybium refert, (jui rompublicam Uomanam suis teinporiliuH niixlam fuisse ait. At liene notandum, Polybium non lo(|ui do mixturi, status sed admuiis- tratioiiis : forma onim republica; erat mere popularis, sed administratio divisa fuit inter consules, sena- tum, et populum."
VOL. II. 48
378 NOTES AND ILLUSTRATIONS.
reditary legislators. Few perhaps but the natives of Great Britain are fully aware, how very remote from the truth are both these suppositions.
I transcribe the following passage from an article in the French Encyclopedic ; written by an author of some distinction both for talents and learning ; and which, it is not impossible, may be quoted at some future period in the history of the world, as an authentic document with respect to the state of English society in the eighteenth century. The writer had certainly much better access to information than was en- joyed by those to whom we are indebted for our experimental knowledge of the an- cient systems of policy.
" En Angleterre, la loi des successions attribue aux aines dans les families nobles les biens immeubles, a I'exclusion des cadets qui n'y ont aucune part. Ces cadets sans bien cherchent a reparer leurs pertes dans I'exercice du negoce, et c'est pour eux un moyen presque sur de s'enrichir. Devenus riches, ils quittent la profession, ou meme sans la quitter, leurs enfans rentrent dans tons les droits de la noblesse de leur famille ; leurs aines prennent le titre de milord si leur naissance et la possession d'une terre pairie le leur permettent. — II faut neanmoins remarquer, que quelque fiere que soit la noblesse Angloise, lorsque les nobles entrent en apprentissage, qui selon les reglemens doit etre de sept ans entiers, jamais ils ne se couvrent devant leurs maitres, leur pariant et tiavaillant tete nue, quoique souvent le maitre soit roturier et de race marchande, et que lesapprentifs soient de la premiere noblesse." — Encyclop. Method. Commerce, Tom. 3. Article JSToblesse.
Note (AA.) page 325.
" Metaphysicse pars secunda est finalium causarum inquisitio, quam non ut prseter- missam, sed ut male collocatam notamus. Solent eniminquiri inter physica non inter metaphysica. Quanquam si ordinis hoc solum vitium esset, non mihi fuerit tanti. Ordo enim ad illustrationem pertinet, neque est ex substantia scientiarum. At hsec ordinis inversio defectum insignem peperit, et maximam philosophias induxit calami- tatem. Tractatio enim causarum finalium in physicis, inquisitionem causarum phys- icarum expulit et dejecit, effecitque ut homines in istiusmodi speciosis et umbratilibus causis acquiescerent, nee inquisitionem causarum realium, et vere physicarum, strenue urgerent, ingenti scientiarum detrimento. Etenim reperio hoc factum esse non solum a Platone, qui in hoc littore semper anchoram figit, verum etiam ab Aristotele, Gale- no, et aliis, qui sEepissime etiam ad iila vada irapingunt. Etenim qui causas adduxe- rit hujusmodi, palpebras cum pilis pro sepi et vallo esse, ad munimentum oculorum : Aut coriujn in animalibus firmitudinem esse ad propellendos calores etfrigora: Aut ossapro columnis et trabibus a naturd induci, quibus fabrica corporis innita- tur : Aut folia arborum emitti, quofructus minus patiantur a sole et vento .- Aut nubes in sublimi fieri, ut terram imbribus irrigent : Aut terram densari et solidari, ut statio et manslo sit animalium : et alia similia : Is in metaphysicis non male ista allegarit ; in physicis autem nequaquam. Imo, quod coepimus dicere, hujusmodi sermonum discursus (instar remorarum, uti fingunt, navibus adhaerentium) scientiarum quasi velificationem et progressum retardarunt, ne cursum suum tenerent, et ulterius progrederentur : et jampridem effecerunt, ut physicarum causarum inquisitio neglecta deficeret, ac silentio prseteriretur. Quapropter philosophia naturalis Democriti, et aliorum, qui Deum et mentem a fabrica rerum amoverunt ; et structuram universi in- finitis naturaj prselusionibus et tentamentis (quas uno nomine fatu7n a,\itfortuna7n vocabant) attribuerunt ; et rerum particularium causas, materise necessitati, sine inter- mixtione causarum finalium, assignarunt ; nobis videtur, quatenus ad causas physicas, multo solidior fuisse, et altius in Naturam penetrasse, quam ilia Aristotelis, et Plato- nis : Hanc unicam ob causam, quod illi in causis finalibus nunquam operam trive- runt ; hi autem eas perpetuo inculcarant. Atque magis in hac parte accusandus Aristotiles quam Plato : quandoquidem fontem causarum finalium, Deum scilicet, omiserit, et naturam pro Deo substituerit, causasque ipsas finales, potius ut logicse amator quam theologiee, amplexus sit. Neque hffic eo dicimus, quod causae illaB finales verae non sint, et inquisitione admodum dignse in speculationibus metaphysi- cse, sed quia dum in physicarum causarum possessiones excurrunt et irruunt, misere earn provinciam depopulantur et vastant." — Be Augm. Scient. Lib. III. Cap. 4.
Note (BB.) page 333.
Among the earliest opponents of Descartes's doctrine concerning the Final Causes, was Gassendi ; a circumstance which I remark with peculiar pleasure, as he has been
NOTES AND ILLUSTRATIONS. 379
so unjustly represented by Cudworth and others, as a partisan, not only of the physi- cal, but of the atheistical opinions of the Epicurean school. For this charge I do not see that they had the slightest pretence to urge, but that, in common with Bacon, he justly considered the physical theories of Epicurus and Democritus as more analogous to the experimental inquiries of the moderns, than the logical subtilties of Aristotle and of the schoolmen. The followino; passage is transcribed in Gassendi's own words, from his Objections to the Meditations of Descartes.
" Quod autem aphysicd consideratione rejicis usum causarumjinalium, alia for- tassis occasione potuisses recte facere : at de Deo cum agitur, verendum profecto, ne prjBcipuum argumentum rejicias, quo divina sapientia, providentia, potentia, atque adeo existentia, lumine naturae stabiliri potest. Quippe ut mundum universum, ut coelum et alias ejus et praecipuas partes praeteream, undenam, aut quomodo melius argumentare valeas, quam ex usu partium in plantis, in animalibus, in hominibus, in te ipso (aut corpore tuo) qui similitudinem Dei geris ? Videraus profecto magnos quosque viros ex speculatione anatomica corporis humani non assurgere modo ad Dei notitiam, sed hymnum quoque ipsi canere, quod omnes partes ita conformaverit, collocaveritque ad usus, ut sit omnino propter solertiam atque providentiam incom- parabilem commendandus." — Objectiones Quintal in Meditationem IV. De Vera et falso.
I do not know if it has hitherto been remarked, that Gassendi is one of the first modern writers, by whom the following maxim, so often repeated by later physiolo- gists, was distinctly stated ; " Licet ex conformatione partium corporis humani, con- jecturas desumere adfunctiones merenaturales." It was from a precipitate appli- cation of this maxim, that he was lead to conclude, that man was originally destined to feed on vegetables alone ; a proposition which gave occasion to several memoirs by Dr. Wallis and Dr. Tyson, in the Philosophical Transactions of the Royal Society of London.
Note (CC.) page 344.
The theories of Hume, of Paley, and of Godwin, how differently soever they may have figured in the imaginations of their authors, are all equally liable to the fundamental objections stated in the text. The same objections are applicable to the generous and captivating, but not always unexceptionable morality inculcated in the writings of Dr. Hutcheson. — The system, indeed, of this last philosopher, may be justly re- garded as the parent stock on which the speculations of the others have been suc- cessively grafted.
Mr. Hume entered on his Inquiries concerning Morals, at a period when Dr. Hutcheson's literary name was unrivalled in Scotland. The abstract principles on which his doctrines are founded, differ widely from those of his predecessor, and are unfolded with far greater ingenuity, precision, and elegance. In various instan- ces, however, he treads very closely in Dr. Hutcheson's footsteps : and in the final result of his reasonings, he coincides with him exactly. According to both writers, a regard to general expediency affords the only universal canon for the regulation of our conduct.
It is a curious circumstance in the History of Ethics, that the same practical rule of life, to which Dr. Hutcheson was so naturally and directly led by his cardinal vir- tue of disinterested benevolence, has been inferred by Dr. Palej' from a theory which resolves moral obligation entirely into prudential calculations of individual ad- vantage. For the very circuitous, and (in my opinion) very illogical argument, whereby he has attempted to connect his conclusion with his premises, I must refer to his work.*
The Political Justice of Mr. Godwin is but a new name for the principle of gene- ral expediency or utility. " The term justice " lie observe, " may be assumed as a general appellation for all moral dut}'. — That this appellation," he continues, " is sulRcicntly expressive of the subject, will appear, if we consider for a moment, mercy, gratitude, temperance, or any of those duties which, in looser speaking, are
* Principles of Moral and Political Philosophy, Book ii. Chap. 1, 2, 3, 4, 5, 6.
The theory of Dr. Paley hag been very ably examined by Mr. Gisborne, in a treatise entitled tho Principles of Moral Philosophy investigated, and brielly applied to the Constitution of Civil Society. (London, 1790.) ITk) objections to it there stated appear to me quite unanswerable ; and they possess tho additional merit of being urged with all the detbronco «o justly duo to Dr. Paley's charactsr atid talents.
380 ]VOTES AND ILLUSTRATIONS.
contradistinguished from justice. Why should I pardon this criminal, remunerate this favor, abstain from this indulgence ? If it partake of the nature of morality, it must be either right or wrong, just or unjust. It must tend to- the benefit of the in- dividual, either without entrenching upon, or with actual advantage to the mass of individuals. Either way, it benefits the whole because individuals are parts of the whole. Therefore, to do it is just, and to forbear it is unjust. If justice have any meaning, it is just that I should contribute every thing in my power to the benefit of the whole."— PoZii. Justice, Vol. I. pp. 80, 81.
It is manifest, that, in the foregoing extract, the duty of justice is supposed to co- incide exactly as a rule of conduct with the affection of benevolence ; whereas, ac- cording to the common use of words, justice means that particular branch of virtue which leads us to respect the rights of others ; a branch of virtue remarkably distin- guished from all others by this, that the observance of it may be extorted by force ; the violation of it exposing the offender to resentment, to indignation, and to punish- ment. In Mr. Godwin's language, the woid justice must either be understood to be synonymous with general benevolence, or — assuming the existence of such an affec- tion— to express the moral fitness of yielding, upon all occasions, to its suggestions. " It is just," says Mr. Godwin, " that I should contribute every thing in my power to the benefit of the whole. — My benefactor ought to be esteemed, not because he bestowed a benefit upon me, but because he bestowed it upon a human being. His desert will be in exact proportion to the degree in which the human being was wor- thy of the distinction conferred. Thus, every view of the subject brings us back to the consideration of my neighbour's moral worth, and his importance to the general weal, as the only standard to determine the treatment to which he is entittled. Grati- tude, therefore, a principle which has so often been the theme of the moralist and the poet, is no part either of justice or virtue." (Ibid. p. 84.) The v/ords just and justice can, in these sentences, mean nothing distinct from morally ^^ ov reasonable ; so that the import of the doctrine amounts merely to the following proposition. That it is reasonable or right, that the private benevolent affections should, upon all occa- sions, yield to the more comprehensive ; — which is precisely the system of Hutche- son disguised under a different and much more exceptionable phraseology.
This abuse of words is not without its effect in concealing from careless readers the fallaciousness of some of the author's subsequent arguments; for although the idea he professes to convey by the term jMsfice, be essentially different from that commonly annexed to it, yet he scruples not to avail himself for his own purpose, of the received maxims which apply to it in its ordinary acceptation. In discussing, for example, the validity of promises, he reasons thus : " 1 have promised to do some- thing just and right. — This certainly 1 ought to perform. Why ? Not because I prom- ised it, but hecoMse justice prescribes it. I have promised to bestow a sum of money upon some good and respectable purpose. In the interval between the promise and my fulfilling it, a greater and nobler purpose offers itself, which calls with an imperi- ous voice for my co-operation. Which ought I to prefer? That which best deserves my preference. A promise can make no alteration in the case. I ought to be guided by the intrinsic merit of the objects, and not by any external and foreign con- sideration. No engagements of mine can change their intrinsic claims. If every shilling of our property, every hour of our time, and every faculty of our mind, have already received their destination from the principles of immutable justice, promises have no department left upon which for them to decide. Justice, it appears, there- fore, ought to be done, whether we have promised it or not." — Ibid. p. 151.
It is quite evident, that, in this passage, the paramount supremacy indisputably be- longing io justice in its usual and legitimate sense, is ascribed to it when employed as synonymous with benevolence ; and of consequence, that the tendency of the new system, instead of extending the province oi justice, properly so called, is to set its authority entirely aside, wherever it interferes with views of utility. In this respect, it exhibits a complete contrast to all the maxims hitherto recognised among moralists. The rules of justice are happily compared by Mr. Smith to the strict and indispensable rules of grammar ; those of benevolence to the more loose and general descriptions of what constitutes the sublime and beautiful in writing that we meet with in the works of critics. According to Mr. Godwin, the reverse of this com- parison is agreeable to truth ; while, at the same time, by a dexterous change in the meaning of terms, he assumes the appearance of combating for the very cause which he labors to betray.
Of the latitude with which the word justice had been previously used by many ethical writers, a copious and choice collection of instances may be found in the
JNTOTES ANB ILLUSTRATIONS. 381
learned and philosophical notes subjoined by Dr. Parr to his Spital Sermon. (Lon- don, 1801.) " By none of the ancient philosophers, however," as he has well ob- served, " is justice set in opposition to any other social duty ; nor did they employ the colossal weight of the term in crushing the other moral excellencies, which were equally considered as pillars in the temple of virtue." pp. 28, 29, 30, 31.*
Note (DD.) page 345.
As the main purpose of this section is to combat the logical doctrine which would exclude the investigation of Final Causes from natural philosophy, I have not thought it necessary to take notice of the sceptical objections to the theological inferences commonly deduced from it. The consideration of these properly belongs to some inquiries which I destine tor the subject of i separate Essay. On one of them alone I shall offer at present a few brief remarks, on account of the peculiar stress laid upon it in Mr. Hume's Posthumous Dialogues.
" When two species of objects," says Philo, "have always been observed to be conjoined together, I can infer, by custom, the existence of one wherever I see the existence of the other : and this I call an argument from experience. But how this argument can have place, where the objects, as in the present case, are single, indi- vidual, without parallel, or specific resemblance, maybe difficult to explain. And will any man tell me, with a serious countenance, that an orderly universe must arise from some thought and art, like the human, because we have experience of it ? To ascertain this reasoning, it were requisite that we had experience of the origin of worlds ; and it is not sufficient surely, that we have seen ships and cities arise from human art and contrivance. — Can you pretend to show any similarity between the fabric of a house, and the generation of the universe .' Have you ever seen Nature in any such situation as resembles the first arrangement of the elements ? Have worlds ever been formed under your eye ; and have you had leisure to observe the whole progress of the phenomenon, from the first appearance of order to its final con- summation ? If you have, then cite your experience, and deliver your theory."
This celebrated argument appears to me to be little more than an amplification of that which Xenophon puts into the mouth of Aristodcmus, in his conversation with Socrates, concerning the existence of the Deity. " I behold," says he, '• none of those governors of the world whom you speak of ; whereas here, I see artists actual- ly employed in the execution of their respective works." — The reply of Socrates, too, is in substance the same with what has been since retorted on Philo, by some of Mr. Hume's opponents. "Neither, yet, Aristodemus, seestthou thy soul, which, however, most assuredly, governs thy body ; although it may well seem, by thy man- ner of talking, that it is chance and not reason which governs thee."
AVhatever additional plausibility Philo may have lent to the argument of Aristode- mus, is derived from the authority of that much abused maxim of the inductive logic, that'' all our knowledge is entirely derived from experience." It is curious, that So- crates should have touched with such precision on one of the most important excep- tions with which this maxim must be received. Our knowledge of our own exist- ence as sentient and intelligent beings, is (as I formeily endeavoured to show) not an inference from experience, but a fundamental law of human belief. All that expe- rience can teach me of ray internal frame, amounts to a knowledge of the various mental operations whereof I am conscious ; but what light does experience throw on the origin of my notions of personality and identity ? Is it from having observed a constant conjunction between sensations and sentient beings ; thoughts and think- ing beings ; volitions and active beings ; that I infer the existence of that individual and permanent mind, to which all the phenomena of my consciousness belong ? Our conviction that other men are, like ourselves, possessed of thought and reason ; together with ail the judgments we pronounce on their intellectual and moral char- acteis, cannot (as is still more evident) be resolved into an experimental perception of the conjunction of different objects or events. They are inferences of design from
*riaving mentioned the name of tliis eminent person, I eagerly embrace the opportunity of acknowl- edging the instruction I have received, not only from liis various publications, but from tlie private literary communications witli whicli ho lias repeatedly favored mc. From one of these (containing animadversions on some passages in my Essay on tlie Su1)lime,) I entertain hopes of being permitted to make a few extracts in a future edition of that performance. By his candid and liberal strictures, I have fell mvsilf liiijlily honored; and should be proud to record, in his own words, the corrections lie has sunu'' si' d of i-rrtain critical and philological judgments, which, it is highly probable, I may havo too lightly hazarded.
382 NOTES AND ILLUSTRATIONS.
its sensible effects, exactly analogous to those whichj in the instance of the universe, Philo would reject as illusions of the fancy.*
But leaving for future consideration these abstract topics, let us, for a moment, at- tend to the scope and amount of Philo's reasoning. — To those who examine it with attention, it must appear obvious, that, if it proves any thing, it leads to this general conclusion. That it would be perfectly impossible for the Deity if he did exist, to ex- hibit to Man any satisfactory evidence of design by the order and perfection of his works. That every thing we see is consistent with the supposition of its being pro- duced by an intelligent author, Philo himself has explicitly acknowledged in these remarkable words : " Supposing there were a God, who did not discover himself im- mediately to our senses ; would it be possible for him to give stronger proofs of his existence, than what appear on the whole face of nature ? What, indeed, could such a Divine Being do, but copy the present economy of things ; — render many of his ar- tifices so plain, that no stupidity could mistake them ; — afford glimpses of still greater artifices, which demonstrate his prodigious superiority above our narrow apprehen- sions ; — and conceal altogether a great many from such imperfect creatures ? " The sceptical reasonings of Philo, therefore, do not, like those of the ancient Epicureans, hinge, in the least, on alleged disorders and imperfections in the universe, but en- tirely on tlie impossibility, in a case to which experience furnishes nothing parallel or analogous, of rendering intelligence and design manifest to our faculties by their sen- sible effects. — In thus shifting his ground from that occupied by his predecessors, Philo seems to me to have abandoned the only post from which it was of much im- portance for his adversaries to dislodge him. The logical subtilties, formerly quoted about experience and belief, (even supposing them to remain unanswered,) are but little calculated to shake the authority of principles, on which we are every moment forced to judge and to act, by the exigencies of life. For this change in the tactics of modern sceptics, we are evidently, in a great measure, if not whdfly, indebted to the lustre thrown on the order of nature, by the physical researches of the two last centuries.
Another concession extorted from Philo by the discoveries of modern science is still more important. I need not point out its coincidence with some remarks in the first part of this section, on the unconscious deference often paid to final causes by those inquirers who reject them in theory ; — a coincidence which had totally escaped my recollection when these remarks were written. I quote it here, chiefly as a pleasing and encouraging confirmation of the memorable prediction with which Newton concludes his Optical Queries ; that, " if JVatural Philosophy, in all its parts, by pursuing the inductive method, shall at length be perfected, the bounds of Moral Philosophy will be enlarged also."
" A purpose, an intention, a design," says Philo, " strikes every where the most careless, the most stupid thinker ; and no man can be so hardened in absurd systems as at all times to reject it. That JSfature does nothing in vain, is a maxim, estab- lished in all the schools, merely from the contemplation of the works of Nature, without any religious purpose ; and from a firm conviction of its truth, an anatomist, who had observed a new organ or canal, would never be satisfied till he had also dis- covered its use and intention. One great foundation of the Copernicajv system is the maxim. That JVature acts by the simplest methods, and chooses the most proper means to any end ; and astronomers often, without thinking of it, lay this strong foundation of piety and religion. The same thing is observable in other parts of philosophy : And thus all the sciences lead us almost insensibly to acknowledge a first intelligent author ; and their authority is often so much the greater, as they do not directly profess that intention."
* This last consideration is ably stated by Dr. Reid. (See Essays on the Intellectual Powers, pp. 631, 632, 4to. Ed.) The result of his argument is, that " according to Philo's reasoning we can have no evidence of mind or design in any of our fellow-men." — At a considerably earlier period, Buffier had fallen into the same train of thinking. Among the judgments which he refers to common sense, he as- signs the first place to the two following : " 1. 11 y a d'autres etres, et d'autres homines que moi au monde. 2. Jl y a dans eux quelque chose qui s'appelle verite, sagesse prudence," &c. &c. (Cours de Sciences, p. .566. Paris, 1732.) I have already objected to tlie application of the phrase common sense, to such judgments as these ; hut this defect, in point of expression, does not detract from the sagacity of the author in perceiving, that in the conclusions we form concerning th? minds and characters of our follow creatures, (as well as in the inferences drawn concerning the invisible things of God from the things which are made,) there is a perception of the understanding implied, for which neither rea- soning nor experience is sufficient to account.
NOTES AND ILLUSTRATIONS. 383
* P. 73.
Since this sheet was cast off, I have been informed from the best authority, that the conversation here alluded to, which I had understood to have taken place be- tween Lord Chief Justice Mansfield, and the late Sir Basil Keith, really passed be- tween his Lordship and another very distinguished officer, the late gallant and ac- complished Sir Archibald Campbell. I have not, however, thought it worth while, in consequence of a mistake which does not affect the substance of the anecdote, to cancel the leaf ; — more especially, as there is at least a possibility that the same ad- vice may have been given on more than one occasion.
APPENDIX.
Article I. (See page 117.) •
The following article relates entirely to the question, — " How far it is true, that all mathematical evidence is resolvable into identical propositions." The discus- sion may, in one point of view, be regarded as chiefly verbal ; but that it is not, on that account, of so trifling importance as might at first be imagined, appears from the humiliating inference to which it has been supposed to lead concerning the narrow limits of human knowledge. " Put the question," says Diderot, " to any candid mathematician, and he will acknowledge, that all mathematical propo- sitions are merely identical ; and that the numberless volumes written (for example) on the circle, only repeat over in a hundred thousand forms, that it is a figure in which all the straight lines drawn from the centre to the circumference are equal. The whole amount of our knowledge, therefore, is next to nothing.'' — That Diderot has, in this very paradoxical conclusion, stated his own real opinion will not be easily believed by those who reflect on his extensive acquaintance with mathemat- ical and physical science ; but I have little doubt, that he has expressed the amount of the doctrine in question, agreeably to the interpretation put on it by the great majority of readers.
As the view of this subject which I have taken in the text, has not been thought satisfactory by my friend M. Prevost, I have thought it a duty, both to him and to myself, to annex to the foregoing pages, in his own words, the remarks subjoined to the excellent and faithful translation with which he has honored this part of my work, in the Biblioth^que Britannique. Among these remarks, there is scarcely a proposition to which I do not give my complete assent. The only difference between us turns on the propriety of the language in which some of them are expressed ; and on this point it is not surprising, if our judgments should be somewhat biassed by the phraseology to which we have been accustomed in our earlier years. The few sentences to which I am inclined to object, 1 have distinguished from the rest, by printing them in small capitals. — Such explanations of my own argument as ap- pear to be necessary, I have thrown into the form of notes, at the foot of the page.
In the course of M. Pre vest's observations on the point in question, he has intro- duced various original and happy illustrations of the important distinction between conditional and absolute truths ; — a subject on which I have the pleasure to find, that all our views coincide exactly.
"A la fin de I'article que Ton vient de lire,* I'ingenicux autcur renvoie a ce qu'il a dit au commencement. II pense y avoir suflisammcnt prouve quo I'eAidcnce particulierc qui accompagnc Ic raisonncmcnt mathematiquc nc pent pas se resoudre dans la perception dc I'idcnlite. Recourons done a cctte preuve. Elle se trouve consister toute entiero on refutation.
" I. L'autcur commence par remarquer, que quelques ])crsonnes fondcnt I'opin- ion qu'il rejctte sur ceJle qui prend Ics axiomes pour premiers principes. Et coinme il a combattu celle-ci, il en conclut que sa consequence doit etre fausse. Un tel argument a en cfTel bcaucoup de force pour ceux qui sont partis d'unc ccrtaine the- crie sur Ics axiomes pour en conclure I'assertion contestec ; mais 11 n'cn a point pour les autres. Le redacteur dc cet article se range parmi ces derniers. II a dit et i
• Chap. II. Sect. 3. Art. II. of this volume.
VOL. II. 49
386 APPENDIX.
pense encore, que le math^maticien avance de supposition en supposition ; que c'est en letouinant sa pensee sous diveises formes, qu'il arrive a d'utiles resultats ; que c'est la reconnoissance de quelque identite qui autorise chacune DE sEs CONCLUSIONS ; et toutefois il a dit et il persiste a croire, que les axiomes raathematiques ne font que tenir la place ou de definitions ou de theoremes ; et que les definitions sont les seuls principes des sciences de la nature de la geoinetrie. Voici ces propres expressions.* ' J'observe que de bonnes definitions initiates sont les seuls principes rigoureusement suffisans dans les sciences de raisonnement pur
C'est dans les definitions que sont veritablement contenues les hypotheses
dont ces sciences partent On pourroit concevoir, [toujours dans ces memes
sciences,] que les principes fussent si nettement poses, que Ton n'y trouvat autre chose que de bonnes definitions. De ces definitions retournees, resulteroient toutes les propositions subsequentes. Les diverses proprietes du cercle que sont-
ELLES autre CHOSE, QUE DIVERSES FACES DE LA PROPOSITION QUI DEFINIT
CETTE COURSE .' — C'est donc I'imperfection (peut-etre inevitable) de nos concep- tions, qui a engage a faire entrerles axiornes pour quelque chose dans les principes des sciences de raisonnement pur. Et ils y font un double office. Lesunsremplacent des definitions. Les autres remplacent des propositions susceptibles d'etre demontrees.'
" II est manifeste que celui qui a tenu de tout temps ce langage n'a pas fonde son opinion, vraie ou fausse, relativement a I'evidence mathematique, sur une opinion fausse relativement aux axiomes ; ou du moins, qu'etant si parfaitement d'accord avec Mr. Dugald Stewart en ce qui concerne les premiers principes des mathema- tiques, ce n'est point de la que derive I'apparente discordance de ses expressions et de celles de son ami, sur ce qui concerne le principe de I'evidence mathematique dans la deduction demonstrative. Des lors il est evident que ce premier argument de I'auteur reste pour lui comme nul.
" IL Passons au second. Celui-ci est encore purement negatifet personnel. li s'addresse a ceux qui derivent, d'un principe propre a la geometric, I'assertion que I'auteur combat. De ce que I'egalite en geoinetrie se demontre par la congruence, ces philosophes se pressent de conclure, que, dans toutes les mathematiques, les verites reposent sur I'idenlite. Ceux donc qui n'ont jamais songe a donner un tel appui a I'assertion contestee ne peuvent absolument pas se rendre a I'attaque dirigee centre cet appui. II est probable qu'un tres-grand nombre de partisans du principe de I'identite, considere comme base de la demonstration, se trouvent (comme le ledacteur peut ici le dire de lui-menie) tout a fait etrangers a la maniere de raisonner que I'auteur refute ; et n'ont point forme leur opinion relativement a I'evidence ma- thematique d'apres la congruence (reelle ou potentielle) de deux espaces. C'est ce que le redacteur affirme ici, quant a lui, de la maniere la plus positive ; et de la re- sulteque I'argument personnel, f dirige contre ceux qui ontete menes d'une de ces opinions a I'autre, ne I'atteint point.
" II est un peu plus difficile de prouver cette affirmation, que quand il etoit ques- tion des axiomes, parce que ceux-ci ne peuvent pas manquer de s'offiir aux recher- ches du logicien, au Hen qu'il n'est pas appelle a prevoirl'application inconsideree du principe de superposition a toute espece de demonstration. Si cependant il fait voir que son opinion sur la demonstration derive de principes universels et tout differens de celui qu'ona > n vue, il aura fait, je pense, toutce qu'il est possible d'attendre de lui.
" Qu'il soit maintenant permis au redacteur de quitter la tierce personne, et pour eviter quelques longueurs et ruelques expressions indirectes, d'etablirnettement son opinion et la marche qu'il a tenue en I'exposant.
" Des les premieres pages de ma logique, je pars de la distinction a faire entre les deux genres de verite ; la conditionelle et Vabsolue. Puis j'ajoute :
" Le MOYEN unique, par LEQUEL nous CONNOISSONS si une PROPOSITION CON- DITIONNELLE EST VRAIE, OU I.E CARACTERE d'uNE TELLE VERITE, EST l'iDENTITE BIEN ETABUE ENTRE LE PRINCIPE ET LA CONSEQUENCE. CeTTE IDENTITE n'eST pas COMPLETE SANS DOUTE ; MAIS ELLE EST TELLE A QUELQUE EGARD, QUE LA CONSEQUENCE DOIT ETRE TOUTE ENTIERE COMPRISE DAKS LE PRINCIPE." \
* Essais de Philos.Tom. II. p. 29, a Geneve, chez Paschoud, 1804.
t Adhominem.
j Essais de Phil. Tom. II. p. 2. " Le lecteur equitable voudra bien se rappeler que I'ouvrage, dont ce passage est tire, n'est que I'esquisse d'un cours fort etendu, dans lequel se trouvent developpes, par des exemples et de toute maniere, les sim- ples enonces du texte. A peine est-il necessaire de dire ici en explication ce que
APPENDIX. 387
" Traitant ensuite des sciences selon leur genre, j'appelle sciences de raisonne- ment pur ceWcs qui ne s'occupent que de la veiite conditionelle. Je cherche, d'une maniere geneiale etabstiaite, les caracteres de ces sciences. J'en fais ensuite I'ap- plication aux mathematiques dans les deux branches qu'elles comprennent ; et c'est par cette vote, que je me trouve avoir determine la nature de la demonstration. J'ai soin du reste de faire remarquer que la nature du raisonnement pur, ou proprement dit, ne depend nullement du sujet, et qu'il n'est propre aux mathematiques qu'en ce sens que ces dernieres s'occupent dc raisonnement d'une maniere exclusive et n'y melent point des propositions de veiite absolue, comrae font les sciences de/az7 ei d" experience. En voilaassez, je crois, pour faire voir que ce n'est pas temerairement quej'affirme n'avoir enaucune fao,on concu la nature de la demonstration d'apres le point de vue borne de la superposition. Je ne puis done, quant a moi, donner mon assentiment a un argument qui n'attaque que ceux dont I'opinion a cette base.
" III. On est toujours long quand on refute une refutation. J'aurois done tort de m'etendre au-dela de ce qui est strictement necessaire pour etablir nettement I'etat de la question. Je ne discuterai pas des opinions qui me sont etrangeres, telles que celles de Leibnitz, de I'auteur d'une Dissertation latine imprimee a Berlin en 1764, de Barrow, Condillac, Destutt-Tracy. II me suffit d'avoir repondu, pour moi et pour ceux qui pensent corame moi, aux deux seuls argumens de I'auteur, contre I'opinion que j'ai des long-temps adoptee.
" J'ajouterai cependant un mot au sujet d'une remarque, que I'auteur introduit en disant, qu'elle est applicable a toutes les tentatives que Von a faites j)onr etablir I'opinion dontils'agit. ' Accordant,' difil, ' que toutes les propositions mathemati- ques puissent etre representees par la formule a=a, il ne s'en suivroit nullement que chaque pas du raisonnement, qui conduit a ces conclusions, soit une proposition de meme nature.' Je prie I'auteur de cette objection de vouloir bien reHechir un in- stant sur le sens du mot pas ramene a son expression propre et non figuree. Cer- tainement un pas dw raisonnement n'est autre chose qu'une proposition. Si done on accorde que toute proposition est representee par a^^a, il faudra bien que toutpas soit de meme nature.*
" Quant a la lettre chiffree, certainement clle differe de la nonchiffree quant aux signes ecrits ; comme aussi les plus exageres partisans du principe de I'identite ne nieront pas que I'expression deux plus deux ne soit differente de I'expression quatre. Dans I'un et I'autre cas le signe differe, le sens que Ton a en vue est le meme.
" IV. Les observations precedentes ont pour but de prouver que, dans les pro- cedes de raisonnement, (precedes que les mathematiques ofTrent degages de tout melange,) on deduitles consequences en s'appuyant constamment sur le peincipe d'identite. Je dois dire un mot maintenant de la raison pour laquelle je crois ne- cessaire d'etablir solidement ce principe et de la mettre au-dessus de tout attaque. Cette raison est, qu'a I'instant oii on le perd de vue, on court risque de confondre deux genres de verites, que nous savons tous qu'il faut distingucr. Ce qu'il importe
j'entends par I'identite complete ou non complete entre le principe etsa consequence. Si je conclus, par example, du genre a I'especc, il y aidcntite incomplete ; comme lorsqu'ayant prouve une verite de tout polygene, je I'affirme du triangle en particu- lier. II y a identite complete dans une equation. Et on entend bien que I'identite dont il s'agit est celle dc la quantite, (du nombre des unites,) et non de toulc autre. Ces deux exemples me semblent suffire pour prevenir toute equivoque."
* That the word pas ov step is a figurative expression, when applied to a process of reasoning, cannot be disputed ; and the same remark may be extended to the word proposition, and to almost every other term employed in discussions connect- ed with the Human Mind. It maybe doubted, however, whether it can be correctly asserted, that a step of reasoning differs in no respect from -a proposition. In our language, at least, the word sttp properly denotes, not a proposition, but the transi- tion to a new proposition from others already known. Thus, when I say, " the area of a triangle, having the circumference of a circle for its base, and the radius for its altitude, is greater than the area of any polygon inscribed in the circle," I enunciate a proposition. When I say, that '' tlie area of the same triangle is less than that of any circumscribed polygon," I enunciate another proposition. But when I infer from these two propositions, that the areas of the triangle and circle are equal, I ob- tain possession of a new truth distinct from either ; nor is it easy to imagine a more significant metaphor for expressing this acquisition, than to say, that 1 have advanced or gained a step in the study of geometry.
388 APPENDIX.
de prevenir, c'est le passage inapercu du relalif k I'absolu ; c'est une conclusion vici- euse, deduite regulierement d'une hypothese, et temerairement appliquee a ce qui est independant de cette hypothese. Ce sophisme, qui parolt grossier, a neanmoins ete commis plus d'une fois et le sera, dans quelques occasions deceptrices, par ceux qui n'auront pas pleinement analyse le travail du raisonnement. ■
" Tout se reduit, sans doute, en fait de raisonnement, a reconnoitre que la conse- quence est bien deduite du principe. Mais quel est le caractere auquel on reconnoi- tra que cette deduction a ete bien faite ^ C'est ce que ne disent pas ceux qui rejet- tent le caractere de I'identite. Et j'avoue que je ne con(^.ois pas quel autre on pour- roit tenter d'y substituer. Celui-la est simple et clair.* On peut, a chaque proposition, s'arreter pour voir si elle n'est que le developpement d'une precedente ; et si, par inadvertance on sort du genre, en melant des fails aux hypotheaes, on est ramene forcement a celles-ci.
" Si Jean Bernouilli et Leibnitz avoient reconnu leurs hypotheses aussi nettement qu'Euler les reconnut plus tard, ils n'auroient pas ete divises d'opinion sur la nature des logarithmes des noinbres negatifs et irnaginaires. Si Huyghens n'avoit vu, dans le travail du mathematicien, que le retournement de ses propres hypotheses, il ne se seroit pas servi peut-etre de I'expression que rapporte Leibnitz. Ce dernier lui ayant montre, qu'une quantite melee d'imaginaires pouvoit etre convertie en quantite reelle, ' Huyghens,' dit Leibnitz, ' trouva cela si admirable, qu'il me repondit qu'ily a la-dedans quelque chose qui nous est incomprehensible.' f
" Je connois un professeur de logique, qui a coutume, dans ses cours, d'embarras- ser a dessein ses eleves par des questions relatives aux rapports des quantites nega- tives et positives. Si un paradoxe les arrete, ils se tiennent pour avertis, qu'il ne peut y avoir dans les consequences, que ce qui est implicitement contenu dans le principe ; et ils se donnent le soin de bien affermir celui ci, je veux dire, de le reduire a des termes parfaitement clairs ; apres quoi, il ne leur en coute point de lever les difficultes. Mais si Ton n'est pas bien preoccupe de cette verite fondamentale, on ne saura a quoi imputer I'anonialie, ou I'apparente contradiction, des consequences.
" Personne n'adoiire plus sincerement que je ne fais le genie de Jaq. Bernouilli, qu'il a si heureusement applique a la theorie des probabilites ; et je ne fais certaine- ment aucune injure a sa memoiie, en le produisant comme un exemple de la facilite avec laquelle le mathematicien, seduit par ses belles decouvertes, oublie un instant quel est le genre de verite qui lui est propre. J'ai en vue la derniere reflection de son Art de conjectiirer. D'une formule (tres-belle sans doute et tres-ingenieuse) par laquelle ce profond penseur a apprecie la probabilite d'approcher du rapport des causes en multipliant les effets ; tout-a-coup il conclut a la regularite des lois qui gouvernent I'univers. J
" On ne me reprochera pas d'avoir tire mes exemples des ecrits de quelques rai- sonneurs mediocres ; etl'on voudrabien croire, que si j'avois voulu puiser a de telles sources, j'aurois eu beaucoup de facilite a multiplier mes citations.
" Je pense done enfin, qu'il faut que celui qui travaille dans les sciences de raison- nement pur soit bien averti, qu'il ne fait autre chose que retourner ses hypotheses, et que c'est la le seul moyen de prevenir des erreujs assez dangereuses. L'opinion que jesoutiens n'est done point simplement une affaire de speculation, dont il me seroit aise de faire le sacrifice ; c'est une regie pratique qui doit servir de base a la partie dela logique qui s'occupede cette espece de verite.
" V. Je dirai maintenant pourquoi, attache, comme je le suis, au principe de l'identite, je crois neanmoins pouvoir esperer de ne differer qu'en apparence de I'excellent philosophe qui rejette ce principe. C'est parce que nous pensons I'un etl'autre que les definitions sont les vrais principes desmathemaliques, etque toutle reste en derive. C'est la sans doute I'objet principal. Et je m'assure, cue quand ce philosophe viendra a discuter (avec plus de detail que son sujet ne I'appelloit ale
* Would it not be still simpler and clearer to caution mathematicians against ever losing sight of the distinction between absolute and hypothetical truths ?
f Leibnitz, Opera, Tom. IIL p. 372. Lettre a Varignon.
i " Unde tandem hoc singulare sequi videtur, quod si eventuum omnium observa- tiones per totam ieternitatem continuarentur, (probabilitate ultimo in perfectam certi- tudinemabeunte,) omnia in mundo certis rationibus et conslanti vicissitudinis lege contingere deprehenderentur ; adeo ut, etiam in maxime casualibus atque fortuitis, quandam quasi necessitatem, et, ut sic dicam, fatalitatem agnoscere tencamur ; quam nescio annon Plato intendere voluerit, suo de universali rerum apocatastasi dogmate," etc. Art. conj. p. 4, line.
APPENDIX. 389
faire) le vrai caractere de la bonne deduction, il finira par admettre, sinon les memes expressions, du moins au fond le meme principe que j'emploie.
" Je vols en efFet, et par son ouvrage et par sa correspondance, que ce sont les ex- pressions sur-tout qu'il censure ; et quant a ce point la, je serai tres-dispose a y ap- porterles changemens qu'il voudra bien lui-meme me suggerer, pourvu toutefois qu'elles rendent correctement ma pensee.
" Ainsi apres lui avoir expose, dans une lettre, mes idees au sujet du principe d'identite, j'ajoutois : ' Tout cela revient a dire, que la consequence est contenue toute entiere dans le principe. Ne pourroit-on pas donner a toutes les propositions mathematiques cette tournure : Dire telle chose, c'est dire telle autre chose ? ' Mr. Dugald Stewart me repond la-dessus : 'Je suis paifaitement d'accordavec vous, quant a I'esprit et a la substance de votre remarque. Celui qui admet la definition ouV hypothdse ne pent pas nierses diverses consequences logiques, pourvu qu'il soit en etat de comprendre chaque pas de la marche par laquellele principe et les conse- quences sont lies ensemble. Je ne suis pas siir toutefois que, pour le gros des lec- teurs, vous ne presentiez pas cette proposition d'une maniere trop concise et trop fig- uree, quand vous dites que la consequence cstcontenue dans le principe, ou qu'afiirra- er I'une c'est affirmer I'autre. Tout au moins je pense qu'il y a lieu de craindre que ces expressions ne suggerent de fausses idees a ceux qui ne prendront pas garde au sens precis que vous donnez aux mots que vous employez.' Je suis done tout pret a remplacer le mot contenue par un equivalent. Mais ce mot me semble pris ici dans un sens familier aux logiciens ; car c'est precisement ainsi que Ton dit com- munement que I'espece est comprise dans le genre.*
" Un autre mot, que releve Mr. Dugald Stewart, est celui de proposition identi- que.\ II me fait remarquer, que plusieurs bons logiciens ont appelle de ce nom les propositions qui ne font que repeter le meme mot aux deux termes, (A est A,) et qu'ils designent ces propositions comme inutiles et nugatoires. Je renoncerai sans discussion, sur I'autorite de ces logiciens, a I'expression que j'ai adoptee, quoique je puisse opposer autorite a autorite. Mais je desire conserver un mot qui exprime, de maniere ou d'autre, ma pensee. Comme dit Campbell, J cette phrase ' quatre est quatre,' n'offie qu'une proposition inutile et veritablement nugatoire. Mais dire ' deux fois deux font quatre,' c'est presenter la meme idee sous deux faces ; et un tel travail est, comme on salt, fort utile. Je m'etois accoutume a appeller tautologi- qiies les premieres, et identiques les secondes. Je suis tout pret a changer cette habitude, pourvu que Ton me fournisse un mot a substituer.§
* " Si Ton pent dire que la notion de triangle est comprise dans cello de polygene, on pourra dire de certaines propositions sur les triangles qu'elles sont comprises dans leurs analogues sur les polygenes. Si done on a prouve, par example, que dans tout polygene, les angles exterieurs sont egaux a quatre droits, on pourra de ce principe tircr la consequence pour les triangles. Et cette consequence semble pouvoir etre dite contenue dans son principe."
With this remark I perfectly agree ; for he who knows the general theorem, is in actual possession of all its particular cases ; insomuch that, after this theorem has been once brought to light, no other person can afterwards lay claim to any one of the cases as an original discovery. After it had been demonstrated, for instance, that in every rectilineal figure, the exterior angles are equal to four right angles, no geometer could well think of announcing, as a new proposition, that the same theo- rem holds with respect to every triangle. The particular cases, therefore, may all be said, with perfect propriety, to be contained in the general theorem. But how widely docs this differ from the meaning annexed to the same word, when it is said, that all the properties of the circle, whether discovered or undiscovered, are contain- ed in Euclid's definition of that curve !
t " Mr. Dugald Stewart reproche aussi quclque part au mot d'identite d'etre em- prunte des scolastiques, mais ce n'est point la une tache a mon avis ; car (comme disoit Leibnitz en parodiant un mot de Virgile) il y a de Tor dans ce fumier. De plus en Anglais on pourroit peut-ctre se passer de ce mot, en Fran(jais on ne le pent pas. Nous parlous une languc timide, qui s'cffraie du moinilre neologisme."
I Voyez Bibl. Brit. p. ;32 de ce volume.— Littcrat. Vol. LVIII. No. 3, Mars 1S15.
<§i Tiie distinction marked in the above |)assage, between tautological and identical propositions is precise and important ; but the meaning annexed to the latter cijithct does not appear to me agreeable to established use ; according to which, identical propositions arc exactly of that description to wliich the name of tautological is
390 APPEIVDIX,
" Enfin Mr. Dugald Stewart joint a ces critiques une remarque, qui fait voir qu'un des motifs, pour lesquels il s'est eleve contre le principe d'identite, est la crainte qu'il n'entraine dans quelques consequences fausses ou meme dangereuses. Voici comrae 11 s'exprime sur la fin de la lettre, dont je viens d'extraire les observations preceden- tes : 'A toutes ces propositions, comme vous les entendez, je souscris sans difficulte. Mais n'est-il pas a craindre qu'elles ne fassent naitre dans I'esprit de quelques lec- teurs des idees differentes de celles que vous y attachez ? Et n'ont-elles pas une tendance a donner un air paradoxal a une doctrine, qui, lors-qu'elle est proposee d'une maniere un peu pleine, ne donne aucune prise au doute ou a I'hesitation ? Quelle etrange consequence a ete tiiee de I'usage de ce mot identity, par un philo- sophe, tel que Diderot ! Interrogez, dit-il, des mathematiciens de bonne foi, et Us vous avoueront que leurs propositions sont toutes identiques ; et que tant de vo- lumes sur le cercle,par exemple, se reduisent a nous repeter en cent mille faqons differentes, que c^est une figure, oic toutes les lignes tirees du centre a la circonfe- rence sont egales. Nous ne savons donc presque rien.' *
" Cette derniere conclusion, a laquelle arrive Diderot, est d'autant plus etrange, comme le dit celui qui la cite, qui c'est precisement parce que les mathematiques travaillent sur la verite conditionnelle, qu'elles sont douees d'une pleine certitude, ainsi que j'ai tache de la faire voir ailleurs,f et que c'est par consequent a ce titre qu'elles meritent eminemment le nom de science. Mais de ce qu'un philosophe, tel que Diderot, s'est egare dans une consequence a laquelle sans doute il aspiroit, je ne crois pas que Ton doive conclure a la necessite de changer un langage philosophique et conforme a la verite. Si ce langage a une apparence de paradoxe, ce que je ne sens pas, il faut tacher de la reformer, a quoi je suis bien dispose a cooperer.
" Dans tout le volume que j'extrais, il n'est plus question de la discussion qui vient de nous occuper. Je ne crois pas en consequence avoir occasion d'y revenir. Ce n'est pas meme sans regret, et sans une sorte de repugnance, que je I'ai entreprise. Je ne la terminerai pas sans rapeller encore une fois que I'espece d'opposition qui regno entie nos opinions est moins reelle qu'apparente, et que Mr. Dugald Stewart a juge lui-meme que c'etoit sur les mots que nous differions, plutot que sur le fond des choses."
Article II. (See page 222.)
For the contents of this Article, as well as of the former, I am indebted to M. Pre- vost. They are extracted from a letter, dated Geneva, 9th April 1815. — My readers ■will thus be put in possession of the opinion of my learned friend on the only two questions of any moment which we have had occasion to discuss in the course of our long literary correspondence. The difference between us in both instances, I per- fectly agree with him in thinking, is more apparent than real.
here applied. I have looked into every book of logic within my reach, and find their language on this subject perfectly uniform. Locke defines identical proposi- tions to be those in which a term is affirmed of itself ; and he gives as instances, " a soul is a soul," " a spirit is a spirit," " a law is a law," " right is right," and " wrong is wrong." — The definition of identical propositions given by Crousaz coincides ex- actly with that of Locke : " Quando sulyecti et attiibuti sedem idem occupat termi- nus, eodem sensu prorsus veniens ; propositio talis dicitur identica ; et nugatoria est." — Condillac, one of the highest authorities, certainly, among French logicians, expresses himself in the same manner, " Tout le systeme des connoissances hu- maines peut etre rendu par une expression plus abregee et tout-a-fait identique : les sensations sont des sensations. Si nous pouvions, dans toutes les sciences, suivre egalement la generation des idees, et saisir le vrai systeme des choses, nous verrions d'une verite naitre toutes les autres, et nous tronverions I'expression abregee de tout ce que nous saurions, dans cette proposition identique ; le meme est le MEME." Does not the last of these propositions, as well as the first, fall under the class of tautological or nugatory propositions .' and, if this be the case, will it not follow, that the assertion which gave rise to this discussion requires some modifica- tion ? — " C'est en repetant sans cesse, le meme est le m6me, que le geometre opere tous ses prodiges."
* Lettre sur les Aveugles.
f Des Signes, p. 15 et 25 et suiv. — Essais de Philos. Tom. 11. p. 12 et 13.
APPENDIX. 391
" Mais il y a une autre question sur laquelle nous differons, ou du moins nous
ne nous exprimons pas de meme. C'est ce qu'etablit d'une manieie positive, et dans des expressions bien honorables pour moi, la note qui se trouve au bas de la page 311 1 de ce meme 2d volume de vos Elem. of the Phil. &.c. — Ce qu'il y a de singu- lier, c'est qu'encore ici, j'ai lieu de cioire que notie dissentitnent est moins reel qu'cpparent, et que la controverse sur ce point n'est pas moins verbale que sur I'autre, peut-etre plus, ou du moins plus evidemment telle. La chose vaut la peine d'etre eclaircie. — Et d'abord, vu la distance qui nous separe, oserois-je vous prier de relire ici ce que je dis a la page viii et ix de ma preface a la traduction de votre premier volume. Vous y verrez que je n'etablis, aucune difTerence entre nous relativement a la nature des causes physiques.* En citant a la p. 311 f du 2d vol. les deux phrases auxquelles vous reduisez mes opinions a ce sujet, il vous a echappe que la premiere de ces phrases etoit modifiee par celle qui la suit et que vous avez omise. Cette mo- dification est tout-a-fait essentielle. ' Si Ton analyse le mot force ou 6nergie, et qu'on se borne aux causes naturelles ; on verra que cela signifie que I'effet suit con- stamment la cause par quelque loi de la nature." Dans mes cours d'enseignement, j'insiste beaucoup sur cette definition, a laquelle je ne crois pas que (dans vos idees telles que je les connois) vous ayez rien a objecter. Ellepresente en eflfet le meme caractere des causes physiques que Hume et vous ; et elle repond en meme temps a une difficulte de Keid, tres-fondee si on n'y met aucune limite. Est-il besoin avec vous de details et d'exemples .' Je ne le pense pas. Cependant la crainte d'etre obscur me f'era ajouter un mot. A la nouvelle lune de Mars, les Mahometans se tiennent prets a voir, et des qu'ils I'apercjoivent ils jettent un cri. Ce cri est bien un signe, mais non une cause de I'apparition que j'aurai devant les yeux en les tournant vers le ciel. II precede, mais ce n'est pas en vertu d'une loi. Reciproquement, ua corps electrique etant frotte un autre corps s'en approche, je dis indifTeremment que I'un de ces corps attire I'autre, ou que I'electricite est cause de ce mouvement. C'est que ces faits se suivent en vertu des lois de I'electricite. Et il est entendu que I'on remonte, tant que Ton pent, de cause en cause. Ainsi Ton pourroit demander la cause de I'electricite ; comme on pourroit demander celle de la fievre,qui elle-meme est cause du delire, &c. &c. Je dis done que nous sommes pleinement d'accord sur la nature des causes physiques, a moins (ce que je ne prevois pas) que vous ne me contestiez la distinction que j'etablis entre cause et signe. — Le point sur lequel nous ne sommes pas d'accord (et oii j'ai contre moi, outre vous, plusieurs nobles autorites) est une question de physique pure ; savoir : la cause de la gravitation est-elle au nombre de celles dont on doit s'occuper ? Persistons a cet egard chacun dans notre opinion. II est probable que ce champ de discussion ne nous engagera pas dans une controverse directe, et je m'en feliciterai. — Je passe a remarquer la difTerence entre loi et cause. Une loi est un rapport, ou mieux, un rapport de rapports, une propor- tion. C'est une chose theorique ; c'est une generalisation ; une loi ne pent ao-ir. II faut done un agent ; une cause, pour realiser un changement. Exemple. "' Si le
* Page 222 of this edition.
f The passage here referred to by M. Prevost is as follows :
" Je n'entend pas toutefois souscrire implicitemcnt a toutes les opinions de I'auteur. Je me suis prescrit dans cette traduction de rendre fidelement ses pensees, et je n'aj pas cru devoir toujours lui opposer les miennes, dans les cas rares ou je ne me trouvois pas d'accord avec lui. J'en donnerai un seul exemple. L'auteur envisage comme contraire aux principes d'une saine philosophic la recherche de la cause ou du me- canisme de la gravitation. Ceux qui ontconnoissance des travaux entrepris et execu- tes par G. L. Le Sage sur cette matiere, savent qu'une telle recherche est compatible avec la methode philosophique la plus rigoureuse. Je suis pleinement d'accord avec M. Stewart, quant a la regie generale a laquelle cette maxime particuliere se rapporte. II y a une limite, que le philosophe doit reconnoitre, et au-dcli de laquelle il ne doit pas pousser ses recherches. Maisje differe sur la place ou cette limite doit etre posee ; en convenant toutefois, que la recherche du mecanisme de la gravitation a ete I'occasion d'une multitude d'erreurs, et que c'est un veritable ecueil qui doit etre soigneusement evite par ceux qui debutent dans la carrlere des sciences pliilosophi- ques. Quoique cette question soit tres intcrcssante en physique, elle Test moins en metaphysique, ou plutot en logique ; puisque dans cette derniere science ce n'est qu'un exemple d'une regie qui a beaucoup d'applications. Par cette raison, je ra'ab- stiendrai d'cntrcr ici dans la discussion de ce point conteste."
II Page 222 of this edition.
392 APPENDIX.
pole nord d'un aimant est approch6 du pole sud d'un autre aimant, il y a attraction.' C'est une loi. Mais ce simple enonce ne produit rien. Maintenant j'ai sur ma table deux aimans, j'oppose leurs poles antagonistes ; la cause y est; I'attraction (ou approche) suivra d'apres la loi. — J'ai risque de proposer que le mot agent fut plus particulierement consacre aux causes impulsives, parce-qu'elles sont celles qui pro- duisent des phenomenes tres cominuns, tres-bien discutes, et universels. Je n'ai propose cela qu'avec une expression de doute ; et je n'ai rien a dire a ceux qui s'y refusent. — Pour mieux montrer que la distinction de loi et cause est necessaire en physique, j'userai d'un example. Un homme, venu de je ne sais ou, voit un cheval qui traine un chariot ; mais il n'aper^oit point les traits. A chaque pas que fait le cheval, il voitle chariot avancer.* II en conclut que le cheval est cause du mouve- ment du chariot. II penetre plus avant et trouve les traits ; il reconnoit que ce mouvement se rapporte a I'impulsion. Tout cela suppose qu'il connoit les lois de celle-ci. Le cheval est une cause, le trait est une cause plus reculee. C'est celle-ci que j'appellerois un agent. Mais pour cette derniere denomination je ne dois pas tropy retenir. — Quant a la fiction de Boscovich, purement hypothetique ; j'avoue que je ne vois pas qu'elle soit d'un grand poids en faveur de ceux qui inculpent la recher- che de la cause dela gravitation. J'aurois sur ce sujetplus a dire ; mais comme c'est purement un point de physique, il me semble que je puis ici m'en abstenir."
* " II est entendu que ce fait se repete souvent d'une maniere uniforme sur plusieurs chariots pareils et iterativement sur chacun."
END OF VOL. II.
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