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HANDBOUND AT THE
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UNIVERSITY OF TORONTO PRESS
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BOHN'S CLASSICAL LIBRARY.
THE
ORGANON, OR LOGICAL TREATISES,
ARISTOTLE
THE
ORGANON, OR LOGICAL TREATISES,
ARISTOTLE.
WITH
l1
THE INTRODUCTION OF PORPHYRY,
LITERALLY TRANSLATED, WITH NOTES, SYLLOGISTIC EXAMPI ES, ANALYSIS, AND INTRODUCTION.
BY
OCTAVITJS FREIRE OWEN, M. A.
OF CHRIST CHURCH, OXFORD. RECTOR OF BURSTOW, SURREY; ASD DOMESTIC CHAPLAIN TO THE DUKE OF PORTLAND.
IN TWO VOLUMES. VOL. I.
LONDON: GEORGE BELL & SONS, YOKE STKELT, COVENT .GAUDtN. 18H0.
NOV - 7 1988
DAI-
LONDON :
PRINTED BY WILLIAM CLOWES AND SONS, LIMITED, STAJIFOUD STKEBT AND CHARING CKOSS.
6
VI
INTRODUCTION.
The investigation of the science of Mind, especially as to its element, Thought, is of so interesting a charac- ter as in great measure to reconcile the inquirer to the abstruseness of formal reasoning. The beauty of the flower, whilst concealing the ruggedness, is apt to with- draw our attention from the utility, of the soil on which it grows ; and thus in like manner the charms of Idealism, ending but too frequently in visionary specu- lation, have obstructed the clear appreciation of the design and use of Logic. Not that we deny the con- nexion which must ever subsist between Logic, as the science of the laws of reasoning, and psychology ; in- ^/ deed the latter is constantly introduced in several topics of the Organon ; but if we would derive real practical benefit from logical study, we must regard it as enun- ciative of the universal principle of inference, affording a direct test for the detection of fallacy, and the estab- lishment of true conclusion.
IV INTRODUCTION.
Wherefore, while primarily connected with the laws of Thought, Logic is secondarily and practically allied to language as enunciative of Thought. To enter into the mental processes incident thereto, though so tempt- ing a theme as already to have seduced many from the direct subject of the science, would far exceed the limits of this Introduction. We shall therefore content ourselves with a few observations upon the utility of the study connected with the Organon itself.
It is a quaint remark of Erasmus, that the human un- derstanding, like a drunken clown lifted on horseback, falls over on the farther side the instant he is supported on the nearer ; and this is the characteristic of human praise and censure. From an ignorant and exaggerated notion of its purport, Logic, instead of being limited to its proper sphere, was supposed commensurate with the whole investigation of abstract truth in relation to matter, cause, and entity, — in fact, the substance of a folio volume, describing every phase of human life, compressed into a few pages of Boethius and Aldrich. Thus, not having effected what nothing short of a mi- raculous expansion of the understanding could effect, it sunk into insignificance, until recently vindicated, and placed upon its proper footing, by Whately, Mansel, and others.
It is true that, whether viewed as an art or a science,
INTRODUCTION. v
Logic does not solve the origin of mental conception; but it furnishes the rules on which all reasoning is constructed ; and it would be strange indeed if we re- fused the practical assistance of surgery because it does not exhibit in theory the operation of will upon matter. We may learn Logic and yet not be able to think ; but the science cannot be blamed for the imperfection of the element worked upon, any more than the artificer for the inferiority of the only material within his reach. It is sufficient that Logic, without entering into all the phenomena of mind, provides certain forms which an argument, to be legitimate, must exhibit, certain tests by which fallacy may be detected, and certain barriers against ambiguity in the use of language.
Hence, the utility of a science which enables men to take cognizance of the travellers on the mind's highway, and excludes those disorderly interlopers verbal fallacies, needs but small attestation. Its search- ing penetration by definition alone, before which even mathematical precision fails,1 would especially com- mend it to those whom the abstruseness of the study does not terrify, and who recognise the valuable results which must attend discipline of mind. Like a medi- cine, though not a panacea for every ill, it has the health of the mind for its aim, but requires the de- termination of a powerful will to imbibe its nauseating
' Prior Analyt. ii. 16.
VI QTTROI'UCTION.
vet wholesome influence : it is no wonder therefore that punv intellects, like weak stomachs, abhor and reject it. What florid declaimer can endure that the lux- uriant boughs of verdant sophistry, the rich blossoms of oratorical fervour, should be lopped and pared by the stern axe of a syllogism, and the poor stripped trunk of worthless fallacy exposed unprotected to the nipping atmosphere of truth ?
Like the science of which it treats, not only has the term " Logic " been variously applied,1 but even the Or- ganon, as a whole, presents no great claim to unity. The term is neither found, as belonging to an art or science, in Aristotle, nor does it occur in the writings of Plato, and the appellation " Organon," given to the treatises before us, has been attributed to the Peripatetics, who maintained against the Stoics that Logic was " an instrument " of Philosophy. The book, according to M. St. Hilaire, was not called " Organon " before the 15th century,2 and the treatises were collected into one volume, as is supposed, about the time of Andronicus of Rhodes ; it was translated into Latin by Boethius about the 6th century. That Aristotle did not compose the Organon as a whole, is evident from several portions having been severally regarded as logical, gram- matical, and metaphysical, and even the Aristotelian names themselves, Analytic and Dialectic, are applica- 1 Scotus super Univ. Qu. 3. 2 Cf. Waitz, vol. ii. p. 294.
INTRODUCTION. vii
ble only to certain portions of the Organon. Still the system is so far coherent in the immediate view taken of Logic, as conversant with language in the process of reasoning, that any addition to the structure of the Stagirite can never augment the compactness with which the syllogism, as a foundation, is built. The treatises themselves are mentioned under distinct titles by their author, and subsequent commentators have discussed the work, not as a whole, but according to its several divisions. It is remarkable also, that no quot- ations from the Categories, de Interpretatione, or So- phistical Elenchi, are found in the extant writings of Aristotle, since those given by Hitter l of the first and last must be considered doubtful.
In the present Translation my utmost endeavour hus been to represent the mind and meaning of the author as closely as the genius of the two languages admits. The benefit of the student has been my especial ob^eci; hence in the Analysis, the definitions are given in the very words of Aristotle, and the syllogistic examples, introduced by Taylor, have been carefully examined and corrected. In order also to interpret the more con- fused passages, I have departed somewhat from tht usual plan, and in addition to foot-notes have affixec explanations in the margin, that the eye may catch, ix the same line, the word and its import. Whereve)
• Vol. iii. p. 28.
Vlll INTRODUCTION.
further elucidation was necessary, I have referred to standard authorities, amongst whom I would gratefully commemorate the works of Mr. Mansel and Dr. Whately, not forgetting my solitary predecessor in this laborious undertaking, Thomas Taylor, whose strict integrity in endeavouring to give the meaning of the text deserves the highest commendation. For books placed at my disposal I have especially to express my sincere acknowledgments to the Rev. Dr. Hessey, Head Master of Merchant Tailors' School, and John Cuninghame, Esq. of Lainshaw.
By an alteration in the original plan, it has been found requisite, in order to equalize the size of the volumes, to place Porphyry's Introduction at the dose, instead of at the commencement, of the Organon.
O. F. O.
£>n^ttow, Jane £3, 1853.
\%
ERRATA.
r<ige 219, line 2, in head of chapter xvii., for an account read on account
— 273, in marginal note 4, for Instance of a syllogistic argument read
Instance of asyllogistic argument, i. e. not syllogistic
— 594, at head of chapter xxv., for from what is simply read fron.
what is not simply
ARISTOTLE'S OKGANON.
THE CATEGORIES.1
Chap. I. — Of Homonyms,"1 Synonyms, Paronyms.
Things are termed homonymous, of which the *■ ^at "» name alone is common, but the definition (of sub- stance according to the name) is different ; thus " man "
1 Categories, or Predicaments, so called because they concern things •which may always be predicated, are the several classes under which all abstract ideas, and their signs, common words, may be arranged. Their classification under ten heads was introduced by Archytas and adopted by Aristotle. The reason why, in this treatise about them, Aristotle does not begin from these, but from Homonyms, &c, is that he might previously explain what was necessary to the doctrine of the Categories to prevenl subsequent digression. Vide Porphyr. in Praedicam. After comparing various opinions of Alexander Aphrodisiensis, Syrianus, Simplicius, and others, it appears agreed by all, that Aristotle's intention in this treatise was, to discuss simple primary and general words, so far as tin;/ are sig- nificant of things ; at the same time to instruct us in things and conceptions, so far as they are signified by icords. A recollection of this digested ■ t- planation, will much assist the student in the enunciation of the plan.
2 " Homonyms," equivocal words,-- ■" Synonyms," uiiivocal,— " Paro- nyms," derivative. We may remark here, that analogous nouns o trite only one species of equivocal : that the synonyms of Aristotle musl be distinguished from the modern synonyms, which latter are defined by Boethius, "those which have many names, but one definition;" and lastly, that paronyms have been limited by the schoolmen to certain con- crete adjectives, a limitation which is not warranted by Aristotle, and is expressly rejected bv his Greek commentators.— Mansel's Rudiments oi Logic. See also Simplicius Scholia, p. 43, b. 5. "The reason, ' says Syrianus, "why things polyonomous, and heteronomous, are omitted I Aristotle, is because they rather pertain to ornament of diction, than to the consideration of things ; they are therefore more properly discussed in the Rhetoric and Poetics."
2 aristotle's organon. [chap. u.
and " the picture of a man " are each termed " animal," since of these, the name alone is common, but the definition (of the substance according to the name) is different : ' as if any one were to assign what was in either, to constitute it " animal," he would allege the peculiar definition of each. But those are called synonyms, of which both the syiwnymsT' narae is common, and the definition (of the sub- stance according to the name) is the same,2 as both " a man " and " an ox " are " animal," for each of these is predicated of as " animal " by a common name, and the definition of the substance is the same, since if a man gave the reason of each as to what was in either, to constitute . „ it " animal," he would assign the same reason.
3. Paronyms. . . ' & .
Again, things are called paronyms which, though differing in case, have their appellation (according to name) from some thing, as " a grammarian " is called so from "gram- mar," and " a courageous man " from " courage."
Chap. II. — Of the logical division of Things and their Attributes}
1 Subjects of Op tilings discoursed upon, some are enunciated discourse com- after a complex, others after an incomplex, man-
plex and in- .-i i » .,
Complex. ner » the complex as " a man runs, " a man con-
quers," but the incomplex as " man," " ox,"
1 Taylor translates \6yog sometimes " reason," at others " definition." It is better to preserve the latter as far as may be, though the student will do well to remember that it is capable of both significations. The brack- ets are retained from the Leipsic and other copies.
2 Ovaia, " a thing sufficient of itself to its own subsistence." Taylor. He translates it " essence," rather than " substance," because this latter word conveys no idea of self-subsistence. See his Introduction of Por- phyry. It must be observed, however, that whilst by continued abstrac- tion from the subject and different predicates of Propositions, the predi- cates arrive at the nine other categories, the subject will ultimately end in " substance." Cf. Phys. Ausc. lib. iii.
3 This chapter, containing the several divisions of terms, into abso- lute and connotative, abstract and concrete, respectively, has presented endless difficulties to commentators ; and the question of relation seems as far from being settled as ever. The whole subject may perhaps be properly condensed in the following manner. All bvra are divided by Aristotle into four classes, Universal and Singular Substances, and Uni- versal and Singular Attributes; the former existing per se, the latter in the former. Universals are predicable of singulars, but attributes, in
CIIAl*. II. 1
THE CATEGORIES.
" runs," " conquers." Likewise also some things 2. varieties of are predicated of a certain subject, yet are in no Pr^lcatlon- subject, as "the man" is predicated of a subject, i. e. of
their original state, are not predicable of substances ; but by the mental act, we may so connect an attribute with a subject, as to render tin- former predicable of the latter, as a difference, property, or accident. When a predicate is thus formed from an attribute, it is called connota- tive, or, as Whately justly remarks, " attributive," and signifies primarily, the attribute, and secondarily, the subject of inhesion. Original uni- versal or attributes, as "man," "whiteness," are called "absolute;" but terms may be made to cross, so that by an act of mind, that which signifies substance may be conceived as an attribute, and as no longer predicable of the individuals ; in this sense they are called " abstract," as " humanitas" from " homo ; " but when they are primarily or secondarily predicable of individuals, they become "concrete," e. g. "man" is con- crete and absolute; " white," concrete and connotative ; "whiteness," abstract and absolute ; it must be remembered only, that no abstract term is connotative. Vid. Occam, Log. p. i. ch. 5, 10. Simplicius enumerates eleven modes of predication, arising from the relations of genus and spe- cies. Aristotle, in the Physics, divides substance in eight modes, omit- ting " time"— considering subject as both composite and individual. The division into universals and particulars was probably taken from the categorical scheme of Pythagoras.
We annex a scheme of the relation of subject to predicate, in respect of consistency and inhesion.
Contrary to or inconsistent with
|
Substance |
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Sub-contrary in |
inconsistent with |
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4 Aristotle's organon. [chap. in.
" some certain man," yet is in no subject. Others, again, are in a subject, yet are not predicated of any subject, (I mean by a thing being in a subject, that which is in any thing not as a part, but which cannot subsist without that in which it is,) as "a certain grammatical art" is in a sub- ject, " the soul," but is not predicated of any ; and " this white thing" is in a subject, "the body," (for all "colour" is in " body,") but is predicated of no subject. But some things are both predicated of and are in a subject, as " sci- ence" is in a subject — "the soul," but is predicated of a subject, namely, "grammar." Lastly, some are neither in, nor are predicated of, any subject, as "a certain man" and " a certain horse," for nothing of this sort is either in, or 3. individuals predicated of, a certain subject. In short, indi- not predicated viduals, and whatever is one in number, are pre- a su jec . Seated 0f no subject, but nothing prevents some of them from being in a subject, for " a certain grammatical art" is amongst those things which are in a subject, but is not predicated of any subject.
Chap. III. — Of the connexion between Predicate and Subject.
1. statements When one thing is predicated of another, as of !£s"metnt in a subject, whatever things are said of the predi- cate, may be also said of the subject,1 as " the man" is predicated of "some certain man," but "the animal" is predicated of "the man," wherefore "the animal" will be predicated of "some certain man," since "the certain man" is 2 Difference of Dotn "man" and "animal." The differences of distinct genera different genera, and of things not arranged under
1 Genera, species, and differences, differ according to their predica- ments, hence in each predicament, there are genera, species, and differ- ences. Those genera also, have a mutual arrangement, one of which is under the other, as " flying " under " animal," but those are not mutually arranged, one of which, is not ranked under the other, as "animal" and r> science." Upon the application of this general rule, see Whately and Hill's Logic, especially the latter, in respect to summa and subaltern genera, and their cognates, pages 56, 57. Properly speaking, there can be only one highest genus, namely, Being ; though relatively a subaltern term, may at any time, be assumed as the summum genus, as " sub- stance," " auimal; ' etc.
CHAP. IT.] THE CATEGORIES. 5
each other, are diverse also in species,1 as of " ani- induces differ mal" and "science." For the differences of " ani- unfcrthem.'* raal" are "quadruped," "biped," "winged," "aquatic," but none of these, forms the difference of "science," since "sci- ence," does not differ from " science," in being 3 Not so as " biped." But as to subaltern genera, there is subaltern ge- nothing to prevent the differences being the same, as the superior are predicated of the genera under them ; so that as many differences as there are of the predicate, so many will there also be of the subject.
Chap. IV. — Enumeration of the Categories.
Of things incomplex enunciated, each signifies j ofincom- either Substance, or Quantity, or Quality, or Re- pie* "re- lation, or Where, or When, or Position, or Pos- session, or Action, or Passion.2 But Substance is, (to speak generally,) as "man," "horse;" Quantity, as "two" or "three cubits ;" Quality, as "white," a "grammatical thing ;" Relation, as " a double," " a half," " greater ; " Where, as " in the Forum," "in the Lyceum ;" When, as "yesterday," "last year;" Position, as "he reclines," "he sits;" Possession, as " he is shod," " he is armed ; " Action, as " he cuts," " he burns ; " Passion, as " he is cut," " he is burnt." 2. categories Now each of the above, considered by itself, is by themselves,
' •> .' neither affirm-
predicated neither affirmatively nor negatively, ative nor nega- but from the connexion of these with each other, tive- affirmation or negation arises. For every affirmation or nega- tion appears to be either true or false, but of things enun-
1 Difference joined to genus constitutes species — it is called specific difference, when it constitutes the lowest species, as of individuals. Cf. Crakanthorpe Logica, lib. ii. The common definitions of the heads of the predicables, are those of Porphyry, adopted by subsequent logicians. Vide Porph. Isagoge.
2 The principle of distinction above is shown to be grammatical, by Trendelenburg, Elementa, section 3rd. The six last may be reduced to Relation, see Hamilton on Reid, p. 688. The categories are enu- merated and exemplified in the following verses, for the student's recol- lection.
Summa decern : Substantia, Quantum, Quale, Relatio, Actio, Passio. Ubi, Quando, Situs, Habitus. Presbyter exilis, specie pater, orat et ardet. In campo, semper rectus, et in tunica.
6 Aristotle's organon. [chap. v.
ciated without any connexion, none is either true or false, as "man," "white," "runs," "conquers."
Chap. V. — Of Substance}
1. Primary sub- Substance, in its strictest, first, and chief sense, stance is net js that which is neither predicated of any subject,
ther in, nor is . . l . „ J J .
predicated of, nor is in any ; as " a certain man. or " a certain ^Secondary horse." But secondary substances are they, in substances con- which as species, those primarily-named sub- stances are inherent, that is to say, both these and the genera of these species ;2 as "a certain man" exists in "man," as in a species, but the genus of this species is " animal ; " these, therefore, are termed secondary substances,
1 On the various modes in which Aristotle employs the term oixria, cf. Metaphy. lib. iv., and Phys. lib. iii. Without entering into the dispute relative to the real existence of genera and species, as substances independent of us, between the old Realists and the modern Conceptual- ists, it will be sufficient to state that Aristotle here employs the term as
' the summum genus, under which, by continued abstraction of differences, > all things may be comprehended as a common universal. Thus also Plato in Repub. lib. vii. Whether called Entity, Being, Substance, or Subsistence, it may be defined, " That which subsists independently of any other created thing," and in this view may be affirmatively predi- cated of every cognate term, though no cognate term can be so predi- cated of it : thus all bodies, all animals, all lions, etc., are substances or things, according as we adopt either of these last as summum genus. Archytas places essence first ; Plotinus and Nicostratus doubt its generic affinity altogether ; but all regard the principle laid down, of some one, independent, existence, or conception.
2 But in getting to this ultimate abstraction, the first common nature of which the mind forms conception from individual comparison, is called the lowest primary or most specific species, and of this, every cognate term may be universally predicated, though itself canno* be predicated of any cognate term. Between these extremes, all intermediate notions (and their verbal signs) are called subaltern, each of which, like the step of a lad- der, is at once superior to some and inferior to others, and becomes a genus in relation to some lower species, and a species to some higher genera. The annexed " Arbor Porphyriana" is given by Aquinas, Opusc. 48. Tract. 2, cap. 3. In all the earlier specimens, "animal rationale" is placed between "Animal" and "Homo," as the proximum genus, divided into " mortale" and " immortale," in accordance with Porphyry's definition of man. We shall here observe also, that a summum genus can have no constitutive differences, which are represented at the side, though a summum genus may have properties.
ch'ap. V ]
THE CATEGORIES.
as both "man" and "animal."1 But it is evident , T A.
3. In predica-
from what has been said, that or those things tion the name which are predicated of a subject, both the name ofth^subjeet and the definition must be predicated of the sub- must be predi- ject, as "man" is predicated of "some certain man," as of a subject, and the name, at least, is predicated, for you will predicate "man" of "some certain man," and the
Substantia
,\sV*
Corporea
Animatum
Sensibile
Rationale
Incorporea
Inanimatum
Insensibile
Irrationale
Socrates
Plato
» For the method of predication, vide Huyshe, Aldrich, or Whately. Also compare the Topics iv. 2, Isagoge 2, Aquinas Opusc 48, cap. 2. Genus and species are said " praedicari in quid," l. e. are expressed by a substantive ; Property and Accident " in quale," or by an adjective. This whole chapter, brings forcibly to the mind, Butler's satirical bur- lesoue of Hudibrastic acumen, in discovering
" Where entity and quiddity,
The ghosts of defunct bodies fly ! "
Iludibras, Part i. Can. 1. Though very necessary, the initiative processes of Logic, indeed present
" A kind of Babylonish dialect,
Which learned pedants much affect"
8 Aristotle's organon. [chap. v.
definition of man will be predicated of " some certain man," for "a certain man" is both "man" and "animal;" where-
fore both the name and the definition will be pre- happens in the dicated of a subject. But of things which are in inneskinT113' a SUDJect> for the most part, neither the name nor
the definition is predicated of the subject, yet with some, there is nothing to prevent the name from being some- times predicated of the subject, though the definition cannot be so; as "whiteness" being in a body, as in a subject, is predicated of the subject, (for the body is termed "white,") but the definition of "whiteness" can never be predicated of body. All other things, however, are either predicated of primary substances, as of subjects, or are inherent in them as in subjects ; l this, indeed, is evident, from several obvi- ous instances, thus " animal " is predicated of " man," and therefore is also predicated of some " certain man," for if it
5. Theuni- were predicated of no "man" particularly, nei- versai involves ther could it be of " man " universally. Again,
"colour" is in "body," therefore also is it in "some certain body," for if it were not in "some one" of bodies singularly, it could not be in "body" universally; so that all other things are either predicated of primary sub- stances as of subjects, or are inherent in them as in subjects ; if therefore the primal substances do not exist, it is impossible that any one of the rest should exist. '
6. species more But °f secondary substances, species is more a substance substance than genus ; 2 for it is nearer to the
primary substance, and if any one explain what the primary substance is, he will explain it more clearly and appropriately by giving the species, rather than the genus ; as a person defining " a certain man " would do so more clearly, by giving " man " than " animal," for the former is more the peculiarity of " a certain man," but the latter is more common. In like manner, whoever explains what "a certain tree " is, will define it in a more known and appropri-
7. Primary sub- ate manner, by introducing "tree" than "plant." subjects^au6 Besides the primary substances, because of their predicates; subjection to all other things, and these last being
1 Plato, in the Philebus, observes, that a philosopher ought not to de- scend, below wholes, and common natures.
s Vidt supra, note ; also Metaph. lib. iv. and vi.
CHAP. V.] THE CATEGORIES. 9
either predicated of them, or being in them, are for hence tb<?!<- this reason, especially, termed substances. Yet the name* same relation as the primary substances bear to all other things, does species bear to genus, for species is subjected to genus since genera are predicated of species, but species 8. Genus a pre are not reciprocally predicated of genera, whence d.icat e of sPe_ the species is rather substance than the genus. „ vice vend. Of species themselves, however, as many as are 9. infimffi not genera, are not more substance, one than an- species are other, for he will not give a more appropriate not being 'sub- definition of " a certain man," who introduces stance- " man," than he who introduces " horse," into the definition of "a certain horse:" in like manner of primary substances, one is not more substance than another, for " a certain man " is not more substance than a " certain ox." With reason therefore, after the first substances, of the rest, species and genera alone are termed secondary genera alone" substances, since they alone declare the primary are secondary
* Sli list in pp'n
substances of the predicates ; thus, if any one were to define what "a certain man" is, he would, by giving the species or the genus, define it appropriately, and will do 30 more clearly by introducing "man" than "animal;" but whatever else he may introduce, he will be introducing, in a manner, foreign to the purpose, as if he were to introduce " white," or " runs," or any thing else of the kind, so that with propriety of the others, these alone are termed sub- stances. Moreover, the primary substances, be- cause they are subject to all the rest, and all the ^'atfo^be-5 °f others are predicated of, or exist in, these, are most tween cognate properly termed substances, but the same relation species.3" which the primary substances bear to all other things, do the species and genera of the first substances bear to all the rest, since of these, are all the rest predicated, for you will say that " a certain man " is " a grammarian,'' and therefore you will call both " man" and " animal" " a grammarian," and in like manner of the rest.1
1 Archytas adopts a different division of substance, into matter, form, and a composite of the two, and this division Aristotle shows in his Physics, and Metaphysics, and Physical Auscultation he knew, but doflfl not employ it in this treatise, as not adapted for its subject matter, namely, logical discussion. Cf. Physica Ausc. lib. iii., and Metaph. lib. ri. and xi.
10 akistotle's organon. [chap. V
i? No sub- It ^s common however to every substance, not to
stance m a sub- be in a subject,1 for neither is the primal substance in a subject, nor is it predicated of any ; but of the se- condary substances, that none of them is in a subject, is evident from this; "man" is predicated of "some certain" subject " man," but is not in a subject, for " man " is not in " a cer- tain man." So also " animal " is predicated of " some certain " 13 of inhe- subject "man,"*but " animal" is not in "a certain sives the name man." Moreover of those which are, in the sub- catedof thee '" ject, nothing prevents the name from being some- subject;, but not tjmes predicated of the subject, but that the defi-
the definition. . . r •> > .
nition should be predicated ot it, is impossible. Of secondary substances however the definition and the name are both predicated of the subject, for you will predicate the
definition of " a man" concerning; " a certain man,"
o
may b^ predi- and likewise the definition of " animal," so that cated of second- substance, may not be amongst the number, of those
ary substances. . J . . °
things which are in a subject. is. Difference This however is not the peculiarity of sub- does not exist stance, but difference also is of the number of
m subject. ' . .
those things not in a subject;2 lor "pedestrian ' and " biped " are indeed predicated of " a man " as of a subject, but are not in a subject, for neither " biped " nor " pedestrian " is in " man," The definition also of differ- ence is predicated of that, concerning which, difference is pre- dicated, so that if " pedestrian " be predicated of "man," the definition also of " pedestrian " will be predicated of man, for
" man" is " pedestrian." Nor let the parts of sub- substances' are stances, being in wholes as in subjects, perplex us, also sub- so that we should at any time be compelled to say,
that they are not substances ; for in this manner,
1 Simplicius observes that Aristotle discusses the things which sub- stance has in common with the other predicaments ; Iamblichus, what is common to it, and also its property and difference. Some may doubt how essence, will not be in a subject, as ideas according to Plato are in intellect, yet these are neither as in a subject, but are as essence in an- other essence: Aristotle discusses this in the 12th book of the Metaphysics.
2 Generic difference, it must be remembered, constitutes subaltern spe- cies— specific difference, forms the lowest species — the former difference is predicated of things different in species, the latter of things differing in number. In the scholastic theory, the properties of the summum genus were regarded as flowing from the simple substance, those of all subor- dinate classes, from the differentia. See Hill's Logic on the Predicables
CHAP. V.] THE CATEGORIES. ) 1
things would not be said to be in a subject, which are in any as parts. It happens indeed both to substances and to differences alike, that all things should be ^S™ predicated of them univocally, for all the cate- substance nre-
r . ,. ,, t . i -,1 • dicated univo-
gones from them are predicated either in respect caUy. of individuals or of species, since from the primary substance there is no category, for it is predicated in respect of no subject. But of secondary substances, species indeed is predicated in respect of the individual, but genus in respect to species and to individuals, so also differences are predicated as to species and as to individuals. Again, the primary substances take the definition of species and of genera, and the species the definition of the genus, for as many things as are said of the predicate, so many also will be said of the subject, likewise both the species and the indi- viduals accept the definition of the differences : those things at least were univocal, of which the name is common and the definition the same, so that all which arise from substances and differences are predicated univocally.
Nevertheless every substance appears to signify 19 A11 sub. this particular thing : • as regards then the pri- stance signifies
1 . ° . D.. ,, \ , some one thing.
mary substances, it is unquestionably true that they signify a particular thing, for what is signified is indi- vidual, and one in number, but as regards the secondary sub- stances, it appears in like manner that they signify this par- ticular thing, by the figure of appellation, when any one says " man " or " animal," yet it is not truly so, but 20 SecoI,dary rather they signify a certain quality, for the sub- substances sig-
1 It was the opinion of Kant, as well as of Reid and Stewart, that in mind, as in body, substance and unity are not presented but represented, but what the thine/ itself is, which is the subject and owner of the several qualities, yet not identical with any one of them, can only be conceived, in as far as we can attain to any single conception of the to ov — through its many modifications, which attainment is itself questionable. \ ide some admirable remarks in Mansel's Prolego. Log. '277. Generally it suffices to retain the quaint form of the schools noticed above upon pre- dication of genus and species. Vide Aldrich's Logic. Genus is a whole logically, but species metaphysically, or, as they may be better expressed, the first is Totum Universale, the second Totuui Essentiale. Cf. Cra- kanthorpe Logica, lib. ii. cap. 5. Since writing the above, the striking illustration occurs to me, used by Lord Shaftesbury, of " the person left within, who has power to dispute the appearances, and redress, the ima- gination." Shaftesbury's Charac. vol. i. p. 325. The passage has mora sense than, yet as much sound as, any of his Lordship's writing.
12 Aristotle's organ on. [chap. v.
r.ify a certain ject is not one, as the primary substance, but " man '' "quale. an(j « anmiai " are predicated in respect of many.
Neither do they signify simply a certain quality, as " white," for " white " signifies nothing else but a thing of a certain quality, but the species and the genus determine the quality, about the substance, for they signify what quality a certain substance possesses : still a wider limit is made by genus than by species, for whoever speaks of " animal," comprehends more than he who speaks of " man."
v It belongs also to substances that there is no su'bstlrlce ad- contrary to them, * since what can be contrary to the mits no con- primary substance, as to a certain " man," or to a certain " animal," for there is nothing contrary either at least to " man " or to " animal ? " Now this is not the peculiarity of substance, but of many other things, as for in- stance of quantity ; for there is no contrary to "two" ttewes™ in" cubits nor to " three " cubits, nor to " ten," nor to any thing of the kind, unless some one should say that " much" is contrary to " little," or " the great" to " the small ; " but of definite quantities, none is contrary to the other. Sub- stance, also, appears not to receive greater or less ; 2 greaternorie'ss! I mean, not that one substance is not, more or less, substance, than another, for it has been already said that it is, but that every substance is not said to be more or less, that very thing, that it is ; as if the same sub- stance be " man " he will not be more or less " man ;" neither himself than himself, nor another " man " than another, for one " man " is not more " man " than another, as one " white thing" is more and less "white" than another, and one " beautiful" thing more and less " beautiful" than another, and "the same thing" more or less than "itself;" so a body being " white," is said to be more " white " now, than it was before, and if " warm " is said to be more or less " warm." Substance at least is not termed more or less substance, since " man " is not said to be more "man" now, than before, nor any
1 This, says Simplicius, is doubted by some, and indeed in his Physics, lib. i., Aristotle apparently contradicts his own statement above by in- stancing Form as the contrary to Privation, both being substantial ; but Form is but partly, substance, and partly, habit, and only in so much as it is the latter, is it contrary to Privation, not " quoad substantiam."
2 This is true, discrete quantities being unchangeable, and definite ia quantity.
CIIA.P. V.] THE CATEGORIES. 13
one of such other things as are substances : hence substance is not capable of receiving the greater and the less.
It appears however, to be especially the pecu- 24. individu- liarity of substance, that being one and the same ceweVontr"^- in number, it can receive contraries, which no one ries.> in wnicn can affirm of the rest which are not substances, those which we as that being one in number, they are capable of not substanc*s- contraries.1 Thus " colour," which is one and the same in number, is not " white " and " black," neither the same action, also one in number, both bad and good ; in like manner of other things as many as are not substances. But substance being one, and the same in number, can receive contraries, as " a certain man " being one and the same, is at one time, white, and at another, black, and warm and cold, and bad and good. In respect of none of the rest does such a thing appear, ex- cept some one should object, by saying, that a sentence and opinion are capable of receiving contraries, for the same sen- tence appears to be true and false ; thus if the statement be true that " some one sits," when he stands up, this very same statement will be false. And in a si- objection by a milar manner in the matter of opinion, for if j^g nce t0 the any one should truly opine that a certain person sits, when he rises up he will opine falsely, if he still holds the same opinion about him. Still, if any one, should even admit this, yet there is a difference in the mode. 2e x h For some things in substances, being themselves in substances changed, are capable of contraries, since cold, be- change'tTcapa- ing made so, from hot, has changed, for it is ble ot contra- changed in quality, and black from white, and good from bad : in like manner as to other things, each one of them receiving change is capable of contraries. The sen- tence indeed and the opinion remain themselves altogether immovable, but the thing being moved, a contrary is pro- duced about them; the sentence indeed remains the same, that " some one sits," but the thing being moved, it becomes at one time, true, and at another, false. Likewise as to opinion,
1 He does not mean that contraries exist in substance at one and the same time, as may be perceived from the examples he adduces. Archy- tas, according to Simplicius, admits the capability of contraries to be the peculiarity of substance ; " thus vigilance is contrary to sleep, slowness to swiftness, disease to health, ot'all which, one and the same man, is capa- ble." Simp, in Anst. Cat. Compare also Wai'.z, Organ, p. 2'Jl, Comment.
14 aristotle's organon. [ciiap. vi.
so that in this way, it will be the peculiarity of substance, to receive contraries according to the change in itself, but if any one admitted this, that a sentence and opinion can receive contraries, this would not be true. For the sen- 5J"„.S5U^n tence and the opinion are not said to be capable
QT. paSSlOll 111 -*■ J-
the example as of contraries in that they have received any thing, opinion but, in that about something else, a passive qua-
lity has been produced, for in that a thing is, or is not, in this, is the sentence said to be true, or false, not in that itself, is capable of contraries.1 In short, neither is a sen- tence nor an opinion moved by any thing, whence they can- not be capable of contraries, no passive quality being in them ; substance at least, from the fact of itself receiving contraries, is said in this to be capable of contraries, for it receives dis- ease and health, whiteness and blackness, and so long as it receives each of these, it is said to be capable of receiving contraries. Wherefore it will be the peculiarity of substance, that being the same, and one in number, according to change in itself, it is capable of receiving contraries ; and concerning substance this may suffice.2
Chap. VI.— Of Quantity?
1. Quantity Of Quantity, one kind is discrete, and another two-fold, dis- continuous;4 the one consists of parts, holding
1 Simplicius alleges that certain Peripatetics asserted that matter itself was susceptible of TrdBoQ. It must be remembered however that Aris- totle's definition of irdOt] (Rhet. lib. i.) is, that they are certain things added to substance, beyond its own nature. Vide Scholia ad Categorias, ed. Waitz, p. 32. Leip. 1844.
2 The union between ovaia and v\r] is laid down in the treatise de Anima, lib. ii. 1 , sec. 2 : the latter term was used by the schoolmen to signify the subject matter upon which any art was employed, in which sense, it was tantamount to primal substance.
3 Some say that quantity, is considered in juxta-position with substance, because it subsists together with it, for after substance is admitted, it is necessary to inquire whether it is one or many ; others, because among other motions, that which is according to quantity, viz. increase and diminution, is nearer to the notion of substance, viz. generation and cor- ruption, than " alliation " is, which is a motion according to quality. Taylor. Vide ch. 8, and Sulpicius, concerning the nature of this last. See also, Arist. Phys. lib. iii. et v., also cf. Cat. ch. 14.
4 Conf. Metaphy. lib. iv. cap. 13, Yloabv Xkytrat to Siaiperbv etQ fvviraQXovra, k. t. X. The reader will do well (o compare the above chapter, throughout, with that quoted from the Metaphysics, where these terms are all used equivocally.
CI1A.P. VI.] THE CATEGORIES. 15
position with respect to each other, but the other crete and eonu- of parts, which have not that position. Dis- occ^yingreia* crete quantity is, as number and sentence, but the position,
i. j ? and tiic con-
continuous, as line, superficies, body, besides trary. place and time. For, of the parts of number, |*is^et™plea there is no common term, by which its parts con- I. Number. join, as if five be a part of ten, five and five, conjoin at no common boundary, but are separated. Three, and seven, also conjoin at no common boundary, nor can you at all take a common limit of parts, in number, but they are always separ- ated, whence number is of those things which
0 „ 2. uratio.
are discrete. In like manner a sentence, ior that a sentence is quantity is evident, since it is measured by a short and long syllable ; l but I mean a sentence produced by the voice, as its parts concur at no common limit, for there is no common limit, at which the syllables concur, but each is distinct by itself. A line, on the contrary, is 3 Examples continuous, for you may take a common term, at continuous.
.... i ■ , jj?1-A line.
which its parts meet, namely, a point, and ot a superficies, a line, for the parts of a superficies coalesce in a certain common term. So also you can take a common term in respect of body, namely, a line, or a superficies, 2 Asuperficies by which the parts of body are joined. Of the same sort are time and place, for the present time is joined both to the past and to the future. Again, place 3. Time and is of the number of continuous things, for the Place- parts of a body occupy a certain place, which parts join at a certain common boundary, wherefore also the parts of place, which each part of the body occupies, join at the same bound- ary as the parts of the body, so that place will also be con- tinuous, since its parts join at one common boundary.
Moreover, some things consist of parts, having 4 Relative position with respect to each other, but others of sition of some parts not having such position ;2 thus the parts of ^as t0 the a line have relative position, for each of them lies
1 Aristotle means by Xoyoc, a sentence subsisting in voice, not in intel- lect. Sulpic. He adds also, that Archytas, Athenodorus, and Ptolemy condemn the division of quantity into two kinds, and prefer that ot num- ber, magnitude, and momentum, but the reply is, that the last is a quality, the same as density.
2 Plotinus, in his first book on the Genera of Being, says, if the con- tinued, is quantity, discrete, cannot be ; but he questions it as existing in
16 Aristotle's okganon. [chap. vi.
some where, and you can distinguish, and set out, where each lies, in a superficies, and to which part of the rest, it is joined., 83 also the pans of a superficies, have a certain position, for it may be in like manner pointed out where each lies, and what have relation to each other, and the parts of a solid, and of a place, in like manner. On the contrary, in
5. Parts have . 0 , .... mip
no relation in respect or number, it is impossible tor any one to respect of num- show that its parts have any relative position, or
ber or time. *. J r . '
that they are situated any where, or which ot t he- parts are joined to each other. Nor as regards parts of time, for not one of the parts of time endures, but that which does not endure, how can it have any position ? you would rather say, that they have a certain order, inasmuch as one part of time is former, but another latter. In the same man- ner is it with number, because one, is reckoned before two, and two, before three, and so it may have a certain order, but
you can, by no means, assume, that it has position.
A speech likewise, for none of its parts en- dures, but it has been spoken, and it is no longer possible to bring back what is spoken, so that there can be no position of its parts, since not one endures : some things therefore consist of parts having position, but others of those which
have not position. What we have enumerated named aretfie are alone properly termed quantities ; all the rest only proper being so denominated by accident, for looking
quanta— all ,,0 n , i • • • , • °
others reduci- to these, we call other things quantities, as white-
ExampiesT _ ness *s sa*^ *° ^e mucn? because the superficies is great, and an action long, because of its time be- insr lone, and motion also, is termed, much. Yet each of
*o
these is not called a quantity by itself, for if a man should explain the quantity of an action, he will define it by time, describing it as yearly, or something of the sort ; and if he were to explain the quantity of whiteness, he will define it by the superficies, for as the quantity of the superficies, so he would say is the quantity of the whiteness ; whence the par- ticulars we have mentioned are alone properly of themselves termed quantities, none of the rest being so of itself, but ac-
the intellect, and confounds the distinction between order, in discrete, and position, in continued quantities. The point is touched upon also in lib. vi. of the Physics. Compare also ch. 12, on Priority, in the Cate- gories, as to the relation in respect of number and time.
CHAP. VI.] THE CATEGORIES 17
cording to accident. Again, nothing is contrary 8 Quant:ty to quantity,1 for in the definite it is clear there is perse, imsno nothing contrary, as to " two cubits " or to " three," or to " superficies," or to any thing of this kind, for there is no contrary to them ; except indeed a man should allege that " much " was contrary to " little," or the " great " to the " small." Of these however, none is a quantity, but rather be- longs to relatives, since nothing, itself by itself, is described as great or small, but from its being referred to something else. A mountain, for instance, is called ^^n^oimded " little," but a millet seed " large," from the fact upon the con- of the one being greater, but the other less, in re- toyman? srea' spect of things of the same nature, whence the relation is to something else, since if each were called " small " or "great" of itself, the mountain would never have been called " small," nor the seed " large.j We say also that there are " many " men in a village, but " few " at Athens, although these last are more numerous, and " many " in a house, but " few " in a theatre, although there is a much larger number in the latter. Besides, " two cubits," " three," and every thing of the kind signify quantity, but "gi'eat " or " small " does not signify quantity, but rather relation, for the " great " and " small " are viewed in reference to something else, so as evi- dently to appear relatives. Whether however any one does, or does not, admit such things to be quantities, still there is no contrary to them, for to that which cannot of itself be assumed, but is referred to another, how can there be a contrary ? Yet more, if " great " and " small " be contraries, it will happen, that the same thing, at the same time, receives contraries, and that the same things are contrary to themselves, for it happens that the same thing at the same time is both " great " and " small." Something in respect of this thing is " small," but the same, in reference to another, is " large," so that the same thing happens at the same time to be both "great" and "small," by which at the same moment it receives contraries. Nothing 12 simuitane- however appears to receive contraries simultane- °us contrariety ously, as in the case of substance, for this indeed injpos
1 I^tor rov ttoctov nwilioKav tiviq to fi7}Siv fxfiv tvavriov, ttooq dva- rpoTn)v d'e tovtov oil ^wpci, Sid to Trpo(n\wg £t?a£ai, on ovfii Ty ovoiq itiv tvavTiov. — Magent. Schol. ed. Waitz. Cf. Metaph. lib. ix. c. 4, h, and 7.
G
18 Aristotle's organon. [chap. vi.
seems capable of contraries, yet no one is at the same time " sick " and " healthy," nor a thing " white " and " black " together, neither does any thing else receive contraries at one and the 13 same time^ | It happens also, that the same things
are contrary to themselves, since if the " great " be opposed to the " small," but the same thing at the same time be great and small, the same thing would be contrary to itself, but it is amongst the number of impossibilities, that the same thing should be contrary to itself, wherefore the great is not contrary to the small, nor the many to the few, so that even if some one should say that these do not belong to relatives, but to quantity, still they will have no contrary. H. The contra- The contrariety however of quantity seems titet'yc°hieflan especially to subsist about place, since men admit subsistent in " upward " to be contrary to " downward," calling space. t|ae piace toward the middle " downward," because
there is the greatest distance from the middle, to the extremities of the world ; l they appear also to deduce the definition of the other contraries from these, for they define contraries to be those things which, being of the same genus, are most distant from each other.
is. Quantity is Nevertheless quantity does not appear capable incapable of tie- of the greater and the lessj as for instance "two
cubits," for one thing is not more " two cubits " than another ; neither in the case of number, since " three " or " five " are not said to be more than " three " or " five," nei- ther "five" more "five" than "three" "three;" one time also is not said to be more " time " than another ; in short, of none that I have mentioned is there said to be a greater or a less, wherefore quantity is not capable of the greater and less. 16. But of Still it is the especial peculiarity of quantity
equality and to be called " equal" and "unequal,"2 for each of mequaiy. ^ akOVe-mentioned quantities is said to be
1 The " upward " and " downward " do not signify place, but the pre- dicament where, just as " yesterday " and " to-day " do not signify time, but the predicament when. Simplicius. Andronicus also assents to this. Compare the 4th book of Arist. Physics, where he defines piace to be the boundary of that which it contains ; the Pythagoreans, who in words agree with Aristotle, in effect differ most widely from him. Phys. lib. vi. and viii.
2 This may be shown thus : Quantity, quoad se, is measurable ; but the measurable can be measured by the same, or by more or by fewer measures; in the first case therefore, equal1 ty, in the second, inequality,
CHAP. VII. ] THE CATEGORIES. 19
"equal" and "unequal," thus body is called "equal" and "unequal," and number, and time, are predicated of as "equal " and " unequal ; " likewise in the case of the rest enumerated, each one is denominated " equal " and " unequal." Of the remainder, on the contrary, such as are not quantities, do not altogether appear to be called " equal " and " unequal," as for instance, disposition is not termed entirely "equal" and "un- equal," but rather "similar" and "dissimilar;" and white- ness is not altogether " equal " and " unequal," but rather "similar" and "dissimilar;" hence the peculiarity of quan- tity will especially consist in its being termed " equal " and " unequal."
Chap. VII.— Of Relatives? Such things are termed " relatives," which are , r, - ... .
., , ° , '. ~^ 1.. Definition of
said to be what they are, from belonging to other relatives, and things, or in whatever other way they may be re- mstances- ferred to something else ; thus " the greater" is said to be what it is in reference to another thing, for it is called greater than something ; and " the double " is called what it is in reference to something else, for it is said to be double a certain thing ; and si- milarly as to other things of this kind. Such as these are of the number of relatives, as habit,2 disposition, sense, knowledge, po- sition, for all these specified are said to be what they are, from belonging to others, or however else they are referrible to another, and they are nothing else ; for habit is said to be the habit of some one, knowledge the knowledge of something, position the position of somewhat, and so the rest. Relatives, therefore, are such things, as are said to be what they are, from belonging to others, or which may somehow be referred to an- other ; as a mountain is called "great" in comparison with an- other, for the mountain is called "great" in relation to something, and " like " is said to be like somewhat, and other things of this
subsists. Archytas divides the equal and unequal triply, according to the three differences of quantity. Taylor.
1 Compare the divisions of relation given in the Metaphys. lib. iv. c. 15.
* This must not be confounded with the action of habit alluded to in b. ii. c. 2, of the Ethics. Plotinus doubts whether habit in things re- lated be other than a mere name. This chapter is a thorough specimen of Aristotelian prolixity, of which, by a slight change in the Horatiau line, we may say, —
" Et facundia deseret hunc et lucidus ordo." Ars Poet 41.
c 2
20 Aristotle's organon. [chap. vit.
sort, are similarly spoken of, in relation to something. Re- clining, station, sitting, are nevertheless certain positions, and position is a relative ; but to recline, to stand, or to sit, are not themselves positions, but are paronymously denominated from the above-named positions.
2. Some reia- Yet there is contrariety in relatives, as virtue
tives admit is contrary to vice, each of them being relative, and knowledge to ignorance ; ' but contrariety is not inherent in all relatives, since there is nothing contrary to double, nor to triple, nor to any thing of the sort.
3 Aisod Relatives appear, notwithstanding, to receive
the more and the less, for the like and the unlike are said to be so, more and less, and the equal and the un- equal are so called, more and less, each of them being a relative, for the similar is said to be similar to something, and
4 e. r *ne une(lual> unequal to something. Not that all
relatives admit of the more and less, for double is not called more and less double, nor any such thing, but all
5. Relatives relatives are styled so by reciprocity, as the servant reciprocally is said to be servant of the master, and the master,
master of the servant ; and the double, double of the half, also the half, half of the double, and the greater, greater than the less, and the less, less than the greater. In like manner it happens as to other things, except that some- times they differ in diction by case, as knowledge is said to be the knowledge of something knowable, and what is know- able is knowable by knowledge : sense also is the sense of
6. Except the sensible, and the sensible is sensible by sense, where the attri- Sometimes indeed they appear not to recipro-
butionofthe . „ . , J rr . , ... -
relation is er- cate, if that be not appropriately attributed to roneous. which relation is made, but here he who attributes
errs ; for instance, a wing of a bird, if it be attributed to the bird, does not reciprocate, for the first is not appropriately
1 These are relatives, according to their genus, which is habit in this case. It may, however, be inquired how Aristotle afterwards ranks sci- ence, virtue, and their opposites, amongst qualities? Because the same thing, as he shows throughout, according to its connexion with different relations, occupies often a different predicament. Hence, also, contrariety is only partly inherent in relatives, since they derive their contrariety from the contrariety of their predicaments : thus in habit or in quality they receive contrariety, but not in the double or triple, because quantity does not receive it. To admit contraries therefore, is not the peculiarity of relatives, since contrariety is not in all relatives, nor in them alone,
CHAP. VII.] THE CATEGORIES. 21
attributed, namely " wing " to " bird," since " wing " is not predicated of it so far as it is " bird," but so far as it is " winged," as there are wings of many other things which are not birds, so that if it were appropriately attributed, it would also reciprocate ; as " wing " is the wing of " a winged crea- ture," and " the winged creature " is " winged " by the " wing." It is sometimes necessary perhaps even to invent .
7 NgcgssHv of
a name,1 if there be none at hand, for that to sometimes in- which it may be properly applied : e. g. if a rudder f^^reulta"6 be attributed to a ship, it is not properly so attri- buted, for a rudder is not predicated of a ship so far as it is " ship," since there are ships without rudders ; hence they do not reciprocate, inasmuch as a ship is not said to be the ship of a rudder. The attribution will perhaps be more appro- priate, if it were attributed thus, a rudder is the rudder of something ruddered, or in some other way, since a name is not assigned ; a reciprocity also occurs, if it is appropriately attributed, for what is ruddered is ruddered by a rudder. So also in other things ; the head, for example, will be more ap- propriately attributed to something headed, than to animal, for a thing has not a head, so far as it is an animal, since there are many animals which have not a head.
Thus any one may easily assume those things to 8 Rule for no_ which names are not given,, if from those which mination of re- are first, he assigns names to those others also, ciproc with which they reciprocate,2 as in the cases adduced, "winged" from "wing," and "ruddered" from "rudder." All relatives therefore, if they be properly attri- 9 A11 proper buted, are referred to reciprocals, since if they relatives reci- are referred to something casual, and not to that proc to which they relate, they will not reciprocate. I mean, that neither will any one of those things which are admitted to be referrible to reciprocals, reciprocate, even though names be assigned to them, if the thing be attributed to something ac- cidental, and not to that to which it has relation : for ex-
1 Conf. Top. i. 5, 1, also Anal. Post, ii. 7, 2. Definable objects are of two classes, producing a corresponding variety in the form of defini- tion. 1st, Attributes, which include things belonging to every other cate- gory but that of substance. 2nd, Substances, which not existing in a sub- ject, but per se, must be assumed before their attributes or relatives can be demonstrated. The definition of an attribute is to be found in its cause.
7 See Blair's Lectures on Rhetoric, under Figurative Language.
22 aristotle's organon. [chap. vii.
ample, a servant, if he be not attributed as the servant of a master, but of a man, of a biped, or any thing else of the kind, will not reciprocate, for the attribution is not appropriate. If however that, to which something is referred, be appropri- ately attributed, every thing else accidental being taken away, and this thing alone being left, to which it is appropri- ately attributed, it may always be referred to it, as " a servant," if he is referred to " a master," every thing else ac- cidental to the master being left out of the question, (as the being " a biped," and " capable of knowledge," and that he is "a man,") and his being "a master" alone, left, here the " servant " will always be referred to him, for a " servant " is said to be the servant of a " master." If again, on the other hand, that to which it is at any time referred is not ap- propriately attributed, other things being taken away, and that alone left, to which it is attributed, in this
lxiste°ncheaofthe case it; wil1 not be referred to it. For let a " serv- one depends ant " be referred to " man," and a " wing " to vm" infra, i"' "bird," and let the being " a master " be taken away from " man," the servant will no longer refer to man, since "master" not existing, neither does "serv- ant " exist. So also let " being winged " be taken away from " bird," and " wing " will no longer be amongst relatives, for what is " winged " not existing, neither will " wing " be the wing of any thing. Hence it is necessary to attribute that, to which a thing is appropriately referred, and if indeed a name be already given to it, the application is easy ; but if no name be assigned, it is perhaps necessary to invent one ; but being thus attributed, it is clear that all relatives are referred to reciprocals^/ ^ Naturally, relatives appear simultaneous, and by naturelie-s ^is is true of the generality of them, for " double " muitaneous, and "half" are simultaneous, and "half" existing, caption™6 ' ' ' double " exists, and " a master" existing, the " serv- ant " is, and the " servant " existing, the "master " is, and other things are also like these. These also are mutually subversive, for if there is no "double" there is no "half," and no "half" there is no "double" ; likewise as to other things of the same kind. It does not however appear to be true of all re- 12 As science Stives, that they are by nature simultaneous, for and its object, the object of " science " may appear to be prior apparen y. ^o i( gcjencej" smce for the most part we derive
CHAP. VIT.J THE CATEGORIES. 23
science from things pre-existing, as in few things, if even in any, do we see science and its object originating together. Moreover, the object of science being subverted, 13 Sometimes co-subverts the science, but science being sub- tut not always, verted, does not co-subvert the object of science, for there being no object of science, science itself becomes non-existent, (since there will be no longer a science of any thing) ; 1 but on the contrary, though science does not exist, there is nothing to prevent the object of science existing. Thus the quadrature of the circle, if it be an object of scientific knowledge, the science of it does not yet exist, though it is itself an object of science : 2 again, " animal " being taken away, there will not be " science," but still it is possible for 14 Instance of many objects of science to be. Likewise also do things pertain- things pertaining to sense subsist, since the sens- ] s ible seems to be prior to the sense, as the sensible being sub- verted co-subverts sense, but sense does not co-subvert the sensible. For the senses are conversant with body, and are in body, but the sensible being subverted, body also is subverted, (since body is of the number of sensibles,) and body not existing, sense also is subverted, so that the sensible co-subverts sense. Sense on the other hand does not co-subvert the sensible, since if animal were subverted, sense indeed would be subverted, but yet
1 This is self-evident, as also that there are some few things in which science is the same as its object, e. g. things without matter are certainly present at the same time as the intellectual science which abides in energy. On the contrary, in the other case, as Simplicius observes, if in- dolence reject the knowledge of things, yet the things themselves remain, as music, etc. Vide also Brewer's Introduction to the Ethics, book v., as to the position occupied by tTri<jT>ifi.ij in the scheme of the rive habits. It will thence appear second, and correspond to deduction from certain prin- ciples, the latter being a subdivision of abstract truth, thus :
Abstract truth
Principles Deductions from
voiig Principles
I iTTicrr))/!)]
« v <
together | crocpia.
' Aristotle selects this instance, as the quadrature of the circle does not appear from this, to have been known in his time, but Iamblichus asserts that it was known to the Pythagoreans, and Sextus Pythagoricus re- ceived it by succession. Archimedes is stated to have discovered the quadrature of the circle by a line called the line of Nicomedes : he himself Styled it the quadratrix.
24 aristotle's organon. [chap. vii.
the sensible will remain ; such for instance as "body," " warm," " sweet," " bitter," and every thing else which is sensible. Be- sides, " sense " is produced simultaneously with what is " sensi- tive," for at one and the same time " animal " and " sense " are produced, but the " sensible " is prior in existence to " animal " or " sense," for fire and water, and such things as animal con- sists of, are altogether prior to the existence of animal or sense, so that the sensible will appear to be antecedent to sense. 15 Primary ^ *s doubtful however whether no substance is
substance has among the number of relatives, as seems to be the case, or whether this happens in certain second sub- stances ; for it is true in first substances, since neither the wholes, nor the parts, of first substances are relative. " A cer- tain man " is not said to be a certain man of something, nor " a certain ox" said to be a certain ox of something ; and so also with respect to the parts, for a " certain hand " is not said to be a cer- tain hand of some one, but the hand of some one ; and some head is not said to be a certain head of some one, but the head of some one, and in most secondary substances the like occurs. Thus man is not said to be the man of some one, nor an ox the ox of some one, nor the wood the wood of some one, but they are said to be the possession of some one ; in such things therefore, it is evident, that they are not included amongst re- 16. But some latives. In the case of some secondary substances secondary sub- there js a doubt, as " head," is said to be the head of
stances seem to ' , >
possess reia- some one, and " hand, ' the hand ol some one, and in question1 is*6 like manner, every such thing, so that these may solved by an appear amongst the number of relatives. If then definition of e the definition of relatives has been sufficiently ™' "'"iv"' T'- framed, it is either a matter of difficulty, or of impossibility, to show that no substance is relative ; l but if
1 Plato's favourite method of definition, which however was rejected by Speusippus, was to take a wide genus, and by the addition of successive differentia, to arrive at a complex notion, co-extensive with the desired definition. Aristotle, on the other hand, to discover definition, employed the inductive method, (he does not name this however,) which consisted in examining the several individuals, of which the term to be defined is predicable, and observing what they had in common. This will apply to relatives and co-relatives equally, and hence we perceive that, properly speaking, all definition is an inquiry into attributes. Every substance definable must be a species, every attribute a property. Vide Scholia. Edinburgh Review, No. cxv. p. 236. Pacius on Anal. Post, 11, 13, 21.
CHAP. VII.] THE CATEGORIES. 25
the definition has not been sufficiently framed, but those things are relatives, whose substance is the same, as consists with a relation, after a certain manner, to a certain thing ; somewhat, perhaps, in reply to this, may be stated. The ^ former definition, however, concurs with all relatives, yet it is not the same thing, that their being, consists in relation, and that being what they are, they are predicated 17. one reia- of other things. Hence it is clear, that he who ,tive bei"?
i i • 1 A • . 1 mi 1 i known, the co-
knows any one relative, definitely, will also know relative can be what it is referred to, definitely. ( Wherefore also known- from this it is apparent, that if one knows this particular thing to be among relatives, and if the substance of relatives is the same, as subsisting in a certain manner, with reference to something, he will also know that, with reference to which, this particular thing, after a certain manner, subsists ; for if, in short, he were ignorant of that, with reference to which, this particular thing, after a certain manner, subsists, neither would he know, whether it subsists, after a certain manner, with re- ference to something. And in singulars, indeed, ,„ „. ,
,.. ., n •/> 1 -i^^i 18- Singulars.
this is evident ; lor 11 any one knows definitely, that this thing is " double," he will also forthwith know that, definitely, of which it is the double, since if he knows not that it is the double, of something definite, neither will he know that it is " double," at all. So again, if a man knows this thing, to be more beautiful than something else, he muse straightway and definitely know that, than which, it is more beautiful. (Wherefore, he will not indefinitely know, that this, is better, than that which is worse, for such is opinion and not science, since he will not accurately know that it is better than something worse, as it may so happen that there is nothing worse than it, j whence it is necessarily evident, that whoever definitely knows any relative, also definitely knows that, to which it is referred. It is possible, ,„ _
19. lhc con-
notwithstanding, to know definitely what the verse true of head, and the hand, and every thing of the sort ss^edsary sub are, which are substances ; but it is not necessary to know that to which they are referred, since it is not neces- sary definitely to know whose, is the head, or whose, is the hand ; thus these will not be relatives, but if these be not relatives, we may truly affirm no substance to be among re- latives. It is, perhaps, difficult for a man to assert assuredly
26 aristotle's organon. [chap, vin,
any thing of such matters, who has not frequently considered them, yet to have submitted each of them to inquiry, is not without its use.1
Chap. VIII. — Of the Quale and of Quality ?
1. Quality and By quality, I mean that, according to which, cer- its species; the ta;n things, are said to be, what they are. Quality,
latter of four ° . . J . ,\
kinds. however, is among those things which are predi-
dtspo^ftion— d cate(i multifariously ; hence one species of quality these ex- is called "habit" and "disposition," but habit,
p ame . differs from disposition, in that it is a thing more
lasting and stable.3 Of this kind too, are both the sciences and the virtues,4 for science appears to rank among those things, which continue more stable, and are hardly removed, even when science is but moderately attained, unless some great change should occur from disease, or from something of the sort ; so also virtue, as justice, temperance, and so forth, does not appear capable of being moved or changed with facility. But those are termed dispositions, which are easily moved and quickly changed, as heat, cold, disease, health, and such things ; or a man is disposed, after a manner, accord- ing to these, but is rapidly changed, from hot becoming cold, and from health passing to disease, and in like manner as to other tilings, unless some one of these qualities has, from
1 Cf. Metaph. lib. iv. c. 15.
2 JloioTrjg. Def. " That which imparts what is apparent in matter, and what is the object of sense." Taylor's Explanation of Aristotelian Terms. See also Metaphys. lib. iv. c. 14, 19, and 20, Leip. The distinction in the text has been remarked upon, as exemplifying Aristotle's passion for definition, but it would be more correct to remember that it was perhaps less his inclination than his judgment, which induced him to lay down strict notions of verbal definition primarily, knowing that the thing signi- fied, or idea, could never hold its proper position in the mind, if any doubt existed as to the meaning of the term or verbal symbol of it, ab origine. It is a great pity that modern controversialists so frequently neglect this.
3 Cf. Ethics, book ii. ch. 5, and book ii. ch. 1. In the latter place, Aristotle shows that moral virtue arises from habit, in opposition to Plato, who taught that the virtues were not produced by learning or nature, but were divinely bestowed. Aristotle's opinion resembled Locke's, in the de- nial of innate ideas, the soul having nothing within it but inclination, rd TTHpvKoe. The»student will profitably refer here to Bishop Butler's Analogy, on the growth of mental habits. Anal, part i. ch. 5. Bohn's Stand. Lib.
4 So Cicero, de Off. lib. iii., connects these two, " temperantia est scientia." See also Montaigne's Essays, ch. xl. b. i., and ch. ii. b. iii.
CHAP. VIII.] THE CATEGORIES. 27
length of time, become natural, immovable, or at least dif- ficult to be moved, in which case we may term it a habit. But it is evident that those ought to be called habits, which are more lasting, and are with greater difficulty removed, for those persons who do not very much retain the dogmas of science, but are easily moved, are said not to possess a scientific habit, although they are in some manner disposed as to science, either worse or better ; so that habit differs from disposition in the one being easily removed, but the former is more lasting, and less easily removed. Habits are dispositions also,1 but dispositions not necessarily habits, for those who have habits are also, after a manner, disposed according to them, but those who are disposed are not altogether possessed of the habit^
Another kind of quality is, that, according 2nd species of to which, we sav that men are prone to pugilism, quality, that
J ill i- . which compre-
or to the course, or to health, or to disease, in hends the fa- short, whatever things are spoken of according to culties- natural power, or weakness ; for each of these is not denomi- nated from being disposed after a certain manner, but from having a natural power or inability of doing something easily, or of not suffering ; thus, men are called pugilistic, or fitted for the course, not from being disposed after a certain man- ner, but from possessing a natural power of doing something easily. Again, they are said to be healthy, from possessing a natural power of not suffering easily from accidents, but to be diseased, from possessing a natural incapacity to resist suffer- ing easily from accidents : similarly to these, do hard and soft subsist, for that is called "hard" which possesses the power of not being easily divided, but " soft," that which has an impo- tence as to this same thincr.
The third kind of quality consists of passive qua- 3rd Passive lities and passions, and such are sweetness, bitter- qualities.
1 The "H0o£ signifies the habitual disposition or " humour," as in Every Man out of his Humour, by Ben Jonson.
"When some one peculiar quality
Doth so possess a man, that it doth draw
All his affects, his spirits, and his powers,
In thoir confluctions, all to run one way —
This may be truly said to be a humour." Vide Aristotle's Rhetoric, (Bonn's Class. Lib.). And again, Coriolanus, act iii. scene 2, — Away my disposition, and possess me
Some harlot's spirit ! Or, act iii. sc. 1, " Men: His nature, is too noble for the world," etc.
28 ARISTOTLE;S ORGANON. [CHAP. VIII.
ness, sourness, and all their affinities, besides warmth, and cold- ness, and whiteness, and blackness. Now that these are qualities, is evident from their recipients being called from them, "qua- lia," ' as honey from receiving sweetness, is said to be sweet, and the body white, from receiving whiteness ; in like manner in other things. They are called passive qualities,2 not from the re- cipients of the qualities suffering any thing, for neither is honey said to be sweet from suffering any thing, nor any thing else of such a kind. " In like manner to these are heat and cold called passive qualities, not from the recipients themselves suffering any thing, but because each of the above-mentioned qualities produces passion in the senses, they are denominated passive qualities ; for as sweetness, produces a certain passion in the taste, and warmth, in the touch, so also do the rest. Whiteness, 1 Exception in an<^ blackness, and other colours are, on the con- the case of co- trary, not called passive qualities in the same man- ner with the above-mentioned, but from themselves being produced from passion ; for that many changes of co- lours spring from passion is evident, since when a man blushes he becomes red, and when frightened, pale, and so every thing of this sort^ Whence also if a man naturally suffers a passion of this nature, he will probably have a similar colour, since the disposition which is now produced about the body when he blushes, may also be produced in the natural constitution, so as that a similar colour should naturally arise. Whatever such symptoms then originate from certain passions diffi-
1 Simplicius doubts whether the same thing is signified by quale, and quality : probably the latter signifies the peculiarity itself, but quale that which participates in the peculiarity, as in the examples given above. As to the term " quality," Plato in his Thesetetus insinuates that he was the author of it, and indeed some ancient philosophers, as Antisthenes, subverted certain qualities, and allowed only the subsistence of qualia, which they deemed incorporeal. The Stoics, on the contrary, thought the qualities of incorporeal natures incorporeal, and of bodies, corporeal. Simplicius defines qualities — " powers, active, yet not so, primarily, nor alone."
2 It may perhaps seem strange that Aristotle distinguishes passions and passive qualities by the same characteristics as he has before used about habit and disposition ; but it may be replied, that here he considers the passions and passive qualities which by nature are easily or hardly re- moved. Heat, so far as it disposes a subject, is a disposition ; so far as that disposition is permanent, is a habit ; if it be superficially effected by an agent, it is called a passion, and so far as the passion is produced perma- nently and intrinsically, it is called passive quality. Taylor.
CHAP. VIII.] THE CATEGORIES. 29
cult to be removed and permanent are called passive qualities. For whether in the natural constitution, paleness, or blackness, be produced, they are called qualities, (for according to them we are called " quales ;") or whether through long disease or heat, or any such thing, paleness or blackness happens, nei- ther are easily removed, or even remain through life, these are called qualities, for in like manner, we are called " quales " in respect of them. Notwithstanding, such as are produced from things easily dissolved, and quickly j^ ™"e may restored, are called passions,1 and not qualities, for men are not called " quales" in respect of them, since neither is he who blushes, in consequence of being ashamed, called red, nor he who turns pale, from fear, called pale, they are rather said to have suffered something, so that such things are called passions, but not qualities. Like these also are 3 Also affec_ passive qualities, and passions denominated in the tions of the soul. For such things as supervene immediately upon birth from certain passions difficult of removal, are called qualities ; as insanity, anger, and such things, for men ac- cording to these are said to be " quales," that is, wrathful and insane. So also as many other mutations as are not natural, but arise from certain other symptoms, and are with difficulty removed, or even altogether immovable, such are qualities, for men are called " quales " in respect of them. Those which, on the other hand, arise from things easily and rapidly restored, are called passions, as for instance, where one being vexed becomes more wrathful, for he is not called wrathful who is more wrathful in a passion of this kind, but rather he is said to have suffered something, whence such things are called passions, but not qualities.2
The fourth kind of quality is figure and the form, 4th species of which is about every thing, besides rectitude and quality— form curvature, and whatever is like them, for accord- an gure' ing to each of these a thing is called " quale." Thus a tri- angle or a square is said to be a thing of a certain quality, also a straight line or a curve, and every thing is said to be " quale " according to form. The rare and the dense, the rough and the smooth, may appear to signify a certain quality,
1 Cf. Ethics, b. ii. ch. 5; also Metaphys. lib. iv. ch. 21; where the same examples of inanimate objects are given.
* Ethics, book ix. ch. 8. The being loved is like something passive.
30 Aristotle's organon. [chap, vm,
but probably these are foreign from the division of quality, as each appears rather to denote a certain position of parts. For a thing is said to be " dense," from having its parts near each other, but "rare," from their being distant from each olher, and " smooth," from its parts lying in some respect in a right line, but " rough," from this part, rising, and the other, falling. 5. Things call- There may perhaps appear to be some other nymousiy from rnode of quality, but those we have enumerated these qualities. are most commonly called so.
The above-named therefore are qualities, but " qualia " are things denominated paronymously according to them, or in some other manner from them ; most indeed and nearly all of them are called paronymously,1 as "a white man" from "whiteness," " a grammarian " from "grammar," a "just man " from "justice," and similarly of the rest. Still in some, from no names having been given to the qualities, it is impossible that they should be called paronymously from them ; for instance, a " racer " or " pugilist," so called from natural power, is paronymously denominated from no quality, since names are not given to those powers after which these men are called "quales," as they are given to sciences, according to which men are said to be pugilists or wrestlers from disposition, for there is said to be a pugilistic and palaestric science, from which those dis- posed to them are paronymously denominated "quales." Sometimes however, the name being assigned, that which is called " quale " according to it, is not denominated parony- mously, as from virtue, a man is called worthy, for he is called worthy, from possessing virtue, but not paronymously from virtue ; this however does not often happen, wherefore those things are called " qualia," which are paronymously denomin- ated from the above-mentioned qualities, or which are in some other manner termed from them.2
1 Vide supra, Cat. i. Massinger's employment, of the very word, we are now discussing, presents a peculiar difficulty, in establishing the paronymous or denominative relation. In the Roman Actor, act i. scene 3, and also in the Picture, act ii. scene 1, the word quality is limited to actors and their profession. See Gifford's notes on Massinger. In fact, most of our ancient dramatists confined the word chiefly to histrionic performers.
a The name " conjugata " is more properly applied to derivatives from the same primitive, as sapiens, sapienter, sapientia ; the avaToixcc of Aris totle. Cf. Topics ii. 9, 1. Cic. Top. c. ih.
CHAP. VIII.] THE CATEGORIES. 31
In quality, there is also contrariety,1 as justice
t 1 . • • f J uv j. 1.1 i 6- Quality
is contrary to injustice, and whiteness to black- sometimes sus. ness, and the like; also those things which sub- fePt.ible °f con-
7 . ° trariety.
sist according to them are termed qualia, as the unjust to the just, and the white to the black. This however does not happen in all cases, for to the yellow, or the pale, or such like colours, though they are qualities, there is no con- trary.2 Besides, if one contrary be a quality, the other, will also be a quality, and this is evident to any one con- sidering the other categories. For instance, if justice be contrary to injustice, and justice be a trary be a quale ' quality, then injustice will also be a quality, for o»e other will none of the other categories accords with injustice, neither quantity, nor relation, nor where, nor in short any thing of the kind, except quality, and the like also happens as to quality in the other contraries.
Qualia also admit the more and the less,3 as one thing is said to be more or less " white " than another, and one more and less "just" than another ; the same thing also 8 It can also itself admits accession, for what is " white," can be- admit degree. ^ome more, "white." This however, does not hap- pen with all, but with most things, for some one may doubt whether justice, can be said to be more or less justice, and so also in other dispositions, since some doubt about such, and as- sert that justice cannot altogether be called more and less, than justice, nor health than health, but they say, that one man has less health, than another, and one person less justice, than an- other, and so also of the grammatical and other dispositions. Still the things which are denominated according to these, do without question admit the more and the less, for one man is said
1 See below, Cat. xi. 5.
- Repugnance is not synonymous with contrariety, e. g. red and blue are repugnant, but not opposed. Archytas says, " Certain contraries are conjoined to quality, as if it received a certain contrariety and privation."
3 Here he evidently means qualities by qualia, as the examples indi- cate. There were four opinions entertained, upon the admission by qualia, of degree. Plotinus, and the Platonists, asserted that all qualia, and qua- lities alike, received the greater and the less ; others, limited intension, and remission, to the participants ; the Stoics avowed that the virtues are inca- pable of either ; and the fourth opinion, which Porphyry opposes, allows degree, to material, but denies it, to immaterial, and self-subsistent, qua- lities. Vide Simp, in Catego. Iamb. Opera. Aristotle, below, seems tc refer to the second, of these opinions.
32 Aristotle's organon. [chap. vm.
to be more grammatical, than another, and more healthy, and more iust, and similarly in other things. Tri-
Form incapable 1 j ,11 i 1
of degree. (Cf. angle and square appear nevertheless incapable w^ateiy, b. ii. 0f ^he more, as also every other figure, since those things which receive the definition of a triangle, and of a circle, are all alike triangles or circles, but of things which do not receive the same definition, none can be said to be more such, than another, as a square, is not more a cir- cle, than an oblong, for neither of them admits the definition of the circle. In a word, unless both receive the definition of the thing propounded, one cannot be said to be more so and so, than another, wherefore all qualities do not admit the more and the less.
Of the above-mentioned particulars then, no perVyo/quaHty one *s peculiar to quality, but things are said to that similitude he similar, and dissimilar, in respect of qualities
is predicated in ■, n .... ... ... ,
respect of it. alone, lor one thing is not like another in respect of any thing else, than so far as it is quale, so that it will be peculiar to quality, that the like and the unlike should be termed so in respect of it.1
Yet we need not be disturbed lest any one should say that, 10 r 1 t proposing to speak of quality, we co-enumerate objection— that many things which are relatives, for we said that position are1S" habits and dispositions are among the number of re- reckoned latives, and nearly in all such things the genera are tiveTas weifas called relatives, but not one of the singulars. Sci- amongst qua- ence, for example, although it is a genus, is said to be what it is, with respect to something else, for it is said to be the science of a certain thing, but of singulars not one is said to be what it is, with reference to something else, as neither grammar is said to be the grammar of something, nor music the music of something. But even perhaps these, are called relatives, according to genus, as grammar is said to be the science of something, not the grammar of something, and music the science of something, not the music of some-
1 If impression and character produce similitude, and quality consists in character, it will justly have its peculiarity according to the similar and dissimilar. Archytas observes, " The peculiarity of quality is the si- milar and the dissimilar ; for we say that all those things are similar in colour which have the same colour, and the same idea of character; but those are dissimilar which subsist in a contrary manner."
CIIA.P. IX."1 THi: CATEGORIES. 33
thing ; so that singulars are not of the number of Relatives. Still, we are called quales from singulars,1 for these we possess, as we are called scientific from not included assessing certain singular sciences ; so that these ta™ecsnfclf ^tivs nay be singular qualities, according to which Logic, de Divi- de are sometimes denominated quales, but they ire not relatives ; besides, if the same thing should happen to be both a particular quality and a relative, there is no absurdity in its enumeration under both genera.
Chap. IX. Of Action, Passion, and the other categories of Position : When : Where : and Possessio?i.
Action and Passion admit contrariety, and the more and the less, for to make warm, is contrary pas^f0tn°admit to making cold ; to be warm, contrary to the being contrariety and cold, to be pleased, contrary to being grieved ; so that they admit contrariety. They are also capable of the more and the less, for it is possible to heat, more and less, to be heated, more and less, and to be grieved, more and less ; where- fore, to act, and to suffer, admit the more and less, and so much may be said of these. T5ut we have spoken of the being situ- ated in our treatment of relatives,2 to the effect that it is paronymously denominated, from positions : as re- 2 Reca gards the other categories, when, where, and to tion of the other have, nothing else is said of them, than what was cateeones-
1 ralg Ka9' tKaara, etc. It may be useful here to give a general defin- ition of the several meanings applied by Aristotle to peculiar uses of the preposition as regards relative action and relation. At' 6, on account of which, then signifies— the final cause ; Si' 6v through which — the instru- mental cause ; s? bv or iv </7, from or in which — the material cause ; KaQ' 6 — according to which — form is thus denominated ; 7rpoc o, with re- lation to which — or the paradeigmatic cause ; and v(j>' 6v, by which — the demiurgic or fabricative cause. Cf. Top. lib. iv. c. 15, et seq. Taylor makes one continual mistake in the translation of Ka9' tKaara, by ren- dering it " particular," whereas the latter is " iv fitpu." Buhle, on the contrary, is correct in this translation throughout.
2 Aristotle here refers the reader to the category of relation, but as re- gards the opinion entertained of the remaining categories, Porphyry and lamblichus consider them as accessorial relatives; e. g. " When " and " where" are not, per se, place and time, but when these two latter exist primarily, the former accede to them. Thus also " having" signifies some- thing distinct from the existing thing, at the same time that it exists with it. Upon the reduction of the latter six categories to relation, see Hamilton on lieid, p. 688 ; also St. Hilaire's Translation, Preface, p. 08, et acq.
»
34 ARISTOTLE'S ORGANON. [ CHAP. X.
mentioned at first, because they are evident ; e. g. that "to have," signifies to be shod, to be armed ; "where," as in the Lycreum, in the Forum, and the rest which are spoken of these. Of the proposed genera therefore, suflicient has been stated.
Chap. X. — Of Opposites*
i Opposites WE must now speak of opposites, in how many are of four ways opposition takes place.) One thing then is
said to be opposed to another in four ways, either as relative, or as contrary, or as privation and habit, or as affirmation and negation. Thus speaking summarily, each thing of this kind is opposed, relatively, as " the double " to " the half," contrarily, as " evil " to " good," privatively and habitually, as " blindness " and " sight," affirmatively and ne- gatively, as " he sits," " he does not sit."
Whatever things then are relatively opposed, are posufontive °P sa^ to be what they are with reference to opposites,
or are in some manner referred to them, as " the double of the half," is said to be what it is, with reference to something else, for it is said to be the double of something ; and " knowledge " is opposed relatively to the object of knowledge, and is said, to be what it is, in reference to what may be known, and what may be known, is said to be what it is, in reference to an opposite, namely, " knowledge," for " the ob- ject of knowledge " is said to be so, to something, namely, to "knowledge."
1 For a brief exposition of this chapter, the reader is referred to the nature and laws of logical opposition in necessary, impossible, and con- tingent matter, given in Aldrich, Huyshe, Whately, Hill, and Man- sel. It will be remembered however that he here speaks of the opposi- tion of terms, the rules for the opposition of propositions being more especially considered in the Interpretation : still a reference to that treatise, as well as to the authors cited above, will be useful, as elucidating the grounds on which all logical opposition is founded. Archytas (says Simplicius) does not omit, but seems to have more accurately explained the differences of contraries adduced by Aristotle. He says : Of contra- ries, some are in the genera of genera, as good and evil, the first being the genus of the virtues, the second of the vices : some again in the genera of species, as virtue to vice, the first being the genus of prudence, temperance, etc. ; the other of imprudence, intemperance : lastly, some in species, as fortitude to timidity, etc. : but he adds, " there is nothing to prevent the contraries of genera being reduced under one genus, as gcod and evil unJer quality."
CHAP. X.] THE CATEGORIES. 35
Things therefore relatively opposed are said to be, what they are, with reference to opposites, or in whatever manner, they are referrible to each other, but those which are opposed as contraries, are by no means, said opposulon17 to be what they are, with reference to each other, but are said to be contrary to each other, for neither is "good" said to be the "good" of "evil," but the contrary of eviL nor is "white," denominated the " white " of "black," but its contrary, so that these oppositions differ from each other. Such contraries however, as are of that kind, that one of them must necessarily be in those things, in which it can naturally be, or of which it is predicated, these have nothing intermediate ; but in the case of those, in which it is not necessary, that one should be inherent, there is something intermediate. For instance, health and disease may na- turally subsist in the body of an animal, and it is necessary that one, should be therein, either disease, or health ; the odd and even are also predicated of number, and one of the two, either the odd or the even, must necessarily be in number, yet there is nothing intermediate between these, neither between disease and health, nor between the odd and the even. Those contraries, again, have something intermediate, in which one of them need not be inherent, as black and white are naturally in body, but it is not necessary, that one of these, should be inherent in body, for every body, is not white or black. Vileness, also and worth, are predicated of man, and of many others, yet one of these, need not be in those things of which it is predicated, for not all things are either vile or worthy ; at least, there is something intermediate, as between white and black, there is dark brown, and pale, and many other colours, but between vileness and worth, that, is intermediate, which is neither vile, nor worthy. In some instances, the inter- mediates have names, thus, the dark brown, and the pale, and such colours are media between white and black, but in other cases, it is not easy to assign a name to the intermediate, but the latter i3 defined, by the negation of either extreme, as, for exam- ple, whatever is neither good nor bad, nor just nor unjust.1
Privation, however,2 and habit are predicated 3. opposition
' Vide Whately, book ii. ch. 5, sect. 1 ; also book ii. ch. 3, sect. 4 ; also Metaph. lib. iv. c. 10. 8 Cf. Metaph. lib. iv. c. 22 and 23. Examples of Positive, Privative,
d 2
36 aristotle's organon. [chap. x.
of habit and of something identical, as sight and blindness of the privation. eye^ an(j universally, in whatever the habit is natu-
rally adapted to be produced, of such is either predicated. We say then, that each of the things capable of receiving habit is deprived of it, when it is not in that, wherein it might naturally be, and when it is adapted naturally to possess it ; thus we say that a man is toothless, not because he has no teeth, and blind, not because he has no sight, but because he has them not, Avhec he might naturally have them, for some persons from their birth, have neither sight nor teeth, yet they are neither called tooth- i. Distinction less nor blind. To be deprived of, and to possess in the meaning habit, then, are not privation and habit, for the
of habitual and .,.,,. , , . .. . , ,. -, • ,
privative op- sight is habit, but the privation is blindness, but position. ^0 p0Ssess sight is not sight, nor to be blind, blind-
ness, for blindness is a certain privation, but the being blind is to be deprived, and is not privation, for if blindness were the same as being blind, both might be predicated of the same person, but a man is said to be blind, yet he is never called blindness. To be deprived also, and to possess habit, appear to be similarly opposed, as privation and habit, since the mode of opposition is the same, for as blindness is opposed to sight, so likewise is the being blind, opposed to the possession of sight.1 4. opposition Neither is that, which falls under affirmation and of affirmative negation, affirmation and negation ; for affirmation is an affirmative sentence, and negation a negative
and Negative words are given in Hill's Logic, p. 27. Aldrich's definition of the three will be remembered here, namely, that the first signifies the presence of an attribute ; the second, its absence from a subject capable of it; the last, its absence from a subject incapable of it. A definite noun and its corresponding indefinite noun together, constitute a perfect division.
1 This opposition between propositions is said to be as to their quality ; to this may be appended that contrariety of quality which exists between two particulars, properly called the opposition of sub-contraries. It may here be observed, that though this last-named form of contrariety is ad- mitted by Aristotle, (Int. ch. 7,) he does not use the term v-nevavrnoQ as expressive of it, but calls it, in Anal. Prior, ii. 1 5, an opposition /card tt)v \iZiv. The term is used by the Greek commentators, (Ammonius Schol. p. 115, a. 15,) Boethius Int. ad Syll. p. 564. A poetical example of the mutual subversion of some relative opposites may be found in Shaks- peare's King John, act iii. scene 1 :
" Indirection thereby grows direct. And falsehood falsehood cures : as fire cools fire Within the scorched veins of one new burn'd."
CHAP. X.] THE CATEGORIES. 37
sentence, but nothing which falls under affirmation and nega- tion is a sentence (but a thing). Still these are said to be mutually opposed, as affirmation and negation, since in them the mode of opposition is the same, for as affirmation is some- times opposed to negation, for example, "he sits" to "he does not sit," so that thing which is under each is opposed, as " sitting " to " not sitting."
But that privation and habit, are not opposed as relatives, is evident, since what a thing is, is and habit not not asserted of its opposite, for sight is not the relative]y op- sight of blindness, nor in any other way spoken in reference to it, so also blindness, cannot be called the blind- ness of sight, but blindness indeed is said to be the privation of sight, not the blindness of sight. Moreover, all relatives are referred to reciprocals, so that if blindness were relative, it would reciprocate with that to which it is referred, but it does not reciprocate, for sight is not said to be the sight of jlindness.
From these things, also, it is manifest that those which are predicated, according to privation and habit, are not ;ontrarily opposed, for of contraries which have [rarity?* C°" no intermediate, one must always necessarily be inherent, wherein it is naturally adapted to be inherent, or of which it is predicated, but between these, there is no inter- mediate thing wherein it was necessary that the one should be in what was capable of receiving it, as in the case, of disease and health, in odd and the even number. Of those however between which there is an intermediate, it is never necessary that one should be inherent in every thing ; for neither is it necessary that every thing capable of receiving it, should be white or black, or hot or cold, since there is no prevention to an interme- diate being between them. Again, of these also there was a cer- tain medium, of which it was not requisite that one should be in its recipient, unless where one is naturally inherent, as in fire to be hot, and in snow to be white : still in these, one, must of necessity be definitely inherent, and not in whatever way it may happen, for neither does it happen that fire is cold, nor that snow is black.1 Wherefore it is not necessary that one of them should be in every thing capable of receiving it, but
' Vide Whately and Hill's Logic, De terminorum distributione : also the former upon Fallacies, book i. sections 1 and 13.
38 Aristotle's organon. [chap. x.
only in those wherein the one is naturally inherent, and in these, that which is definitely and not casually, one. In privation however, and habit, neither of the above-men- tioned particulars is true, since it is not always necessary that one should be inherent in what is capable of receiv- ing it, as what is not yet naturally adapted to have sight, is neither said to be blind nor to have si°rht ;
6. Nature of
intermediates wherefore these things will not be of such contra- ct posTtion'0 r*es as nave nothing intermediate. But neither, on the other hand, will they be amongst those which have something intermediate, since it is necessary that at some time, one of them, should be inherent in every thing ca- pable of receiving it : thus when a man is naturally fitted to have sight, then he will be said to be blind, or to have sight, and one of these, not definitely, but whichever may happen, since he need not necessarily be blind, nor see, but either, as it may happen. In respect nevertheless of contraries, which have an intermediate, it is by no means necessary that one, should be inherent in every thing, but in some things, and in these, one of them definitely, and neither casually, so that things which are opposed according to privation and habit, are evi- dently not in either of these ways opposed, as contraries.
Again, in contraries, when the recipient exists, a change into each other may happen, unless one is naturally inherent in something, as for instance, in fire to be hot. It is possible also for the healthy to be sick, the white to become black, cold to become hot, (and the hot to become cold) ; from good it is possible to become bad, and from bad good, for he who is depraved, being led to better pursuits and discourses, advances, though but a little, to be better, and if he once makes an advancement ever so little, he will evidently become either altogether changed, or have made a very great proficiency,1
1 Vide Ethics, book ii. ch. 1 ; <ilso Magna Moralia, and Metaph. lib. viii. It will be observed that here, as elsewhere, he speaks of moral, not intellectual advancement: Truth, however, he considers the work of both the intellectual parts of the soul. Ethics, book vi. ch. 2. See Mer- chant of Venice, act iv. scene 1 ; and Massinger's beautiful lines on the progress of moral habit in the 5th act, 2nd scene, of the Virgin Martyr : also the duty of increasing the mental powers, Hamlet, act iv. sc. 4 :
" Sure he that made us with such large disccurse,
Looking before and after, gave us not
That capability and godlike reason
To fas In us unused."
CHAP. X.J THE CATEGORIES. 39
since he ever becomes more disposed to virtue, even if he has ob- tained the smallest, increase, from the beginning. Wherefore he will probably acquire greater increase, and this perpetually occurring, he will at last be transformed entirely to a contrary habit, unless he be prevented by time ; but in privation and habit, it is impossible for a mutual change to occur, since it may take place from habit to privation, but from privation to habit is impossible, as neither can he who has become blind, again see, the bald again have hair, nor has the toothless ever yet again got teeth.
Whatever things are opposed, as affirmation 7 The u and negation, are evidently opposed according to Harity of affir-
j?.-, , ,. •• j • • ., mative, and ne-
none or the above-mentioned modes, since in these sative opposi-
alone it is always necessary that one should be ti.on> **' one
* *> should be true
true, but the other false ; l as neither, is it al- and the other ways necessary in contraries that one should be false' true but the other false, nor in relatives, nor in habit and privation. For instance, health and disease, are contrary, yet neither of them is either true or false ; so also the double and the half are relatively opposed, and neither of them is either true or false ; nor in things which are predicated as to priva- tion and habit, as sight and blindness. In short, nothing pre- dicated without any conjunction, is either true or false, and all the above-named are predicated without conjunction. Not but that a thing of this kind may appear, to happen in contraries, which are predicated conjunctively, for " Socrates is well" is opposed to " Socrates is sick," 2 yet neither in these is it always necessary, that one should be true and the other false, for while Socrates lives, one will be true and the other false, but when he is not alive, both will be false, since neither is it true that Socrates is sick, nor that he is well, when he is not
1 Vide rules of natural opposition in the common Logical Treatises.
2 These are properly contradictories, one being true and the other false, but the definition of contradictories does not include them as being given by Aldrich only of universals ; the definition however given in Anal. Post, i. 2, 6, will include them — avrityaoiQ Si avriQtaiq ?)c oi>k sort fi(ra£,v Kaff avTt]\'. Some logicians call the opposition of singulars secondary contradiction. Boethius, p. 613, regards such instances as con- tradictories ; also Wallis, lib. ii. ch. 5. Compare Aldrich's Logic upon rules of contradiction : it is remarkable that he does not mention the op- position of singulars until he comes to the causes of opposition of propo- sitions. Cf. Interpretation 7, Anal. Prior, xi. 15.
40 Aristotle's organon. | chap, xi
in existence at all. In privation and habit, then when the sub- ject is non-existent, neither is true, but when the subject exists, the one is not always true, nor the other false. " Socrates sees " is opposed to " Socrates is blind," as privation and habit, and whilst he exists, one need not be true or false, for when he is not naturally fitted to possess them, both are false, but when Socrates does not exist at all, both will thus be false, that he sees, and that he is blind. In affirmation and negation always, if Socrates be or be not, one will always be false and the other true ; for it is evident with respect to these two, " Socrates is sick," and " Socrates is not sick," that when he exists one of them is true and the other false ; and in like manner when he does not exist, for in the latter case that he is ill is false, but that he is not ill is true ; so that in those things alone which are affirmatively and negatively opposed will it be the pecu- liarity that one of them is either true or false.
Chap. XL — Opposites continued, especially as to the contrariety be- tween the Evil and the Good.
1. Opposition " Evil " is of necessity opposed to good, and of good and this is evident from an induction of singulars,
as disease to health, and cowardice to courage, and similarly of the rest. But to evil, at one time, good, is contrary, and at another, evil, for to indigence being an evil, Rhet. b i. c. 7 excess *s contrary, which is also an evil ; in like and Eth. t>. n. manner, mediocrity, which is a good, is opposed to
each of them. A man may perceive this in re- spect of a few instances, but in the majority the contrary to evil is always good.1
Again, of contraries it is not required, if one is, contrary6exists that the remainder should be; for when every
1 Compare note in the preceding chapter relative to the observation of Archytas as to generic and specific contrariety, whence it will be seen that this chapter is nothing else than an elaboration of the principle he lays down. He adds in his treatise on Opposites, " There are three dif- ferences of contraries ; for some things are opposed as good to evil, as for instance health to sickness, some as evil to evil, as avarice to prodigality, and some as neither to neither, as the white to the black, and the heavy to the light." What he calls " neither," and Aristotle " the negation of extremes," subsequent philosophers called " indifferent," adtaQopa. Comp. Cic. ad Atticum, also Sanct. Chrys. in Ep. ad Ephes. c. 5.
CHAP. XII. J
THE CATEGORIES.
41
man is well, there will indeed be health, and not it is not neces- disease, and so also when all things are white, there other 'shouw will be whiteness, but not blackness. Besides, if exist— but * Socrates is well" be the contrary of " Socrates is destroys the ill," and both cannot possibly be inherent in the other- same subject, it follows, that when one of the contraries exists^ the other cannot possibly exist, for " Socrates is well " exist- ing, " Socrates is ill" cannot exist.1
Contraries, however, evidently are, by their na- ture, adapted to subsist about the same thing, genwan^nhe- either in species or genus, since disease and health rent in similar naturally subsist in the body of an animal, but cTensera °r spe" whiteness and blackness simply in body, and jus- tice and injustice in the soul of man.
Notwithstanding, it is requisite that all contraries be either in the same genus, or in contrary genera, or be ge- nera themselves ; for white and black are in the same genus, as " colour '* is the genus of them ; but justice and injustice in contrary genera, for "virtue" is the genus of one, but "vice " of the other ; lastly, "good" and "bad "are not in a genus, but are themselves the genera of certain things.
4. They must be either in the same genus, or in contrary ge- nera, or be ge- nera them- selves.
Cha p. XII.-— Of Priority?
A thing is said to be prior to another in four respects : first and most properly, in respect of fourfold! y time, according to which, one is said to be older 1st. in respect
• — f • i i ■ • • n i of time.
and more ancient than another, since it is called
older and more ancient, because the time is longer. Next,
when it does not reciprocate, according to the „ , __
. L . . ° 2nd, When
consequence ot existence : thus one is prior to two, there is no re- for two existing, it follows directly that one ex- ^^^ t0 ists ; but when one is, it is not necessary that two quence of ex- should be, hence the consequence of the re- mainder's existence does not reciprocate from the existence of the one ; but such a thing appears to be prior, from which the consequence of existence does not reciprocate.
1 Logic taking no cognizance of understood matter, the necessary, im- possible, and contingent should be omitted from the table of opposition.— Mansel. Compare also Whately de Oppositione, cited above.
a Cf. Metaph. lib. iv. c. 11.
42 ARISTOTLE'S ORGANON. [CHAP. Xn.
3rd, in respect Thirdly, the prior is that predicated according of order. to a certam order, as in the instance of sciences and
discourses, for in demonstrative sciences, the prior and the posterior, subsist in order, since the elements are prior in order, to the diagrams, and in grammar, letters are before syllables ; so also of discourses, as the proem is prior, in order, to the narration.
Moreover, besides what we have mentioned, the kn '• In eXCel" better and more excellent appear to be prior by nature. The common people are accustomed to say, that those whom they chiefly honour and especially re- gard, are prior in their esteem;1 but this is nearly the most foreign of all the modes, wherefore such are (nearly) the modes of priority which have been enumerated. 2 Another Besides the above-mentioned, there may yet
mode of prior- appear to be another mode of the prior ; as of edy,"vhereeone things reciprocating, according to the consequence thing is the 0f existence, that which in any respect is the cause
CiillSt' 01 3.11-
other's exist- of the existence of the one, may justly be said to be ing- by nature prior, and that there are, certain things
of this kind, is manifest. For that man exists, reciprocates, according to the consequence of existence, with the true sen- tence respecting him, since if man is, the sentence is true, by which we say, that man is, and it reciprocates, since if the sentence be true, by which we say that man is, then man is. Notwithstanding, a true sentence, is by no means the cause of a thing's existence, but in some way, the thing appears the cause of the sentence being true, for in consequence of a thing existing, or not existing:, is a sentence said to be true or false. Wherefore one thing may be called prior to another, according to five modes.2
1 In the text, rovg Evrifiwrepovg. The adverbial construction repre- sented in Greek by the neuter plural, was frequently the form of employ- ing -n-pwToc in this sense : thus Herod, vi. 100, Ato-%(V»/£ 6 NoOwi'oe iwv twv 'Epsrpiewv rd npiora. In Latin the same expression occurs for great men, primates equivalent to optimates, and sometimes primores ; thus Liv. Primoribus patrum ; Hor. Populi primores, etc. An odd in- stance of "first" for "noblest" occurs in Coriolanus, act iv. scene 1,
" My first son, Whither wilt thou go ?" where see note, Knight's ed.
2 The tautological baldness of this whole chapter, it is hopeless to remedy, its arrangement also is slovenly : for the latter portion, the next
CHAP. XIII.] THE CATEGORIES. ■ 43
Chap. XIII. — Of things simultaneous.
Things are called simultaneous simply and most , Those thi properly, whose generation occurs at the same are simuitane-
• ous which at
time, for neither is prior or posterior ; these, the same time therefore, are said to be simultaneous as to time. are produced,
' . and which re-
mit by nature those are simultaneous, which re- ciprocate, but
ciprocate according to the consequence of exist- cause'the*1"
ence, although one, is by no means the cause of other's exist-
the existence of the other, as in the double and
the half, for these reciprocate ; thus the double existing, the
half also exists, and the half existing, the double exists, but
neither is the cause of existence to the other.
Those, also, which being derived from the same „ _
'.,... b ,-, , . , 2. Or which as
genus, are by division mutually opposed, are said species of the to be naturally simultaneous ; ' but they, are said l^slTin'the to have a division opposite to each other, which same relation subsist according to the same division ; thus the winged is opposed to pedestrian and aquatic, as these being derived from the same genus, are by division mutually opposed, for animal is divided into these, viz. into the winged, the pe- destrian, and aquatic, and none of these is prior or posterior, but things of this kind appear naturally simultaneous. Each of these again, may be divided into species, for instance, the winged, the pedestrian, and the aquatic ; wherefore, those will be naturally simultaneous which, derived from the same genus, subsist according to the same division. But genera are al- ways prior to species, since they do not reciprocate according to the consequence of existence ;2 for the aquatic existing, ani- mal exists, but though animal exists, it is not necessary that the aquatic should.
Hence those are called naturally simultaneous, which in- deed reciprocate, according to the consequence of existence ; but the one is by no means the cause of existence to the other, which is also the case with things that, derived from the same
chapter will appear elucidatory, and, in fact, is the same statement of the whole, in reverse.
1 Porphyry recognises only a relative difference between two given species. See Introduction ; also Hill's Logic.
2 See Whately, book ii. ch. 5.
44 aristotle's organon. [chap. xiv.
genus, have by division a mutual opposition ; those, how- ever, are simply simultaneous whose generation is at the same time.1
i Chap. XIV.— Of Motion?
i. Motion of Of motion, there are six species, generation, cor- six kmds. ruption, increase, diminution, alteration, and
change of place.
The other motions then evidently differ from each other, for neither is generation, corruption, nor increase, diminu- tion, nor alteration, change of place, and so of the rest. In 2. Alteration the case of alteration however, there is some reiItiventobthe doubt, wnether it be not sometimes necessary that rest, this dis- what is altered, be so, in respect to some one, of proved. tjie other motions, but this is not true, for it hap-
pens that we are altered, as to nearly all the passions, or at least the greater part of them, without any participation of the other motions, for it is not necessary that what is passively moved should be either increased or diminished. Wherefore, alteration will differ from the other motions, since 1st, By no in- if it were the same, it would be necessary that
nutlon n'ecJs""" wnat is altered> be forthwith increased or dimin- sariiy occurring ished, or follow some of the other motions, but tered!at ls al" this is not necessary. Similarly, also, what is in- 2nd, By no creased or moved with any other motion, ought
change taking ,. ., ,,. .., N J , ,.' °
place in to be altered (in quality) ; but some things are
quality. increased which are not so altered, as a square
is increased when a gnomon3 is placed about it, but it has
1 The office of Logic being to guard against ambiguity in the use of terms; it is clear that by nominal division alone, species from the same genus will often have a subordinate opposition, as antagonistic in its na- ture, as opposite genera ; for example, purple, yellow, etc., under colour. Boethius uses division in three senses : 1. Of a genus into species. 2. Of a whole into its parts. 3. Of an equivocal term into its several significa- tions. Cicero, Top. vi. ch., calls the first, divisio, the second, partitio. Aristotle approves division by contraries. See Top. vi. 6, 3, de part. Anim. i. 3.
2 Compare the Physics, books iii. v. vi. vii. viii., also Metaph. lib. x. ch. 9, 11, 12. ^ In the 11th ch. of the 10th book, Meta., he defines motion, H icivrjoig tvepyua fikv tlvat Soicti rtc are\?)g SL Vide also the Scholia Marc. ed. Waitz, 'H Kivqoig kanv l^dWa^ig icai tKcrracrig.
3 The following figure will illustrate this comparison : the use of the yvwfiov being the ascertainment of right angles.
oriAP. xv.]
THE CATEGORIES.
3. Generic and specific contra- riety to motion.
not become altered (in quality) ; and in like manner with other things of this kind, so that these motions will differ from each other.
Nevertheless simply, rest is contrary to motion, the several rests to the several motions, corrup- tion to generation, diminution to increase, rest in place to change in place ; but change to a contrary place seems especially opposed, as ascent to descent, downwards to upwards. Still it is not easy, to define the contrary to the re- mainder of these specified motions, but it seems to have no contrary, unless some one should oppose to this, rest according to quality, or change of quality into its contrary, just as in change of place, rest according to place, or change to a contrary place. For alteration is the mutation of quality, so that to mo- tion according to quality, will rest according to quality, or change to the contrary of the quality, be opposed ; thus becoming white is opposed to becoming black, since a change in quality occurs, there being an alteration of quality into contraries.
Chap. XV.— Of the verb « to Haver
To have, is predicated in many modes ; either as habit and disposition or some other quality, for we are said to have knowledge and virtue ; l
|
3 \ \ |
1st / / Square |
|
/ a / s m / |
1 O N. \ |
I. Having pre- dicated in many ways. 1. Quality. 1
1 This form is often cognate, and almost identical with the 7th, of pos- session, thus St. Paul's Ep. 2 Cor. iv. 7 ; as to the 2nd, the idiom of the English does not fully correspond with the Greek Ixuv, our word in re- lation to quantity being " to hold." A rare use of the word "havings " occurs in the Lover's Complaint of Shakspeare ; see Knight's edition : " Whose rarest havings made the blossoms dote."
46 Aristotle's organon. [chap. i.
2. Quantity or as to quantity, as the size which any one has ; thus he is said to have the size of three or four cubits ; or
3. investiture, as things about the body, as a garment or a
4. in a part. tunic ; ' or as in a part, as a ring in the hand ;
5. As to a part, or as a part, as the hand or the foot ; or as in a
6. in measure, vessel, as a bushel has wheat, or a flagon, wine, for the flagon is said to have2 the wine, and the bushel the wheat ; all these therefore are said to have, as in a vessel ; or
as a possession, for we are said to have a house or
7. Possession. , -1
land. A man is also said to have a wife, and the wife a husband, but the mode now mentioned, of " to have," seems the most 8 Also indi- foreign, for we mean nothing else by having a wife, rectiy or by than that she cohabits with a man ; there may analogy. perhaps appear to be some other modes of having,
but those usually mentioned have nearly all been enumerated.
ON INTERPRETATION.3
Chap. I. — What Interpretation is, which is here discussed: of the Symbols or Exponents of the Passions by the voice — of Nouns and Verbs.
l. Things enun- We must first determine what a noun, and what
cia.ted h? the a verb, are ; next, what are negation, affirmation,
bois of the pas- enunciation, and a sentence, sions in the Those things therefore which are in the voice,
1 This is Shakspearian usage also. Sometimes this form is applied generally to condition or estate, and even attire, and manner. See Win- ter's Tale, iv. 3. The next are in the sense of " holding," again.
3 More properly \wpeTv. It is evident throughout this chapter, that the elliptical modes in which we employ " have " as an auxiliary verb are endless, and in the use of it, the assimilation of the English to the Greek is peculiar. Sometimes a very decided verb is omitted, and the auxiliary made to stand alone; thus, in K. Henry VIII. act ii. sc. 2,
"All the clerks,
I mean the learned ones, in Christian kingdoms,
Have their free voices " for " have sent " their free voices.
For the Aristotelian usages of the word, compare Metaph. lib. iv. c. 23.
3 Having discussed in the Categories the doctrine of simple terms, Aristotle, in the following treatise, proceeds to the discussion of Proposi-
CHAP. 1.1 ON INTERPRETATION. 47
are symbols of the passions of the soul, and when written, are symbols of the (passions) in the voice, and as there are not the same letters among all men, so neither have all the same voices, yet those passions of the soul, of which these are primarily the signs, are the same among all, the things also, of which these are the similitudes, are the same. About these latter, we have spoken in the treatise " Of the Soul," ' for they are parts be- longing to another discussion, but as in the soul, there is sometimes a conception, without truth or falsehood, and at another time, it is such, as necessarily to have one of these, inherent in it, so also is it with the voice, for false- 2 Truth and hood and truth are involved in composition and falsehood of division.2 Nouns therefone and verbs of them- dependent on
tion, which, is the result of the conjunction of simple terms, and discard- ing the other species of sentence, confines himself to the categoric form of the enunciative sentence simply, preparatory to the systematic inquiry into the nature of syllogism, hereafter to be conducted in the Analytics. Indeed, for this reason, as occupying a middle place between simple terms and syllogism, this treatise is more properly introduced here, as Waitz, Buhle, Averrois, and Taylor place it, than after the Topics, as by Bekker. So highly is it esteemed by Ammonius, (in librum Aris. de Int., Vend. 1545,) that he states his gratitude to the god Hermes if he shall be able to add any thing to its elucidation, from what he recollects of the interpret- ations of Proclus, the Platonist, his preceptor.
As to the title, notwithstanding much difference of opinion, the fruit of primary misconception of the term (7rfp< tpurjvtiag), its application here seems well grounded, as descriptive of language in its construction, being enunciative of the gnostic powers of the soul ; it may therefore, we think, (with the learned author of the Prolegomena Logica, Mansel,) be adequately Anglicized, " Of language as the interpretation of thought." Boethe defines it, " Interpretatio est vox significativa, per se ipsam, aliquid significans," to which Waitz adds the remark, " latius patet tpfirjvtia quam XtSic." Isidore of Seville observes : " Omnis elocutio concept® rei interpres est : inde perihermeniam nominant quam interpretationem nos appellamus." For various interpretations of the word, see St. Hilaire, de la Logique d' Aristote, p. i. ch. 1(3. The treatise itself may be divided into four parts : First, concerning the principles of the enunciative sen- tence, including definitions of its component parts ; the three othera in- forming us of proposition : as, 1st, purely enunciative ; 2nd, more complex, wherein something is added to the predicate, making in fact a fourth term ; 3rd, modal : at the end he annexes an inquiry connected with a case of problematic contrariety.
1 Vide de Anim. iii. 6 ; also Metaph.
2 This is evident, since logic itself is psychological; but observe, he does not say all truth is conversant with composition and division, the last is indeed excluded from the idealities of Plato. Thought, per se, has no need of systematic language, the most accurate development of which does
48 atcistotle's organon. [chap n.
composition selves resemble conception, without composition wodrdds!Vlsi0symf and division, as "man," or "white," when some- bois. ' thing is not added, for as yet it is neither true nor
false, an instance of which is that the w6rd rpayiXacpoc1 sig- nifies something indeed, but not yet any thing true or false, unless to be, or not to be, is added, either simply, or according to time.
Chap. II. — Of the Noun and its Case.
1 Definition ^ noun therefore is a sound significant 2 by of the noun— compact without time, of which no part is separ- ately signi-" ately significant ; thus in the noun KdWnnrog, the ficant— distinc- '[n7r0Q signifies nothing by itself, as it does in the
tion between °
simple and sentence koXoq 'Ltttvoq ; neither does it happen with composite. simple nouns as it does with composite, for in tbe former there is by no means the part significant, but in the latter a part would be, yet signifies nothing separately, as in the word iwaKvpoKeXric, 3 the KeXng signifies no-
conffcflf*11*0' tninS ty itself>- But il is according to compact,4 because naturally there is no noun ; but when it
not touch, in all cases, its subtlety. On the distinction between cn]/xt1ov and 6fj.oiw[xa, see Waitz, vol. i. 324. It will be remembered that the legi- timate office of logic is not establishment of the truth or falsehood of the subject matter, except in so far as that truth or falsehood results from certain relations of original data according to fixed rules. (Vide Whately , Hill, Huyshe.) It is needless to quote the definition given by Aldrich of Proposition here.
1 That is, an animal partly a goat and partly a stag. Compare with this and the following chapters, ch. xx. of the Poetics.
2 <boj)>rj <ji)ixavriKr), called by Aldrich vox, by Boethius and Petrus Hispanus, vox, signiticativa ad placitum. Logical nouns are equivalent to simple terms, or categorems, in opposition to syncategorems, which are not, per se, significative. Here Aristotle mentions the noun and the verb : Dut (ch. xx. Poetics) he elsewhere adds the conjunction and article ((pwvai aaiifioi). Cf. Harris Hermes, ch. iii. ; also Hill's Logic*
3 A piratical ship. The word is a vox complexa — <pwv>), avfiTmrXtyfikvi}, a compound word, whereof each part has a meaning in composition, 001)'?} aTrXij, where the parts have no meaning. Vide Sanderson's Logic.
4 Primo quidem declarat conceptum deinde supponit pro re. Aldrich. When Aristotle makes the assertion in the text, he does not dissent from that of Socrates in the Cratylus ; but whilst he denies the subsistence of names from nature, an opinion adopted by Heraclitus, he shows in his Physical Auscultation, and various other places, that names accord with things. In this very treatise the name of " an indefinite noun," or of " contradic-
CnAP. III.] ON INTERPRETATION. 49
becomes a symbol, since illiterate sounds also signify some- thing, as the sounds of beasts, of which there is no noun.
" Not man," however, is not a noun, neither is a name instituted by which we ought to call it, since n'itJnot'anoun it is neither a sentence, nor a negation ; ' but let it be an indefinite noun because it exists in respect of every thing alike, both of that which is, and of that which is not.2 (friXwrog indeed, or <bi\u>vi, and such like words . _
i 4. Chscs of tne
are not nouns, but cases of a noun,3 but the de- noun differ finition of it (that is, of the case) is the same as {^Sajbein™ to other things (with the definition of a noun), but joined to the (it differs in) that, with (the verb) "is" or "was" they'slgnily1 a' or " will be," it does not signify what is true or neither truth
n , , , , ° /. .„ i ■ \ nor falsehood.
false, but the noun always (signifies this), as
" Philonus is," or " is not," for as yet, this neither signifies
what is true, nor what is false.
Chap. III. — Of the Verb, its Case, and of those called Verbs
generally*
A verb, is that which, besides something else, sig- 1 Definjti0n nifies time ; of which no part is separately signifi- of the verb or cant, and it is always indicative of those things which pw°'
tion," given by him, clearly shows his opinion about names. The suppo- sitio of Aldrich is not found in Aristotle, but may be traced to the Greek Logic of Michael Psellus.
1 Not a noun, that is, not a true and perfect noun, nor a sentence, since it is neither " verum vel falsum significans;" neither is it a negation, for it wants a verb, without which there is no negation.
2 Signifies as well being as non-being : in the original bfioiiog t<p' utovovv virdpxt1- Waitz omits the rest of this sentence from "indefi- nite noun."
3 Aristotle considers the oblique cases of a noun (tttojchiq), not the nomi- native, the Stoics regarded the nominative (IvOtia) also a case. Oblique cases are syncategorematic, that is, can only form part of a term, the nominative may be a term by itself.
4 Aristotle does not employ the term categorematic, but defines his simple terms, opot ilg oi)e SiaXitrai r) Ttporaaig, — with him categorema- tic words are the noun as subject, and the verb as predicate. Vide Boeth Introd. ad Syll. and Pet. Hisp. Tract i. Cf. Trendelenburg, Elementa, § 3. Waitz, vol. i. 267. The copula has been called the only logical verb, but is, properly speaking, no verb at all, and cannot correspond with the pi\fia \,i Aristotle, except by coalescing with the predicate. Vide Mansel's
50 ARISTOTLE'S ORGANON. [CHAP. m.
are asserted of something else. But I say that it signifies time, besides something else, as for instance, "health" is a noun, but "is well" is a verb ; for it signifies, besides being well, that such is the case now : it is always also significant of tilings asserted of something else, as of those which are predicated of a subject, or which are in a subject.
Nevertheless I do not call, "is not well," and, "is ed withMga"" not iU " — ver bs 5 for incleed they signify time, be- tion, or in its sides something else, and are always (significant) of theSpresent°, is something, yet a name is not given to this difference, not a proper jet either be therefore an indefinite verb, because
it is similarly inherent both in whatever does, and does not exist.1 So also "was well" or "will be well" are not verbs, but they are cases of a verb, and differ from a verb, because the latter, besides something else, signifies present time ; but the others, that which is about the present time. Verbs therefore so called, by themselves, are nouns, and have
a certain signification, for the speaker establishes properly nouns. tne conception, 2 and the hearer acquiesces, but they
do not yet signify 3 whether a thing " is " or " is not," for neither is " to be" or "not to be" a sign of a thing,
Logic ; also Pacius de Interp., c. 3. The ovo/xa is aviv xpovov, the verb Trpod(jr]fiaivii xQ0V°v '■ this distinction is lost by those who, with Aldrich, resolve the verb into copula and predicate. Vide Ammonius Scholia, p. 105, b. 29. The infinitive is not included under "verb," for it is a noun-substantive, nor the participle, which is a noun-adjective, neither can the former ever be the predicate, except when another infinitive is the subject. Vide Whately, b. ii. c. i. § 3. For case as appertaining to verbs, see post, ch. 20. By Aristotle, number, tense, and mood, were all reckoned cases, tttuxsuq, or fallings, of the noun and verb, so our Eng- lish word " fall " in music.
1 Boeth. translates aopiarov, infinitum. The translation is blamed by Vives de Caus. Corr. Art. lib. iii. Sir W. Hamilton uses the word in- designate.
2 That is, in the mind of the hearer. The expression 'ivrrjoi T-qv Sta- voiav is rendered by Taylor " stops the discursive power " — a meaning which is however equivalent to " establishes the conception," since ciavoia being properly the movement of the intellect towards investi- gating truth, is "arrested," when a conception is fixed upon it: thus Buhle, " constituit conceptionem." Taylor's translation is strictly exact, but besides being obscure, enforces the introduction of many words into the text. Aiavoid. is more nearly akin to logical discursus than to any •other energy : see the note upon Anal. Post, lib. i. ch. 33.
3 i. e. before they are enunciatively joined with nouns.
CHAP. IV. 1 ON INTERPRETATION 51
nor if you should say merely, " bein^r," for that *■ They are in-
,,/ , • m? v i -j significant ex-
is nothing ; they signify however, besides some- cept mcompo-
thing else, a certain composition, which with- Sltl0n-
out the composing members it is impossible to under- stand.1
Chap. IV. — Of the Sentence.2
A sentence is voice significant by compact,* of , Definiti which any part separately possesses signification, of the sentence as indeed a word, yet not as affirmation or nega- •'KtX'a,'am«i,- tion; now I say for example "man" is signifi- ^.omitted by cant, but does not imply that it " is " or " is not;"3 it will however be affirmation or negation, if any thing be added to it. One/ syllable of the word uvBpunog, is not however (significant),4 neither the " vg " in " pig," but it is now merely sound ; still in compound words a part is significant, but not by itself, as we have observed.
Now every sentence is significant, not as an instrument, but, as we have said, by compact, still not every sentence is enunci- ative,5 but that in which truth or falsehood is inherent, which things do not exist in all sentences, as prayer is a sentence, but it is neither true nor false. Let therefore the „ _t.
, i t • i i • 2- Other kinds
other sentences be dismissed, their consideration of sentence t>e- belongs more properly to Rhetoric or Poetry; ^wc— Logic" but the enunciative sentence to our present conversant
.i with the enun-
ttieoiy. ciative alone.
1 Cf. Mansel's Prol. Log. p. 63. I follow Waitz and Bulile; Taylor's rendering is altogether erroneous.
2 Compare Poetics, ch. '20; also this treatise, ch. 5; Analy. Post, lib. ii. cap. 10; Metap. vii. 4; also Aldrich, sub vocis speciebus.
3 That is, it neither affirms nor denies something ; a verb must be added to make it significant.
4 In the Poetics, c. 20, he defines a syllable, a sound without signifi- cation, composed of a mute and an element which has sound, (i. e. a vowel or semi-vowel). An article, again, is a sound insignificant, showing the finals or distinctions of a word. Buckley has well called the de- scription most obscure : Aristotle, the star of definition, is at last confused by his own ray !
5 ' AtrotyavTiKoq 8k ov nag. The quality of signifying either what is true or false is the logical property of proposition, and is the immediate consequence of its difference, namely, affirmation or negation. Hill's Logic, p. 90. Vide also Whately, Aldrich, and the other treatises on Logic.
e 2
52 aristotles organon. [chap. v.
Chap. V. — Of Enunciation?
1. Divisions of ^NE nrs* enunciative sentence2 is affirmation; the enunciative afterwards negation, and all the rest are one by
sentence — \6- • ,. T, . , .,
roc uitoipovTi- conjunction. It is necessary however that every ***' enunciative sentence should be from a verb, or
from the case of a verb, for the definition of " man," unless " is," or " was," or " will be," or something of this kind, be added, is not yet an enunciative sentence. Why indeed is the sentence " a terrestrial biped animal " one thing, and not many things ? for it will not be one, because it is consecutively pro- nounced : this however belongs to another discussion.3 One enunciative sentence, moreover, is either that which signifies one thing,4 or which is one by conjunction,5 and composite.01 many (such sentences) are either those which sig- nify many things6 and not one thing, or which are without conjunction.7 Let therefore a noun or a verb be only a word, since we cannot say that he enunciates who thus
1 Cum disseramus de oratione cujus varlae species sunt — est una inter has ad propositum potissima qua? pronuntiabilis appellatur, absolutam sententiam comprehendens, sola ex omnibus verilati at falsitati obnoxia, quam vocat Sergius, " effatum," Varro, " proloquium," Cicero, " enunci- atum," Grace " protasin," turn "axioma; " — familiarius tamen dicetur "propositio." — Apuleius de Dogm. Platonis, lib. iii. As Mansel ob- serves justly, he has not distinguished between airofpavaig and Trporacng. the former of which is rendered by Boethius " enunciatio," the latter "pro- positio." Vide Elem. sect. 2, Trendelenburg ; Aquinas, Opusc. 48, Tract, de Enunc. The distinction drawn by the latter is not implied by Aris- totle either here or Anal. Pr. i. 1, 2.
2 Aoyof anotyavTiKOQ. Oratio indicativa, Pet. Hispanus. Boethius, " Oratio enunciativa." F or Kara^aaig, &c. see next chapter. Aldrich's de- finition errs against the third rule, and hardly presses on the second — for good definition.
3 Definition is a sentence, but not as if one enunciation ; its consider- ation belongs to the first philosophy, and the reader will find the question solved in lib. 6, of the Metaphysics.
4 As " a man runs," the purely categorical.
5 This may be disjunctive, which is a species of hypothetical or com- pound, as " it is either day or night." Vide Whately, book ii. ch. ii. sect. 1.
6 These come under the class ambiguous, founded often on one equi- vocal term only, as the " dog is moved," where dog may signify many things.
7 As " I congratulate you," &c. Compare Hill and Whately ; in the former many examples are given.
CHAP. VI.] ON INTERPRETATION. 53
expresses any thing by his voice whether he is * i. e. simple
interrogated by any one or not, but that he speaks ^™atsii°I^" le
from deliberate intention.1 Now of these enun- negation.
ciations one is simple, for instance something of * \*y\ not n^ht."
something, or fromt something, but another is 3- Definition
,° i> ,1 j. i • i i • i • of simple enun-
composed of these,;}: as a certain sentence which is datum, amavT- already a composite ; simple enunciation, then, is ?£jrepe'I™" voice significant about something being inhe- rent, or non-inherent, according as times are di- § i.e. into past,
. , , P0 present, and fu-
Vlded.CJ a ture.
Chap. VI. — Of Affirmation and Negation.3
Affirmation is the enunciation of something 1. Distinctive concerning something, but negation is the enun- ^l6™*1?.",,0^
? . a o affirmation (xa.
ciation of something from something.4 Since, ™0a<nr) and
1 This form arises from our usual elliptical method of expression, in regard to interrogatives, when the repeated verb is understood but not expressed ; as, " Who reads ? Socrates," i. e. " Socrates reads."
2 These sentences are known by the barbarous name of propositions de inesse, that is, denoting the inherency or inbeing of the predicated qua- lity in the class or thing expressed by the subject. The expression tov virapxtiv in Aristotle, has two meanings, one in which the pre- dicate is said to be in the subject, which is equivalent to Karijyopnrai, as all B is A, to A Karriyopilrai Kara iravroq roii B ; and Elvai iv, whereby the subject is said to be in the predicate, as all A is B, A iariv iv o\y ry B., which is exactly the reverse of Karriyopelrai. See note 3, p. 80. On the different species of sentences alluded to in the above chapter, see also Petrus Hispanus, Sum. Log. Tract 1. " Vocum signifi- cativarum ad "placitum, alia complexa ut oratio, alia incomplexa ut nomen et verbum. Orationum perfectarum, alia indicativa, ut ' Homo currit ; ' alia imperativa, ut ' Petre fac ignem ; ' alia optativa, ut " Utinam esset bonus clericus ! " alia subjunctiva, ut " si veneris ad me dabo tibi equum ; " alia deprecativa, ut " miserere mei Deus ! " Harum autem orationum sola indicativa oratio dicitur esse propositio." Cf. Boeth. de Syll. Cat. p. 582, also Poet. c. 20.
3 Upon the import of Propositions, see Mill's Logic, book i. ch. 5 Reid defines judgment after the above manner : " an act of the mind whereby one thing is affirmed or denied of another." Affirmative judg- ment is called by Aldrich, " compositio," negative, " divisio," (rvv9tcng and diaiptaig : comp. 1st ch. of this treatise. Apuleius calls the sentence either Propositio dedicativa or abdicativa.
4 My translation is identical with that of Boethius : Aldrich's defini- tion is applicable only to propositions " tertii adjaceniis," and is in fact acci- dental. Vide Huyshe, p. 5t.
5-i Aristotle's organon. [chap. vn.
negation (aTro- however, a man may enunciate what is inherent as *a<7,t') though it were not,1 and what is not 2 as though it
were ; that which is, as if it were, and that which is not, as if it were not, and in like manner about times external to the pre- sent ; it is possible that whatever any one affirms may be denied, and that whatever any one denies may be affirmed, whence it is evident that to every affirmation there is an op- posite negation, and to every negation an opposite affirma- tion.3 Let this be contradiction, affirmation and betweenaffim- negation being opposites,4 but I call that opposi- ative and nega- tion which is of the same respecting the same,5 not
tive constitutes . ,. , , , * ~. , /» ,
contradiction equivocally, and such other particulars ot the uirn'fMunr). cf. jjjn(j as we have concluded against sophistical importunities.6
Chap. VII. — Of Contraries and Contradictories.
Of things, since some are universal, but others between^he"1 singular,7 (and by universal I mean whatever may universal (to naturallv be predicated of many things, but by sin-
KaDoXov) 1 ji i i ■• 1 it n • • i
and the singu- gular, that which may not : as " man is universal,
«»"►""" but " Callias " singular,) it is necessary to enunciate
that something is, or is not, inherent, at one time, in
' A false negation, (2) a false affirmation : of the subsequent examples, the first is a true affirmation, and the second a true negation.
3 This classification originates in the logical difference of propositions, see Hill's Logic, page 96.
4 al avriKei^isvai (irporacreig), this term is sometimes by Aristotle limited to contradictories.
5 " When having the same subject and predicate they differ in quan- tity, or quality, or both." Whately. Vide also some general remarks on this subject in Huyshe, p. 51, note.
6 Vide " Sophistical Elenchi."
7 Taylor has mistaken Ka9' tKaarov, by translating it " particular," as usual : see note, page 33. Compare An. Pr. i. 1,2. Omnis is the sign of an universal proposition taken distinctively, as Omnis homo est animal ; when collectively, the proposition is singular. Individual names are distinguished as individua signata, as " Socrates : " individua demonstra- tiva, by a demonstrative pronoun, hie homo : individua vaga, by an inde- finite pronoun, aliquis, quidam : this distinction is found in the Greek commentators. Cf. Albert de Predicab. Tract, iv. cap. 7. Aquinas. The two first form singular propositions ; a doubt has been entertained as to the last, whether they form singulars or particulars. Mansel's Logic,
CHAP. VII.] ON INTERPRETATION. 55
an universal, at another in a singular thing. Now, if any one universally enunciates of an universal, that something is or is not inherent, these enunciations will be contrary : 1 I mean universally enunciates of an universal, as contrariety— that " every man is white," " no man is white." ¥avT1?' al When on the other hand he enunciates of univer- sals, not universally,2 these are not contraries, though the things signified may sometimes be contrary ; but I mean by not universally enunciating of universals, as that " man is white," "man is not white :" for man being universal, is not employed as an universal in the enunciation, since the word " every " does not signify the universal, but (shows that the subject is) uni- versally (taken). Now to predicate universally of what is univer- sally predicated is not true, for no affirmation will be true in which the universal is predicated of an universal predicate,3 as for in- stance, "every man" is "every animal." Where- 3 0fcontradic fore I say affirmation is opposed to negation contra- tion : {hrtubarX- dictorily, the affirmation which signifies the uni- «"•»»*««'»<»>■ versal to that which is not universal, as " every man is white," "not every man is white," "no man is white," "some man is white." But contrarily is between universal affirmative and uni- versal negative, as " every man is white," " no man is white," " every man is just," "no man is just." 4 Wherefore it is impossi-
p. 46. When a singular term is the predicate, it must of course be co- extensive with its subject. On the above chapter compare Whately, book ii. 2, 3, and Hill, 9, et seq. : in fact, a slight acquaintance even with Aldrich's -Logic will suffice to place the principle of opposition, as copied here, clearly before the reader ; for mere simplification we have annexed the usual scheme of opposition.
1 That is, adds the universal mark, or sign, " every " or " none." It should be recollected also, as Taylor observes here, " that contraries may at one and the same time be absent from a subject, but they cannot at one and the same time be inherent in it;" this Aristotle indeed points out in this chapter. (2) " Not universally, i. e. does not add the universal mark" — he adds, " the things signified may be contraries, that is to say, the mental conceptions may be, whilst the enunciations are still indefi- nite. The extent of the indefinite is regulated by the matter of the pro- position, and is universal in necessary and impossible matter."
3 For example, to say, every man is every animal, is false, unless man is horse, ox, etc. ; or to say every man is every visible thing will be false, be- cause the predicate of every man may be also said of Socrates, hence So- crates would be every thing visible. Socrates would therefore be Plato, and Aristotle, and every thing visible, which is absurd. — Taylor.
4 These contraries cannot be at one and the same time true, but they may be both false, or one true, and the other false. In necessary matter, at*
56 Aristotle's organon. [chap. vti.
ble that these should at one and the same time be
4. Contraries , u , ,, .. .
themselves true, but the opposites to these may sometimes pos- caiinot at the sibly be co- verified about the same thing, as that
eiiniC time DG , , *3'
true, though not every man is white, and "some man is white."1 their opposites 0f guch contradictions then of universals, as are
universally made, one must necessarily be true or false, and also such as are of singulars, as " Socrates is white," " Socrates is not white ; " but of such contradictions as are indeed of universals, yet are not universally made, one is not always true, but the other false. For at one and the same time we may truly say that " man is white," and that " man is not white," and " man is handsome," and " man is not handsome," for if he is deformed he is not handsome, and if any thing is becoming to be, it is, not. This how- ever may at once appear absurd, because the assertion " man is not white," seems at the same time to signify the same thing, as " no man is white," but it neither necessarily signi- fies the same thing, nor at the same time.2 5. one nega- Notwithstanding it is evident that of one af-
tion incident firmation there is one negation, for it is necessary
Urinatives are true, negatives false, in impossible matter negatives true, affirmatives false, in contingent matter both false. Properly speaking, it is contrary to the very nature of logical inquiry to admit any reference whatever to the understood matter of proposition, of which Logic can take no cognizance, its province being, to establish argument when necessarily deducible from propositions placed in a certain connexion. From the truth of the universal or the falsehood of the singular we infer the accidental quality of all the opposed propositions ; but from the falsehood of an uni- versal or truth of a singular, we only know the quality of the contradictory.
1 He means " singular sub-contraries," which contradict the universals mutually contrary to each other, hence are co-verified in the same thing, i. e. in contingent matter, as in the above instance. The expression sub- contrary ({nrtvavriojg) is not used by Aristotle, though he admits the op- position above ; he calls it in Anal. Prior, ii. 15, an opposition Kara rrjv X'tliv, but not Kar akijOtiav. subalterns (vira\\r)\oi) are not noticed by Aristotle, the first who gave the laws of this species of opposition was Apuleius De Dogmate Platonis, lib. iii., who was followed by Marcianus Capella, and Boethius. The three kinds of opposition are called by the earlier writers, Alterutrae, Incongrus, and Suppares.
2 Viz. what he has said, that indefinites are at one and the same time true. Indefinite enunciation may seem to be universal, because it has an universal subject, but it is not universal, because it wants the universal mark, " every " or "no one." It is not requisite that the universal and indefinite should be at one and the same time true nor false, for one may be true and the other false.
CHAP. VII.*]
ON INTERPRETATION.
57
that tbe negation should deny the same thing toeachaffirm- which the affirmation affirmed, and also from the atl0n- same, (i. e.) either from some singular or some universal, uni- versally or not universally ; I say, for instance, that " Socrates is white," " Socrates is not white." If however there is something else from the same thing, or the same thing from something else, that (enunciation) will not be opposite, but different from it ; ' to the one, " every man is white," the other (is opposed) " not every man is white," and to the one, " a cer- tain man is white," the other, " no man is white ;" and to the one, " man is white," the other, " man is not white."
That there is then one affirmation contradictorily opposed to one negation, and what these are, has been shown, also that there are other contraries, and what they are, and that not every con- tradiction is true or false, and why and when it is true or false.
1 That is, if the negative differs from the affirmative in the predicate or the subject. The instance " Socrates is white," Socrates is not white, is contradictory, the one being true always, and the other false ; which con- stitutes the essential feature of contradictories included in the definition given Anal. Post, i. 2, ' Avr'npaaiQ 6k avTiQiaiQ i/c oi»K tort fitra^v tcaff avri)v. Some logicians call the opposition of singulars " secondary con- tradiction." Vide Boethius, p. 613. Wallis, lib. ii. c. 5. For the rules of contradiction, vide Aldrich, Whately, Huyshe. The following scheme from Aldrich gives the opposition of necessary, impossible, and contingent matter (n. i. c.) as to universal contraries A. E., and sub-contraries I. and O., with their verity (v.) or falsity (f.). See also scheme page 3.
Subcontraries
58 aristotle's organon. [chap. viii. ix.
Chap. VIII. — Of Opposition when there is not one Affirmation,
nor one Negation}
, m. The affirmation and negation are one, which indi-
1. What con- .
Btitutes single cate one thing of one, either of an universal, being affirmation and taken universally, or in like manner if it is not, as
negation, is the J ' '
unity of the "every man is white,' " not every man is white," theJpredicate° " man is white," "man is not white," "no man is without equi- white," " some man is white," if that which is white signifies one thing. But if one name be given to two tilings, from which one thing does not arise, there is not one affirmation nor one negation ;2 as if any one gave the name " garment " to a "horse," and to "a man;" that " the garment is white," this will not be one affirmation, nor one negation, since it in no respect differs from saying " man " and " horse " are " white," and this is equivalent to " man is white," and " horse is white." If therefore these signify many things, and are many, it is evident that the first enunciation either signifies many things or nothing,3 for " some man is not a horse," wherefore neither in these is it necessary that one should be a true, but the other a false contradiction.4
, . . Chap. IX. — Of Opposition in contingent Futures.
In those things which are, and have been,5 the past affirms- affirmation and negation must of necessity be true tionmustneces- or fa^se 5 *n universals, as universals, always one saniy be true true but the other false, and also in singulars, as otherwise in we have shown ; but in the case of universals not respect of the universally enunciated, there is no such necessity,
and concerning these we have also spoken, but as
1 Vide Whately, b. ii. c. 2, sect. 3.
2 That is, enunciation is equivocal.
3 " The garment is white " signifies many things, i. e. if the word " garment" be assumed for "man " and "horse;" or it signifies nothing, that is, if it is sc assumed as to signify one thing, since being taken for man, horse, the latter is not one thing, but nothing.
4 For both may be true, as every garment (i. e. man) is rational, not every garment (i. e. horse) is rational; or they may be both false.
5 Taylor reads ywofitvtov, after the Laurentian MS. Waitz, Bekker, and Buhle ytvofih'wv. In iis quae sunt et quie facta sunt. Averrois. Of course Aristotle does not mean by the assertion in the text, other than that one is true and the other false.
CHAP. IX __ ON INTERPRETATION. 59
to singulars and futures, this is not the case. For if every affirmation or negation be true or false, it is also necessary that every thing should exist or should not exist, for if one man says that a thing Avill be, but another denies the same, one of them must evidently of necessity speak truth, if every affirmation or negation be true or false, for both will not subsist in such things at one and the same time. Thus if it is true to say that " a thing is white," or that " it is not white," it must of necessity be "white" or not "white," and if it is white or not white, it wa3 true to affirm or to deny it : also if it is not, it is falsely said to be, and if it is falsely said to be, it is not ; so that it is necessary that either the affirmation or the negation should be true or false. In- deed there is nothing which either is, or is gene-
9 WVi t
rated fortuitously, nor casually, nor will be, or trueaffirma-
not be, but all things are from necessity, and not M0" ?r nesa-
casually, for either he who affirms speaks truth, futures ex-
or he who denies, for in like manner it might clu.d5s casual
° existence.
either have been or not have been, lor that which
subsists casually neither does nor will subsist more in this
way than in that.1 Moreover if a thing is now "white," it
1 Pluribus modis Aristoteles repetit et inculcat quod si aut affirmatio aut negatio necessario sit vera de rebus futuris item e veritate in dicendo colligi possit quomodo res ipsae evenire debeant atque ex ipsis rebus ju- dicetur quid sit verum, quid falsum : etenim si certum est et derinitum utrum verum sit, utrum falsum in iis quae de rebus futuris pronuntiantur, prsestituta sunt omnia, et qua? eveniunt, necessario eveniunt. Waitz. It is well observed by Ammonius, that the observations here made by Aristo- tle " are conversant not only with logic, but with every part of philosophy." Not all things are assumed to exist from necessity, but some are supposed to be in our own power; this constitutes the doctrine of moral responsibi- lity with the theologian, the scientific investigation of the philosopher, and the division into necessary and contingent of the logician : with respect to the last, the inquiry here seems to be whether all contradiction defi- nitely or only indefinitely comprehends these. The fatalist looks to the doc- trine of necessity as authorizing his " affections and antipathies " to become "the laws ruling his moral state," (Vide Shelley's Queen Mab,) forgetful of the moral faculty of self-approval and the contrary, (SoKifiaariid)) and {diroSoKifiaGTiKi)) , admitted by Epictetus, (Arr. Epict. lib. i. Capt. 1,) whilst others are led by it into the " visionary presumption of a peculiar destiny." Vide Foster's Essays on the Epithet Romantic. For the Ethical discussion of the subject, the reader is referred to Butler's Ana- logy, and so far as certain laws of thought form the basis of logical ne- cessity, he will find an admirable paper in chap. vi. of Mansel's Prolego- mena Logica. It is sufficient for our present purpose to state that
60 ARISTOTLE'S ORGANON. [CHAP. IX.
was true to say before that it will be "white," so that it was always true to say of any thing generated that it either is, or that it will be ; but if it was always true to say that it is, or will be, it is impossible that this is not, nor should be ; and whatever must of necessity be, it is impossible that it should not have been generated, and what it is impossible should not have been generated must of ne- cessity have been generated ; wherefore all things that will be, it is necessary should be generated, and hence there will be nothing casual nor fortuitous, for if it were fortuitous it would not be of necessity. Nor is it possible to say, that neither of them is true, as that it will neither be, nor will not be, for in the first place the affirmation being false, the nega- 3. Result of ^on Wi^ not De true> and this being false, it re- denying the suits that the affirmation is not true. And besides,
truth of both. .« ., ,, ,, . . . ,,
it it were true to say that a thing is at the same time " white " and " great," both must of necessity be, but if it shall be to-morrow, it must necessarily be to-morrow, and if it will neither be nor will not be to-morrow, it will not be a casual thing, for example, a naval engagement, for it would be . requisite that the engagement should neither oc-
cur nor not occur.
These and similar absurdities then will hap- surdity follows pen, if of every affirmation and negation, whether tnencasuaiins *n resPec* °f universals enunciated universally, or of singulars, it is necessary that one of the op- posites be true and the other false, but that nothing happens casually in those things which subsist, but that all are, and are generated of necessity ; so that it will neither be necessary to deliberate nor to trouble ourselves, as if we shall do this thing, something definite will occur, but if we do not, it will not occur. For there is nothing to prevent a person for ten thousand years asserting that this will happen, and another person denying it, so that of necessity it will have been then true to assert either of them. And it makes no difference whether any persons have uttered a contradiction or not, for
Aristotle traces here the institution of a word to the primary concept of the thing, so that if affirmation is true, a thing is, if negation is true, a thing is not. If either be true or false, he who affirms or denies says truly or falsely, so that if affirmative be true or false, a thing must necessarily exist or not exist. He alleges two enthymematic proofs, terminating in a reductio ad absu -dum.
CHAP. IX.] ON INTERPRETATION. 61
it is evident that the things are so, although the one should not have affirmed any thing, or the other have denied it, since it is not, because it has been affirmed or denied, that therefore a thing will or will not be, neither will it be more so for ten thousand years than for any time whatever. Hence if a thing so subsisted in every time that one of these is truly asserted of it, it was necessary that this should take place ; and each thing generated, always so subsisted, as to have been generated from necessity, for when any one truly said that it will be, it was not possible not to have been generated, and of that which is generated, it was always true to say that it will be. But* if these things are impossible — (for * vide Bekter, we see that there is a beginningr of future Waitz, Buhie,
o o ana trie -Ltipsic
things, both from our deliberation and practice, edition. Tay- and briefly in things which do not always energize, lor omits the "• there is equally a power of being and of not being, in which both to be and not to be occurs, as well as to have been generated and not to have been generated ; and, indeed, we have many things which evidently subsist in this manner, for example, it is possible for this garment to have been cut in pieces, and it may not be cut in pieces, but be worn out be- forehand, so also it is possible that it may not be cut in pieces, for it would not have been worn out before, unless it had been possible that it might not be cut in pieces, and so also in re- spect of other productions, which are spoken of according to a power of this kind — ) then it is evident that all things neither are, nor are generated of necessity, but 5. Many things that some things subsist casually, and that their have a casual
. . ~ % • subsistence as
affirmation is not more true than their negation, and to the nature of that there are others in which one of these subsists don^rnegs^ more frequently, and for the most part,1 yet so, that tion- either might possibly have occurred,but the other not.2
Wherefore, being, must of necessity be when it is,3 and non-being, not be, when it is not ; but it is not ne- cessary that every being should be, nor that non-being should not be, since it is not the same thing for every being
1 As for instance, finding a treasure ; here the negation is oftener true than the affirmation: except recently in California and Australia.
2 That is, the rarer may occur, but the more common may not.
3 Hypothetically. i. e. a thing must be, if it is supposed to be, because being and non-being cannot concur in eodem, eodem tempore.
62 ARISTOTLE S OKGA.NON. [CHAP. IX.
to be from necessity, when it is, and simply to be from neces- . „ „ , sity, and in like manner as to non-being. There
6. Parallel rea- . J" . . . . °„
soning as to is the same reasoning also in the case 01 contra-
and^difficuity Miction ; to be or not to be is necessary for every
as to the neces- thing, also that it shall, or shall not be, yet it is not
falsehood of* requisite to speak of each separately, but I say,
contingent fu- for instance, that it is necessary for a naval action
tures, solved. »
to occur or not occur to-morrow, yet it is not necessary that there should be a naval action to-morrow, nor that there should not be ; it is necessary, however, that it should either be or not be. Wherefore, since assertions and things are similarly true, it is evident that things which so subsist, as that whatever have happened, the contraries also were possible, it is necessary that contradiction should subsist in the same manner, which happens to those things which are not always, or which not always, are not. For of these, one part of the contradiction must necessarily be true or false, not indeed this or that, but just as it may happen, and one must be the rather true, yet not already true nor false ; 1 so that it is evidently not necessary that of every affirmation and nega- tion of opposites, one should be true, but the other filse ; 2 for it does not happen in the same manner with things which are not, but which either may or may not be, as with things which are, but it happens as we have said 3
1 When the contingents of course are unequal.
2 That is, definitely.
3 Quae ex casu pendent et esse possunt et non esse ; quare in his affir- matio et negatio (r) avricpaaig) quum nihil praestitutum sit, eodem jure vera? vel falsae pronuntiantur ( 6 juoi'wc i%ti) altera utra enim admittenda erit neque tamen, altera alteri praeferenda, tanquam sit destinatum, et certum quod eventurum sit ; quamvis enim alteram veram fore magis sit probabile quam alteram (/uaWov aXrjOi)) nondum vera est donee eventus earn comprobaverit. Waitz. Aristotle's object, whilst he admits the contingent, is to reduce it, for all logical purposes, to a necessary certainty of consequence. The whole of this chapter proves at once the practical turn of his mind, opposed alike to the ideal of Plato, the merely probable (as a result) of the Academics, and the versatile scepticism of Pyrrho, against whom Montaigne ushers in his own Philippic (Essay 12, book ii.) by the famous quotation from Sextus Err.piricus.
" Nil sciri si quis putat, id quoque nescit
An sciri possit quo se, nil sciri fatetur." Compare the philosophical principle of formal necessity in this chapter with Bp. Butler's distinction between, " by necessity," and acting "neces- sarily," Analogy, ch. 6, also his Introduction, and part ii. ch. 2, upon the nature of the contingent and proof.
CHAP. X._ ON INTERPRETATION. 63
Chap. X. — Of Opposition with the addition of the Copula.*
Since affirmation signifies something of something, and this is either a noun, or anonymous,2 (i. e. indefinite,) but what is in affirmation must be one and of one thing,3 all affirmation and negation will be either from a enmictatfon! °* noun and a verb, or from an indefinite noun and verb. (But what a noun is, and what the anonymous, has been shown before, for I do not reckon " not man " a noun, but an indefinite noun, for an indefinite noun signifies in a certain respect one thing, just as "is not well" is not a verb, but an indefinite verb.) Still without a verb there is _, , „
• i «. ■' . /• L, • » Cf. ch. 2, and 3.
neither an affirmation nor negation, tor " is, or " will be," or " was," or " is going to be," and so forth, are verbs, from what has been already laid down, since in addition to something else they signify time. Hence the first affirmation and negation (will be), "man is," "man is not," afterwards "non-man is," "non-man is not." Again, " every man is," " every man is not," " every non-man is," "every non-man is not," and the same reasoning holds in times beyond (the present).4 But when " is," is additionally
1 This is called oppositio tertii adjacentis, and a proposition is so de- nominated -where the copula is separated from the predicate ; otherwise where the two form one word, as " He walks," the proposition is called secundi adjacentis ; hitherto the latter has been treated of, and the co- pula and predicate considered equivalent to a single verb, as Xevkuv (De Int. ch. 2) to Xsvkov tan. I have followed Taylor in finishing the sen- tence before the bracket.
2 'At'uivvixov vocat to aopiarov ovo/ia quod ex sequentibus apparet, quamquam to dpwvvfiov alium sensum habere solet apud Arist. Waitz. Vide supra. " Something of something," means of which something is asserted.
3 This is true also of negation. The statement has already been made, ch. 8, that there must be one subject, and one predicate. Vide Whately, b. ii. c. 2.
4 Literally, " external times," twv ektoi; fit \pov(ov. On the distinc- tion between the copula and the third per. sing, of elfii, as predicating existence, see Pacius de Int. c. 3, and Biese, vol. i. p. 95. — Upon the pre- dicate having the negation added to it for the sake of obtaining a parti- cular affirmative premise, see Whately. b- ii. ch. 2 : where of course it is added to the subject, as in the text, it becomes an indefinite subject, to which the finite is stated prior, as being of an incomplex nature, and by this means the character of the proposition is sometimes changed, and the
64 aristotle's organon. [chap, x
predicated as the third thing, then the oppositions are enun- ciated doubly ; l I say for instance, " a man is just ; " here the word " is," I say, is placed as a third thing, whether noun or verb, in the affirmation, so that on this account, these will be „ ,,.1. , four, of which two will subsist with respect to
2. If the copula „ ' . . ... , r „
be added, there affirmation and negation, according to the order ot
MundaUons— consequence, as privations, but two will not.2 But
their subsist- I say that the word " is," will be added to "just " or
ence exemp i- ^ « no^ just," * so that also negation is added, where-
* Manornon- fore there will be four. We shall understand,
man, Waitz. . . „ .'
however, what is said from the under-written examples :3 " A man is just," the negation of this is, " a man isnotjust;" "he is not a just man," the negative of this is, "he is not not a just man," for here the word "is," and "is not," will be added to the "just" and the "not just," wherefore An. Pr. 46. these things, as we have shown in the Analytics,
are thus arranged. The same thing will happen with°ttieirpe™' ^ tne affirmation be of a noun taken universally.4 cuiiarity, uni- as for instance, "every man is just ;" of this the
versals. ,. . ,. . • , „ ,,
negation is, " not every man is just, " every man is not just," "not every man is not just," except that it does not similarly happen that those which are diametrically op- posed are co- verified ;5 sometimes, however, this does hap-
subject admits an affirmative. Vide Huyshe, 51, and the translator's note, AMrich's Log., Oxford, 1843.
1 That is, besides the two terms, (man) subject, and (just) predicate.
* The enunciations will be four which have the same predicate, and »n a certain respect the same subject. Two of these, he says, will subsist with respect to affirmation and negation according to the order of con- sequence, because " man is not just," man not is not just, are referred to J' man is just," " man not is just," as privations are referred to habits. By the word negation here, he does not mean the whole proposition, but the words " not is." Farther on he calls " not " negative.
3 'Ek tH)v v-iroyiypa.iip.ivwv. Tabula hoc modo disponenda erit
ovk tanv oil SLiccuog avOphnrog "\~ ~p ovk sfsrt oiicaiog avOpajnog
tan, SiKaiog avQpwTrog — -^ "Etrriv ov Biicaiog avOpunrog.
Waitz. The place subsequently referred to in the Analytics, is upon the opposition of indefinites.
4 That is, of a distributed subject, which is the case in universal pro- position. Vide Whately, book ii. ch. 2, sect. 2. 4 Since indefinites are compared to particulars, in contingent matter
CHAP. X.] ON INTERPRETATION". 65
pen, these two therefore are opposed to each other. 4 others witi But the other two (are opposed) in respect to an indefinite " non-man," as to a certain added subject, as su Ject' "non-man is just," "non-man is not just," "the non-just is not man," "the not non-just is not man:" there are not, however, more oppositions than these, but these without those, will be by themselves, as using the noun, " non-man." In those, however, wherein, " is," is not adapted, — as in " he enjoys health," and " he walks," — here it produces the same when thus placed, as if "is" were added; as " every man enjoys health," " every man does not enjoy health," " every non-man enjoys health," "every non-man does not enjoy health." For it must not be said, " not every man," but the negation, "not," must be added to " man ;" for "every" does not signify universal, but that (the thing is taken) universally.1 This is however evident, from " a man enjoys health," " a man does not enjoy health," " non-man is well," " non-man is not well," these differ from those, in not being universally (taken).2 Hence " every," or " no one," signifies nothing else, than that affirmation or negation is of a noun universally (assumed) ; wherefore it is necessary to add other things of the same kind.3 But because the contrary negation to this, " every animal is just," is that which signifies that "no animal is just," it is evident that these will never be either true at the same time, nor in respect to the same subject, but the opposites to these will sometimes be so, as "not every animal is just," and "some animal is just."4 But these follow; 5 consequence the one, "no man is just," follows "every man of the negative
opposite enunciations may be true. Contraries are both false in contin- gent matter, never both true ; subcontraries both true in contingent mat- ter, never both false ; contradictories always one true, another false. Vide scheme of opposition.
1 " Every," " all," " no," etc., are called universal signs, and show that the subject is distributed ; but when the common term has no sign at all, the indefinite is decided by the propositional matter, i. e. is uni- versal in impossible, aud particular in contingent matter. Vide the com- mon Logics.
2 The enunciations, " man is well," " man is not well," differ from " every man is well," " every man is not well."
3 That is, as the indefinite is made indefinite by the addition of nega- tion to the subject, the same should be done in a definite enunciation, as " every man is well," every non-man is well, rd ovv aWa ra avrd ctl irpooTtOtvcu, " reliqua ergo eadem oportet (dicentem) apponere." Buhle
* These are the particulars, or subcontraries.
$
66 aristotle's organon. [chap. x.
upon the af- is not just," but the opposite, " some man is just." firmative, and f0nows « not every man is not i ust ," for it is neces-
sary that some man should be just. In the case also of singulars, it is evident that if a man being questioned denies truly, he asserts also truly, as, "Is Socrates wise? No ! " Socrates therefore is not a wise man. But in the case of universals, what is similarly asserted is not true, but the negation is true, as, " Is every man wise ? No ! " Every man
therefore is not wise ; for this is false, but this, hvTMeitxevrr- t( not every man then is wise," is true, and this is
opposite, but that is contrary. Opposites, however, as to indefinite nouns and verbs, as " non- man " and "non-just," may seem to be negations without a noun and verb, but they are not so, for the negation must always of necessity be either true or false, but he who says " non-man " does not speak more truly or falsely, but rather less, than he who
says " man," except something be added. Still the nitenoWie- assertion, "every non-man is just," does not sig- gitimate enun- njfy fae game as any one 0f those (propositions), nor
the opposite to this, namely, " not every non-man is just ;" but the assertion, " every one not just is not a man," means the same with, " no one is just who is not a man."
Nouns and verbs indeed, when transposed, have the same sig- nification, as, " he is a white man," " he is a man white," for unless it be so, there will be many negations of the same thing, but it has been shown that there is one of one ; of this, " he is a white man," there is the negation " he is not a white man," and of the other, " he is a man white," (except this be the same with " he is a white man,") the negation will either be " he is not, not a man white," or " he is not a man white." 7. No differ- But the one is a negation of this, " he is not a ence in affirm- man white," and the other of this, " he is a white
ation or nega- .. , , ' , .., , ,• e
tion produced man (so1 that there wdl be two negations ot one
1 This parenthetical sentence is omitted by Taylor, but given by Bek- ker, Waitz, Buhle, and Averrois ; the last gives the following scheme of
Enunciationum indefinitarum dispositio.
. f Affirmativa simplex Negativa simplex ) B
\ Homo est Justus Homo non est Justus J
r I Negativa infinita Affirmativa infinita ) D
( Homo non est non Justus Homo est non Justus J
p ( Negativa privatoria Affirmativa privatoria ) p
\ Homo non est injustus Homo est injustus )
CHAP. XI. | ON INTERPRETATION'. 67
affirmation) ; wherefore it is evident that when a by transposi- noun and verb are transposed, the same affirmation tI0"' and negation result.
Chap. XL — Of the Composition and Division of Propositions.
To affirm, and deny, one thing of many, or many ( 0ne thino,
of one, is not one affirmation nor one negation, cannot be said
except that is some one thing which is manifested lany nJi one,
from the many ; I mean by one, not if one name b>' one affirma-
, ,-, • • r. i • i tIon or nega-
be given to many things, nor it jne thing result tion.— Excep- from them, as "man" is perhaps " animal," and tlon' "biped," and "mild," yet one thing results from these ; but from " white" and " man," and " to walk," one thing does not re- sult, so that neither if a person affirm one certain thing of these is it one affirmation, but there is one articulate sound indeed,1 yet many affirmations, nor if he affirmed these things of one, (would there be one affirmation,) but in like manner, many. If, then, dialectic interrogation be the seeking of an answer, either of a proposition, or of either part of a contradiction, (but a proposition is a part of one contradiction,) there would not be one answer to these, for neither is there one interrogation, not even if it be true : we have, however, spoken of these in the Topics, at the same time it is evident that, Topics, vm. 7.
What is it ? is not a dialectic interrogation,2 for a s°p'>- .EL .
... . „ ° . tf. Prior An.
. c. 6.
A'rinr
choice should be given from the interrogation to i. i.
He divides also "universals" and "particulars" after the same manner. The whole treatise he distinguishes into two books, the 2nd commencing with this chapter, and treating of indefinite enunciations generally. The Greeks resolved it into five sections ; Boethius, sometimes into two, and at others into six books ; the Latin translators generally, into two books. These differences, in the earlier commentators, have given rise to much confusion in quotation, amongst their successors.
1 Or (ptuvrj fiia — una vox. Aristotle's doctrine in the Topics differs from that of Porphyry, as the latter does from Aldrich. The word Ka.Tt)y6pi}(ia, occurrent lower down, signifies a predicable — the expres- sions categorematic and syncategorematic are not Aristotelian, but are met with in Michael Psellus. Cf. Trendelenburg, Elem. sect. 9. Waitz, vol. i. p. 267.
2 On the nature of the interrogation, see Whately ii. 2, 1, and upon interrogational fallacy, book iii. sect. 9. Si quis vero quoerit ita ut quod responderi debeat unum quidem sit, sed detinitione data exponendum, unum quidem est quod quaeritur et quod respondetur, quoestio vero dia-
F 2
68 Aristotle's organox. [chap, xi
irpo3.op.'<ru<rflai. enunciate this or that part of the contradiction ; Taylor. ^ut ^ie interrogator must besides define, whether
this particular thing, or not this, be a man.
As, however, there are some things predicated
as composites, so that there is one whole predicable, of those which are predicated separately, but others are not so, what is the difference ? For in respect of " man," we may truly and separately predicate "animal " and " biped," and these as one thing ; also "man" and "white," and these as one thing ; but not if he is " a shoemaker" and " a good man," is he therefore
also a good shoemaker. For if, because each of not to be as- these is true, both, conjointly, should be of neces- sumed, as con- gjty true, many absurdities would follow, for
junctively true. J ' J . '
" man and " white are truly predicated ol a man, so that the whole together may be ; ' again, if the thing "is white," the whole conjointly "is white," wherefore, it will be " a man white, white," even to infinity ; again, " a musician white walking," and these frequently involved to infinity. Once more, if " Socrates" is " Socrates" and "man," " Socrates" is also " Socrates man," and if he is "man" and "biped." he is also "man biped ;" wherefore it is evident, if a man says conjunctions are simply produced,2 the result will be that he will utter many absurdities.
Let us now show how they are to be placed. Of things predicated, and of those of which it happens to be predi- cated, whatever are accidentally enunciated, either in respect of the same, or the one of the other, these will not be one ; as "man is white," and "a musician;" but "whiteness" and
lectica, quoniam qtiaestione dialectics non interrogator quae sit hominis definitio, sed utrum haec sit hominis definitio, an non sit. Waitz.
1 Since " man " and " white" are predicated at the same time, and the subject may be said to be " a white man." The rule is, that we cannot use a separate predicate when there is in the subject any thing so opposed to a portion of the predicate, as to cause any contradiction, as if a dead man were called a man. If there is any contradiction between the pre- dicate and subject, the proposition will be false, yet if there be no such contradiction, it does not follow that the latter is always true. In most cases, however, of this sort, we find a fourth term surreptitiously intro- duced, by the ambiguity of the copula.
2 Tag avfiTrXoKag a.Tr\oJg yivtaOai, si quis simpliciter dicat com- plexiones fieri. Averrois. Compare Whately, book i. and ii. ch. 5 ; also book iii. sect. 9 ; also Hill's Logic, 10S, et seq., and observations upon logical division.
CIIA.P. XII.] ON INTERPRETATION. 69
" music" are not one tiling, for both are accidents to the same thing. Neither if it be true to call what is white musical, yet at the same time will "musical" "white" be one thing, for what is "white" is " musical " per accidens, so that " white musical" will not be one thing, wherefore neither is a man said to be "a good shoemaker" singly, simple and™ but also " a biped animal," because these are not |j°™£°snite pre" predicated of him per accidens. Moreover, nei- ther are such things which are inherent in another (to be added), hence, neither is " whiteness " (to be predicated) repeatedly, nor is "a man" "a man animal," nor (a man) " biped," since both animal and biped are inherent in man ; still it is true to assert it singly of some one, as that " a cer- tain man is a man," or that " a certain white man is a white man," but this is not the case always. But when some op- position is in the adjunct which a contradiction follows, it is not true, but false, as to call a dead man a man, but when such is not inherent, it is true. Or when something (contra- dictory) is inherent, it is always not true ; but when it is not inherent, it is not always true, as " Homer" is something, "a poet," for instance, "is" he therefore, or "is" he not? for "is" is predicated of Homer accidentally, since "is" is predi- cated of Homer because he is a poet, but not per se (or essen- tially). Wherefore, in whatever categories, contrariety is not inherent, if definitions are asserted instead of nouns, and are essentially predicated, and not accidentally, of these a parti- cular thing may be truly and singly asserted ; but non-being, because it is a matter of opinion, cannot truly be called a certain being, for the opinion of it is, not that it is, but that it is not.
Chap. XII. — On Modal Proposition.1
These things then being determined, let us con- i. of thenega- sider how the affirmations, and negations of the tions -7"~v \mf
. - . . , p TOV aval, 6i 0€-
possible and impossible to be, subsist with reter- pwwe^., ence to each other, also of the contingent and the
1 Aristotle here enumerates four modes, but in Anal. Prior, i. 2, they are reduced to two, the necessary and contingent. See St. Hilaire's Translation. The Greek commentators have multiplied the modes, by allowing any adverb, added to the predicate, or adjective qualifying the Bubject to constitute a modal. The word rpo7roe, as applied to the modes
70 aristotle's organon. [chap. xir.
non-contingent, and of the impossible and necessary, since this has some doubtful points. For if among the complex, those contradictions are mutually opposed, which are arranged ac- cording to the verb " to be," and " not to be," (as for instance the negation "to be a man," is "not to be man," not this, " to be not a man," and the negation of " to be a white man " is " not to be a white man," and not this " to be not a white man," since if affirmation or negation be true of every thing, it will be true to say " that wood is not a white man,") — if this be so, in those things to which the verb " to be " is not added, that which is asserted instead of the verb " to be," will pro- luce the same thing. For example, the negation of " a man walks," will not be " non-man walks," but, " a man does not walk," for there is no difference in saying that " a man walks," or that " a man is walking," so that if this is every where the case, the negation of " it is possible to be," will be " it is pos- sible not to be," and not " it is not possible to be." But it appears that it is possible for the same thing both to be, and not to be, for every thing which may possibly be cut, or may possibly walk, may also possibly not be cut, and not walk, and
the reason is that every thing which is thus pos- oiJLVw^f- sible? cloes not always energize,1 so that negation
will also belong to it, for that which is capable of walking, may not walk, and the visible may not be seen. Still however it is impossible that opposite affirmations and negations should be true of the same thing, wherefore the ne-
of propositions and of syllogisms, comes from the Greek commentators, but is not Aristotelian. (Ammonius Schol. p. 130, a. 16.) The ad- mission of modals into Logic, has been strongly advocated and opposed ; the determination of the implied matter of a pure proposition is extra- logical of course, but respecting the expressed matter of a modal, the reader will find some valuable remarks in Mansel's Logic. The authorities are, on one side of the question Sir W. Hamilton, on the other Kant and St. Hilaire. A modal is reducible to a pure categorical, by uniting the modal word to the predicate, or to the subject when the mode only expresses the nature of the matter of the proposition, e. g. a fish neces- sarily lives in the water, i. e. all fish live in the water. Though the man- ner of connexion between the extremes is expressed in a modal, yet it does not thereby test the quantity of the proposition, as there are uni- versal and particulars in each mode. On the distinction of propositional matter, see Sir. W. Hamilton, Ed. Rev. No. 115, p. 217. Also the com- mentary of Ammonius, de Int. 7, (Scholia, p. 115, a. 14).
1 " Non semper in actu est.'' Averrois. Cf. Metap. lib. ii. 4, and books " and 8 ; also Physics, lib. ii.
CHAP. XII.] ON INTERPRETATION. 71
gation of "it is possible to be," is not "it is possible not to be." Now it results from this that we either at the same time affirm and deny the same thing of the same, or that the affirmations and negations are not made according to the ad- ditions, " to be " or " not to be ; l " if therefore, that, be im- possible, this, will be to be taken, wherefore the negation of "it is possible to be," is "it is not possible to be," (but* not it is possible not to be). Now there is *B?k™'*]ed by the same reasoning also about the being contingent, for the negation of this is, not to be contingent, and in like manner as to the rest, for example the necessary and impossible, since as in those it happens that, " to be," and, " not to be," are additions, but "whiteness" and "man" are subjects, so here " to be " and "not to be," become as subjects, but " to be possi- ble," and " to be contingent," are additions which determine the true and false in the (enunciations) "to be possible" and "to be not possible," similarly as in those, " to be," and " not to be." 2 But of "it is possible not to be," the negation is not, "it is not possible to be," but "it is not possible not to be," and of " it is possible to be," the negation is not, "it is possible not to be," but, "it is not possible to be ;" wherefore, "it is possible to be," and, "it is possible not to be," will appear to follow each other ; for it is the same thing, " to be possible to be," and "not to be," since such things are not contradictories of each other, namely, "it is possible to be," and, " it is possible not to be." But " it is pos-
1 Sequitur enim hinc aut idem vere simul affirmari et negari de eodeni aut non secundum apposita quatenus ea, sunt et non sunt, fieri afiirma- tiones et negationes. Si ergo illud fieri nequit (ut negatio propositionis modalem negativam effieiat) hoc (tit negatio modi efficiat modalem nega- tivam) eligendum fuerit. Buhle.
3 Vide Huyshe's Logic, p. 50. As regards modality, judgments accord- ing to Kant are problematical, assertorial, and apodeictieal. The first are accompanied by a consciousness of the bare possibility of the judgment; the second by a consciousness of its reality ; the third by a consciousness of its necessity. Modality is thus dependent on the manner in which a certain relation between two concepts is maintained, and may vary ac- cording to the state of different minds, the given concepts, and conse- quently the matter of the judgment, remaining unaltered. Mansel's Prol. Log., and Appendix, note G. The real state of the case appears to be that, in the endeavour to combine psychological variation with logical distinct- ness, philosophers have sacrificed the proper office of the latter. As far as proposition is concerned, modals may be tuined at once into pure ea- tegoricals, in fact, they affect not the relation between the terms, but sim- ply the subject or predicate, in other words, the terms themselves alone.
72 Aristotle's organon. [chap. xm.
sible to be," and " it is not possible to be," are never true of the same thing at the same time, for they are opposed, neither at least are, " it is possible not to be," and " it is not possible not to be," ever true at the same time of the same thing. Like- wise of, "it is necessary to be," the negation is not, "it is necessary not to be," but this, " it is not necessary to be," and of, "it is necessary not to be," (the negation) is this, "it is not necessary not to be." Again, of, "it is impossible to be," the negation is not "it is impossible not to be," but "it is not impossible to be," and of, " it is impossible not to be," (the negation) is, " it is not impossible not to be." In fact, uni- versally, as we have said, "to be" and "not to be," we must 2. The elvat necessarily regard as subjects, but those things and uh eivat to which produce affirmation and negation we must
be considered r »
as subjects, connect with "to be and "not to be : we ought Tfflrlnltion and a^so to consider these as opposite affirmations and negation is to negations ; possible, impossible, contingent, non- contingent, impossible, not impossible, necessary, not necessary, true, not true.
Chap. XIII. Of the Sequences of Modal Propositions.
The consequences are rightly placed thus : " it thod^fdis^os- happens to be," follows, " it is possible to be," and coL^uences. tms reciprocates witn that ; also, " it is not impos- sible to be" and "it is not necessary to be." But, " it is not necessary not to be," and, "it ' is not impossible not to be;" follow, "it is possible not to be," and, "it may happen not to be ; " and, " it is necessary not to be," and, " it is im- possible to be," follow, " it is not possible to be," and, " it does not happen to be;" but, "it is necessary to be," and also, "it is impossible not to be," follow, "it is not possible not to be," and, " it is not contingent not to be : " what we say how- ever may be seen from the following description :
1 3
It is possible to be It is not possible to be
It may happen to be It may not happen to be
1 Bekker, Buhle, and Waitz read this clause differently : as all are, however, agreed in the scheme given, I have reconciled their variation by a reference to that. Taylor appears to have done the same.
CIIAP. XIII.] ON INTERPRETATION. 73
It is not impossible to be It is impossible to be
It is not necessary to be. It is necessary not to be.
2 4
It is possible not to be It is not possible not to be
It may happen not to be It may happen not to be It is not impossible not to be It is impossible not to be
It is not necessary not to be. It is necessary to be.
Therefore the impossible, and the not impossi- i.
to aoi'i
aoovaroV'
ble, follow contradictorily the contingent, and the liai °'"t d : possible, and the non-contingent, and the not »*. reciproce. possible, and vice versa ; * for the negation of the impossible, namely, " it is not impossible to be," follows, " it is possible to be," but affirmation follows negation, for, "it is im- possible to be " follows " it is not possible to be," since " it is impossible to be," is affirmation, but, " it is not impossible to be," is negation.
Let us next see how it is with necessary matter, now it is evident that it does not subsist thus, but contraries follow, and contradictories (are placed) separately,1 for, " it is not ne- cessary to be," is not the negation of " it is ne- „ , ,
„ . , Mil 2. to avayxaioi',
cessary not to be, since both, may possibly be true its peculiarity, of the same thing, as that which necessarily, is not, ana^roof.6*50" need not of necessity, be. But the reason why the necessary follows not, in like manner, other propositions, is that the impossible being enunciated contrarily to the ne- cessary, signifies the same thing ; for what it is impossible should exist, must not of necessity be, but not be, and what is impossible should not be, this must of necessity be ; so that if these similarly follow the possible and the not possible, these (do so) in a contrary mode,2 since the necessary and the impossible do not signify the same thing, but, as we have said,
1 Contrarias eas appellat, quum propterea quod non est aliud nomen, quod its melius conveniat, turn maxime propter locos, quos occupant in tabula quam adscripsit • nam in hac e£ tvavrlaq collocate sunt ovk dvay- kcuov tlvai et avay. /xtj tlvai Waitz. In the table given above the two former in each column are contraries to the two former in the opposite ; and the two latter in each are contrary sequences from the two former. Necessity, according to Aristotle, (Ethics, ch. iii.,) was either absolute (airXwg), or hypothetical (t£ vTroOkuewg), the former immutable, the lat- ter only conditional. See also Metap. lib. iv.
* Namely, " it is necessary and it is net necessary."
74 Aristotle's organon. [chap, xiii,
Buhie and v^ce vers^- Or is it impossible that the contra- Averrois omit dictories of the necessary should be thus disposed ? equeaion. g^ what, "is necessary to be" is "possible to be," since if not, negation would follow, as it is necessary eithei to affirm or deny, so that, if it is not possible to be, it is im- possible to be, wherefore it would be impossible for that to be, which necessarily is, which is absurd, but the enunciation, "it is not impossible to be" follows the other, "it is possible to be," which again is followed by, " it is not necessary to be," whence it happens that what necessarily exists does not necessarily exist, which is absurd. But again neither does, "it is necessary to be" follow "it is possible to be," nor does the proposition, " it is necessary not to be," for to that, both, may occur, but whichever of these is true,1 those2 will be no longer true, for at one and the same time, it is possible to be, and not to be, but if it is necessary either to be or not to be, both, will not be possible. It remains therefore, that "it is not necessary not to be," follows " it is possible to be ;" for this3 is also true in respect of what is necessary to be, since this becomes the contradiction of that proposition which follows, viz. "it is not possible to be;" as "it is impossible to be," and " it is necessary not to be," follow that, of which the negation is, " it is not necessary not to be." Wherefore these contradictions follow according to the above-mentioned mode, and nothing absurd results, when they are thus disposed.4
Still it may be doubted whether " it is possible diileiuy™ °tfoa to be," follows " it is necessary to be," for if it the above, by does not follow, the contradiction will be conse-
the distinction . ' . .. , . „ , .„
between ration- quent, namely, "it is not possible to be, and it a ai potenUainy " man should deny this to be a contradiction, it will be necessary to call, " it is possible not to be," a contradiction, both which are false in respect of necessary matter. Nay, on the contrary, it appears to be possible that the same thing should " be cut" and " not be cut," should " be" and "not be," so that what necessarily "is," may happen "not to be," which is false. Nevertheless it is evident that not every thing which can " be," and can " walk," is capable also of the op- posites, for in some cases this is not true. In the first place,
1 That is, it is necessary to be, and it is necessary not to be.
7 It is possible to be, and it is possible not to be.
* It is not necessary not to be. * As above.
CHAP. XIII.] ON INTERPRETATION. 75
in those things which are potent irrationally,1 as fire is calorific, and has irrational power ; rational ^^"Jfx°7°" powers then are those of many things, and of the contraries ; but not all irrational powers, for, as we have said, fire cannot heat, and not heat, nor such other things as always energize. Yet even some irrational powers can at the same time receive opposites ; but this has been stated by us, because not every power is susceptible of con- traries, not even such as are predicated, according to the same species. Moreover, some powers are equivocal, for the possible is not predicated, simply ; but one thing is (called so), because it is true, as being in an energy, as it is possible for a man to walk, because he walks, and in short, a thing is pos- sible to be, because that is already in energy which is said to be possible ; on the other hand, another thing (is said to be possible), because it may be in energy ; as it is possible to walk, because a man may walk. Now this power exists in movable natures only, but that in immovable ; but with re- spect to both, it is true to say, that it is not impossible to walk or to be, and that a man is now walking and energizing, and has the power to walk, hence it is not true2 to predicate that which is thus possible, in respect of necessary matter, simply, but the other is true. Wherefore since the universal follows the particular, to be able to be, but not all ability, fol- lows that which is of necessity, and indeed the 3 The iyayKaX. necessary and the non-necessary may perhaps be ov km uh a*,
1 Non secundum rationem possibilia. Buhle. " Non secundum ratio- nem possunt." Averrois. Compare Metaph. lib. ii. and iv. and viii. In the last place, the same distinction between rational and irrational powers is maintained ; the reader will find also that the whole of the 8th chapter turns on the difference between SwdfiiQ and ivepyeia. Briefly, the former is (as here) simple potentiality ; the latter, that active state, in which potentiality may be. Aristotle places the ivepytia, and properly, ante- cedent to the dvi'a/iic. Vide also Ethics, book i. ch. 2. Aw(i/j«j con- sidered as faculties were five, of which vegetables possessed one, brutes four, and man all. Compare Aristot. de Animu. The resistance given, has respect to the potentiality of the will, which of course is excluded from irrational subjects, hence they are, in a sense, unsusceptible of con- traries ; man's will, being potential, has power to restrict his Zvvapuq, or place them in tvtpytiq, but irrational subjects have no potential will, hence the difference.
2 It is only truly asserted of what is hypothetically necessary, because a thing must of necessity be, when it will be, though it will not neces- sarily be.
76 ARISTOTLE'S ORGANON. [CHAP. XIT.
are the &px4 the principle of the existence, or of the non-exist- *«>™* «»«"• '" ence of all things, and we should consider other things as consequent upon these.1 Hence from what we have stated, it is clear that whatever exists of necessity, is in energy, so that if eternal natures are prior in existence, 4. The to if, energy also is prior to power, and some things, as faAyiwhv. icar" the first substances, are energies without power, Priority. but others with power, namely, those which are
prior by nature, but posterior in time : lastly, there are some which are never energies, but are capacities only.
Chap. XIV. Of Contrary Propositions.2
1. Those opin- But whether is affirmation contrary to negation, ions are con- or affirmation to affirmation ? and is the sentence
1 The following order will explain :
1 3
It is necessary to be It is not necessary to be
It is not possible not to be It is possible not to be
It may not happen not to be It may happen not to be
It is impossible not to be. It is impossible not to be.
2 4
It is necessary not to be It is not necessary not to be
It is not possible to be It is possible to be
It may not happen to be It may happen to be
It is impossible to be. It is not impossible to be.
Waitz observes that he does not consider the Trpwrjj ovaia here as in the Categories, but as in the Metaphysics. Vide Metap. b. iii. 4, 6, etc., also Physics, lib. ii. and De Anima, i. 1, 2, and ii. 1, 2. Ed. Trendelenburg. The learned note of Ammonius, too long to insert, tends to show no more than what can be gleaned by the student from a reference to the places quoted, namely, that with Aristotle, energy is prior to capacity, and that the necessary being invariably the same in subsistence, can only be predicated of things which are always in energy : this conclusion being syllogistically educed, he proceeds to evolve the contingents and consequences, placing form in energy, matter in capacity. In the Meta. 12th book, he calls the gods— essences in energy. Composites are those which participate of matter, and either may or may not retain form : thus beings are, first, energies simple and immutable, next, those which are mutable, yet connected with energy, others, which precede energy as to time, but do not always obtain it, lastly, others which subsist as to capa- city alone, and are not naturally adapted to energy. Vide Ammonius in librum de Interpretatione.
2 This chapter is not given separately in the text, by Waitz: with Ammonius it forms the fifth section of the treatise. He considers it eithei
CIIAI*. XIV. J
ON INTERPRETATION. 77
which says, "every man is just," contrary to the trary wMch are one, "no man is iust," or the sentence "every of contrary
. . „ ,, ■ l_ » -c rt l matter, and the
man is just, to, "every man is unjust, as Ual- prepositional lias is just," " Callias is not just," " Callias is un- r^f^ just," — which of these are contraries ? For if the contrariety things in the voice, follow those which exist in of °Pimon- the intellect,1 but there the opinion of a contrary is contrary, ' as for instance, that "every man is just," is contrary to, " every man is unjust," it is necessary that affirmations also in the voice should subsist in the same manner, but if there, the opinion of a contrary be not contrary, neither will affirm- ation be contrary to affirmation, but the before-named ne- gation. Hence it must be considered what false opinion is contrary to the true opinion, whether that of negation or that which opines it to be the contrary. I mean in this way, there is a certain true opinion of good that it is good, but an- other false opinion that it is not good, lastly, a third, that it is evil, which of these therefore is contrary to the true opinion ? and if there is one, according to which is it contrary ? If then a man should fancy contrary opinions to be defined by this, that they are of contraries, it would be erroneous, for of good that it is good, and of evil that it is evil, there is perhaps the same opinion, and it is true whether there be many (opinions) or one : but these are contraries, yet not from their being of contraries are they contraries, but rather from their subsist- ing in a contrary manner.2 If then there is an opinion of good that it is good, but another that it is not good, and there is also something else, which is neither inherent, nor can be, in good, we cannot admit any contrary of the rest, neither
as spuriously introduced by some one posterior to Aristotle, or written by him to exercise the reader's judgment upon what has been said, as in the Categories he contends that what is sensible is prior to sense, explaining the system of relation generally in his Physical Auscultation.
1 Vide supra, ch. i. ; also Ethics, book vi. ch. 1 and 2. As Waitz ob- serves, he seems to refer to the same subject in the Metaphysics, where he takes for granted that ivavria kari 86%a SoKy r) rrje avriipcMTtwQ, and again in the Topics. Waitz, 363. Vide also Whately, book ii. ch. 2, 3, and Huyshe, sect. 4 : whose remarks will fully explain this chapter. The example, Callias is just— is unjust, is in fact a contradiction. (Vide De Interpreiatione, ch. 7.)
2 fiaWov T(p tvavriwg, in a form of logical contrariety. On the three- fold division of good, by the Pythagoreans and Peripatetics, see Cic. Acad. i. 5 ; Tusc. v. 85. Ethics, book i. 8.
78 Aristotle's organon. [citap. xrv.
such opinions as imagine the non-inherent to be inherent, nor the inherent to be non-inherent, (for both are infinite,1 both as many as imagine the non-inherent to be inherent, and the inherent to be non-inherent) ; but in those things in which there is deception, (therein we admit contraries,) and these are from which there are generations ; generations however are from opposltes, wherefore deceptions also. If then good is good and not evil, and the one is essential, but the other accidental — (for it is accidental to it not to be evil) and of every thing the opinion is more true and false which is essential, if the true (be assumed) — the opinion that good is not good, is false in respect of that which is essentially inherent, but the opinion that it is evil is false of that which is from acci- dent, so that the opinion of the negation of good would be more false than the opinion of the contrary. He is however especially deceived about every thing who holds a contrary opinion, for contraries belong to things which are the most diverse about the same thing. If then one of these is con- trary, but the opinion of the negation is more contrary, it is evident that this itself will be (truly) contrary ; but the opinion that the good is evil is complex, for it is necessary perhaps, that the same man should suppose (good) not good. Once more, if it is requisite for the like to occur in other things, it may seem to have been well said in this case also ; for the (opposition) of negation is either every where or no where ; but whatever things have no contraries, of these, the opposite to the true opinion is false, as he is mistaken who fancies " a man " " not a man," if then these (negations) are contrary the other (opinions) also, of negation, are. Besides, it is the same as to the opinion of good that it is good, and of what is not good, that it is not good ; and also the opinion of good, that it is not good, and of what is not good that it is good ; to the opinion then of the not good that it is not good, which is true, 2. Nature of what will be the contrary ? Certainly not that contrariety be- -which says that it is evil, since it may at one
tween affirma- J . »
tion and nega- and the same time be true ; but truth is never tion" contrary to truth, for whatever is not good is evil,
so that it will happen that these opinions, shall be at one and the same time, true. Nor again will that (opinion) that it is not
1 This parenthesis is omitted by Taylor. I follow the reading of Buhle and Waitz.
CHAP. XIV. J ON INTERPRETATION. 79
evil, be (the contrary), for that is also true, and these may exist at the same time, wherefore (the opinion) of what is not good, that it is good, remains as a contrary to the opinion of what is not good, that it is not good, and this will be false, so that the opinion of good that it is not good, will be the contrary to that of what is good, that it is good. That there will be no difference though we should propose universal affirmation is evident, for universal negation will be the contrary ; as for in- stance, to the opinion which supposes every thing good to be good, that nothing of good things is good (will be the contrary opinion), for the opinion of good that it is good, if good be universal, is the same with that which opines that whatever is good is good, and this differs in no respect from the opinion that every thing which is good is good, and the like takes place as to that which is not good. So that if this be the case in opinion, and affirmations and negations in the voice are S)'m- bols of (conceptions) in the soul, it is clear that the universal negation which is about the same thing, is contrary to affirm- ation. For instance, to " every thing good is good," or that "every man is good," (the negation is contrary,) that " nothing or no man is good ;" but this, that " not every thing, or not every man," (is good, is opposed) contradictorily. It is however evident, that true opinion can neither possibly be contrary to true opinion, nor true negation (to true negation), for those are contraries which subsist about op- _ „
r 8. Contraries
posites ; but about the same things the same may cannot co-exist be verified, but contraries cannot possibly be in- uua fc" T<fJ avl't' herent in the same thing, at one and the same time.1
1 Vide the canones oppositarum. Aldrich. Also notes upon the 7th chap, de Interpret.
80 aristotle's organon. [book
THE PKIOR ANALYTICS.1
BOOK I.
Chap. I. — Of Proposition, Term, Syllogism, audits Elements.
i. Purport of It is first requisite to say what is the subject, the8 attainment concerning which, and why, the present treatise of demonstra- is undertaken, namely, that it is concerning de- monstration, and for the sake of demonstrative science ; we must afterwards define, what is a proposition, what a term, and what a syllogism, also what kind of syllo- gism is perfect, and what imperfect; lastly, what it is for a thing to be, or not to be, in a certain whole, and what we say it is to be predicated of every thing, or of nothing (of a class).
2. Definition of A proposition then is a sentence which affirms or (irpoTa™) pro- denies something of something,2 and this is uni-
position. It is , . °. . n °. T ,
either, versal, or particular, or indefinite ; 1 denominate
versfi°Xo",uni" universal, the being present3 with all or none; 2. huepet, par- particular, the being present with something, or 3?or^ii6punov, n°t with something, or not with every thing ; indefinite. but the indefinite the being present or not being present, without the universal or particular (sign) ; as for example, that there is the same science of contraries, or that
1 Aristotle herein analyzes syllogism and demonstration into their prin- ciples ; the names Prior and Posterior were given to these treatises in the time of Galen, but it is remarkable, that when Aristotle cites them, he denominates the former, " Concerning Syllogism," and the latter " Concerning Demonstration." Upon the subject of title, compare St. Hilaire, Memoire, vol. i. p. 42, with Waitz, vol. i. p. 367 ; and for general elucidation of the treatise itself, much information has been derived from the valuable commentary of Pacius.
8 Oratio indicativa, etc., Aldrich, " Oratio enunciativa," Boethius. The latter's definition is the better.
3 The word vTrapxtw, inesse, has given ample scope for the exercise of logical contention : Taylor objects to translating it, the being inherent, and points out an anomaly arising from Pacius' use of it in this way, in the next chapter. He asserts that the real Aristotelian sense is " being present with.*' For the account of the word, see note, p. 53.
CHAP. I.] THE PRIOR ANALYTICS. 81
pleasure is not good. But a demonstrative „ _._
to 3. Difference
proposition differs from a dialectic in this, that between the the demonstrative is an assumption of one part of f™°£**™*™}e the contradiction, for a demonstrator does not in- ana the 3.aA«- terrogate, but assume, but the dialectic is an in- terrogation of contradiction.1 As regards however forming a syllogism from either proposition, there will be no difference between one and the other, since he who demonstrates and he who interrogates syllogize, assuming that something is or is not present with something. Wherefore a syllogistic proposition will be simply an affirma- tic proposition tion or negation of something concerning some- thing, after the above-mentioned mode : it is however demon- strative if it be true, and assumed through hypo- theses from the beginning,2 and the dialectic pro- s{rJt^vedemon position is to him who inquires an interrogation of contradiction, but to him who syllogizes, an assumption of what is seen and probable, as we have shown in the Topics. What therefore a proposition is, and wherein the syllogistic demonstrative and dialectic differ, will be shown accurately
1 The oldest Greek commentator, Alexander Aphrodisiensis, speaks of the Xoyitcr) (cat uvWoyiaTtKr) TrpayfiaTiia as containing under it, airo- SttKriKt), StaXtKTiKt], Trnpaarticr], and aocpiariKt]. Schol. p. 149, a. 19.
2 These are d^nofiara, the truth of which are self-evident. Waitz. They correspond to the Koivai ivvotai of the mathematicians. The place referred to is the 1st book of the Topics. As assumption by the name of hypothesis forms one of the Aristotelian apxai, or principles of science, we annex the following table of the latter from Mansel's Appendix.
'Apxcu
I Koivai (iK u>v) Iciai {irtpi b)
I I
a^idifiara vifftig
(original premises)
opiafioi vTroQkaiiQ
Definitions. assumptions of the
real, of the subjects, existence of the subjects, as
nominal, of the attributes. a necessary condition
to their definition. (N. B. The attributes are not assumed, but proved to exist in their subjects.) 0
82 Aristotle's organon. [book i.
in the following treatises, but for our present requirements
what has now been determined by us may per-
6 Definition of h suffice. Again, I call that a " term," into
a term — apos. i . V . , .
which a proposition is resolved, as for instance, the predicate and that of which it is predicated, whether to be or not to be is added or separated. ^Lastly, a Byiiogismfa syllogism is a sentence in which certain things being laid down, something else different from the premises necessarily results, in consequence of their ex- istence.1^ I say that, "in consequence of their existence," something results through them, but though something happens through them, there is no need of any external term in order to the existence of the necessary (consequence). either perfect, Wherefore I call a perfect syllogism that which zf areAncf' requires nothing else, beyond (the premises) as- sumed, for the necessary (consequence) to appear : but an imperfect syllogism, that which requires besides, one or more things, which are necessary, through the supposed terms, but have not been assumed through propositions.2 But for one thing to be in the whole of another, and for one thing to be predicated of the whole of another, are the same thing, „ „ c ... and we say it is predicated of the whole, when no-
8. Definition J l ' .
of predication thing can be assumed of the subject, of which the nulio""1 et other may not be asserted, and as regards being predicated of nothing, in like manner.3
1 Vide Aldrich. Aristotle's definition is translated by Aulus Gellius, xv. 26. Oratio in qua, consensis quibusdam et concessis aliud quid, quam qua? Concessa sunt, per ea, quae concessa sunt necessario conficitur. On the subject of the syllogism being a petitio principii, vide Mansel's Logic, Appendix D.
8 Cf. Aquinas Opusc. 47. de Syll. cap. viii. Scotus, lib. i. Anal. Prior, Quaest. xxii. seqq. Occam, Log. p. 3, cap. 6. The direct and in- direct syllogisms of the Schoolmen must not be confounded with the per- fect and imperfect of Aristotle : an indirect syllogism has the minor term the predicate, and the major the subject, of the conclusion.
3 That is, when nothing can be assumed of the subject of which the other can be predicated. With Aristotle the " dictum de omni et nullo," is the principle of all syllogism. Vide Whately, b. i. sect. 4. See also the same principle, Categor. 3.
CHAP. II.] THE PRIOR A-NALYTIC S. 83
Chap. II. — On the Conversion of Propositions.
Since every proposition is either of that which is present (simply), or is present necessarily or converse. contingently, and of these some are affirmative, ^onveislon but others negative, according to each appellation ; in e, univer- again,sinceof affirmative and negative propositions sa y' some are universal, others particular, and others indefinite, it is necessary that the universal negative proposition of what is present should be converted in its terms ; for instance, if " no pleasure is good," " neither will any good be pleasure." But an affirmative proposition we must of neces- 2 A and j (0 sity convert not universally, but particularly,1 as be converted if "all pleasure is good," it is also necessary that par "a certain good should be pleasure;" but of particular pro- positions, we must convert the affirmative proposition parti- cularly, since if " a certain pleasure is good," so also " will a certain good be pleasure ;" a negative proposition however need not be thus converted, since it does not follow, 3 Conversion if " man " is not present with " a certain animal," of o unneces- that animal also is not present with a certain man.
Let then first the proposition A B be an universal nega- tive ; if A is present with no B, neither will B be present with any A, for if it should be present with some A, for ex- ample with C, it will not be true, that A is present with no B, since C is something of B. If, again, A is pre- . „ ,
• i n -n -ii i i • i 4- Examples.
sent with every B, B will be also present with some A, for if with no A, neither will A be present with any B, but it was supposed to be present with every B. In a similar manner also if the proposition be particular, for if A
1 Aristotle's account of conversion differs from that of Aldrich, since he divides conversion into universal and particular, having respect to the qua- lity of the proposition after conversion. 'AttXi) avncrpo^r; is mentioned by Philoponus Scholia. On the conversion per accidens, of the logicians, see Whately, b. ii. sect. 4. Boethius uses the expressions generalis and per accidens. Whately's term, conversion by limitation, is far better. The example in the text is worked out more shortly by Theophrastus and Eudemus. It is to be noticed that, having in Inter, ch. 12, spoken of four modes, he here reduces them to two Vide St. Hilaire's Translation, Preface, p. 66.
g 2
Pi Aristotle's organon. [book i.
be present with some B, B must also necessarily be present with some A, for if it were present with none, neither would A be present with any B, but if A is not present with some B, B need not be present with some A, for example, if B is " animal," but A, " man," for man is not present with " every animal," but " animal " is present with " every man."
Chap. III. — On the Conversion of Modal Propositions}
l Rule for The same system will hold good in necessary pro- modai conver- positions, for an universal negative is universally
sion the same ,., , , .,1 /v. r. ...
as for pure pro- convertible, but either affirmative proposition par- positions. Ex- ticularlv ; for if it is necessary that A should be
ample of the " . -n ■ • i t -r-»
necessary mo- present with no B, it is also necessary that B lal' should be present with no A, for if it should hap-
pen to be present with any, A also might happen to be pre- sent with some B. But if A is of necessity present with every or with some certain B, B is also necessarily present with some certain A ; for if it were not necessarily, neither would A of necessity be present with some certain B : a particular negative however is not converted, for the reason we have before assigned.
In contingent propositions, (since contingency is mul- tifariously predicated, for we call the necessary, and the not necessary, and the possible, contingent,) in all affirmatives, conversion will occur in a similar manner, for if A is con- tingent to every or to some certain B, B may also be con- tingent to some A ; for if it were to none, neither would
A be to any B, for this has been shown before.
The like however does not occur in negative propositions, but such things as are called contingent either from their being necessarily not present, or from their being not necessarily present, (are converted) similarly (with the
1 Modality is not altogether excluded from Logic ; but is admitted by Aristotle, only when, being expressed in a proposition, it necessitates un- der certain conditions a corresponding modification of consequence. Logic has nothing to do with deciding the truth or falsity of proposition, per se, necessarily or contingently ; it only ascertains the necessary infer- ence of conclusion from premises according to certain canons. Vide some admirable remarks by Sir W. Hamilton on this subject. Psellus and Petrus Hispanus are both extra-logical in their consideration of matter.
CHAP. IV.] THE PRIOR ANALYTICS. 85
former); e. g. if a man should say, that it is 2 of the con- contingent, for "a man,' not to be "a horse," tingent, with or for " whiteness " to be present with no " gar- examp e* ment." For of these, the one, is necessarily not present, but the other, is not necessarily, present ; and the proposition is similarly convertible, for if it be contingent to no " man " to be " a horse," it also concurs with no " horse " to be " a man," and if " whiteness " happens to no " garment," a " garment " also happens to no " whiteness ; " for if it did happen to any, "whiteness" will also necessarily happen to "a certain gar- ment," and this has been shown before, and in (Ch 2 , like manner with respect to the particular negative
-r> j i ,,• 11 ? 3. Of things
proposition. But whatever things are called con- calied contin- tingent as being for the most part and from their sent, with the
o o x . differences m
nature, (after which manner we define the contin- conversion oe- gent,) will not subsist similarly in negative conver- tween E and °- sions, for an universal negative proposition is not converted, but a particular one is, this however will be evident when we speak of the contingent. At present, in addition to what we have said, let thus much be manifest, that to happen to nothing, or not to be present with any thing, has an affirma- , Cf ch 12 de tive figure,* for " it is contingent," is similarly ar- interpreta- ranged with "it is," and "it is" always and entirely produces affirmation in whatever it is attributed to, e. g. "it is not good," or, " it is not white," or in short, " it is not this thing." This will however be shown in what follows, but as regards conversions, these will coincide with the rest.
Chap. IV. — Of Syllogism, and of the first Figure.
These things being determined, let us now de- i. syllogism scribe bv what, when, and how, every syllogism is being mo,Tf,
J ' ' „ ' i n T universal than
produced, and let us afterwards speak ol demon- demonstration stration, for we must speak of syllogism prior to ed^to^ature demonstration, because syllogism is more uni- and constmc- versah since, indeed, demonstration is a certain syllogism, but not every syllogism is demonstration.
When, then, three terms so subsist, with reference to each other, as that the last is in the whole of the middle, and the mid- dle either is, or is not, in the whole of the first, then it is neces- sary that there should be a perfect syllogism of the extremes.
86 Aristotle's oroanon. [book i.
. But I call that the middle,1 which is itself in an-
«'m«Vo«, and of other, whilst another is in it,2 and which also be- tfPs-ii0egXismPle comes tne middle by position,3 but the extreme4 that which is itself in another, and in which an- other also is.5 For if A is predicated of every B, and B of every C, A must necessarily be predicated of every C, for it has been before shown, how we predicate " of every ; " so also if A is predicated of no B, but B is predicated of every C, A will not be predicated of any C. But if the first is in every
1 That is, in the first figure, because the middle is piaced otherwise in the second and third figures.
2 That is, in the first figure ; the middle is the subject of the major pre- mise, and predicate of the minor.
3 That is, the middle is placed between the extremes. Aristotle, in his figures, regards rather the extension of the middle, than its position in the two premises. Vide Trendelenburg, Elem. sect. 28. Waitz, Anal. Pr. 23.
4 The majus extremum, to fitl^ov olkdov, is called also to Tzpu>Tov. An. Pr. book i. ch. 31 ; the minus, to iXcittov, also to taxarov- An. Pr. book ii. ch. 8. Cf. Aldrich, cap. iii. sect. 3.
5 The minor extreme is the subject of the middle in the minor pre- mise ; and the major extreme is the predicate of the middle in the major premise.
Ex. 1. Every man is an animal Every man is an animal
No horse is a man No stone is a man
Every horse is an animal. No stone is an animal.
Ex. 2. No line is science No line is science
No medicine is a line No unity is a line
Every medicine is science. No unity is science.
Ex.
Some Habit { » not } good Some habit { |J not } good
All prudence is a habit All ignorance is a habit
All prudence is good. No ignorance is good.
l£x. 4. Some horse j . . J white Some horse | •„ n t } white
No swan is a horse No crow is a horse
Every swan is white. No crow is white.
Kx 5. Every man is an animal Every man is an animal
Something white (i. e. a swan) Something white (i. e. snow) is not
is not a man a man
Every swan is an animal. No snow is an animal.
Ex. 6. No man is inanimate No man is inanimate
Something white (i.' e. snow) Something white (i. e. a swan) id
is not a man not a man
A 11 snow is inanimate. No swan is inanimate.
CHAP. IV.] THE PRIOR ANALYTICS. 87
middle, but the middle is in no last, there is not a syllogism of the extremes, for nothing necessarily results from the ex- istence of these, since the first happens to be present with every, and with no extreme ; so that neither a particular nor universal (conclusion) necessarily results, and nothing neces- sary resulting, there will not be through these a syllogism. Let the terms of being present universally, be " animal," "man," " horse," and let the terms of being present with no one be "animal," "man," "stone."* Since, then, neither
. -ii -in i .Lxample (1.)
the first term is present with the middle, nor the middle with any extreme, there will not thus be a syllogism. Let the terms of being present, be " science," " line," " medi- cine," but of not being present, " science," " line," f Ex ,e (2 <(unity;"f the terms then being universal, it is manifest in this figure, when there will and when there will not be a syllogism, also that when there is a syllogism, it is necessary that the terms should subsist, as we have said, and that if they do thus subsist there will evidently be a syllogism But if one of the terms be universal and the other particu Iar, in relation to the other, when the universal is joined to the major extreme, whether affirmative or negative, but the par- ticular to the minor affirmative, there must necessarily be a perfect syllogism, but when the (universal) is joined to the minor, or the terms are arranged in some other way, a (syl- logism) is impossible. I call the major extreme
i ^ • i_- l xi •!,, • j ,i • xi 3. Definition of
that in which the middle is, and the minor that T(, ucr£0„, and which is under the middle. For let A be present 7° <^aTTO" with every B, but B with some C, if then to be predicated " of every " is what has been asserted from the first, A must necessarily be present with some C, and if A is pre- sent with no B, but B with some C, A must necessarily not be present with some C, for what we mean by the being predi- cated of no one has been defined, so that there will be a perfect syllogism. In like manner, if B, C, being affirm- 4 syllogistic ative, be indefinite, for there will be the same syl- ratio the same logism, both of the indefinite, and of that which as for thes- is assumed as a particular. Ocular.
If indeed to the minor extreme an universal af- 5- No syllogism urinative or negative be added, there will not be Univeisai,°bute a syllogism, whether the indefinite, or particular, the major par-
J & > , . . x ticular, or m-
affinns or denies, e. g. 11 A is or is not present definite.
88 Aristotle's organon. [book i,
with some B, but B is present to every C ; let the terms of affirmation be "good," "habit," "prudence," and those •Example (3.) of negation> "good," "habit," " ignorance." *
Again, if B is present Avith no C, but A is
present or is not present with some B, or not with every
B ; neither thus will there be a syllogism ; let the terms of
. being present with every (individual) be " white," f
"horse," "swan;" but those of being present with no one, be " white," " horse," " crow." The same also
may be taken if A, B be indefinite. Neither will the major is" there be a syllogism, when to the major extreme AorE.butthe the universal affirmative or negative is added;
minor O. , , , ° . .
but to the minor, a particular negative, whether it be indefinitely or particularly taken, e. g. if A is present with every B ; but B is not present with some, or not with every C, for to what the middle is not present, to this, both to every, and to none, the first will be consequent. For let the terms, "animal," "man," "white," be supposed, afterwards from among those white things, of which man is not predicated, let "swan" and "snow" be taken ; hence "animal" is predi- cated of every individual of the one, but of no individual of the , ,_ , other, wherefore there will not be a syllogism. t
% Example (5.) . . * . -n i
Again, let A be present with no B, but B not be present with some C, let the terms also be " inanimate," " man," " white," then let " swan" and " snow" be taken from those white things, of which man is not predicated, for inani- mate is predicated of every individual of the one, but of no . Exam j . . individual of the other. § Once more, since it is
indefinite for B not to be present with some C, (for it is truly asserted, that it is not present with some C, whether it is present with none, or not with every C,) such terms being taken, so as to be present with none, there will be no syllogism (and this has been declared before). Where- fore it is evident, that when the terms are thus, there will not be a syllogism, since if one could be, there could be also one in these, and in like manner it may be shown, if even an uni- , XT . versal negative be taken. Nor will there by any
7. Nor when ° . - . / J
both are parti- means be a syllogism, it both particular mter- cuiar, etc. vajg i ke pre(jiCated either as affirmative or nega-
1 Propositions. " Propositio ipsa vocatur passim ab Aristotele, ' inter-
CHAP. V.J THE PRIOR ANALYTICS. 89
tive, or the one affirmative and the other negative, or the one indefinite, or the other definite, or both indefinite ; but let the common terms of all be "animal," "white," "man," „ Example (7 } "animal," "white," "stone."*
From what has been said, then, it is evident, that if there be a particular syllogism in this figure, the terms must ne- cessarily be as we have said, and that if the terms be thus, there will necessarily be a syllogism, but by no 8 2x-ua wpS. means if thev are otherwise. It is also clear, that ™>- The first
* . , . „ s% , n figure com-
all the syllogisms in this figure are perfect,1 tor Piete,andcom- all are perfected through the first assumptions ; and £[aeshs*"d0sf *" that all problems are demonstrated by this figure, firmation and for by t'his, to be present with all, and with none, nesatlon- and with some, and not with some, (are proved,) and such I call the first figure.2
o
Chap. V Of the second Figure.
When the same (middle term) is present with every 1 , jXnu». b„ individual, (of the one,) but with none, (of the ^^ other,) or is present to every or to none of each, position of the
vallum,' ' Siaor^a,' quoniam duobus extremis terminis includitur, eorum- que intervallutn efficit." Buhle.
Ex. 7. Something white I J* nQt ] an Something white j ^ no(. | an ani-
animal mal
Some man { |j not } white Some stone { J nQt } white
Every man is an animal. No stone is an animal.
1 For the special and general rules of syllogism, see the common Logics. It is sufficient to observe here, that the Aristotelian dictum is directly applicable only to the first figure, which is therefore the type of all syllogisms, and that the special rules, as laid down by Petrus Hispa- nus, may all be found in this and the following chapters.
2 On the term 7rpo/3\//f<ara, compare Alexander Schol. p. 150, b. xl. with this place, and also with Topics, i. 4. Schol. p. 256, a. 14, here, it is used as lr\roi\itva, or " qusestiones," upon which vide Aldrich, cap. 3. The term oxwara, is employed, as Pacius thinks, by Aristotle, because of his illustration of syllogisms by geometrical figures. Vide Waitz, vol. i. 384. The invention of the fourth figure (disowned by Aristotle) is attributed by Averrois to Galen. TpoVoc, or mood, is not used in Aid- rich's sense by Aristotle, except, perhaps, in the 28th chapter of this book. In the same meaning, Aristotle uses 7rrt5<Tic in An. i. 26. Upon the perfect and imperfect moods, vide Whately and Aldrich, (Mansel'z Ed.)
0:
- 7 - - 1_ - -- =■: >" :•- :c
v-rx m M : i»n: M "was • nyy i n ni A »e pre-
; —•••: - >" -_ :* :----—- z~: I.
__~ liar ieenpnweo Defies. AgmiiF Mh p !■■* ■iflt
■
— w l ...,. .." i_-: : — Z
i
_
"_j -
-
;
-__ -
I = "
: i -
~.~ _"_ r_
- Z - . r-- .'.. -
_
! -.1
■ -" :
:_--
c: ^ " r^z -zr.i aSjlLtzz: 9i
i ?dbffl«, Let t&e lens of
■ ;.-- - -
■ syTiflgiwa, wheat 31 is rerefaer pc
• : . ■ " .- • -
-- ~" :::-•;: . :
^armr.-. ' - - "-
H-:.t .: - - - - .- - - . - -..
|
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' iio£am" X. |
|
— ^ |
|
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■ . - . |
-
:: - _ - it'ifae
:- i - - - 7" " . . _ :~ - . " " ■ _ . " - - . ■'— ■ — ■ . - ■ - §1 T-li r— _:. 7 : .: - : :--- " - - " r
:- ;:";-:_:. 2- — L ' -. ~ :-. -.- :: " i . - - " :" . :- : — -"" — :_ i
A I — _ i <
■ ■ : - - ~ - -
.: .- - - . - - ' - '-
Ex. -
V ;
--
92 Aristotle's organon. [book i.
M must necessarily be present with every 0, but it was sup- posed not to be present with a certain 0, and if M is present with every N, and not with every 0, there will be a syllogism, that N is not present with every O, and the demonstration will be the same. But if M is predicated of every O, but not of every N, there will not be a syllogism ; let the terms of presence be " animal," " substance," " crow," and of absence " animal," "white," "crow ;"* neither will there be a syllogism when M is predicated of no 0, but of a certain N, let the terms of presence be "animal," "substance," . ,„ . " stone," but of absence, " animal," " substance,"
t Example (4.) . ,, .
" science, j When therefore universal is opposed to particular, we have declared when there will, and when there will not, be a syllogism ;
but when the propositions are of the same quality,1 4. if both pre- as both being negative or affirmative, there will not Tz^quafitT by any means be a syllogism. For first, let them be no syllogism negative, and let the universal belong to the major
extreme, as let M be present with no N, and not be present with a certain O, it may happen therefore that N shall be present with every and with no 0 ; let the terms of . _ , ,, , universal absence be " black." " snow," " ani-
| Example (5.) ■ ' .
mal ; J but we cannot take the terms or universal presence, if M is present with a certain O, and with a certain O not present. For if N is present with every O, but M with no N, M will be present with no 0, but by hypothesis, it was present with some O, wherefore it is not possible thus to assume the terms. We may prove it nevertheless from the indefinite,2
1 Taylor forgets that the affirmation and negation of proposition con- stitute its quality, so construes 6/joioo-x»j/xoi/£c, " of the same figure," — a classical exactitude procured by an illogical ambiguity. Buhle, "eadem forma."
Ex. 5. No snow is black
Some animal is not black No animal is snow.
8 Called dStopiorog, or indefinite, because it does not explain whether the attribution is true, alone in a part, or universally. Taylor.
Ex. 6. Every swan is white
Some stone is white
No stone is a swan.
Ex. 7. Every swan is white Every swan is white
Some bird is not white Every bird is a swan
Every bird is a swan. Every bird is white.
CHAP. V.] THE PRIOR ANALYTICS. 93
for since M was truly asserted not to be with some certain O,
even if it is present with no 0 ; yet being present with no O,
there was not a syllogism, it is evident, that neither now will
there be one. Again, let them* be affirmative,
and let the universal be similarly assumed, e. g. p0s'iu0n0sth pro"
let M be present with every N, and with a certain
O, N may happen therefore to be present, both with every
and with no O, let the terms of being present with none, be
"white," "swan," "snow;"t but we cannot as- . _ , „,
' ' . ' ' . ... e t Example (6.)
sume the terms ot being present with every, tor
the reason which we have before stated, but it may be shown
from the indefinite.! But if the universal be + _ . ,„ ,
.., . + -, -nr • • 1 t Example (7.)
joined to the minor extreme, and M is present with
no O, and is not present with some certain N, it is possible
for N to be present with every and with no O ; let the terms
of presence be " white," " animal," " crow," but of absence,
" white," " stone," " crow." § But if the proposi- . Exam le .
tions are affirmative, let the terms of absence be
" white," " animal," " snow," of presence, " white," " animal,"
"swan." II Therefore it is evident, when the pro- „_ , ...
e .i, i\J J *v || Example (9.)
positions are ot the same quality, and the one universal, but the other particular, that there is by no means ja syllogism. Neither, however, will there be one, if a thing be present to some one of each term, or not present, or to the one, but not to the other, or to neither universally, or indefinitely, let the common terms of all be "white," "ani- _„ , ,..,
• • • iim- "Example (10.)
mal, "man; "white, "animal, "inanimate. 1
Wherefore it is evident, from what we have stated, that if the terms subsist towards each other, as has been said, there is necessarily a syllogism, and if there be a syllogism, the terms must thus subsist. It is also clear that all syllogisms
Ex. 8. Some animal is not white Some stone is not white
No crow is white No crow is white
Every crow is an animal. No crow is a stone.
Ex. 9. Some animal is white Some animal is white
All snow is white Every swan is white
No snow is an animal. Every swan is an animal.
Ex. 10. Some animal j j* . \ white Some animal I ^ not 1 white
Some man | j* , j white Something inanim. I ^ uot I whiU Every man is an animal. Nothing inanimate is an animal.
94 akistotle's organon. [book I.
in this figure are imperfect, for all of them are produced from certain assumptions, which are either of necessity in the terms, or are admitted as hypotheses, as when we demonstrate by the 5 No affirma- iniP0SSit»le. Lastly, it appears that an affirmative tive conclusion syllogism is not produced in this figure, but all m this figure. are negativej fr^ t}ie universal and also the
particular.1
Chap. VI. — Of Syllogisms in the third Figure.
1. •zxnu-iT' When with the same thing one is present with gurejts cha- every, but the other with no individual, or both racteristic— the with every, or with none, such I call the third subject of both - figure ; and the middle in it, I call that of which PerfecTs7io- we Pre^icate both, but the predicates the ex- gism in this tremes, the greater extreme being the one more figure. remote from the middle, and the less, that which
is nearer to the middle. But the middle is placed beyond the extremes, and is last in position ; now neither will there be a
perfect syllogism, even in this figure, but there gism!'asyll° may De one,* when the terms are joined to the
middle, both universally, and not universally. Now when the terms are universally so, when, for instance, P and R are present with every S, there will be a syllogism, so that P will necessarily be present with some certain R, for since an affirmative is convertible, S will be present to a cer- tain R. Wherefore since P is present to every S, but S to some certain R, P must necessarily be present with some R, for a syllogism arises in the first figure. We may also make
the demonstration through the impossible, and by &T h?*°r exposition.2 For if both are present with every
S, if some S is assumed, (e. g.) N, both P and R
1 For the special rules and necessary negative conclusion in this figure, vide Whately and Aldrich ; and for the principles of the several figures, compare Hill's Logic. The enumeration of distinct axioms for the second and third figures, occurs in Lambert Nues Organon, part i. ch. 4, sect. 232. According to him, the use of the second figure is for the discovery and proof of differences in things ; and of the third, for those of examples and exceptions.
2 The method called tKQtaiq signifies by exhibiting an individual case. ; exponere sensui," hence a syllogism with singular premises is caned
" syllogismus expositorius." It is doubtful whether Aristotle regarded
CHAP. VI.] THE PRIOR ANALYTICS. 95
will be present with this, wherefore P will he present with a certain R, and if R is present with every S, but P is present with no S, there will be a syllogism, so that P will be neces- sarily inferred as not present with a certain R ; for the same mode of demonstration will take place, the proposition R S being converted ; this may also be demonstrated by the im- possible, as in the former syllogisms. But if R is present with no S, but P with every S, there will not be a syllogism ; let the terms of presence be "animal," "horse," "man," but of absence "animal," "inanimate," "man."* „ , „,
•xt • i i ii t ip o -n * Example (1.)
JN either when both are predicated ot no b, will there be a syllogism, let the terms of presence be " animal," " horse," " inanimate," but of absence " man," . _ , .„, " horse," inanimate," the middle " inanimate." f Wherefore also in this figure it is evident, when there will, and when there will not, be a syllogism, the
, . . , n , . ■'., f ' 2. When both
terms being universal, tor when both terms are premises are affirmative, there will be a syllogism, in which it fffirmat.i,,;ev.
' •> ° . ' , there will be a
will be concluded that extreme is with a cer- syllogism, but tain extreme,1 but when both terms are negative "re negative- there will not be. When however one is negative the major and the other affirmative, and the major is nega- be°negatfv™ana tive but the other affirmative, there will be a syl- *he minor> at-
... . . firmative.
logism, that the extreme is not present with
a certain extreme, but if the contrary there will not be.
If indeed one be universal in respect to the middle,2 and the other particular, both being affirmative, syllogism is necessarily produced, whichever term be universal. For if R is present
the tKOeaig as a syllogism at all. Vide Aquinas, Opusc. 47. ZabareUa, cap. 7.
Ex. 1. Every man is an animal Every man is an animal
No man is a horse No man is inanimate
Every horse is an animal. Nothing inanimate is a horse.
Ex. 2. Nothing inanimate is an ani- Nothing inanimate is a man mal
Nothing inanimate is a horse Nothing inanimate is a horsb
Every horse is an animal. No horse is a man.
1 i. e. the major with the minor.
* i. e. Universally predicated of the middle.
Ex. 3. Every animal is animate Some animal is not a man Every man is animate.
9t> Aristotle's organon. [book i.
with every S, but P with a certain S, P must necessarily be present with a certain R, for since the affirmative is convert- ible, S will be present with a certain P, so that since R is present to every S, and S with a certain P, R will also be present with a certain P, wherefore also P will be present with a certain R. Again, if R is present with a certain S, but P is present with every S, P must necessarily be present with a certain R, for the mode of demonstration is the same, and these things may be demonstrated like the former, both by the impossible, and by exposition. If however one be affirm- ative, and the other negative, and the affirmative be universal, when the minor is affirmative there will be a syllogism ; for if R is present with every S, and P not present with a certain S, P must also necessarily not be present with a certain R, since if P is present with every R, and R with every S, P will also be present with every S, but it is not present, and this may also be shown without deduction, if some S be taken with which P is not present. But when the major is affirm- ative there will not be a syllogism, e. g. if P is present with every S, but R is not present with a certain S ; let the terms m F of being universally present with be " animate,"
xamp e (i marij" " animal." * But it is not possible to take the terms of universal negative, if R is present with a certain S, and with a certain S is not present, since if P is present with every S, and R with a certain S, P will also be present with a certain R, but it was supposed to be present with no R, therefore we must assume the same as in the former syllogisms. As to declare something not present with a cer- tain thing is indefinite, so that also which is not present with any individual, it is true to say, is not present with a certain individual, but not being present with any, there was no syl- logism, (therefore it is evident there will be no syllogism).1
1 i. e. when it is assumed not to be present with a certain individual.
Ex. 4. Something wild is an animal Something wild is an animal Nothing wild is a man Nothing wild is science
Every man is an animal. No science is an animal.
Ex. 5. Something wild is n:t an ani- Something wild is not an animal, mal
Nothing wild is science Nothing wild is a man
No science is an animal. Every man is an animaL
CHAP. VI. _, THE PRIOK ANALYTICS. 97
But if the negative term be universal, (yet the particular af- firmative,) when the major is negative, but the minor affirm- ative, there will be a syllogism, for if P is present with no S, but R is present with a certain S, P will not be present with a certain R, and again there will be the first figure, the pro- position R S being converted. But when the minor is nega- tive, there will not be a syllogism ; let the terms of presence be " animal," " man," " wild," but of absence, " animal," "science," "wild," the middle of both, "wild."* # £xam Nor will there be a syllogism when both are ne- gative, the one universal, the other particular : let the terms of absence when the minor is universal as to the middle, be " animal," " science," " wild," (of presence, " ani- mal," "man," "wild)."| When however the p {) major is universal, but the minor particular, let the terms of absence be "crow," "snow," "white ;"t but of , _ , ,„.
' , , -p -r! • t Example (6.)
presence we cannot take the terms, 11 R is present with some S, and with some is not present, since if P is present with every R, but R with some S, P will also be present with some S, but it was supposed to be present with no S, indeed it may be proved from the indefinite. Neither if each ex- treme be present or not present with a certain middle, will there be a syllogism ; or if one be present and the other not ; or if one be with some individual and the other with not every or indefinitely. But let the common terms of all be, "animal," "man," "white," "animal," "inanimate," "white." S Wherefore , ^ , ,„,
,.,.,. i , i -n § Example (7.)
it is clear in this figure also, when there will and when there will not be a syllogism, and that when the terms are disposed as we have stated, a syllogism of necessity subsists, and that there should be a syllogism, it is necessary that the terms should be thus. It is also clear 3. No universal that all syllogisms in this figure are imperfect, for conclusion de- Ex. 6- Nothing white is a crow
Not every thing white is snow No snow is a erjw.
Ex
7. Something white j |S^ol j an Something white j . > an ani-
animal mal
Something white j l* a .Something white 1 J > inani-
man mate.
Every man is an animal. Nothing inanimate is an animal.
V-
98 Aristotle's organon. ["book i.
rived from tMa they are all perfected by certain assumptions, and figure. t[iat an universal conclusion either negative or af-
firmative, cannot be drawn from this figure.1
Chap. VII. — Of the three first Figures, and of the Completion of Incomplete Syllogisms.
In all the figures it appears that when a syllogism is not pro- duced, both terms being affirmative, or negative, (and par- ticular,2) nothing, in short, results of a necessary character ; but if the one be affirmative and the other nega-
1. If one pre- . , ... . .. . , .,
mise be a or i, tive, the negative being universally taken, there
therehwmhoeEa *s always a syllogism of the minor extreme with the
conclusion in major. For example, if A is present with every
norfe predi™1 or with some B, but B is present with no C, the
oated of the propositions being converted, C must necessarily
major. , . » i • 1 1
not be present with some A ; so also in the other figures, for a syllogism is always produced by conversion : again, it is clear that an indefinite taken for a particular affirm- ative, will produce the same syllogism in all the figures.
Moreover it is evident that all incomplete syllogisms are completed by means of the first figure, for all of them are concluded, either ostensively or per impossibile, but in both ways the first figure is produced : being osten- sively*3 completed, (the first figure is produced,) because all of them were concluded by conversion, but conversion produces the first figure : but if they are de-
1 Vide Hill, p. 196; also Whately, pp. 60 and 61. For the uses of the three figures also Aldrich, iii. 8.
2 The words " and particular " are omitted by Waitz.
3 Taylor translates this " demonstratively." " Simplici et rect& de- monstratione." Buhle. Reduction is expressed by the verb avaytaQai, never aTraytoQai. Mansel. He is also right in drawing attention to the incorrectness of the phrase, " reductio ad impossibile;" it ought to be " per deductionem ad impossibile, or elliptically, per impossibile." The general phrase is a palpable absurdity. Vide An. ii. 11, C. Upon the nature of the dirayu/yr] els to dSvvarov, wherein, after all, the word does not mean reduction, see Mansel's Logic, Appendix, note G. The anti- thesis to duicTiicbg, is t£ V7ro9ecno)g. Cf. ch. 23 of this 1st book of Ana- lytics: also Whately, book ii. ch. 3, sect. 5 and 6. Although the in- direct moods have been attributed to the invention of Theophrastus, by Alexander, (Schol. p. 153,) we find two of them recognised here by Aristotle, and the other three in Anal. Prior, ii. 1.
CHAP. VII.] THE PRIOR ANALYTICS. 99
monstrated per impossibile, (there will be still the first figure,) because the false being assumed, a syllogism arises in the first figure. For example, in the last figure, if A and B are present with every C, it can be shown that A is presentwith some B, for if A is present with no B, but B is present with every C, A will be present with no C ; but it was supposed that A was present with every C, and in like manner it will happen in other in- stances.
It is also possible to reduce all syllogisms , A11 llo to universal syllogisms in the first figure. For gisms may be those in the second, it is evident, are completed vers^inth* through these, yet not all in like manner, but first figure the universal by conversion of the negative, and the various each of the particular, by deduction per impos- methods- sibile. Now, particular syllogisms in the first figure are com- pleted through themselves, but may in the second figure be demonstrated by deduction to the impossible. For example, if A is present with every B, but B with a certain C, it can be shown that A will be present with a certain C, for if A is present with no C, but is present with every B, B will be present with no C, for we know this by the second figure. So also will the demonstration be in the case of a negative, for if A is present with no B, but B is present with a certain C, A will not be present with a certain C, since if A is present with every C, and with no B, B will be present with no C, and this was the middle figure. Wherefore, as all syllogisms in the middle figure are reduced to universal syllogisms in the first figure, but particular in the first are reduced to those in the middle figure, it is clear that particular will be reduced to universal syllogisms in the first figure. Those, however, in the third, when the terms are universal, are immediately completed through those syllogisms ; * ' but when particular , . (terms) are assumed (they are completed) through versais of the particular syllogisms in the first figure ; but these j j! ^e^particu- have been reduced to those,J so that also particu- ia«. lar syllogisms in the third figure (are reducible niversa s- to the same). Wherefore, it is evident that all can be re- duced to universal syllog'»;ms in the first figure ; and we have therefore shown how syllogisms de inesse and de non inesse
1 By a deduction to an absurdity. h 2
100 Aristotle's organon. [book i.
subsist, both those which are of the same figure, with refer- ence to themselves, and those which are of different figures, also with reference to each other.
Chap. VIII. — Of Syllogisms derived from two necessary Propositions.
Since however to exist, to exist necessarily, and syllogisms, viz. to exist contingently are different, (for many xe°if— and those tnmgs exist, but not from necessity, and others to? 'avaticatov neither necessarily, nor in short exist, yet may hap- tl7/xe<rt>a™cL pen to exist,) it is evident that there will be a whateiy, b. 2. different syllogism from each of these, and from the
terms not being alike ; but one syllogism will con- sist of those which are necessary, another of absolute, and a third „ „ of contingent. In necessary syllogisms it will
2. Necessary ° J . J .. °
syllogisms re- almost always be the same, as m the case of abso- any those "er~ mte subsistences,1 for the terms being similarly which are abso- placed in both absolute existence, and in existing, or not of necessity, there will and there will not be a syllogism, except that there will be a difference in neces- sary or non-necessary subsistence being added to the terms. For a negative is in like manner convertible, and we assign similarly to be in the whole of a thing, and to be (predicated) of every. In the rest then it will be shown by the same manner, through conversion, that the conclusion is necessary, as in the case of being present ; but in the middle figure, when the universal is affirmative, and the particular negative, and again, in the third figure, when the universal is affirmative, but the particular negative, the demonstration will not be in the like manner ; but it is necessary that proposing something with which either extreme is not present, we make a syllogism of this, for in respect of these there will be a necessary (conclu- sion). If, on the other hand, in respect to the proposed term, there is a necessary conclusion, there will be also one (a neces- sary conclusion) of some individual of that term, for what is proposed is part of it, and each syllogism is formed under its own appropriate figure.
1 i. e. Pure categoricals.
CHAP. IX.] THE PRIOR ANALYTICS. 101
Chap. IX.— Of Syllogisms, whereof one Proposition is necessary, and the other pure in the first Figure.
It sometimes happens also that when one pro- , ConclUii-
position is necessary, a necessary syllogism arises,1 of a syllogism
not however from either proposition indifferently, Jtae necePs-e"
but from the one that contains the greater ex- sar>' often fo1.-
treme.2 For example, if A is assumed to be premLt-ex-'
necessarily present or not present with B, but B 3£,pfc*nd.
to be alone present with C, for the premises beino- versais and
thus assumed, A will necessarily be present or partKUlars- not with C ; for since A is or is not necessarily present with every B, but C is something belonging to B, C
will evidently of necessity be one of these.* If. *.V,e- wln °f
A r> / i ■ \ ■ W1" not "e A.
again, A ±$ (the major) is not necessary, but B C (the minor) is necessary, there will not be a necessary con- clusion, for if there be, it will happen that A is necessarily present with a certain B, both by the first and the third figure, but this is false, for B may happen to be a thing of that kind, that A may not be present with any thing of it. Besides, it is evident from the terms, that there will not be a necessary conclusion, as if A were "motion," B "animal," and C "man," for "man" is necessarily "an animal," but neither are "animal" nor "man" necessarily "moved;" so also if A B is negative, for there is the same de- monstration. In particular syllogisms, however, ^ecefeotl if the universal is necessary, the conclusion will also be necessary, but if the particular be, there will not be a necessary conclusion, neither if the universal premise be nega- tive nor affirmative. Let then, in the first place, the universal be necessary, and let A be necessarily present with every B,
1 Theophrastus and Eudemus allowed a necessary conclusion to follow from two necessary premises only. Vide Alex. Aphr.
2 Majori necessaria, necessario aliquid inesse concluditur. Buhle.
Ex. 1. Every animal is moved No animal is moved
It is necessary that something It is necessary that something white
white should be an animal should not be an animal
Therefore something white is Therefore something white is not
moved. moved.
This is not necessary, for it [This is not necessary, because it
might possibly not be moved.] may be moved.]
102 apjstotle's organon. [book I.
but B only be present with a certain C ; it is necessary therefore that A should of necessity be present with a certain toV 1S ^°ined C, for C is under* B, and A was of necessity pre- sent with every B. The same will occur if the syllogism be negative, for the demonstration will be the same, but if the particular be necessary, the conclusion will not be + i. e. though a necessary, for nothing impossible results,! as nei- ron-necessary tner {n universal syllogisms. A similar conse-
conclusion og
admitted. quence will result also in negatives ; (let the
t Example (i.) termg be) « motionj» "animal," " white." J
Chap. X. — Of the same in the second Figure.
l.inthesecond -^N tne second figure, if the negative premise be
figure, when a necessary, the conclusion will also be necessary,
fo1nedSw!thSa but if the affirmative (be necessary, the conclu-
pure premise, s\on) wiH not be necessary. For first, let the
the conclusion ' . -i i . , .1
follows the ne- negative be necessary, and let it not be possible
s^ypremls^- for A to be in any B> but let ik be present with Example and C alone ; as then a negative proposition may be converted, B cannot be present with any A, but A is with every C, hence B cannot be present with any C, § i. e. belongs for C is under § A. In like manner also, if the *°rA- , negative be added tt> C,|| for if A cannot be with
|| The conclu- ° 'II
sion will be any O, neither can O be present with any A, but necessary. j^ -g w^h everv j}, so neither can C be present with any B, as the first figure will again be produced ; wherefore, neither can B be present with C, since it is simi- 2. if the affirm- larly converted. If, however, the affirmative pre- ative be neces- miSe be necessary, the conclusion will not be
sarv, the con- p i a -it • i
elusion will necessary ; tor let A necessarily be present with not be. every B, and alone not be present with any C,
then the negative being converted, we have the first figure ; but it was shown in the first, that when the major negative (proposition) is not necessary, neither will the conclusion be necessary, so that neither in these will there be a necessary _ . . „ conclusion. If Once more, if the conclusion is
IT 1. e. in syllo- . " • ' '
gismsofthe necessary, it results that b is not necessarily pre- with"a neSces! sent w^tn a certain A, for if B is necessarily pre- sary affirma- sent with no C, neither will C be necessarily pre- sent with any B, but B is present necessarily with
CHAP. XI. J THE PRIOR ANALYTICS. 103
a certain A, if A is necessarily present with every B. Hence, it is necessary that C should not be present with a certain A ; there is, however, nothing to prevent such an A being as- sumed, with which universally C may be present. More- over, it can be shown by exposition of the terms, that the conclusion is not simply necessary, but necessary from the assumption of these, e. g. let A be " animal," B " man," C " white," and let the propositions be similarly assumed : for it is possible for an animal to be with nothing " white," then nei- ther will " man " be present with any thing white, yet not from necessity, for it may happen for "man" to be "white," yet not so long as " animal " is present with nothing " white," so that from these assumptions there will be a necessary con- clusion, but not simply necessary.
The same will happen in particular syllogisms, for ^mewith6 par- when the negative proposition is universal and ne- ticuiars. cessary, the conclusion also will 1 >e necessary,but when the affirm- ative is universal and necessary, and the negative * Taylor in- particular,* the conclusion will not be necessary. ^g'g' ™*not First, then, let there be an universal and necessary which words negative, and let A not possibly be present with Bekkertandby any B, but with a certain C. Since, therefore, a Waits. negative proposition is convertible, B can neither be possibly present with any A, but A is with a certain C, so that of necessity B is not present with a certain C. Again, let there be an universal and necessary affirmative, and let the affirm- ative be attached to B, if then A is necessarily present with every B, but is not with a certain C, B is not with a certain C it is clear, yet not from necessity, since there will be the same terms for the demonstration, as were taken in the case of universal syllogisms. Neither, moreover, will the conclu- sion be necessary, if a particular necessary negative be taken as the demonstration is through the same terms.
o
Chap. XI. — Of the same in the third Figure.
In the last figure, when the terms are universally i. in this figure joined to the middle,1 and both premises are mfgehbenece«- affirmative, if either of them be necessary, the sary, and both
1 That is, are predicated of it.
104 aristotle's organon. [book i.
be a, the con- conclusion will also be necessary; and if one be
elusion will be . J ' .
necessary. negative, but the other affirmative, when the negative is necessary, the conclusion will be also necessary, but when the affirmative (is so, the conclusion) will not be
necessary. For first, let both propositions be1
affirmative, and let A and B be present with every C, and let A C be a necessary (proposition). Since then B is present with every C, C will also be present with a certain B, because an universal is converted into a parti- cular : so that if A is necessarily present with every C, and C with a certain B, A must also be necessarily present with • i. e. belongs a certain B, for B is under C,* hence the first figure t0 «*• again arises. In like manner, it can be also de-
2nd case. monstrated if B C is a necessary (proposition), for
C is converted with a certain A, so that if B is necessarily present with every C, (but C with a certain A,) B will also of necessity be present with a certain A. Again let A C be a negative (proposition), but B C affirmative, and let the negative be necessary ; as therefore an affirmative pro- position is convertible, C will be present with some certain B, but A of necessity with no C, neither will A necessarily
be present with some B, for B is under C. But ceptira6 an eX~ ^ tne affirmative is necessary, there will not be a
necessary conclusion ; for let B C be affirmative and necessary, but A C negative and not necessary ; since then the affirmative is converted C will also be with a cer- tain B of necessity ; wherefore if A is with no C, but C with a certain B, A will also not be present with a certain B, but t Vide ch 9 not ^Yom necessity, f°r it bas been shown by the
first figure,f that when the negative proposition is not necessary, neither will the conclusion be necessary. Moreover this will also be evident from the terms, for let A
i
Taylor, by mistake, reads "necessary." Ex. 1. No horse is good
It is necessary that every horse should be an animal
Therefore some animal is not good.
Ex.2. No horse ?Takes I sleeps
It is necessary that every horse should be an animal
. ' . Some animal does not \ ^ake
I sleep.
CHAP. XI.] THE PRIOR ANALYTICS. 105
be "good," B "animal," and C "horse," it happens therefore
that "good" is with no "horse," but "animal" is necessarily
present with every " horse," but it is not however necessary
that a certain " animal " should not be " good," for every
"animal" may possibly be "good."* Or if this
is not possible, (viz. that every animal is good,) we
must assume another term, as "to wake," or "to sleep," for
every " animal " is capable of these. f If then the
terms are universal in respect to the middle, it has
been shown when there will be a necessary conclusion.
But if one term is universally but the other 2. if 0ne pro- particularly (predicated of the middle), and both position be a propositions are affirmative, when the universal is necessary the necessary the conclusion will also be necessary, conclusion 's t
n i i ... in • necessary, but
for the demonstration is the same as before, since not when i is the particular affirmative is convertible. If there- neeessary- fore B is necessarily present with every C, but A is under C, B must also necessarily be present with a certain A,1 and if B is with a certain A, A must also be present necessarily with a certain B, for it is convertible ; the same will also occur if A C be a necessary universal proposition, for B is under C. But if the particular be necessary, there will not be a neces- sary conclusion, for let B C be particular and necessary, and A present with every C, yet not of necessity, B C then being converted we have the first figure, and the universal propo- sition is not necessary, but the particular is necessary, but when the propositions are thus there was not a necessary con- clusion,^: so that neither will there be one in the case of these. § Moreover this is evident from the * Ex^ie tf ) terms, for let A be " wakefulness," B " biped," but C, "animal ;" B then must necessarily be present with a cer-
1 This succeeding clause is omitted by Taylor, though read by Buhle
and Waitz.
Ex. 3. Every C is A.
t. ■ ,, ( C should be B
It is necessary that some < „ , , , £ ~
. • . Some B is A.
Ex. 4. Every animal wakes
It is necessary that some anim:il should be biped . • . Some biped wakes.
106 Aristotle's org axon. [book i.
tain C, but A may happen to be present with every C, and yet A is not necessarily so with B, for a certain " biped " need
not " sleep " or " wake." * So also we may de- t Example (5 ) monstrate it by the same terms if A be particular
and necessary.f But if one term be affirmative and the other negative, when the universal proposition is ne- gative and necessary, the conclusion will also be necessary, for if A happens to no C, but B is present with a certain C, A must necessarily not be present with a certain B. But 3 when the when the affirmative is assumed as necessary, affirmative is whether it be universal or particular, or particular am i?or when negative, there will not be a necessary conclusion, o is assumed, for we mav allege the other same (reasons
there will not \
be a necessary against it), as m the former cases.1 But let the conclusion. terms when the universal affirmative is necessary ♦ it , ,,, be "wakefulness," "animal," "man," the middle
t Example (6.) ' ' , '
"man. J But when the particular affirmative is necessary, let the terms be "wakefulness," "animal," " white," for "animal" must necessarily be with something "white," but "wakefulness" happens to be with nothing "white," and it
is not necessary that wakefulness should not be § Example (7.) wjth a certain animal. § But when the negative
particular is necessary, let the terms be "biped," xampe(.) it mo^on» "animal," and the middle term,
" animal." ||
Ex. 5. It is necessary that some ani- Every animal wakes
mal should be a biped It is necessary that some biped
Every animal wakes should be an animal
. * . Something that wakes is a . ' . Some biped wakes, biped. 1 Because by reduction to the first figure the minor will be necessary, but the major pure ; hence no necessary conclusion can be inferred. (Vide supra.)
Ex. 6. Some man does not wake
It is necessary that every man should be an animal . • . Some animal does not wake.
Ex. 7. Nothing white wakes
It is necessary that something white should be an animal . • . Some animal does not wake.
Ex. 8. It is necessary that some animal should not be a biped Every animal is moved • . Something which is moved is not a biped.
CHAP. Xn. Xm.] THE PRIOR ANALTTICS. 107
Chap. XII. — A comparison of pure loitli necessary Syllogisms?
It appears then, that there is not a syllogism de inesse un- less both propositions signify the being present with,2 but that a necessary conclusion follows, even if one alone is necessary. But in both,* the syllogisms anciniodai6 being affirmative, or negative, one of the propo- sitions must necessarily be similar to the conclu- 1. Distinction sion ; I me in by similar, that if (the conclusion) solute6 and ne*- be (simply) that a thing is present with, (one of cessaryconciu- the propositions also signifies simply) the being pre- th°e" latter^? ab- sent with, but if necessarily, (that is, in the con- pendence upon
,. ,, , . . v . , \ the premises ;
elusion, one of the propositions is also) necessary, theirconnexion Wherefore this also is evident, that there will als0Wlthlt- neither be a conclusion necessary nor simple de inesse, unless one proposition be assumed as necessary, or purely categorical, and concerning the necessary, how it arises, and what differ- ence it has in regard to the de inesse, we have almost said enough.
Chap. XIII. — Of the Contingent, and its concomitant Propositions.
Let us next speak of the contingent, when, and , Definit;on 0f
how, and through what (propositions) there will the_ contingent
be a syllogism ; and to be contingent, and the \™t gVeXn"and
contingent, I define to be that which, not being confirmed.
v 4. l • A 4. -\ 4-U- (VideMetaph.
necessary, but being assumed to exist, nothing ijD. v. 2,) also impossible will on this account arise, for we say InterPret- 13- that the necessary is contingent equivocally. But, that such
1 Vide the previous notes on the subject of modals. The reader who wishes to ascertain how far logic is conversant with the expressed matter of modal proposition, will find arguments " ad rem," and " ad nauseam" both, in relation to the various views of the question, in Ed. Review, No. 118; Kant, Logik, sec. 30; St. Hilaire's preface. In both modals and pure categoricals, the format consequence alone is really the legitimate object of consideration to the logician, with the material he has strictly nothing to do. Whately has shown that a modal may be stated as a pure proposition, by attaching the mode to one of the terms ; this being done, the rule of consequence applies to both equally.
2 i. e. in categoricals both premises must be affirmative for the con- clusion to be so.
108 Aristotle's oroanon. [rook i.
is the contingent, is evident from opposite negatives and affirmatives, for the assertions — " it does not happen to be," and, " it is impossible to be," and, " it is necessary not to be," are either the same, or follow each other ; wherefore also the contraries to these, " it happens to be," " it is not impossible to be," and, " it is not necessary not to be," will either be the same, or follow each other ; for of every thing, there is either affirmation or negation, hence the contingent will be not necessary, and the not-necessary will be contingent. It hap- pens, indeed, that all contingent propositions are Trpimio-e!!- ca- convertible with each other. I do not mean the versfoif C°n affirmative into the negative, but as many as have an affirmative figure, as to opposition ; e. g. " it happens to exist," (is convertible into) " it happens not to exist," and, " it happens to every," into " it happens to none," or, "not to every," and, "it happens to some," into " it hap- pens not to some." In the same manner also with sioifeffectel"" tne rest,* for since the contingent is non-neces- sary, and the non-necessary may happen not to exist, it is clear that if A happens to be with any B, it may also happen not to be present, and if it happens to be present with every B, it may also happen not to be pi'esent with every B. There is the same reasoning also in particular affirmatives, for the demonstration is the same, but such propositions are affirmative and not negative, for the verb " to be contingent," . „.„ „ is arranged similarly to the verb " to be," as we
t Vide c. 3. ° *
have said before. \ „ „, . These things then being defined, let us next
3. The contin- o '
gent predicated remark, that to be contingent is predicated in two
the'rae Serai ways> one tnat which happens for the most part
the other inde- and yet falls short of the necessary — (for instance,
th^of conver- f°r a man t° become hoary, or to grow, or to
sion not the waste, or in short whatever may naturally be, for
Si line to 63.cn
this has not a continued necessity, for the man may not always exist, but while he does exist it is either of necessity or for the most part) x — the other way (the contin- gent is) indefinite, and is that which may be possibly thus and not thus ; as for an animal to walk, or while it is walking for an earthquake to happen, or in short whatever occurs casually, for
i 1 i. e. that he is subject to these things.
CHAP. XIII. ] THE Pivxo.. ANALYTICS. 109
nothing is more naturally produced thus, or in a contrary way. Each kind of contingent however is convertible according to opposite propositions, yet not in the same manner, but what may naturally subsist is convertible into that which does not subsist of necessity ; thus it is possible for a man not to be- come hoary, but the indefinite is converted into what cannot more subsist in this than in that way. Science however and demonstrative syllogism do not belong to indefinites, because the middle is irregular, but to those things which may na- turally exist ; and arguments and speculations are generally conversant with such contingencies, but of the indefinite con- tingent we may make a syllogism, though it is not generally investigated. These things however will be more defined in what follows,1 at present let us show n'ite contingent when and how and what will be a syllogism from of less use in
^ ° syllogism.
contingent propositions.
Since then that this happens to be present with that may be assumed in a twofold respect, — (for it either signifies that with which this is present, or that with which it may be present, thus the assertion, A is contingent to that of which B is predicated, signifies one of these things, either that of which B is predicated, or that of which it may be predicated ; but the assertion that A is contingent to that of which there is B, and that A may be present with every B, do not differ from each other, whence it is evident that A may happen to be present with every B in two ways,) — let us first show if B is contingent to that of which there is C, and if A is contin- gent to that of which there is B, what and what kind of syllo- gism there will be, for thus both propositions are contingently assumed. When however A is contingent to that ' .
. . . . , . 5. An inquiry
with which B is present, one proposition is de in- into the con- esse, but the other of that which is contingent, so contingent'syt- that we must begin from those of similar character, logisms pre-
*— ■* Tin fpfi
as we began elsewhere.2
1 In the Post Analytics, i. c. 8. In Rhetoric, b. ii. c. 24, he admits ac- cident to be an element of apparent argument, but in Metap. lib. v. c> 3, denies that there is any science of it, and regards it as a <xt]fitlov.
7 That is, from syllogisms, each of whose propositions is contingent.
110
ARISTOTLE S ORGANON.
[BOOK I.
Chap. XIV. — Of Syllogisms ivitA two continyeut P rojjusitions in
the first Fiyure.
When A is contingent to every B, and B to every C, there will be a perfect syllogism, so that A is contingent to every C, which is evident from the definition, for thus we stated the universal contingent (to imply). So also if A is contingent to no B, but B to every C, (it may be concluded) that A is contingent to no C, for to affirm that A is contin- gent in respect of nothing to which B is contin- gent, this were to leave none of the contingents which are under B. But when A is contingent to every B, but B con- tingent to no C, no syllogism arises from the as- sumed propositions, but B C1 being converted ac- cording to the contingent, the same syllogism arises as existed before, as since it happens that B is present with no C, it may also happen to be present with every C, which was shown before,* wherefore if B may happen to every C, and A to every B, the same syllogism will again arise. The like will occur also if negation be added with the contingent (mode) to both propositions, I mean, as if A is contingent to no B, and B to no C, no syl- logism arises through the assumed propositions, but when they 2 when the are converted there will be the same as before. It ooXneiLuve *s ev^ent tnen tnat when negation is added to or the minor the minor extreme, or to both the propositions, is6 either no ere there is either no syllogism, or an incomplete one, syllogism or an for the necessity (of consequence) is completed by
incomplete one . T; ; 1 „ ' , l . . J
—case of the conversion. It however one ot the propositions versai with th ^e universal, and the other be assumed as parti- minor particu- cular, the universal belonging to the major ex-
lar, different. treme there ^ bg ft perfect syHogism> for if A
is contingent to every B, but B to a certain C, A is also con- tingent to a certain C, and this is clear from the definition of universal contingent. Again, if A is contingent to no B, but B happens to be present with some C, it is necessary that A should happen not to be present with some C, since the de-
1. With the contingent pre- mises both uni- versal there will be a perfect syllogism.
2nd case.
3rd case.
» Vide ch. 13.
4th case.
That is, the minor negative being made ^Affirmative.
CHAP. XIV.] THE PRIOR ANALYTICS. 1 1 i
monstration is the same ; but if the particular proposition be assumed as negative, and the universal affirmative, and retain the same position as if A happens to be present to every B, but B happens not to be present with some C, no evident syllogism arises from the assumed propositions, but the parti- cular being converted and B being assumed to be contingently present with some C, there will be the same conclusion as be- fore in the first syllogisms.1 Still if the major proposition be taken as particular, but the minor as universal, and 2 Vice versa if both be assumed affirmative or negative, or of different figure, or both indefinite or particular, there will never be a syllogism ; for there is nothing to prevent B from being more widely extended than A, and from not being equally predicated. Now let that by which B exceeds A, be assumed to be C, to this it will happen 2 that A is present neither to every, nor to none, nor to a certain one, nor not to a certain one, since contingent propositions are convertible, and B may happen to be present to more things than A. Besides, this is evident from the terms, for when the propo- sitions are thus, the first is contingent to the last, and to none, and necessarily present with every individual, and let the common terms of all be these ; of being present necessarily 3 " animal," " white," " man," but of not being con- , Example (]>) tingent, "animal," "white," "garment."* There- fore it is clear that when the terms are thus there is no syllo-
1 In the universal imperfect syllogisms mentioned towards the begin- ning of this chapter.
8 Because C is necessarily not present, and the necessary is distin- guished from the contingent.
3 That is, of the major being with the minor.
Ex. 1. It happens that something white j |s > an animal
! every \ c? > man is white
not every / It is necessary that every man should be an animal.
It happens that something white jt not I an animeJ
I every \ n° „ > garment is white oW 1X1 C not every / It is necessary that no garment should be an wiimsj.
112 aristotle's orgajston. [book i,
gism, for every syllogism is either de inesse, or of that which exists necessarily or contingently, but that this is neithei tie inesse, nor of that which necessarily exists, is clear, since the affirmative is subverted by the negative, and the negative by the affirmative, wherefore it remains that it is of the con- tingent, but this is impossible, for it has been shown that when the terms are thus, the first is necessarily inherent in all the last, and contingently is present with none, so that there cannot be a syllogism of the contingent, for the necessary is not contingent. Thus it is evident that when universal terms 3. when the are assumed in contingent propositions, there unTJersaiaAor arises always a syllogism in the first figure, both e, there is ai- when they are affirmative and negative, except Jsm in tL first tnat being affirmative it is complete, but if nega- flgure-the \[Yq incomplete, we must nevertheless assume the
former(A) com- . , . . .
piete— the lat- contingent not in necessary propositions, but ac- piete^ rvide" cor(ling to the before-named definition, and sorae- last chapter.) times a thing of this kind escapes notice.
Chap. XV. — Of Syllogisms with one simple and another contingent Proposition in the first Figure.
. „ „ . If one proposition be assumed to exist, but the
1. No svlloffism
with mixed other to be contingent, when that which contains aodmodai^tf tne maj0r extreme signifies the contingent, all the the major is syllogisms will be perfect and of the contingent, ac- syHoKismwiu6 cording to the above definition. But when the mi- be perfect, not nor rls contingent) they will all be imperfect, and
otherwise.
the negative syllogisms will not be of the contingent, according to the definition, but of that which is necessarily present with no one or not with every ; for if it is necessarily present with no one, or not with every, we say that " it hap- pens " to be present with no one and not with every. Now let A be contingent to every B, and let B be assumed to be present with every C, since then C is (included) under B, and
Ai? contingent to every B, A is also clearly con-
1 Case of a. "
perfect syiio- tingent to every C, and there is a perfect syllo- minorTshpuree S*sm' ^o a^so i* tne proposition A B is negative, but B C affirmative, and A B is assumed as con- tingent, but B C to be present with (simply), there will be a perfect syllogism, so that A will happen to be present with no C.
CHAP. XV.] THE PRIOK ANALYTICS. 113
It appears then that when a pure minor is assumed the syl- logisms are perfect, but that when it is of a contrary charac- ter it may be shown per impossible that there would be also syllogisms, though at the same time it would be evident that they are imperfect, since the demonstration will not arise from the assumed propositions. First, however, we must show that if A exists, B must necessarily exist, and that if A is possible, B will necessarily be possible ; let then under these circum- stances A be possible but B impossible, if therefore the possible, since it is possible to be, may be produced, yet the impossible, because it is impossible, cannot be produced. But if at the same time A is possible and B impossible, it may happen that A may be produced without B ; if it is produced also, that it may exist, for that which has been generated, „ „.
i «i i_ i , . b,L 2- Digression
when it has been so generated, exists. We must to prove the na- however assume the possible and impossible,1 not consequence in only in generation, but also in true assertion, and respect of the
lu t . ,, , possible and
in the inesse, and m as many other ways as the impossible, and possible is predicated, for the case will be the necessary- same in all of them. Moreover (when it is said) if A exists B is, we must not understand as if A being a certain thing B will be, for no necessary consequence follows from one thing existing ; but from there being two at least, as in the case of propositions subsisting in the manner we have stated in syllo- gism. For if C is predicated of D, but D cf F, C will also necessarily be predicated of F ; and if eacli be possible, the conclusion will be possible, just as if one should take A as the premises, but B the conclusion ; it will not only happen that A being necessary, B is also necessary, but that when the former is possible, the latter also will be possible.
This being proved, it is manifest that when 3. From a false there is a false and not impossible hypothesis, the hypothesis, not
n .1 1 f -i, 1 , n , impossible, a
consequence of the hypothesis will also be false similar conciu- and not impossible, e. g. if A is false yet not im- skm follows- possible, but when A is, B also is, — here B will also be false yet not impossible. For since it has been shown that A ex-
1 The possible is either that which may be when it is not, or that which is simply, or that which necessarily is ; and to all these the above rule applies, and the formal consequence follows as directly from the pre- mises, as to its character, as in the case of categoricals. Cf. Metap. 13. The nature of the possible is fully discussed, Rhetoric, b. ii. ch. ID.
i
114 Aristotle's organon. [book i.
isting, B also exists, when A is possible, B will be also pos- sible, but A is supposed to be possible, wherefore B will be- also possible, for if it were impossible the same thing would be possible and impossible at the same time. These things then being established, let A be present with every B, and B contingent to every C, therefore A must necessarily hap- pen to be present with every C ; for let it not happen, but let B be supposed to be present with every C, this is indeed false yet not impossible ; if then A is not con- tingent to C, but B is present with every C, A is not con- tingent to every B, for a syllogism arises in the third figure. But it was supposed (that A was) contingently present with every (B), therefore A must necessarily be contingent to every C, for the false being assumed, and not the im- xampe(. p^g^^i the consequence is impossible.* We may also make a deduction to the impossible in the first figure by assuming B to be present with every C, for if B is with every C, but A contingent to every B, A will also be contin- gent to every C, but it was supposed not to be present with every C.f Still we must assume the being present with every, not distinguishing it by time, as 4 u - rs l " nowj" or " at tms time," but simply ; for by pro- predication has positions of this kind, we also produce syllogisms,2
1 i. e. that A is not contingent to every C.
Ex. 1. Every B is A It is necessary that some C
should not be A
It happens that every C is B Every C is B
. • . It happens that every C is A. . • . Not every B is A.
Ex. 2. Every B is A It happens that every B is A
It happens that every C is B Every C is B
. • . It happens that every C is A. . • . It happens that every C is A.
2 Vide note to chap. 13, also Post Anal. Book i. He takes only pro- positions which are universally and immutably true for the elements of the sciences.
Ex. 3. Whatever is moved is a man Whatever is moved is an animal
It happens that every horse It happens that every man is
is moved moved
It is necessary that no horse It is necessary that every man
should be a man. should be an animal.
Ex. 4. No B is A It is necessary that some C
should be A
It happens that every C is B Every C is B
. • . Ii happens that no C is A. . ' . Some B is A.
CHAP. XV.] THE PRIOR ANALYTICS. 115
since when a proposition is taken as to the pre- no reference to sent it will not be syllogism, since perhaps there ri^an^imr* is nothing to hinder " man " from being present Logic.) some time or other with every thing moved, viz. if nothing else is moved, but what is moved is contingent to every " horse," yet "man" is contingent to no "horse." Moreover, let the first term be " animal," the middle, " that which is moved," and the last, "man ;" the propositions will then be alike, but the conclusion necessary, and not contingent, for " man " is necessarily " an animal," so that it is evident that the universal must be taken simply and not deprived g £xam lg . by time.*
Again, let the proposition A B be universal negative, and let A be assumed to be present with no B, but ■>. Epure. a let B contingently be present with every C ; now contingent, from these positions A must necessarily happen to be present with no C, for let it not so happen, but let B be supposed to be present with C, as before ; then A must necessarily be present with some B, for there is a syllogism in the third figure, but this is impossible, wherefore A can be contingent to no C, for the false and not the impossible being assumed, the impossible results.! Now this syllo- JVWeTupra!)'! gism is not of the contingent according to the definition, but of what is necessarily present with none, for this is a contradiction of the given hypothesis, because A was supposed necessarily present with some C, but the syllogism per impossibile is of an opposite ' contradiction. Besides, from the terms it appears clearly that there is no contingent con- clusion, for let " crow" stand for A, " that which is intelligent " for B, and "man" for C ; A is therefore present with no B, for nothing intelligent is a "crow;" but B is contingent to every C, since it happens to every "man" to be "intelligent," but A is necessarily present with no C, where- £xam le fore the conclusion is not contingent.^ But neither is the conclusion always necessary, for let A be "what is moved," B "science," and C "man," A will then be present with no B, but B is contingent to every C, and the conclusion
! Vide Whately's Logic, b. ii. c. 3, sect. 7.
Ex. 5. Nothing intelligent is a crow
It happens that every man is intelligent It is necessary that no man should be a crow. I -i
116 Aristotle's org anon. [book i.
will not be necessary, for it is not necessary that no "man" should be "moved," but also it is not necessary that a certain man should be moved ; therefore it is clear that the conclu- sion is of that which is necessarily present with no one, hence the terms must be assumed in a better manner.1 But if the 3. Minor nega- negative be joined to the minor extreme, signify - tive contingent. [n„ to ^g contingent, from the assumed propositions there will be no syllogism, but there will be as in the former
1 That is, instead of science, or an abstract term, we must assume one which may concur with man, e. g. "scientific," since a man may be "scientific," though he cannot be "science."
Ex. 6. It happens that ] e^ery I ani_ it happens that j ev - J animal
mal is white is white
No snow is an animal No pitch is an animal
It is necessary that all snow It is necessary that no pitch should
should be white. be white.
Ex. 7. It happens that I •? [ ani- It happens that j ^ > animal
mal is white is white
Some snow is not an animal Some pitch is not an animal
It is necessary that all snow It is necessary that no pitch should
should be white. be white.
Ex. 8. It happens that \ sometnmg I white js an animal
rr I not every thing )
I Every \ No • ,..
Q „ > man is white
Some 1
. Not every / It is necessary that every man should be an animal.
It happens that j ^"etery'thing } white is an animal
! Every ' \ Some ( Sarment is ^hite Not every' It is necessary that no garment should be an animal.
xt° . ° .i, • f white is an animal
Not every thing )
(every ) man is white some f not every , It is necessary that every man should be an animal.
CHAP. XV.] THE PRIOR ANALYTICS. 117
instances, when the contingent proposition is converted. For let A be present with every B, but B contingent to no C, now when the terras are thus, there will be nothing necessary inferred, but if B C be converted, and B be assumed to be contingent to every C, a syllogism arises as before, since the terms have a similar position. In the same man- 4. Both pre- ner, when both the propositions are negative, if A mises negative. B signifies not being present, but B C to be contingent to no individual, through these assumptions no necessity arises, but the contingent proposition being converted, there will be a syllogism. Let A be assumed present to no B, and B contin- gent to no C, nothing necessary is inferred from these ; but if it is assumed that B is contingent to every C, which is true, and the proposition A B subsists similarly, there will be again the same syllogism. If however B is assumed as not present with C, and not that it happens not to be pre- sent, there will by no means be a syllogism, neither if the proposition A B be negative nor affirmative ; but let the com- mon terms of necessary presence be "white," "animal," "snow," and of non-contingency "white," "ani- * Exam le (6) mal," "pitch." * It is evident, therefore, that when terms are universal, and one of the propositions is 5- General law- assumed, as simply de inesse, but the other con- gisms^when"" tangent, when the minor premise is assumed con- !ninor premise
» ' •» . is contingent,
tmgent, a syllogism always arises, except that a syllogism is sometimes it will be produced from the proposi- eitoertoectiy tions themselves, and at other times from the (con- or by conver- tingent) proposition being converted ; when, how- ever, each of these occurs, and for what reason, we have shown. But if one proposition be assumed as universal, and the other particular, when the universal contin- ^
. ... , . , ,1 . i 6. Of partiou-
gent is joined to the major extreme, whether it be larswithar. affirmative or negative, but the particular is a "nj^rsal
.., . n major.
simple affirmative de inesse, there will be a perfect
Something { white is an animal
ssot every thing )
! every \ 110 \ garment is white
not every ) l*. is necessary that no garment should be an animal.
118 auistotle's organon. [book i.
syllogism, just as when the terms are universal, but the
demonstration is the same as before. Now when the major is
2. Major a or universal, simple, and not contingent, but the other
E pure. ^he niinor) particular and contingent, if both
propositions be assumed affirmative or negative, or if one be
affirmative and the other negative, there will always be an
incomplete syllogism, except that some will be demonstrated
per impossibile, but others by conversion of the contingent
proposition, as in the former cases. There will
also be a syllogism, through conversion, when the
universal major signifies simply inesse, or non-inesse, but the
particular being negative, assumes the contingent, as if A is
present, or not present, with every B, that B happens not to
be present with a certain C ; for the contingent proposition
B C being converted, there is a syllogism. Still
when the particular proposition assumes the not
being present with, there will not be a syllogism. Now let
the terms of presence be "white," "animal," "snow," but of
not being present "white," "animal," "pitch," for the demon-
, „ . stration must be assumed through the indefinite.*
* Example (7.) —,...», . ii«*-iii
Yet it the universal be joined to the less extreme, fs If ticuiar^ ^ut Pai*ticular to the greater, whether negative or there win be no affirmative, contingent or pure, there will by no i7bo°thpremU;es means be a syllogism, nor if particular or inde- be particular finite propositions be assumed, whether they take
the contingent, or simply the being present with, or vice versa, will there thus be a syllogism, and the demon- stration is the same as before ; let however the common terms of being present with from necessity be "animal," "white," . „ . ... "man;" and of not being contingent "animal,"
"white, "garment, j Hence it is evident, that if the major be universal, there is always a syllogism, but if the minor be so, (if the major be particular,) there will never be.
Chap. XVI. — Of Syllogisms with one Premise necessary, and the other contingent in the first Figure.
m , When one is a necessary proposition simple, de
1. The law re- . . i .1 fi • •„ , .
lative to syiio- inesse, or non-inesse, and the other signifies being
character*1"8 contingent, there will be a syllogism, the terms
subsisting similarly, and it will be perfect when
CHAP.
XVI.]
THE PRIOR ANALYTICS.
119
the minor premise l is necessary ; the conclusion however, when the terms are affirmative, will be contingent, and not simple, whether they are universal or not universal. Nevertheless, if one proposition be affirmative, and the other negative, when the affirmative is necessary, the conclusion will in like manner signify the being contingent, and not the not-existing or being present with ; and when the negative is necessary, the con- clusion will be of the contingent non-inesse, and of the sim- ple non-inesse, whether the terms are universal or not. The contingent also in the conclusion, is to be assumed in the same way as in the former syllogisms, but there will not be a syllo- gism wherein the non-inesse will be necessarily inferred, for it is one thing "inesse" not necessarily, and another "non- inesse " necessarily. Wherefore, it is evident that 2 When both when the terms are affirmative, there will not be premises are a necessary conclusion. For let A necessarily be not bet neces- present with every B, but let B be contingent to sary conciu- every C, there will then be an incomplete syllo- gism, whence it may be inferred that A happens to be present with every C ; but that it is incomplete, is evident from de-
1 Major premise r) 7rpoc r<f> (itiZ,ovi iXarrovi. dfcpy Tvporauig. Conclusion this last signifies also the minor term.
Ex. 1. It is necessary that no B should be A It happens that every C is B . • . No C is A.
Ex. 2. It happens that j ^ ^ > ani- mal is white It is necessary that no snow
should be an animal It is necessary that all snow should be white.
Ex. 3. It is necessary that something white should animal It happens that \ M man
aKpy TrporaoiQ — minor >/ irpoq ry> 0-vniripa.Gp.a. In Anal. Pr. ii. 14,
It is necessary that no A should
be B Some C is A . • . It is necessary that some C should not be B.
( not be j
an
no J
is white It is necessary that every man
should be an animal.
It happens that j ' > animal is
white It is necessary that no pitch should
be an animal It is necessary that no pitch should
be white.
1 1 is necessary that something white should{notbe}ananimal
It happens that < ver^ £ garment
is white It is necessary that no garment should be an animal.
120 Aristotle's organon. [book i.
monstration, for this may be shown after the same manner as in the former syllogisms. Again, let A. he contingent to every B, but let B be necessarily present with every C, there will then be a syllogism wherein A happens to be present with every C, but not (simply) is it present with every C, also it will be complete, and not incomplete, for it is completed by the first i. Negative propositions. Notwithstanding, if the propositions necessary. are not 0f similar form, first, let the negative one be necessary, and let A necessarily be contingent to no B, but. let B be contingent to every C ; therefore, it is necessary that A should be present with no C ; for let it be assumed present, either with every or with some one, yet it was supposed to be contingent to no B. Since then a negative proposition is convertible, neither will B be contingent to any A, but A is supposed to be present with every or with some C, hence B will happen to be present with no, or not with every C, it , ,, , was however supposed, from the first, to be pre-
* Example (1.) . , \A *. n «n ■ • . -i , .
sent with every C* Still it is evident, that there may also be a syllogism of the contingent non-inesse, as there
2. Affirmative is one of the simple non-inesse. Moreover, let necessary. ^g affirmative proposition be necessary, and let A be contingently present with no B, but B necessarily pre- sent with every C : this syllogism then will be perfect, yet not of the simple, but of the contingent non-inesse, for the proposition (viz. the contingent non-inesse) was assumed from the major extreme, and there cannot be a deduction to the impossible, for if A is supposed to be present with a certain C, and it is admitted that A is contingently present with no B, nothing impossible will arise therefrom. But if the minor
3. Minor nega- premise be negative when it is contingent, there tive contingent. wiu De a syllogism by conversion, as in the former cases, but when it is not contingent, there will not be ; nor when both premises are negative, but the minor not contin- gent : let the terms be the same of the simple inesse " white,''
"animal," "snow," and of the non-inesse "white,"
"animal," "pitch."f The same will also happen in particular syllogisms, for when
the negative is necessary, the conclusion will be of ticuiaresyiio-ar" the simple non-inesse. Thus if A is contingently gisms. present with no B, but B contingently present with
a certain C, it is necessary that A should not be
t Example (2.) , , „ u
CHAP. XVI.] THE PRIOR ANALYTICS. 12)
present with a certain C. since if it is present with every C, but is contingent to no B, neither will B be contingently pres: nt with any A. So that if A is present with every C, B is ci n- tingent with no C, but it was supposed contingent to a cer- tain C. When however in a negative syllogism the particular affirmative is necessary, as for example B C, or the universal in an affirmative syllogism, e. g. A B, there will not be a syllogism tie inesse, the demon- stration however is the same as in the former cases. But if the minor premise be universal, Avhether affirm- ative or negative and contingent, but the major particular necessary, there will not be a syllogism, let the terms of necessary presence be " animal," " white," " man," and of the non-contingent " animal," " white," „ ^ , „ ,
»*. -r. 11 • • * Example (3.)
" garment. * But when the universal is neces- sary, and the particular contingent, the universal being nega- tive, let the terms of presence1 be "animal," "white," "crow," and of non-inesse "animal," "white," . r , ,, .
" pitch." f t Example (4,
But when (the universal) affirms let the terms
of presence be " animal," " white," " swan,'"' but 4-
of the non-contingent be "animal," "white," j Example (5.)
" snow." J Nor will there be a syllogism when in- 4 Case of both
definite propositions are assumed or both particular, premises inde-
let the common terms, de inesse, be "animal," cuiar.°r pam" " white," " man," de non-inesse " animal," " white," " inanimate ;" for " animal " is necessarily and not contingently
' That is, of the major being with the minor.
Ex. 4. It happens that something It happens that something white
white { !s . \ an animal | . . \ an animal
( is not) { is not)
It is necessary that no crow It is necessary that no pitch should
should be white be white
It is necessary that every crow It is necessary that no pitch should
should be an animal. be an animal.
Ex. 5. It happens that something It happens that something white
white I •' . / an animal < .' . J an animal
( is not ) (is not )
I L is necessary that every swan It is necessary that all snow should
should be white be white
It is necessary that every swan It is necessary that no snow should
shou!'! be an anirr-d. be an animal
122 Aristotle's org anon. [book i.
present with something " white," and " white " is also neces- sarily and not contingently present with something " inani-
* Exam i (6i mate »" tne ^^e a^so occurs in the contingent, so that these terms are useful for all.* From what has been said then it appears that when the terms are alike both in simple and in necessary propositions, 5. conclusion a syllogism does and does not occur, except that from the above, if the negative proposition be assumed de inesse there will be a syllogism with a contingent (con- clusion), but when the negative is necessary there will be one of the character of the contingent and of the non-inesse, but it is clear also that all the syllogisms are incomplete,1 and that they are completed through the above-named figures.
Chap. XVII. — Of Syllogisms ivith tico contingent Premises in the
second Figure.
. _ , , In the second figure, when both premises are as-
1. Ruleforcon- , . , .,, , l ,,
titigent syiio- sumed contingent, there will be no syllogism, nei- fg™ in thls ther when they are taken as affirmative, nor nega- tive, nor universal, nor particular; but when, one signifies the simple inesse, and the other the contingent, if the affirmative signifies the inesse, there will never be a syllogism, but if the universal negative (be pure, there will) always (be a
Ex. 6. It happens that something; It happens that something white
white | . 1 an animal ] -S , > an animal
( is not ) \ is not )
It is necessary that some man It is necessary that something in-
should \ , J white animate should < e , > white
It is necessary that every man It is necessary that nothing inani- should be an animal. mate should be an animal.
It is necessary that something It is necessary that something white
white should \ . , ! an should { e. , > an animal ( not be j I not be )
animal
It happens that some man It happens that every thing inani-
( is ) ,.. mate is white
{ ■ ..} white ( is not )
It is necessary that every man It is necessary that nothing inani-
should be an animal. mate should be an animal.
1 Those are syllogisms with a contingent minor, but a necessary or fure maji>
CHAP. XVII.] THE PRIOR ANALYTICS. 123
syllogism). In the same manner, when one premise is assumed as necessary, but the other contingent ; still in these syllogisms we must consider the contingent in the conclusions, as we did in the former ones. Now in the first place, contingent ne- we must show that a contingent negative is not con- &atiTe ,not con_
to b -!-.•• vertible.
vertible, e. g. if A is contingent to no B, it is not necessary that B should also be contingent to no A. For let this be assumed, and let B be contingently present with no A, there- fore since contingent affirmatives, both contrary and contra- dictory, are convertible into negatives, and B is contingently present with no A, it is clear that B may be contingently present with every A ; but this is false, for if this is contingent to all of that, it is not necessary that that should be contingent to this, wherefore a negative (contingent) is not convertible. Moreover, there is nothing to prevent A being contingent to no B, but B not necessarily present with a certain A, e. g. "whiteness" may happen not to be present with every " man," (for it may also happen) to be present ; but it is not true to say, that man is contingently present with nothing " white," for he is necessarily not pre- sent with many things (white), and the necessary is not the contingent. Neither can it be shown convertible per impos- sibile, as if a man should think, since it is false that B is con- tingently present with no A, that it is true that it (A) is not contingent to no one (B), for these are affirmation and negation ; but if this be true B is necessarily present with a certain A, therefore A is also with a certain B, but this is impossible, since it does not follow if B is not con- tingent to no A, that it is necessarily present with a certain A. For not to be contingent to no individual, is pre- dicated two ways, the one if a thing is necessarily preheated neC-y present with something, and the other if it is gatively in two
1 ., . , , . -n i ways — the cha-
necessanly not present with something, t or what racter of the necessarily is not present with a certain A, can- opposi,^1 not be truly said to be contingently not present with every A ; as neither can what is necessarily present with a certain thing, be truly said to be contingently present with every thing ; if, then, any one thinks that because C is not contingently present with every D, it is necessarily not present with a certain D, he would infer falsely, for, per- chance, it is present with every D ; still because a thing is
124 Aristotle's org axon. [book l
necessarily present with certain things, on this account, we say that it is not contingent to every individual. Wherefore the being present necessarily with a certain thing, and the not being present with a certain thing necessarily, are op- posed to the being contingently present with every individual, and in like manner, there is a similar opposition to the being contingent to no individual. Hence it is evident, that when the contingent and non-contingent are taken, in the manner we first defined, not only the necessarily being present with a certain thing, but also the necessarily not being present with it, ought to be assumed ; but when this is assumed, there is no impossibility to a syllogism being produced, whence it is evident, from what we have stated, that a negative con- tingent is not convertible.
4. From two This then being demonstrated, let A be as-
pwamseBTini- sume(| contingent to no B, but contingent to (E) contingent every C ; by conversion, therefore, there will not figure, mfsyiio- De a syllogism, for it has been said that a proposi- gis™ is con- tion of this kind is inconvertible, neither, however,
strutted «
will there be by a deduction per impossibile. For
B being assumed contingently present with every C, nothing
false will happen, for A may contingently be present with
_ , ., . every, and with no C* ' In short, if there is a
* Example (1.) ,, . ... . ... , '„
syllogism, it is clear that it will be ol the contin- gent, (because neither proposition is assumed as de inesse,) and this either affirmative, or negative ; it is possible, how- ever, in neither way, since, if the affirmative be assumed, it can be shown by the terms, that it is not contingently present ; but if the negative, that the conclusion is not contingent, but necessary. For let A be "white," B "man," and C "horse," A therefore, i. e. "whiteness," is contingently present with every individual of the one, though with no individual of the other,
1 Ex. 1. It happens that no B is A It happens that no B is A
It happens that every C is A It is necessary that every or
some C should be B . ' . It happens that no C is B. . • . It happens that every or some
C is not A.
I have followed Waitz here. Buhle reads the letters and statement of premises differently.
Ex. 2. It happens that no man is white
It happens that every horse is white
It is necessary that no horse should be a man.
CHAP. XVIII.] THE PRIOR ANALYTICS.
125
but B is neither contingently present, nor yet contingently not present, with C. It is evident that it is not contingently present, for no "horse" is "a man," but neither does it hap- pen not to be present, for it is necessary that no " horse " should be "a man," and the necessary is not the t contingent, wherefore there is no syllogism.* This may be also similarly shown, if the negative be transposed,1 and if both propositions be assumed affirmative, or negative, for the demonstration will be by the same terms.']' When one proposition also is uni- 5- Norfromone versal, but the other particular, or both particular other par., or6 or indefinite, or in whatever other way it is pos- both pm- orln sible to change the propositions, for the demon- stration will always be through the same terms. J * ExaraPle (*•' Hence it is clear that if both propositions are as- sumed contingent there is no syllogism.2
ure, with one pu b premise, aiil
Chap. XVIII. — Of Syllogisms with one Proposition simple, and the other contingent, in the second Figure.
If one proposition signifies inesse, but the other 1. Rule for the contingent, the affirmative proposition being ""^fig311 simple, but the negative contingent, there will never be a syllogism, neither if the terms be as-
1 i. e. If the major affirm, and the minor deny.
Ex. 3. It happens that j V } man is white
It happens that | M horse is white It is necessarv that no horse should be a man.
Ex
4. It happens that ( every ) man II happens that some man
*no (Is J white
( is not J
is white
It happens that some horse j h ^ { every j ho^[a
!s J white * U° >
{ is not j white
It is necessary that no horse It is necessary that no horse should should be a man. be a man.
It happens that some man { • , } white
It happens that some horse | • , . | white It is necessary that no horse should be a man. • The last sentence is omitted by Taylor.
126
ARISTOTLE S ORGANON.
[book
the other con- sumed universally, or partially, still the demon- stration will be the same, and by the same terms, yet when the affirmative is contingent, but the negative sim- ple, there will be a syllogism. For let A be assumed present with no B, but contingent with every C, then by conversion of the negative, B will be present with no A, but A is contingent to every C, therefore there is a syllogism in the first figure, that B is contingent to no C. So also if the negative be added to C ; but if both propositions be negative, and one signifies the simple, but the other the contingent non-inesse, from these assumed propositions nothing necessary is inferred, but the contingent proposition being converted,1 there is a syllogism, wherein B is contingently present with no C, as in the former, for again there will be the first figure. If, however, both propositions be assumed
1 If the contingent negative proposition be changed into an affirmative.
Ex. 1. It happens that every animal
is well Every man is well It is necessary that every man
should be an animal.
Every animal is well
It happens that every man is
well It is necessary that every man
should be an animal.
Ex. 2. It happens that no animal is
well Some man is well It is necessary that every man
should be an animal.
Every animal is well
It happens that some man is
not well It is necessary that every man
should be an animal.
Ex. 3 Some animal
iis )
( is not )
well
is
is not It happens that some man
{» Jwell
I is not )
It is necessary that every man should be an ariaal.
It happens that every horse is well
Every man is well It is necessary that no man should be a horse.
Every horse is well
It happens that every man is well
It is necessary that no man should be a horse.
It happens that no horse is well
Some man is well It is necessary that no man should be a horse.
Every horse is well
It happens that some man is not
well It is necessary that no man should
be a horse.
Some horse \ . . f well ( is not )
It happens that some man
f-S .Nell ( is not J
It is necessary that no man should
be ahorse.
CHAP. XIX.] THE PRIOR ANALYTICS. 127
affirmative, there will not be a syllogism : let the
terms of presence be "health," "animal," "man,"
but of not being present with " health," " horse,"
" man."* The same will happen in the case of e v
particular syllogisms, for when the affirmative is
pure, taken either universally, or particularly, fylwfsm"lar
there will be no syllogism, and this is shown
in like manner through the same terms as be- , ^ , ,„ ,
r . -r. , , ° ..... t Example (2.)
tore.y .But when the negative is simple, there will be a syllogism by conversion, as in the former cases. Again, if both premises be taken negative, and that which signi- fies simply the non-inesse be universal ; from these propositions no necessity will result, but the contingent being converted as before there will be a syllogism. If however the negative be pure but particular, there will not be a syllogism, whether the other premise be affirmative or negative. Neither will there be one, when both propositions are assumed indefinite, whether affirmative, negative, or particular, and the . _ , ,„,
. . . ' ° tit < t Example (3.)
demonstration is the same and by the same terms.|
Chap. XIX. — Of Syllogisms with one Premise necessary and the other contingent, in the second Figure.
If however one premise signifies the being present , Rule in
necessarily, but the other contingently, when the these when the
negative is necessary there will be a syllogism, mlfe is neces-
wherein not only the contingent but also the simple sary' a syll°"
r i • t> I-, i i «■ £ism may bc
non-inesse (may be inferred), but when the amrma- constructed. tive (is necessary) there will be no syllogism. For '" Case" let A be assumed necessarily present with no B, but contingent to every C, then by conversion of the negative neither will B be present with any A, but A was contingent to every C, wherefore there is again a syllogism in the first figure, so that B is con- tingently present with no C. At the same time it is shown that neither is B present with any C, for let it be assumed to be
It happens that some animal It happens that some horse
?s ,lwell jis J well
I is not ) \ is not j
Some man . •' A well Some man { . . J well
I is not ) \ is not )
It is necessary that every man It is necessary that no man should
should be an animal be a horse.
128 Aristotle's organon. ("book i
present, therefore if A is contingent to no B, but B is present with a certain C, A is not contingent to a certain C, but it was supposed contingent to every C, and it may be shown after the same manner, if the negative be added to C. Again, 2 Caseofane- ^et tne affirmative proposition be necessary, but cessary affirm- the other negative and contingent, and let A be
contingent to no B, but necessarily present with every C ; now when th<=». terms are thus, there will be no syl- logism, for it may happen that B is necessarily not present with C. Let A be " white," B " man," C " a swan ;" " white- ness," then, is necessarily present with " a swan," but is con- tingent to no " man," and " man " is necessarily present with no "swan ;" therefore that there will be no syllogism of the * f contingent is palpable, for what is necessary is not
contingent.* ' Yet neither will there be a syllogism of the necessary, for the latter is either inferred from two ne- cessary premises, or from a negative (necessary premise) ; be- sides, from these data it follows that B may be present with C, for there is nothing to prevent C from being under B, and A from being contingent to every B, and necessarily present with C, as if C is "awake," B " aniftial," and A "motion;" for " motion " is necessarily present with whatever is " awake," but contingent to every " animal," and every thing which is .,„.■" awake " is " an animal."! Hence it appears
+ Example (2.) . . . ' . „ -,•■„,
that neither the non-inesse is interred, since if the terms are thus the inesse is necessary, nor when the enunci- ations are opposite,2 so that there will be no syllogism. There
1 Ex. 1. It happens that no man is white
It is necessary that every swan should be white It is necessary that no swan should be a man.
Ex. 2. It happens that no animal is moved
It is necessary that every thing awake should be moved Every thing awake is an animal.
Alexander Aphrodisiensis observes that the example would be clearer, .f " walking " were assumed instead of " awake." because it is more ob- viously necessary that a thing which walks should be " moved," than a thing which is awake.
' " Will there be a syllogism from such propositions " — there is an el- lipse of these words here. The case is that neither a contingent nor ne- cessary affirmation is to be inferred, since sometimes the non-inesse is necessary.
CHAP. XIX.]
THE PRIOR ANALYTICS.
129
3. Case of hcth negative.
will be also a similar demonstration if the affirm- ative premise be transposed, but if the proposi- tions are of the same character, when they are negative, a syllogism is always formed, the contingent pro- position being converted, as in the former cases. For let A be assumed necessarily not present with B, and contingently not present with C, then the propositions being converted, B
Ex. 3. It is necessary that every swan should be w,hite It happens that every man is white It is necessary that no man should be a swan. Ex. 4. It happens that no man is It happens that no animal is moved white It is necessary that some swan
should be white It is necessary that no swan should be a man. It is necessary that every swan should be white It happens that some man is not white It is necessary that no man should be a swan. Ex. 5. It is necessary that every It happens that every man is white
It is necessary that something awake should be moved
It is necessary that every thing awake should be an animal.
swan should be white It happens that some man is
a swan It is necessary that no man
should be a swan.
It is necessary that some swan
should be white It happens that every man is
white It is necessary that no man
should be a swan.
Ex. 6. It happens that some animal
ilS A white { is not J
It is necessary that some man
(bef, | white ( not be j
It is necessary that every man
should be an animal
It is necessary that some ani.
mal should j^tbe} white
It happens that some man
| 1S ,1 white ( is not )
It is necessary that every man
should be an animal
shouk
It is necessary that some swan
should be white It is necessary that no swan should
be a man.
It happens that some man is white
It is necessary that every swan
should be white It is necessary that no swan should
be a man.
It happens that some animal
I ■ . > white ( is not )
It is necessary that something in- animate should | , , > white { not be )
It is necessary that nothing in- animate should be an animal.
It is necessary that some animal
should ] . , 1 white ( not be )
It happens that something in- animate \ h . > white I is not \
It is necessary that nothing in- animai e should be an animal.
130 Aristotle's organon. [book i.
is present with no A, and A is contingent with every C, and the first figure is produced ; the same would also occur if the negation belongs to C. But if both propositions be affirma- tive, there will not be a syllogism, clearly not of
4. Case of both .,' e vu •
affirmative. the non-inesse, nor ot the necessary non-inesse, because a negative premise is not assumed, nei- ther in the simple, nor in the necessary inesse. Neither, again, will there be a syllogism of the contingent non- inesse, for necessary terms being assumed, B will not be pre- sent with C, e. g. if A be assumed " white," B " a swan," and C "man ;" nor will there be from opposite affirmations, since B has been shown necessarily not present with C, in short, * e 1 therefore, a syllogism will not be produced.* It will happen the same in particular syllogisms, for when the negative is universal and necessary, syllogisms. there will always be a syllogism of the contingent, and of the non-inesse, but the demonstration will be by conversion ; still, when the affirmative (is necessary), there will never be a syllogism, and this may be shown in . _ . .. , the same way as in the universals, and by the
t Example (4.) J ' . J
same terms. j JNor when both premises are as- i Example (5 ) sume<^ affirmative, for of this there is the same
demonstration as before,^: but when both are ne- gative, and that which signifies the non-inesse is universal, and necessary ; the necessary will not be concluded through the propositions, but the contingent being converted, there will be a syllogism as before. If however both propositions are laid down indefinite, or particular, there will not be a syllogism, § Example (6 ) anc^ the demonstration is the same, and by the
same terms. §
It appears then, from what we have said, that an universal,
and necessary negative being assumed, there is always a
syllogism, not only of the contingent, but also of the simple
3 conclusion non-inesse ; but with a necessary affirmative, there
;cf. cap. is.) wiH never be a syllogism ; also that when the
terms subsist in the same manner, in necessary, as in simple propositions, there is, and is not, a syllogism ; lastly, that all these syllogisms are incomplete, and that they are completed through the above-mentioned figures.1
1 Although all incomplete syllogisms are completed through the first figure, yet some are, after a manner, rendered more useful through another
CHAP. XX.] THE PRIOR ANALYTICS. 13 i
Chap. XX. — Of Syllogisms icith both Propositions contingent in the third Figure.
In the last figure, when both premises are contin- gent, and when only one is contingent, there will ruieXr propo- be a syllogism, therefore when the premises sig- sjtions of this nify the contingent, the conclusion will also be contingent ; also if one premise signifies the contingent, but the other, the simple inesse. Still when one premise is as- sumed necessary, if it be affirmative, there will not be a conclu- sion either necesssry or simple, if on the contrary it is nega- tive, there will be a syllogism of the simple non-inesse as be- fore ; in these however the contingent must be similarly taken in the conclusions. First then let the premises , Both be contingent, and let A and B be contingently mises contin- present with every C ; since therefore a particular gem affirmative is convertible, but B is contingent to every C, C will also be contingent to a certain B, therefore if A is con- tingent to every C, but C is contingent to a certain B, it is necessary also that A should be contingent to a certain B, for the first figure is produced. If again A is con- tingently present with no C, but B with every C, A must also of necessity be contingently not present with a certain B, for again there will be the first figure by conver- sion ; i but if both propositions be assumed negative from these the necessary will not result, but the propositions being converted there will be a syllogism as be- fore. For if A and B are contingently not present with C,
figure, as by changing the contingent affirmative proposition into thb negative.
1 That is, by conversion of the minor.
Ex. 1. It happens that something white j 1S [ an animal
It happens that something white \ .' ,1a man rr I is not J
It is necessary that every man should be an animal
It happens that something white -b j a horse
It happens that something white , a man
rr ( is not )
It is necessary that no man should be a horse.
it '2
132 Aristotle's okganon. [book i.
if the contingently not present be changed, there will again be the first figure by conversion. If however one unWersaiand6 term De universal but the other particular, when the other par- they are so, as in the case of simple inesse, there will, and will not, be a syllogism ; for let A be contingently present with every C, and B present with a certain C, there will again be the first figure by con- version of the particular proposition, since if A is contingent to every C, and C to a certain B, A is also contingent to a certain B, and in like manner if the universal be joined to B C. This also will be produced in a similar way if A C be negative, but B C affirmative, for again we shall have the first figure by conversion, if however both are negative, the one universal and the other particular, by the assumed propositions there will not be a syllogism, but 6. Both parti- there will be when they are converted as before. cuiar or indeii- Lastly, when both are indefinite or particular, there will not be a syllogism, for A must neces- sarily be present with every and with no B, let the terms de inesse be "animal," "man," "white," and de non-in- , „ , esse "horse," "man," "white," the middle term
« Example (1.) My^^nm
Chap. XXI. — Of Syllogisms with one Proposition contingent and the other simple in the third Figure.
l. Rule of con- ^F however one premise signifies the inesse, but sequence— a the other the contingent, the conclusion will be Inferred from that a thing is contingent to, and not that it is ami another present with (another), and there will be a syllo- contingent pre- gism, the terms subsisting in the same manner as supra.) (Vlde the previous ones. For, first, let them be affirm- lst case. Both ative,1 and let A be in every C, but B contingent with every C ; B C then being convei ted there will be the first figure, and the conclusion will be that A is contingently present with a certain B, for when one premise in the first figure signifies the contingent, the conclusion also 2nd,Minorsim- was contingent. In like manner if the proposition major contin^' B C2 be of the simple inesse, but the proposition
1 " Predicative." — Averrris. 2 That is, the minor.
CHAP. XXI.] THE PRIOR ANALYTICS. 133
A C be contingent, and if A C ' be negative, but ,-ent and nega- B C affirmative, and either of them be pure ; in t,ve- both ways the conclusion will be contingent, since again there arises the first figure. Now it has been shown that where one premise in that figure signifies the contingent, the con- clusion also will be contingent ; if however the negative be annexed to the minor premise, or both be as- sumed as negative, through the propositions laid gative'minorar down themselves, there will not indeed be a syllo- lrom twonega-
, . -oi -ii i • fives, no syllo-
gism, but by their conversion- there will be, as in g\&m results.
the former cases.
Nevertheless if one premise be universal and 4. cases of the other particular, yet both affirmative, or the Particulars- universal negative but the particular affirmative, there will be the same mode of syllogisms ; for all are com- pleted by the first figure, so that it is evident there will be a syllogism of the contingent and not of the inesse. If however the affirmative be universal and the negative par ticular, the demonstration will be per impossibile ; for let B be with every C and A happen not to be with a certain C, it is necessary then that A should happen not to be with a certain B, since if A is necessarily with every B, but B is assumed to be with every C, A will necessarily be with every C, which was demonstrated before, but by hypothesis A happens not to be with a certain C.
When both premises are assumed indefinite, or particular, there will not be a syllogism, and the demonstration is the „ Exam ]e ., . same as in universals,3 and by the same terms.*
1 Major. 2 i. e. the negative contingent being changed into affirmative.
3 Alexander Aphrodis. thinks we should read ?) Kai t-rri twv t£ au<po- t'(Q(jiv ivStxoy-ii,'»v, (instead of ») Kai ivrdiQ kci06\ov,) i. e. which was in syllogisms, both the propositions of which are contingent.— Taylor, Julius Facius, and Zell approve of this emendation, but I agree with Waitz in thinking it unnecessary. Cf. cap. 20, and '21.
Ex. . Something white | J^ no(. > an animal
It happens that something white j ^ t > a man
It is necessary that every man should be an animal.
Something white I ^ not !■ a horse
( is ) It happens that something white j jg no( a man
It is necessary that no man should be a hon>e.
134 Aristotle's org anon. book
Chap. XXII. — Of Syllogisms with one Premise necessary, and the other contingent in the third Figure.
If one premise be necessary, but the other con- univ"rsaisf(iii tingent, the terms being affirmative there will be the third figure, always a syllogism of the contingent; but when sary, and the one is affirmative but the other negative, if the other contin- affirmative be necessary there will be a syllogism
gent premise. . J , J p
ot the contingent non-inesse ; if however it be negative, there will be one both of the contingent and of the absolute non-inesse. There will not however be a syllogism of the necessary non-inesse, as neither in the other figures. Let then, first, the terms be affirmative, and let A be neces- Each propo- sarily with every C, but B happen to be with every sition, affirma- C ; therefore since A is necessarily with every C, but C is contingent to a certain B, A will also be contingently, and not necessarily, with some certain B ; for thus it is concluded in the first figure. It can be similarly proved * Example (i ) if B C be assumed as necessary, but A C contin- gent.* 2. Major nega- Again, let bne premise be affirmative, but the tive, minor other negative, and let the affirmative be neces- sary ; let also A happen to be with no C, but let B necessarily be with every C ; again there will be the first figure ; l
It happens that something white j ?s ] an animal
Something white | j* J a man
It is necessary that every man should be an animal.
It happens that some animal { ■' 'a horse
(is not )
Something white ] 'S J a man It is necessary that no man should be a horse. Ex. 1. It happens that every man is It happens that every man is
white white
It is necessary that every man It is necessary that some ani-
should be an animal mal should be a man
. • . It happens that some animal . • . It happens that some animal
is white is white.
1 Taylor inserts here — " and the conclusion will be contingent, but ncJ pare" — which is omitted by Waitz.
CHAP. XXII.] THE PRIOR ANALYTICS. 135
for the negative premise signifies the being contingent it is evident therefore that the conclusion will be contingent, for when the premises were thus in the first figure, the conclusion was also contingent. But if the negative premise be neces- sary, the conclusion will be that it is contingent, not to be with something, and that it is not with it ; for let A be supposed necessarily not with C, but contingent to every B, then the affirmative proposition B C being converted, there will be the first figure, and the negative premise will be necessary. But when the premises are thus, it results that A happens not to be with a certain C, and that it is not with it ; wherefore it is ne- cessary also that A should not be with a certain B. „ _
,,,.•'. , . . . .3. Vice versa.
When however the minor premise is assumed ne- gative there will be a syllogism, if that be contingent by the premise being converted as in the former cases, but if it be ne- cessary there will not be, for it is necessary to be with every, and happens to be with none ; let the terms of being with every in- dividual, be"sleep,"a "sleeping horse," "man ;" of „ being with none " sleep," a "waking horse," "man."* It will happen in the same way, if one term be joined to the middle universally, but the other Ucuiars.of par partially, for both being affirmative there will be a syllogism of the contingent, and not of the absolute, also when the one is assumed as negative but the other affirmative, and the affirmative is necessary. But when the negative is necessary, the conclusion will also be of the not being present with ; for there will be the same mode of demonstration, whether the terms are universal or not universal, since it is necessary that the syllogisms be completed by the first figure, so that it is requisite that the same should result, in these,1
Ex. 2. It happens that eve*y man It happens that every man sleeps sleeps
It is necessary that no man It is necessary that no man should
should be a sleeping horse be a waking horse
It is necessary that every It is necessary that no waking sleeping horse should sleep. horse should sleep.
Ex. 3. It happens that some man It happens that some man sleeps sleeps
It is necessary that no man It is necessary that no man should
should be a sleeping horse be a waking horse
It is necessary that every It is necessary that no waking sleeping horse should sleep. horse should be asleep. i. e. in syllogisms of the first tigure.
136 Aristotle's org anon. [book i.
as in those.1 When however the negative, universally as- sumed, is joined to the less extreme, if it be contingent, there will be a syllogism by conversion, but if it be necessary there will not be, and this may be shown in the same mode as in universals, and by the same terms.f Wherefore v ' in this figure it it is evident, when and how there will be a syllogism,2 and when of the contingent, and when of the absolute, all also it is clear are imperfect, and are perfected by the first figure.
Chap. XXIII. — It is demonstrated that every Syllogism is completed
by the first Figure.
That the syllogisms then in these figures are com- prdi'minlry'to8 pleted by the universal syllogisms in the first proving that figure, and are reduced to these, is evident from resuHsyfromSm what has been said ; but that in short every syllo- lVlivsers.aIs of gism is thus, will now be evident, when it shall be
the first figure. «= » , »■%■%*
shown that every syllogism is produced by some one of these figures.
It is then necessary that every demonstration, must demon- and every syllogism, should show either something lute'unive^s-0 inesse or non-inesse, and this either universally ally or particu- or partially, moreover either ostensively or by tensive. e °%~ hypothesis. A part however of that which is by hypothesis is produced per impossible, therefore let us first speak of the ostensive (syllogisms), and when these are shown, it will be evident also in the case of those lead- ing to the impossibile, and generally of those by hypothesis. 3. For a sim- If then it is necessary to syllogize A of B either
we must^av11 as Dem& with or as not being with, we must as- twoproposi- sume something of something, if then A be as- sumed of B, that which was from the first (pro- posed) will be assumed (to be proved), but if A be assumed of C, but C of nothing, nor any thing else of it, nor of A, there will be no syllogism, for there is no necessary result from as- suming one thing of one, so that we must take another pre- mise. If then A be assumed of something else, or something
1 In syllogisms of the third.
2 i. e. there will be a syllogism from hoth propositions being contin- gent, or from one being pure and the other contingent, or from one neces- sary and the other contingent.
CHAP. XXIII. J THE PRIOR ANALYTICS. 137
else of A, or of C, there is nothing to hinder a syllogism, it will not however appertain to B ' from the assumptions. Nor when C is predicated of something else, and that of another, and this last of a third,2 if none of these belong to B, neither thus will there be a syllogism with reference to B, since in short we say that there never will be a syllogism of one thing in respect of another unless a certain middle is assumed, which refers in some way to each extreme in predication. For a syllogism is simply from premises, but that which pertains to this in relation to that, is from premises belonging to this in relation to that,3 but it is impossible to assume a premise re- lating to B, if we neither affirm nor deny any thing of it, or again of A in relation to B, if we assume nothing common, but affirm or deny certain peculiarities of each. Hence a certain middle of both must be taken, nectedTy™"" which unites the predications, if there shall be a ml^le term :
.r , .p which con-
syllogism of one in relation to the other ; now it nexion is three- it is necessary to assume something common to A^rici^"16 both, this happens in a three-fold manner, (since we either predicate A of C, and C of B,4 or C5 of both or both of C, 6) but these are the before-mentioned figures — it is evident that every syllogism is necessarily produced by some one of these figures, for there is the same reasoning, if A be connected with B, even through many media, for the figure in many media will be the same.
Wherefore that all ostensive syllogisms are 2. of syiio- perfected by the above-named figures is clear, also ^s™bl^rt^re that those per impossibile (are so perfected) will is the same appear from these, for all syllogisms concluding method- per impossibile collect the false, but they prove by hypothesis the original proposition, when contradiction being admitted some impossibility results,7 as for instance that the diameter of a square is incommensurate with the side, because, a common measure being given, the odd would be equal to the even.
1 A will r.ot be concluded of B— but something else.
2 i. e. C of D, D of E, E of F.
3 i. e. in which the middle is connected with each extreme.
4 The first figure. 5 The second figure. 6 The third figure.
7 This, as Dr. Hessey remarks, in his valuable tables upon the nature of Enthyinem, corresponds very closely to the definition of IXtyKriicbv iv6v- HT)fia in the Rhetoric ii. 2, 15, and to the instance given Rhetoric ii. '24, '6. He thus exhibits the operation, which the reader will find applied to the instance in the text, in table 4 of Schemata Rhetonca.
138 Aristotle's org axon. [book i.
They collect then that, the odd would be equal to the even, but show from hypothesis that the diameter is incommen- surate, since a falsity occurs by contradiction. This then it 1. what this J8' t0 syllogize per impossibile, namely, to show an kind ofsyiio- impossibility from the original hypothesis, so that
as by reasonings leading to the impossible, an ostensive syllogism of the false arises, but the original propo- sition is proved by hypothesis ; and we have before said about ostensive syllogisms, that they are perfected by these figures — it is evident that syllogisms also per impossibile will be formed through these figures. Likewise all others which are by hypothesis, for in all there is a syllogism of that which is assumed,1 but the original proposition is proved by con- fession, or some other hypothesis. Now if this is true, it is necessary that every demonstration and syllogism should arise 3. Also of syiio- t,ir°ugh the three figures before named, and this gisms, k( Wo- being shown, it is manifest that every syllogism capftu'iltion. is completed in the first figure, and is reduced to
universal syllogisms in it.
Chap. XXIV. — Of the Quality and Quantity of the Premises in Sy Hoy ism. — Of the Conclusion^
i. Oneaffirma- Moreover it is necessary in every syllogism, that tive and one one term should be affirmative and one universal.
universal term v. .,, ., . , . .,, '
necessary.in all for without the universal there will not be a syllo-
syll0(Prooi.') Sism> or one not pertaining to the thing proposed,
or the original (question) will be the subject of
petition.2 For let it be proposed that pleasure from music is
If A is B, then P is Q, But that P is Q is absurd.
. • . If it is absurd to say that P is Q, it is absurd to say that A is B. . • . A is not B. Q. E. D.
1 Trpbq, to HETakanfiavofttvov. — For example, in the hypothetical syllogism— If the soul is moved by itself it is immortal: but it is moved by itself, . • . it is immortal : the assumption is, the soul is moved by itself. The disjunctive syllogism owes its origin to the airaywyij iirjTo advvarov, one of the principal kinds of hypotheticals mentioned by Aris- totle, whose use of the latter expression, it is necessary to remember, is not opposed to categorical, but to ostensive (Suktikoq) syllogism, as in this very chapter. The reader is referred for some valuable observations upon this subject to note G, Appendix, Mansel's Logic. Hypothetical syllogisms, as we employ the term, are not discussed by Aristotle ; vide Aldrich de Syiloeismis Hypotheticis.
' airijatrai. Distinction is not an Aristotelian term, but the rules
CHAP. XXIV.] THE PRIOR ANALYTICS. 139
commendable, if then any one should require it to be granted that pleasure is commendable, and did not add all pleasure, there would not be a syllogism, but if that a certain pleasure is so, if indeed it is a different pleasure, it is nothing to the purpose, but if it is the same it is a petitio principii, this will however be more evident in diagrams, for instance, let it be required to show that the angles at the base of an isosceles triangle are equal.1 Let the lines A B be drawn to the centre of a circle, if then he assumes the angle A C to be equal to the angle B D, not in short requiring it to be granted that the angles of semicircles are equal, and again that C is equal to D, not assuming the whole (angle) of the section, if besides he assumes that equal parts being taken from equal whole angles, the re- maining angles E F are equal, he will beg the original (question), unless he assume that if equals are taken from equals the remain- ders are equal. Wherefore in all syllogism we must have an universal ; universal is also shown from all universal terms, but the particular in this or that way, so that if the conclusion be universal, the terms must of necessity c^uston*"?- be universal, but if the terms be universal, the lows froni uni-
i ■ , i_ ■ i • -r versal premises
conclusion may happen not to be universal. It but sometimes
appears also that in every syllogism either both j^iy a particu-
premises or one of them must be similar to the 3. One premise
conclusion. I mean not only in its being affirm- SStaSSta
ative or negative,but in that it is either necessarv, in character
, i , ,. , , •" and quality.
or absolute, or contingent ; we must also have regard to other modes of predication.2
In a word then it is shown when there will and will not be a syllogism, also when it is possible,3 and when per- fect, and that when there is a syllogism it must have t" RecaPitula-
* ° tion.
its terms according to some one of the above modes.
belonging thereto are implied in his account of the figures. The several directions given by Aldrich, on the construction of syllogistic inquiry, occur successively in this and the succeeding chapters, as comprised in the old memorial — " Distribuas Medium," etc.
1 This is demonstrated in one way by Euclid, and in another by Pap- pus. See also Proclus Commen. lib. i. Euclid. Elem. One of the five modes of the "petitio principii," is not in form distinguishable from the legitimate syllogism. Conf. Top. viii. 13; Anal. Pr. ii. 16.
2 As the impossible, probable, etc.
3 By possible here he means an imperfect, which may be brought into fc perfect syllogism. For the elucidation of tins chapter and the follow-
140 Aristotle's organon. [book l
Chap. XXV. — Every Syllogism cotisists of only three Terms, and
of two Premises.
1. Demor.stra- It appears that every demonstration Avill be by tion is ™™ev~ three terms and no more, unless the same con- terms only— elusion should result through different ' arguments, proof- as E2 through A B,3 and through C D,4 or through
A B, A C, and B C, for there is nothing to prevent many media subsisting of the same (conclusions). But these being (many), there is not one syllogism, but many syllogisms ; or again, when each of the propositions A B is assumed by syl- logism, as A through D E,5 and again B through
g thehmSor°r' F &,* or when the one is hY induction,6 but the other by syllogism. Thus in this manner indeed there are many syllogisms, for there are many conclusions, as A and B and C, and if there are not many but one, it is thus possible, that the same conclusion may arise conciusfoTmay thruugh many syllogisms, but in order that C may maneyfsyno- be Proved through A B, it is impossible.! For gisms. let the conclusion be E, collected from ABCD,
there6 should be it is then necessary that some one of these should more than foe assumed with reference to something else, as a whole, but another as a part, for this has been shown before, that when there is a syllogism, some of the terms should necessarily thus subsist ; let then A be thus with reference to B, from these there is a certain conclusion, which is either E or C or D, or some other different from these.
ing more particularly, the reader is referred to Mansel's, Whalely's, and Hill's Logic.
1 The Leipsic copy omits the example, and Taylor's reading is some- what different to that of Averrois, Buhle, and Waitz. By demon- stration Aristotle here means syllogism generally.
2 The conclusion. 3 A the major, B the minor.
4 C the major, D the minor.
5 A the major of the prosyllogism in which the major of the principal syllogism is proved — E the minor of the same. Though in the first part E signifies the conclusion of the principal syllogism, yet the conclusion is at present called C. — Taylor.
6 As far as induction is logical at all, in its process it is equally formal with, though it proceeds in an inverse order to, syllogism. It is defined by Aristotle, proving the major term of the middle by means of the minor. Anal. Pr. ii. 23, The Sorites is not recognised distinctively by Aristotle, though, as Melancthon observes, it is implied in Cat. 3, and is alluded to in this chapter ; its distinct exposition is attributed to the Stoics.
CHAP. XXV.] THE TRIOR ANALYTICS. 14
Now if E is concluded, the syllogism would be from A B alone, but it' C D are so as that the one is universal, and the other particular, something also will result from these which will either be E or A or B, or something else different from these, and if E is collected, or A or B, there will be either many syllogisms, or, as it was shown possible, the same thing will happen to be collected through many terms. If, however, any thing else different from these is collected, there will be many syllogisms unconnected with each other ; but if C is not so with respect to D, as to produce a syllogism, they will be assumed to no purpose, except for the sake of induction or concealment, or something of the sort. Still if from A B, not E, but some other conclusion is produced, and from C D, either one of these, or something different from these, many syllogisms arise, yet not of the subject, for it was supposed that the syllogism is of E. If, again, there is no conclusion from C D, it will happen that they are assumed in vain, and the syllogism is not of the primary problem, so that it is evi- dent that every demonstration and every syllogism will be through three terms only.1
This then being apparent, it is ako clear that 3 These threg a syllogism consists of two premises and no more j terms are in- for three terms are two premises, unless some- propositTonI° thing is assumed over and above, as we observed Vi<je <vldri^h at first, for the perfection of the syllogisms. Hence it appears, that in the syllogistic discourse, in which the premises, through which the principal conclusion is col- lected, are not even, — (for it is requisite that some of the former conclusions should be premises,) — this discourse is either not syllogistically constructed,2 or has required more than is necessary to the thesis.
When then the syllogisms are taken according to the prin- cipal propositions, every syllogism will consist of propositions
1 The prosyllogism, or antecedent syllogism of Aristotle, is a syllogism used to prove one of the premises of another syllogism. Vide Pucitis Anal. Pr. i. 35. Biese, vol. i. p. 157.
2 Taylor erroneously uses the active here, contrary to Waitz and Averrois, the latter translates (avXXtXoyicrai) similarly to the rendering above — "est nUiocinatu." Aristotle calls a thesis, the consequent "ex- tra syllogismum spectata," as Aldricfa says, that is, the "problem," "question," to '^tov^ivov — the last, however, is used mere extensively in signification. Vid. An. Post, i. 1, and ii. 3.
142 Aristotle's organon. [book i.
which are even, but of terms which are odd for the terms exceed the premises by one, and the conclusic ns will be half part of the premises.1 When, however, the conclusion results through pro-syllogisms, or through many continued middles,2 as A B through C I), the multitude of terms, in .Vt— incidens like manner, will exceed the premises by one, (tor BuhieUS tne *erm interpolated will be added either exter-
nally or in the middle ; but in both ways it will happen that the intervals are fewer than the terms by one,) but the propositions are equal to the intervals, the former, indeed, will not always be even, but the latter odd, but alter- nately, when the propositions are even the terms are odd, but when the terms are even the propositions are odd ; for toge- ther with the term, one proposition is added wherever the term is added.3 Hence, since the propositions
4. Ofthenum- tii i i -.l • ,1
ber of terms, were even, but the terms odd, it is necessary they propositions, should change when the same addition is made ;
and conclu- , _ ° -n i
sions in com- but the conclusions will no longer have the same £'isSms.sy1*0 order, neither with respect to the terms, nor to the propositions, for one term being added, con- clusions will be added less than the pre-existent terms by one, . „,, . because to the last term alone* there is no con-
* 1 he minor.
elusion made ; but to all the rest, e. g. if D is added to ABC, two conclusions are immediately added, the one to A and the other to B. The same occurs in the other cases also, if the term be inserted in the middle after the same manner, for it will not make a syllogism to one term alone, so that the conclusions will be many more than the terms, and than the propositions.
Chap. XXVI. — On the comparative Difficulty of certain Problems, and by what Figures they are proved}
i. The conciu- Since we have those particulars with which syl- figures consti- logisms are conversant, and what is their quality stutes the leia- in each figure, and in how many ways demon-
1 For there is one conclusion to two propositions. * As in Sorites. Vide Mansel's Logic, p. 83.
3 At the beginning, middle, or end. See Waitz, vol. i. p. 440, and 441.
4 Edocemur hoc capite et seq., quomodo ars dialectica cohaereat cuia demunstrandi arte, Topiea cum Analyticis. Waitz.
CHAP. XXVI.] THE PRIOR ANALYTICS. 143
stration takes place, it is also manifest to us, tire facility of
■ i <• » i • ■!•«» ii demonstration.
what kind of problem is difficult, ana what easy Enumeration of proof, for that which is concluded in many £on^t°£cl£ figures, and through many cases, is more easy, but cond figures,. what is in fewer figures, and by fewer cases, is more difficult. An universal affirmative then is proved through the first figure alone, and by this in one way only ; but a negative, both through the first and through the middle, tnrough the first in one way, but through the middle in two ways ; the particular affirmative again through the first and through the last, in one way through the first figure, but in three ways through the last ; lastly, the particular negative is proved in all the figures, but in the first in one way, in the middle in two ways, and in the last in three ways. Hence it appears most difficult to construct an universal affirmative, but easierof sub- most easy to subvert it, in short, universals are ^ticuiars4" easier to subvert than particulars, because the former are subverted, whether a thing is present with nothing, or is not with a certain thing, of which the one, namely, the not being with a certain thing, is proved in all the figures, and the other, the being with nothing, is proved in two. The same mode also prevails in the case of negatives, for the original proposition is subverted, whether a thing is with every, or with a certain individual,1 now thiswas in two figures. In particular problems there is one way (of confutation), either by showing a thing to be with every, or with no individual, and parti- 3 Partjcuiars cular problems are easier of construction, for they easier of con- are in more figures, and through more modes.2 In 3hort, we ought not to forget that it is possible to confute universal mutually through particular problems, and these through universal, yet we cannot construct universal through particular, but the latter may be through the former, at the same time that it is easier to subvert than to construct is plain. In what manner then every syllogism arises, through how
1 This clause is omitted by Taylor.
2 Aristotle employs 7rrioaig here in the sense of rpoirog, which latter is not an Aristotelian expression, except, as some think, in cap. 28 of this book. He shows in each figure what prepositional combinations are admissible. In Apuleius there is a distinction between modi, or moduli, and conjugationes, the former referring to combinations of three propc sitions, the latter to ihose of two.
•44 akistotle's organon. [book I.
many terms and premises, how they subsist with tion.eCaP'tula reference to each other, also what sort of problem
may be proved in each figure, and what in many and in fewer modes, may be gathered from what has been said.1
CHAP. XXVII. — Of the Invention and Construction of Syllogisms?
1. How to pro- We must now describe how we may always obtain gismsylfrom a provision of syllogisms for a proposed question, certain princi- and in what way we may assume principles about p es' each, for perhaps it is not only requisite to con- sider the production of syllogisms, but also to possess the power of forming them.
2. The several Of all beings then, some are of such a nature sons of predi- as not to be truly predicated universally of any
cfltc s Soni6
cannot be truly thing else, as "Cleon," and "Callias," that which
versanyteofUni" *s singular>3 and that which is sensible, but others
other than in- are predicated of these, (for each of these is man
ivi ua s, etc. ancj annlia]) . some again are predicated of others,
but others not previously of these ; lastly, there are some which are themselves predicated of others, and others of them, as "man " is predicated of Callias, and " animal " of man. That some things therefore are naturally adapted to be predicated of nothing is clear, for of sensibles each is almost of such a sort, as not to be predicated of any thing except accidentally, for we sometimes say that that white thing is Socrates, and that the object approaching is Callias. But that we must stop some- videb. i.ch. 19, where in our upward progression we will again Post Anal., et ' show, for the present let this be admitted. Of these things then we cannot point out another predicate,
1 As a digest of the method of proof, we may state that
A is proved in one figure and one mood
E — — two figures and three moods
I — — two — — four
O — — three — — six. Thus A is the easiest to overthrow, and the nearest to establish : 0 the reverse.
2 Averrois, following the old divisions, commences his 2nd section here " De abundantia Propositionum."
3 The employment of singulars as predicates, is open to much objection, in connexion with singular propositions. See the Thesis appended to Wallis's Logic.
CBAP. XXVII.] THE PRIOR ANALYTICS. 145
except according to opinion, but these may be predicated of others, nor can singulars ' be predicated of others, but others of them. It appears however that those which are interme- diate, are capable in both ways (of demonstration), for they may be predicated of others, and others of them, and argu- ments and speculations are almost all conversant with these. Still it is requisite to assume the propositions 2. How to as- about each thing thus : — In the first place, the sP™e Pr°P°- subject, (by hypothesis,) the definitions, and such these,SinSorder peculiarities as exist of the thing ; next, whatever t0 inferenee- things are consequent to the thing, and which the thing fol- lows ;2 lastly, such as cannot be in it ; those however which it cannot be in are not to be assumed, because of the conversion of the negative. We must also distinguish in the consequents what things belong to "what a thing is," what are predicated as properties,3 and what as accidents ; also of these, those which are (predicated) according to opinion, and those, according to truth ; for the greater number any one has of these, the quicker will he light upon a conclusion, h Distinction. and the more true they are, the more will he de- monstrate. We must too select not those which are conse- quent to a certain one, but those which follow the whole thing, e. g. not what follows a certain man, but what follows every man, for a syllogism consists of universal propositions. If therefore a proposition is indefinite, it is doubtful whether it is universal, but when it is definite, this is manifest. So also we must select those things the whole of which a thing follows, for the reason given above, but the whole consequent itself need not be assumed to follow ; I say for instance, (it must not be assumed) that every " animal " is consequent to " man," or every science to music, but only that they are simply conse- quent, as we set forth,4 for the other is useless and impossible,5 as that "every man" is "every animal," or that "justice is every thing good." To whatever (subject) a consequent is attached, the sign "every" is added ; when however the sub-
1 Taylor here falls into his common mistake of translating kci8' Uacra — " particular." Averrois, '« singularia " — which is right.
2 Omitted by Taylor.
3 The idiov, both by Porphyry and Aristotle, is considered as co-exten- sive and convertible with its subject, and answers to the fourth predicable.
1 i. e. as we form propositions. That is, a predicate with the universal sign.
146 Aristotle's organon. [book i.
ject is comprehended by a certain thing,1 the consequents of which we must assume, those which follow or which do not follow the universal, we are not to select in these — for they were assumed in those, since whatever are consequent to " animal," are also consequent to " man," and as to whatever
things are not absolutely present with in like man- sumed. °vlde ner ; but the properties of each thing must be Aidrich and taken, for there are certain properties in species
not common to genus, since it is necessary that certain properties should be in different species. Nor are we to select those in regard to the universal, which the thing com- prehended follows, as those which " man " follows ought not to be assumed to " animal," for it is necessary if animal fol- lows man that it follows all these,2 but these more properly belong to the selection of the antecedents of " man." 3 We must also assume those which are generally consequent and antece- dent, for of general problems the syllogism also is from propo- sitions, all or some of which are general, as the conclusion of each syllogism resembles its principles. Lastly, we are not to select things consequent to all, since there will not be composed a syllogism from them, on account of a reason which will ap- pear from what follows.
Chap. XXVIII. — Special Rules upon the same Subject. , „^ . t ,j Those therefore who desire to confirm any thing
1. What should . . iii-iii i •> •
betheinspec- of a certain universal, should look to the subject
that Munf matter of what is confirmed, in respect of which
versai or parti- it happens to be predicated ; but of whatever ought
ative or nega- to be predicated, of this, he should examine the
tive may be de- consequents : for if one of these happens to be the
monstrated. i » ... j r ._
same, one must necessarily be in the other. But if (it is to be proved) that a thing is not present universally but particularly, he must examine those which each follows,4 for if any of these is the same, to be particularly present is
1 i. e. by an universal predicate.
2 Of which man is predicated.
* That is, the subjects to man ought to be chosen and assumed per »e. The reader is referred for the rules specified here to the commoi Logics, especially Whately, b. ii. c. 111.
* The antecedent of both predicate and subject.
CHAP. XXVIII. J THE PRIOR ANALYTICS. 147
necessary ; but when the presence with nothing is necessary,1 as to what it need not be present with,2 we must look to those which cannot be present with it ;3 or on the contrary, (as regards that) with which4 it is necessary not to be present, we must look to those which cannot be with it, but as to what ought not to be present, to the consequents. For whichever of these are identical, it will happen that the one is in no other, since sometimes a syllogism arises in the first and at other times in the middle figure. If however the particular non-inesse (is to be proved), that with which it ought not to be present, and those which it follows, are to be looked to ; but of that which ought not to be present, those must be considered, which it is impossible can be in it, for if any of these be identical the particular non-inesse is necessary. What has been said how- ever will perhaps be more clear thus. Let the consequents to A be B, but let those to which it is consequent be C ; those again which cannot be in it, D ; again, let the things present with E be F, and those to which it is consequent, G ; lastly, those which cannot be in it, H. Now if a certain C and a certain F are identical, it is necessary that A should be with every E, for F is present with every E, and A with every C, so that A is with every E ; but if C and G are identical, A must necessarily be with a certain E, for A follows every C, and E every G. If however F and D are identical, A will be with no E from a pro-syllog:sm,5 for since a negative is convertible and F is identical with D, A will be with no F, but F is with every E ; again, if B and H are the same, A will be with no E, for B is with every A, but with no E, for it was the same as II, and H was with no E. If D and G are identical, A will not be with a certain E, for A will not be with G, since it is not present with D, but G is under E, so that neither will it be with a certain E. Moreover if B is identical with G there will be an inverse syllogism, for G will be with every A, (since B is with A,) and E with B (for B is the same as G) ; still it is not necessary that A should be with every E, but it is neces-
1 When E was to be proved.
2 i. e. the subject of the question.
3 Taylor inserts with Buhle here tic to. tnofitva, which alters the sense. I follow Waitz.
4 The predicate. The confusion of the various readings here is endless. * In which the major premise of the principal syllogism is proved.
148 Aristotle's organon. Tbook
L-
sary that it be with a certain E, because an universal predi- cation may be converted into a particular one.
Wherefore we must evidently regard what has tion of the pro- been mentioned as to each part of every problem,1 amlned be eX since all syllogisms are from these ; but in conse- quents, and the antecedents of each thing, we must look to first elements, and to those which are for the most part universal, as in the case of E we must look more to K F than only to F,2 hut in the case of A more to K C than to C only. For if A is present with K C it is also present with F and with E,3 but if it is not consequent to this, yet it may be consequent to F ; in like manner we must examine those which the thing itself is consequent to, for if it follows the primary, it also does those which are included under them, and if it does not follow these, yet it may those which are arranged under them.4
Speculation then, plainly, consists of three terms and two
propositions, and all syllogisms are through the
eons-istsof three above-mentioned figures ; for A is shown present
terms and two wjth every E, when of C and F something iden-
propositions. r
tical may be assumed. Now this will be the mid- dle term,5 and A and E the extremes, and there is the first figure, but (presence with) a certain thing is shown when C and G are assumed identical, and this is the last figure, for G becomes the middle. Again, (presence with) none, when D and F are identical, but thus also the first figure and the middle are produced ; the first, because A is with no F, (since a negative is converted,) but F is with every E ; and the middle because D is with no A, but with every E. Not to be present also with a certain one, (is shown) when D and G are the same, and this is the last figure, for A will be with no G, and E with every G. Wherefore all syllogisms are evidently through the above-named figures, and we must not select those which are consequent to all, because no syllogism arises from them ; as, in short, we cannot construct from con-
' As to both subject and predicate.
" K F is the genus of both K and F, and K C stands in the same rela- tion to K and C. 3 F is contained under K, and E under F.
4 Thus if "living" follows "animal," it also follows" man," and though it does not follow "body," it follows that whichis under " body." - — Taylor
* viz. C F — A the major— E the minor.
CHAP. XXVIII.] THE PRIOR ANALYTICS. 149
sequents, nor deduce a negative through an universal conse- quent, for it must be in one, and not in the other.1
TLat other modes of speculation2 also, as regards selection, are useless for the construction of syllogism is apparent ; for instance, if the consequents to each are identical, or if those which A (the predicate) follows, and which can- 4. other modes not be with E (the subject), or again those which J,,™^6^™ cannot concur to be with either, for no syllogism gards selection arises through these. If then the consequents are identical, as B and F, the middle figure is produced, having both premises affirmative ; but if those which A follows, and which cannot be with E, as C and H, there will be the first figure having the minor premise negative ; again, if those are identical which cannot be with either, as D and H,3 both pro- positions will be negative, either in the first or in the middle figure : thus, however, there will by no means be a syllogism.
We see moreover that we must assume in spe- culation things identical, and not what are different, seiecte i™ in ves-
or contrary ; first, because our inspection is for ligation, not , , .. . .in i 1 tna' wherein
the sake 01 the middle, and we must take as a the terms differ, middle, not what is different, but what is identical. theyLreeth Next, in whatever a syllogism happens to be pro- duced, from the assumption of contraries, or of those things which cannot be with the same, all are reduced to the before- named modes, as if B and F are contraries, or cannot be with the same thing ; if these are assumed there will be a syllo- gism that A is with no E : this however does not result from them, but from the above-named mode ; for B is with every A, and with no E, so that B must necessarily be identical with a certain H. Again, if B and G do not concur to be with the same thing, (it will follow) that A will not be with a certain E, and so there will be the middle figure, for B is
1 That is, he who wishes to conclude a negative must take a middle, which concurs with one extreme, and not with the other, but in the case cited both propositions would be affirmative — here KaraoKtva^Hv, "affir- mative colligere," is opposed to a Troartpuv, " negative colligere." Confer. Waltz, vol. i. page 45U.
* artiste rwv Kara rag tfcXoyag dxptloi. — Vide Waitz, vol. i. 451, and Biese, i. p. 160, also Mansel's Logic, page 79. See also the definition of roiroc given by Cicero (Top. ch. ii.) ; the name originally alluded to the plafc in which we look for middle terms. Vide liliei. ii. 2t>. 1 ; also note o'i Top. i. I.
1 Taylor reads G, en ^neously.
1,30 Aristotle's org anon. [hook l
with every A, and with no G,1 so that B must necessarily be identical with some H. For the impossibility of B and G being in the same thing, does not differ from B being the same as a certain H, since every thing is assumed which can- not be with E.
From these observations, then, it is shown that 6. Recapituia- syllogism arises ; but if B and F are contraries,
tion. jo ' .... . TT
B must necessarily be identical with a certain H, and a syllogism arises through these. Nevertheless it occurs to persons thus inspecting, that they look to a different way than the necessary, from the identity of B and H escaping them.
Chap. XXIX.— The same Method applied to other than cate- gorical Syllogisms.
' _ Syllogisms which lead to the impossible subsist
1. The same , r„ , ,
method to be in the same manner as ostensive, tor these also "electing a* ar*se through consequents, and those (antecedents) middle term in which each follows,2 and the inspection is the "ytheTrnpos°si- same in both, for what is ostensively demonstrated hie," as in the may be ais0 syllogistically inferred per impossi- ble, and through the same terms, and what is de- monstrated per impossible, may be also proved ostensively, as that A is with no E. For let it be supposed to be with a cer- tain E, therefore since B is with every A, and A with a certain E, B also will be with a certain E, but it was present with none ; again, it may be shown that A is with a certain E, for if A is with no E, but E is with every H, A will be with no H, but it was supposed to be with every H. It will happen the same in other problems, for always and in all things demonstration per im- possibile will be from consequents, and from those which each follows. In every problem also there is the same considera- tion, whether a man wishes to syllogize ostensively, or to lead to the impossible, since both demonstrations are from the same terms, as for example, if A were shown to be with no E, because B happens to be with a certain E, which is impossible, if it is as- sumed that B is with no E, but with every A, it is evident that A will be with no E. Again, if it is ostensively collected that A
1 Waitz incorrectly reads E.
s i. e. the predicate and subject of the question.
CHAP. XXIX.] THE TRIOR ANALYTICS. 151
is with no E, to those who suppose that it is with a certain E, it may be shown per impossible to be with no E. The like will also occur in other cases, for in all we must assume some common term different from the subject terms to which there will appertain a syllogism of the false, so that this proposition being converted,1 but the other remaining the same, there will be an ostensive syllogism through the same terms. 2. Wherein the But an ostensive syllogism differs from that per ;*^^e impossibile, because in the ostensive both premises syllogisms are laid down according to truth,2 but in that ° er" which leads to the impossible one is laid down falsely.3
These things however will more fully appear by what fol- lows, when we come to speak of the impossible, for the pre- sent let so much be manifest to us, that both he who wishes to syllogize ostensively, and per impossibile, must observe these things. In other syllogisms indeed which are hypo- thetical, such as those which are according to transumption, or according to quality, the consideration will be in the sub- ject terms, not in the original ones, but in those 3 Tliemodeof taken afterwards, but the mode of inspection will investigation be the same ; but it is necessary also to consider, ^Xetkais. and distinguish, in how many ways hypothetical syllogisms arise.
Each problem then is demonstrated thus, and some of them we may infer syllogistically after another method, for example, universals by an hypothetical inspection of particulars, for if C and H are the same, and if E is assumed to be with H alone,
1 That is, the proposition being assumed contradicting the conclusion of the syllogism leading to the impossible. — Taylor.
2 They are assumed as true, though sometimes false.
3 As if false — to be confuted by a conclusive absurdity. Compare the 23rd chap, of this book of the Analytics. In the place just quoted the to /iera\a^j8av6/x£vov is explained by Alexander as applying to the conclusive expression of the syllogism, because it is taken differently to the manner in which it was originally enunciated, being at first part of a conditional agreement, and afterwards a categorical conclusion. For this reason the syllogism is here said to be Kara fitrd\rj\piv. Were it not for this authority it would seem simpler to interpret furdk^ig, " change of question." As to the hypothetical called Kara 7roiorijra, mentioned here, we have no data for even a plausible conjecture — Mansel. Philo- ponus (Scholia, p. 17*, b. 9) says it is a syllogism. U tov paWov 7) Ik tov i)TTov, 7) Ik tov bfioiov. Vide Whately's and Hill's Logic. Waiu identities boih terms. See rol. i. 156'
152 Aristotle's organon. [book i
A will be with every E ; and again, if D and H are the same, and E is predicated of H alone, (it may be shown) that A is with no E. Wherefore the inspection must clearly be in this way after the same manner both in the necessary and contin- gent, for the consideration is the same, and the syllogism both of the contingent and the absolute will be through terms the same in order ; in the contingent however we may assume things which are not with, but which may be, for it has been shown that by these a contingent syllogism is produced, and the reasoning is similar in the case of the other predications. From what has been said then it appears not only that it is allowable for all syllogisms to be formed in this, but that they cannot be formed in any other way, for every syllogism has been shown to originate through some one of the before-named figures, and these may not be consti- tuted through any other than the consequents and antecedents of a thing, for from these are the premises and assumption ©f the middle, so that it is not admissible that a syllogism should be produced through other things.
Chap. XXX. — The preceding method of Demonstration applicable
to all Problems.
1 The method The way then of proceeding in all (problems), of demonstra- both in philosophy and in every art and discipline, previously"^11 is the same, for we must collect about each of them applicable to ail those things which are with, and the subjects losophicai in- which they are with, and be provided with as many quiry" as possible of these, considering them also through
three terms in one way subverting, but in another constructing according to truth (we reason) from those which are truly de- scribed to be inherent, but as regards dialectic syllogisms (we must reason) from probable propositions. Now the princi- ples of universal syllogisms have been mentioned, how they subsist, and how we must investigate them, that we may not direct our attention to every thing which is said, nor to con- structing and subverting the same things, nor both construct- ing universally or particularly, nor subverting wholly or par- tially, but look to things fewer and definite ; as to each however we must make a selection, as of good or of science. The peculiar principles indeed in every science are many,
CHAP. XXXI. J THE PRIOR ANALYTICS. 153
hence it is the province of experience to deliver 2 Ex erience the principles of every thing, for instance, I say is to supply the that astrological experience gives the principles demonstration of astrological science, for from phenomena being m every sd- sufficiently assumed, astrological demonstrations have thus been invented, so also is it in every other art and science. Wherefore if things are assumed which exist in in- dividuals, it is now our duty readily to exhibit demonstrations, for if as regards history nothing is omitted of what is truly present with things, we shall be able about every thing of which there is demonstration to discover and demonstrate this, and to make that clear which is naturally incapable of demon- Station. ~ ,3. The end of
Universally then we have nearly shown how analytical in- propositions ought to be selected, but we have efucidate°sub0 discussed this accurately in the treatise on Dia- jects naturally
... J abstruse.
lectic.1
Chap. XXXI.— Upon Divisioyi ; and its Imperfection as to De- monstration?
That the division through genera3 is but a cer- tain small portion of the method specified, it is l.'^VuVon, its easy to perceive, for division is, as it were, a weak ^argumenTit syllogism, since it begs what it ought to demonstrate, is a species of
1 In the Topics. The dialectic however of Aristotle, as enunciated here, differs from that art as exhibited in the Topics, in that he discusses it in the Analytics as a mere formal method of reasoning, but in the Topics he gives it an entirely material character. The dialectic of Plato corresponds more nearly with the metaphysics of Aristotle : again, the dialectic of Aristotle is an art, but his analytic a science ; see note on Top. i. 1.
2 Vide Whately, b. iii. sect. 11.
3 i. e. by which genera are divided into species by the addition of differ- ences. Plato used division as a means of demonstrating definitions, and the utility of them, according to Aristotle, consists in employing them as tests of definitions when obtained. Amongst the later Peripatetics, di- vision rose in estimation, and Andronicus Rhodius composed a treatise on the subject. Modern logicians have chiefly drawn from Boethius' work de Divistone. Compare Top. vi. 2. Dichotomy, or the division al- luded to above of genus, is approved by Aristotle when effected by con- traries, but not by contradictories. Compare Eth. Nic. vii. 6; tvaut, Logic, sect. 113; Trend. Elem. sect. 5» ; also Categor. 10.
154 atustoti.e's organon. [book I.
weak syiio- an(j alwayS infers something of prior matter.1 Now this has first escaped the notice of all those who use it, and they endeavour to show that demonstration about essence and the very nature of a thing is possible, so that they neither perceive that those who divide happen to syllogize, nor that it is possible in the manner we have said. In demonstrations therefore, when it is requisite to infer ab- solute presence, the middle term by which the syllogism is 2 in demon- produced must always be less, and must not be stmtion of the universally predicated of the first extreme, but on middle must the contrary, division takes the universal for the be less, and not middle term. For let animal be A, mortal B, im-
umversal in re- _ _ ,
spect of the first mortal b, and man ot whom we ought to assume extreme. ^q definition D, every animal then comprehends
either mortal or immortal, but this is that the whole of what- ever may be A is either B or C. Again, he who divides man, admits that he is animal, so that he assumes A to be predicated of D, hence the syllogism is that every D is either B or C, wherefore it is necessary for man to be either mortal or immortal, yet it is not necessary that animal should be mortal, but this is desired to be granted, which was the very thing which ought to have been syllogistically in- ferred.* Again, taking A for mortal animal, B for pedestrian, C without feet, and D for man, in the same manner it assumes A to be either with B or C, for every mortal animal is either pedestrian or without feet, and that A is pre- dicated of D, for it has assumed that man is a mortal animal, so that it is necessary that man should be either a pedestrian
1 i. e. of universals, or of things more nearly approaching to these.
Ex. 1. Every animal is either mortal or immortal. Every man is an animal . • . Every man is either mortal or immortal.
The conclusion here was to have been, that every man is mortal ; but he who divides does not prove this, but desires it to be granted.
Ex. 2. Every mortal animal is pedestrian or without feet Every man is a mortal animal . * . Every roan is pedestrian or without feet.
Ex. 3. Every length is or is not commensurable Every diameter is a length . ' . Every diameter is or is not commensurable.
CHAP. XXXII.] THE PRIOR ANALYTICS. 15-5
animal or without feet, but that he is pedestrian is not neces- sary, but they assume it, and this again is what _ , ,„
i i i i**ci- * Example 2.)
they ought to have proved. Alter tins manner it always happens to those who divide, namely, that they as- sume an universal middle, and what they ought to show, and the differences as extremes. In the last place, they assert nothing clearly, as that it is necessary that this be a man, or that the t question necessarily is whatever it may , „ .
, , ' n *, ^ T to In rou ue-
be, but they pursue every other way, not appre- vo*. (Vjje bending the available supplies. It is clear how- ^"^vision not ever, that by this method we can neither subvert suitable for re- nor syllogistically infer any thing of accident or for various0 property or genus, or of those things of which we ^.inds of iues- are a priori ignorant as to how they subsist, as whether the diameter of a square be incommensurable, for if it assumes every length to be either commensurable or incom- mensurable, but the diameter of a square is a length, it will infer that the diameter is either incommensurable or com- mensurable, and if it assumes that it is incommensurate, it will assume what it ought to prove, wherefore that we cannot show, for this is the way, and by this we cannot do it ; let however the incommensurable or commensurable be A, length B, and diameter C.J It is clear then that this 4 _ , ,„'
' , n ■ ■ A + , .• t Example (3.)
mode oi inquiry does not suit every speculation, neither is useful in those to which it especially appears ap- propriate, wherefore from what sources, and how demonstra- tions arise, and what we must regard in every problem, appear from what has been said.
Chap. XXXII. — Reduction of Syllogisms to the above Figures?
How then we may reduce syllogisms to the above- j Method of
named figures must next be told, for this is the reducing every
remainder of the speculation, since if we have one of the three
noticed the production of syllogisms, and have the *«««* t0}e
. r . , ."V. considered.
power of inventing them, it moreover we analyze (Compare ch. them when formed into the before-named figures, 28-)
1 Averrois commences his third section here, " de syllogismorum reso- lutions." The word dvdytiv, and not ciTrayiiv, as significative of reduction, has been already commented upon ; it is employed in its strict meaning at this place.
156 Aristotle's organon. [book l
our original design will have been completed. At the same
time, what has before been said will happen to be confirmed,
and be more evident that they are thus from what shall now
be said, for every truth must necessarily agree with itself in
every respect.
Rule 1st. First then we must endeavour to select the two
Propositions to propositions of a syllogism, for it is easier to di- ce investigated x . l . i • 1
as to quantity, vide into greater than into less parts,1 and com- posites are greater than the things of which they are composed ; next we must consider whether it is in a whole or in a part, and if both propositions should not be assumed, oneself placing one of them. For those who propose the uni- versal2 do not receive the other which is contained in it,3 neither when they write, nor when they interrogate, or pro- pose these,4 but omit those5 by which these are concluded, and question other things to no purpose. There- Examine their f°re we must consider whether any thing super- superfluities fluous has been assumed, and any thing: necessary
and deficiencies . , . ,. . i 1 • -i -i ■%
as to the proper omitted, and one thing is to be laid down, and syllogism!0" °f anotuer to be removed, until we arrive at two propositions, for without these we cannot reduce the sentences which are thus the subjects of question. Now in some it is easy to see what is deficient, but others escape us, and seem to be syllogisms,6 because something necessarily happens from the things laid down, as if it should be assumed that essence not being subverted, essence is not subverted,7 but those things being subverted, of which a thing consists, what is composed of these is subverted also ; for from these
1 i. e. into propositions than into terms.
* i. e. the major proposition, which is always universal in the first figure.
3 i. e. the minor, which stands towards the major in the relation of particular to universal.
4 i. e. the propositions of the principal syllogism.
5 i. e. the propositions of the pro-syllogism. This last is the antece- dent in a minor premise, which makes it enthymematic. Vide Whately, book ii. eh. 4, sect. 7, note.
9 Vide Whately's table of Fallacies, book iii.
7 In the propositions adduced, the syllogistic form is not present, but syllogistic inferences may be derived from them. In the place of the major, we have an equivalent proposition expressed, and in place of the minor — the major of the pro-syllogism proving that nrnor is added; this major, however, is changed so far, as it is made more
CHAP. XXXII.] THE PRIOR ANALYTICS* 57
positions it is necessary that a part of essence should be essence, yet this is not concluded through the assumptions, but the propositions are wanting. Again, if because man ex- ists, it is necessary that animal should be, and animal exist- ing, that there should be essence ; then, because ^ ^ man exists, essence must necessarily be ; but this consider the is not yet syllogistically inferred,1 for the proposi- ™iity °f infer" tions do not subsist as we have said they should ; 2 but we are deceived in such, because something necessary happens from the things laid down, and because also a syllo- gism is something necessary. The necessary, however, is more extensive than the syllogism, for every syllogism is ne- cessary, but not every thing necessary is a syllogism ; so that if any thing occurs from certain positions, we must not imme- diately endeavour to reduce, but first assume two propositions, then we must divide them into terms, in this manner, that term we must place as the middle which is said to be in both propositions, for the middle must necessarily exist in both, in all the figures. If then the middle predicates, and is predicated of, or if it indeed predicates, Ascertata the but another thing is denied of it, there will be the JsjJ£rg t^ich first figure, but if it predicates, and is denied by problem be- something, there will be the middle figure, and if J^dsdsieby the other things are predicated of it, and one thing is denied, but another is predicated, there will be the last figure ; thus the middle subsists in each figure. In a similar manner also, if the propositions should not be universal, for the deter- mination of the middle is the same,3 wherefore it is evident, that in discourse, where the same thing is not asserted more than once, a syllogism does not subsist, since the middle is not assumed. As, however, we know what kind of problem is deduced in each figure,4 in what the universal, and in what the particular, it is clear that we must not regard all the figures, but that one which is appropriate to each problem, and whatever things are deduced in many figures, we may ascertain the figure of by the position of the middle.
1 i. e. it is not categorical, but hypothetical.
2 They neither affirm nor deny.
3 For an universal does not differ from a particular, by reason of the middle term, but by the circumscription and determination of the verbal sign, "every," "none," called Trpoadiopia^o^. See Hill's Logic, and Whately. * From chapter 26.
158 aristotle's organon. [book t.
Chap. XXXIII. — On Error, arising from the quantity of Propositions.
i. cause of de- It frequently happens then, that we are deceived wftagtam!-^1 about syllogisms, on account of the necessary our inattention (conclusion), as we have before observed, and some-
to the relative . .
quantity of times by the resemblance1 in the position of the propositions. terms, which ought not to have escaped us.
Thus if A is predicated of B, and B of C, there would appear a syllogism from such terms, yet neither is any thing necessary produced, nor a syllogism. For let A be that which always is ; B, Aristomenes the object of intellect ; and C, Aristomenes ; it is true then that A is with B, for Aristomenes is always the object of intellect ; but B is also with C, for Aristo- menes is Aristomenes the object of intellect, but A is not with C, for Aristomenes is corruptible, neither would a syllogism be formed from terms thus placed, but the universal proposi- tion2 A B must be assumed, but this is false,3 to think that every Aristomenes who is the object of intellect always exists, when Aristomenes is corruptible. Again, let C be Miccalus, B Miccalus the musician, A to die to-morrow ; B therefore is truly predicated of C, since Miccalus is Miccalus the musician, and A is truly predicated of B, for Miccalus the musician may die to-morrow, but A is falsely predicated of C. This case therefore is the same with the preceding, for it is not uni- versally true that Miccalus the musician will die to-morrow, and if this is not assumed, there would be no syllogism.4
This deception arises therefore from a small (matter), since we concede, as if there were no difference between saying that this thing is present with that, and this present with evert/ individual of that.
1 In indefinites, which are mistaken for universals.
2 i. e. the major.
3 Because the distributive particle " every " shows that any particular is assumed.
4 Here the fallacy arises from the major not being universal, for it is not said that every Miccalus, a musician, will die to-morrow. Vide Appendix to Hill's Logic.
CHAP. XXXIV.] THE PRIOR ANALYTICS. 159
Chap. XXXIV. — Error arising from inaccurate exposition
of Terms.1
Deception will frequently occur from the terms 1. Nature of dv- of the proposition being improperly expounded,2 2mm„*SSS, as if A should be health, B disease, and C man, terms inaccu- for it is true to say that A cannot be with any B, for health is with no disease, and again that B is with every C, for every man is susceptible of disease, whence it would appear to result that health can be with no man. Now the reason of this is, that the terms are not rightly set out in expression, since those words which are significant of habits being changed, there will not be a syllogism, as if the word " well " were taken instead of "health," and the word "ill" instead of "dis- ease," since it is not true to say, that to be well cannot be pre- sent with him that is ill. Now this not being assumed, there is no syllogism except of the contingent,3 which indeed is not impossible, for health may happen to be with no man. Again, in the middle figure there will likewise be a falsity, for health happens to be with no disease, but may happen to be with every man, so that disease shall be with no man.4 In the third figure however falsity occurs by the contingent, for it is possible that health and disease, science and ignorance, in short, contraries, shall be with the same individual, but it is impossible that they should be present with each other : this, however, differs from the preceding observations,* since when m y.de ch many things happen to be present with the same individual they also happen to be so with each other.
Evidently then in all these cases deception arises from the setting forth of the terms, as if those are changed which relate to the habits, there is no falsity, and it is therefore apparent
1 Vide Hill, on verbal and material fallacy; also Whately, who refers the Aristotelian division of fallacies (oi irapa. ti)v \e£iv and oi t£w Tr";c \e£iwQ) to logical and material, upon a species of conjecture. Confer. Waitz, vol. ii. p. 532.
2 Because an abstract term, "health," is assumed for a concrete, as "sane."
3 For a man now ill, may not hereafter be well ; that to be ill is pre- sent with every man, therefore to be well present with no man.
4 This is against the rule laid down in ch. 2, of the next book, wherein he shows that the false cannot be collected from the true.
160 auisioxle's organon. [book I.
that in such propositions, what relates to hat it1 must always be exchanged and placed for a term instead of habit.2
Chap. XXXV. — Middle not always to be assumed as a particular definite thing, wc roSt ri.
i. One word ^T *s not always necessary to seek to expound the
cannot always terms by a name,3 since there will oftentimes be
someeterms,in- sentences to which no name is attached, wherefore
asmuchasthey it is difficult to reduce syllogisms of this kind,
are sentences. ■, in ■■ • ,-..,.
but we shall sometimes happen to be deceived by such a search, for example, because a syllogism is of things im- mediate.4 For let A5 be two right angles, B a triangle, C an isosceles triangle. A then is with C through B, but no longer with B through any thing else, for a triangle has of itself two right angles, so that there will not be a middle of the propo- sition A B,6 which is demonstrable. The middle then must clearly not thus be always assumed, as if it were a particular definite thing,7 but sometimes a sentence, which happens to be the case in the instance adduced.
Chap. XXXVI. — On the arrangement of Terms, according to nomi- nal appellation ; and of Propositions according to case.*
1. For the con- For the first to be in the middle, and the latter
structionofa .» . •. • . „
syllogism, it is m tlie extreme, it is unnecessary to assume as if not always re- they were always predicated of each other, or in term should be like manner,9 the first cf the middle, and this in
1 The concrete word "well."
2 The abstract, " health." 3 One word.
4 Between which there is no middle — they may be proved, however, by a definition of the subject, as in the Post Ana. Vide Pacius and Biese, vol. i. p. 157; also Aquinas, Op. 48. cap. 1. The word dfitffoc is used by Aristotle, either to express a proposition not proved by any higher middle term, (vide An. Post, i. 2, and ii. 19,) or a premise imme- diate, as regards its conclusion, i. e. not requiring the insertion of lower middle terms, for connexion of its terms withthose of the conclusion.
3 i. e. three angles, equal to two right.
6 A certain middle thing, signified by one word.
7 As one thing expressed by one word.
g Aristotle distinguishes KXijang and tttwvuc, (which last word he uses for rponoQ,) the first as being nouns in the nominatire case, the other the oblique cases. See Hcrmen. c. 2. 9 i. e. in the same case.
CHAP. XXXVI.] THE PRIOR ANALYTICS. 161
the last, and also likewise in the case of non- predicated of inesse. Still in so many ways as to be is predi- »casu recto." cated, and any thins; is truly asserted, it is requi- Since either
. i i . .P . . . major or minor
site to consider that we signify the inesse, as that premise, or of contraries there is one science. an^obHque^6
For let A be, there is one science, and B, things case, contrary to each other, A then is present with B, not as if contraries are one science,1 but because it is true in respect of them, to say that there is one science of them. It sometimes occurs indeed, that the first is predicated of the middle, but the middle not of the third, as if wisdom is science, but wisdom is of'2 good, the conclusion is that science is of good : hence good is not wisdom, but wisdom is science. Some- times, again, the middle is predicated of the third, but the first not of the middle, e. g. if there is a science of every quality or contrary, hut good is a contrary and a quality, the con- clusion then is, that there is a science of good, yet neither good, nor quality, nor contrary is science, but good is these.3 Sometimes, again, neither the first is predicated of the middle, nor this of the third, the first indeed being sometimes predi- cated of the third, and sometimes not,4 for instance, of whatever there is science, there is genus, but there is science of good, the conclusion is that there is a genus of good, yet none of these is predicated of any. If, nevertheless, of what there is science, this is genus, but there is a science of good, the con- clusion is that good is genus, hence the first is predicated of the extreme, but there, is no predication of each other.5
In the case of the non-inesse there must be the 2 Method the same manner of assumption, for this thing not same with ne- being present with this, does not always signify ga lve that this is not this, but sometimes that this is not of this, or that this is not with this, as there is not a motion of motion or generation of generation, but there is (a motion and genera- tion) of pleasure : pleasure therefore is not generation. Again, there is of laughter a sign, but there is not a sign of a
1 Waitz inserts avrwv. 2 Here he also inserts t7rio-ri)/u/. Aristotle means, that in the major proposition the greater extreme is in a direct, but in the minor proposition the middle is in an oblique case.
3 i. e. good is a quality, and is contrary, hence the minor is direct.
4 i. e. " recta predicatione." Buhle.
1 The conclusion ia direct, but the propositions are oblique.
in
162 aristotle's organon. [book i.
sign, so that laughter is not a sign, and similarly in other cases, wherein the problem is subverted from the genus being in some way referred to it.1 Moreover, occasion is not oppor- tune time, for to the divinity there is occasion, but not oppor- tune time, because there is nothing useful to divinity,2 we must take as terms, occasion, opportune time, and divinity, but the proposition must be assumed according to
3. Method of , , <• f . • , . *?, •
assuming pro- the case ot the noun, since, in short, we assert this positions and universally, that we must always place the terms according to the appellations of the nouns, e. g. man, or good, or contraries, not of man, nor of good, nor of contraries, but we must take propositions according to the cases of each word, since they are either to this as the equal, or of this as the double, or this thing as striking, or seeing, or this one as man, animal, or if the noun falls in any other way, ac- cording to the proposition.
Chap. XXXVII. — Rules of Reference to the forms of Predication.
For this thing to be with that, and for one thing absoiuteUpredi- to he truly predicated of another, must be assumed acte°ntThe^eSt *n as man7 wavs as the categories are divided ; the verai varieties latter must also be taken either in a certain re- divTslon0™1' spec*?3 or simply, moreover either as simple 4 or
connected,5 in a similar manner also with regard to the non-inesse ; these however must be better considered and denned.
1 Either directly or obliquely. Aristotle calls the middle term in the second figure, genus, because as the latter is predicated, the middle term in the second figure is also predicated ; otherwise they differ greatly, since genus is predicated of species affirmatively, but the middle in the second figure is partly predicated affirmatively, and partly negatively, since one premise ought to affirm, and the other deny.
2 This syllogism is in the third figure ; the middle term being " divinity."
s As, an Ethiopian has white teeth.
4 As, a swan is an animal.
* As. a swan is a white animal.
CHAP XXXVIII.] THE PRIOR ANALYTICS. 163
Chap. XXXVIII. — Of Propositional Iteration and the Addition
to a Predicate.
Whatever is reiterated*1 in propositions must
be annexed to the major and not to the middle * t*avai,*\oir
term ; I mean for instance, if there should be a
syllogism, that there is a science of justice "because it is
good," the expression " because it is good," or " in j whatever is
that it is good," must be joined to the major. For reiterated
let A be "science, that it is good ;" B, "good ;" "dto theinqjor*
and C, "justice ;" A then is truly predicated of not to the mid'
B, since of good there is science that it is good :
but B is also true of C ; for justice is what is good, thus
therefore the solution is made.t But if, " that it , „
, „ , , , , -r» o •, -li i n < Example (1.)
is good be added to B,2 it will not be true ; for
A will indeed be truly predicated of B, but it will not be
true that B is predicated of C, since to predicate of justice,
good that it is good, is false, and not intelligible. So also it
may be shown that the healthy is an object of science in that
it is good, or that hircocervus is an object of opinion, quoad
its nonentity,3 or that man is corruptible, so far as
he is sensible, for in all super-predications, we t*'«a-m-yopoZ-
must annex the repetition to the (major) term.
1 tirav. dicitur in oratione, quod accedit, praesertim si ita accedit ut sensus aut leviter, aut omnino non mutetur. Waitz. A syllogism is how- ever said to be produced fitra 7rpoo-0/jic?jc, when something is added to the predicate, to tTriicarriyopovfitvov.
Ex. 1. Of good there is science that it is good Justice is good . • . Of justice there is science that it is good. J That is, to the middle.
3 An animal formed from the union of a goat and a stag. The syllogism may be thus constructed.
Non-being is an object of opinion quoad nonentity An hircocervus is a nonentity . • . An hircocervus is an object of opinion quoad nonentity.
Ex. 2. Every being is an object of science Good is being . •. Good is an object of science. Ex. 3. Of being there is science, that it is being Good is being . • . Of good there is science, that it is being.
m 2
164 arijtotle's org anon. [book t.
The position of the terms is nevertheless not
2. The terms r ■ . „ . . ln . c ,
not the same the same when a thing is syllogistically interred t?onThXPr" simply, and when this particular thing, or in a the inference is certain respect, or in a certain way. For instance, a cenain'quaii- I mean, as when good is shown to be an object of ncation. science, and when it is shown to be so because it is
"ood ; but if it is shown to be an object of science simply, we must take " being " as the middle term ; * if (it is * Example (2.) prove(j that it may be scientifically known) to be
good, a certain being (must be taken as the middle). For let A be " science, that it is a certain being," B " a certain being," and C " good ; " to predicate then A of B is true, for there is science of a certain being, that it is a certain bein"- ; but B is also predicated of C, because C is a cer- tain being ; f therefore A will be predicated of C, t 1. e. good. jience there will be science of good that it is good, for the expression "a certain being" is the sign of peculiar or proper essence. If, on the other hand, " being " is set as the middle, and being simply and not a certain being is added to the extreme, there will not be a syllogism that there is a science of good, that it is good, but that it is being : for ex- ample, let A be science that it is being ; B, being ; t Example (3.) ^ ^ good;j. In guch Syii0gisiiis then as are from
a part,1 we must clearly take the terms after this manner.
Chap. XXXIX.— The Simplification of Terms in the Solution of
Syllogism.
We must also exchange those which have the same import ;
nouns for nouns, and sentences for sentences, and a noun and
a sentence,2 and always take the noun for the sentence, for
thus the exposition of the terms will be easier. For example,
l. in syiio- if there is no difference in saying that what is
gistic analysis supposed is not the genus of what is opined, or that
piidty and per- what is opined is not any thing which may be
spicuitytobe supPosed, (for the signification is the same,) in- studied, tfr n ■> 11 1
stead ot the sentence already expressed we must
1 "Ev fitpti vocat eos qui noil anXwg ri sed rode n concludunt. Waitz. Vide Biese, i. p. 179, not. 2.
- Either for either. This is omitted by Taylor, though read by Averrois, Buhle, Waitz. This direction, except carefully done, gives rise to frequent fallacies. Quando pro termino repetendo, substituitur vox illi aequipol- lens. Aldrich. Whately on Fallacies.
CHAP. XL. XLI.] THE PRIOR ANALYTICS 165
take what may be supposed and what may be opined, as terms.
Chap. XL. — Tlxe definite Article to be added according to the nature
of the Conclusion.
Since however it is not the same, for pleasure to
be good, and for pleasure to be the good, we must Idd^tTraof the*
not set the terms alike ; but if there is a syllogism axi^, and
that pleasure is the good, the good (must be taken
as a term) if that it is good, good (must be taken), and so of
the rest.
Chap. XLI. — On the Distinction of certain forms of Universal
Predication.
It is neither in fact nor in word the same thing , The expres.
to assert that A is present with every individual sionKae' ovjob
with which B is present, and to say that A is T\%*at>!i°? T
present with every individual of what B is pre- pe^f^nticai
sent with, since there is nothing to prevent with «a(fot
B from being with C, yet not with every C.1 ™l\*0£r*
For instance, let B be beautiful, but C white, if r<*«-°f"»™A,
, , •<• i • • i . -i ■ • • is equivalent
then beautiful is with something white, it is true to a being pre- to say that beauty is present with what is Avhite, everything of yet not perhaps with every thing white. If then w.nicn B is pre- A is with B, but not with every thing of which B is predicated, neither if B is present with every C, nor if it is alone present, it is necessary that A should not only not be present with every C, but that it should not be present (at all), but if that of which B is truly predicated, with every individual of this A is present, it will happen that A will be predicated of every individual of which B is predicated of every individual. But if A is predicated of that of which B is universally predicated, there is nothing to prevent B from being present with C with not every or with no individual of which A is present, therefore in (three terms it is evident that) the assertion that A is predicated of every individual of which B is predicated, signifies that of whatever B is prcdi-
1 Therefore " that with 'which B is present," and " that with every individual of which B is present," do not mean the same thing.
166 Aristotle's organon. [book i.
cated of all these A is predicated also, and if B is predicated of every, A will also thus be predicated, but if it is not predicated of every individual it is not necessary that A should be predicated of every individual.
Still we need not imagine that any absurdity will occur from this exposition, for we do not use the expression that this is a particular definite thing,1 but as a geometrician says that this is a foot in length, is a straight line, and is without breadth though it is not so, he does not however so use them, as if he inferred 2 from these. In a word, that which is not 2. certain ex- as a whole to a part, and something else in refer- pressions used ence to this as a part to a whole, from nothing of
for illustration. ,, -, , ,°
these can a demonstrator demonstrate, where- fore neither is there a syllogism, but we use exposition as we do sense 3 when we address a learner, since we do not (use it) so as if it were impossible to be demonstrated without these, as (we use propositions) from which a syllogism is con- structed.
Chap. XLII. — That not all Conclusions in the same Sylloghm are produced through one Figure.
1 The conciu- -^ET us not f°r»et tnat a^ conclusions in the same sion an evi- syllogism are not produced by one figure, but one figure the* a through this figure, and another through that, so inquiry is to be that clearly we must make the 4 resolutions in the same manner, but since not every problem is proved in every 5 figure, but arranged in each, it is evident from the conclusion in what figure the inquiry must be made.6
1 Examples are not adduced to prove, but to illustrate.
2 Tanquam ex his ratiocinans. Averrois.
5 Ttp d' iKTidiaQai (exhibere sensui) ovtoj xpwfitGa Ixxsirtp Kai r<£ alaQd- vtoOai. Cf. Aquinas Opusc. 47. Zabarella, cap. vii. alaOrjcriQ, sensa- tion, signifies the perception of the external senses. Vide Ethics, b. vi. chap. 2, and 11 ; Phys. b. iii. and vii.
4 i. e. the several syllogisms to their proper figures.
s As no affirmative in the second nor universal in the third.
* In qua figura quserendum sit problema aliquod. Buhle.
CHAP. XLI1I. XLIV.] THE PRIOR ANALYTICS. 167
Chap. XLIII. — Of Arguments against Definition, simplified.
With regard, however, to arguments against de- 1 For brevity-g
finition, and by which a particular thing in the ?ake the thing
definition is attacked, that term must be laid ^definition,
down which is attacked, and not the whole de- an,d,nojtJe.
»••/>• "ii i iiiii whole defini-
finition, for it will result that we shall be less tion itself, is to disturbed by prolixity, e. g. if we are to show be laid down- that water is humid potable, we must place potable and water as terms.1
Chap, XLIV. — Of the Reduction of Hypotheticals and of Syllogisms
ad impossibile.
We must not endeavour, moreover, to reduce hy- pothetical syllogisms, for we cannot reduce them, 0ur not re- from the things laid down,2 since they are not dheCt£f1gypo~ proved syllogistically, but are all of them admitted by consent. Thus if a man supposing that except there is one certain power of contraries, there will neither exist one sci- ence of them, it should afterwards be dialectically proved that there is not one * power of contraries ; for .
„ r tpi li iratra. Waltz.
instance, ol the wholesome and of the unwhole- some, for the same thing will be wholesome and unwholesome at the same time — here it will be shown that there is not one power of all contraries, but that is not a science, has not been shown. We must yet acknowledge that there is, not however by syllogism, but by hypothesis, wherefore we cannot reduce this, but that, we may, viz. that there is not one power, for this perhaps was a syllogism, but that an hy- 2 Norsyn0. pothesis. The same thing happens in the case of gisms per im-
... i • i • f • possibile.
syllogisms, which inter a consequence per impos- sibile, since neither can we analyze these, though we may a
1 Waitz states that Pacius has misapprehended this place, by following Philoponus, and avers that SiaXiytaOai here is not " disserere contra aliquid," sed " disputare de aliqua re." Pacius thinks that the chapter refers to such syllogisms as impugn the definition.
2 Ik twv KUfiivuiv. Vide Whately, book ii. ch. 4 ; also Mansel's Logic, Appendix, note G. It has been questioned whether hypothetical can be reduced to categorical ; the reader will find the subject well and fully treated in Mansel, p. 88.
168 aristotle's organon. [book i.
deduction to the impossible, (for it is demonstrated by syllo- gism.) but the other we cannot, for it is concluded from hy- pothesis. They differ nevertheless from the before-named,1 because we must in them indeed have admitted some thing previously, if we are about to consent, as if, for example, one power of contraries should have been shown, and that there was the same science of them, now here they admit, what they had not allowed previously on account of the evident falsity, as if the diameter of a square having been admitted commensurable with the side, odd things should be equal to even.
Many others also are concluded from hypothe-
3. Further con- . ,V , ., . . . .. -i \ i
sideration of sis, which it is requisite to consider, and clearly hypotheticais explain ; what then are the differences of these,
deterred. i • i
and in how many ways an hypothetical syllogism is produced, we will show hereafter;2 at present, let only so much be evident to us, that we cannot resolve such syllogisms into figures ; for what reason we have shown.
Chap. XLV. — The Reduction of Syllogisms from one Figure
to another.
* Anal i. 4 ^-s many problems* as are demonstrated in many and 26 ; Topics, figures, if they are proved in one syllogism, may be referred3 to another, e. g. a negative in the first may be referred to the second, and one in the middle to the first, still not all, but some only.4 This will appear l. Whatever from the following : if A is with no B, but B with syllogisms are every C, A is with no C, thus the first figure
proved in many . i , ./> ,, x. -. ,r
figures, may be arises; but it the negative is converted, there reduced from w[\\ be the middle, for B will be with no A, and
one tiffure to
anotner-case of with every C. In the same manner, if the syllo-
pTrticuiar u!d gism be not universal, but particular, as if A is with
the first and no B, but B is with a certain C, for the negative
gures. kejng converted there will be the middle figure.
1 i. e. from syllogisms, by hypothesis.
8 No work is extant of Aristotle's upon this subject; with St. Hilaire, however, we think that though the subject is not worked out by Aristotle, we have ample data from which to elucidate it.
3 avayayilv — vide Mansel's Appendix.
4 i. e. may be reduced, or referred.
CHAP. XLV.] THE PRIOR ANALYTICS. 169
Of syllogisms, however, in the middle figure, the 2 universal universal will be reduced to the first, but only one in the second of the particular,1 for let A be with no B, but with ""the first, but every C, then by conversion of the negative there onlv one Par_ will be the first figure, since B will be with no A, but A with every C. Now if the affirmative be added to B, and the negative to C, we must take C as the first term, since this is with no A, but A is with every B, wherefore C is with no B, neither will B be with any C, for the negative is converted. If however the syllogism be particular, when the negative is added to the major extreme, it will be reduced to the first figure, as if A is with no B, but with a certain C, for by con- version of the negative there will be the first figure, since B is with no A, but A with a certain C. When however the affirma- tive (is joined to the greater extreme), it will not be resolved, as if A is with every B, but not with every C, for the proposi- tion A B does not admit conversion,2 nor if it were made would there be a syllogism.
Again, not all in the third figure will be resolv- able into the first,3 but all in the first4 will be thethirdfigure into the third, for let A be with every B, but B with °,ne onl>- when
,./~i. ,, • -i «• ■ • tne negative is
a certain L, since then a particular affirmative is not universal, convertible, C will be with a certain B, but A was ^firs™"*16 with every B, so that there is the third figure. Also if the syllogism be negative, there will be the same result, for the particular affirmative is convertible, wherefore A will be with no B, but with a certain C. Of the syllogisms in the last figure, one alone is not resolvable into the first,5 when the negative is not placed universal, all the rest however are re- solved. For let A and B be predicated of every C, C there- fore is convertible partially to each extreme, wherefore it is present with a certain B, so that there will be the first figure, if A is with every C, but C with a certain B. And if A is with every C, but B with a certain C, the reasoning is the same,
1 Viz. Festino and not Baroko. Of these reductions it may be generally observed, that only negative syllogisms are reducible to the second, and only particular to the third figure. Barbara, Baroko, and Bokardo cannot be ostensively reduced to any other figure.
a Being A it does not admit simple conversion.
3 For Bokardo is excepted.
4 Darii and Ferio — because universals cannot be reduced to the third figure, in which the conclusion is particular. 5 i. e. Bokardo.
17C Aristotle's organon. [book t.
for B reciprocates with C. But if B is with every C, and A with a certain C, B must be taken as the first term, for B is with every C, but C with a certain A, so that B is with a certain A ; since however the particular is convertible, A will also be with a certain B. If the syllogism be negative, when the terms are universal, we must assume in like manner, for let B be with every C, but A with no C, wherefore C will be with a certain B, but A with no C, so that C will be the middle term. Likewise, if the negative is universal, but the affirmative particular, for A will be with no C, but C with a certain B ; if however the , , negative be taken as particular, there will not be
a resolution,* e. g. if B is with every C, but A not with a certain C, for by conversion of the proposition B C, both propositions will be partial.
4. The conver- It is clear then, that in order mutually to con- sum of the Yer^ these figures,1 the minor premise must be
tumor premise . & *
necessary for converted in either figure, for this being trans- posed a transition2 is effected ; of syllogisms in the middle figure,3 one is resolved,4 and the other is not5 resolved into the third, for when the universal is negative there is a resolution, for if A is with no B, but with a certain C, both similarly reciprocate with A, wherefore B is with no A, but C with a certain A, the middle then is A. When however A is with every B, and is not with a certain C, there will not be reso- lution, since neither proposition after conversion is universal. Syllogisms also of the third figure may be resolved into the middle, when the negative is universal, as if A is with no C, but B is with some or with every C, for C will be with no A, but will be with a certain B, but if the negative be particular, there will not be a resolution, since a particular negative does not admit conversion.
We see then that the same syllogisms6 are not gisms°notSmu°- resolved in these figures,7 which were not resolved tuaiiy reduci- into the first figures, and that when syllogisms
ble into the ° JO
other figures are reduced to the first figure, these only are con- intTtiie^rst0.1 eluded Per impossibile.
How therefore we must reduce syllogisms, and
1 Viz. the first and third.
2 MtrdficHng — transitus fit ex una in aliam figuram. — Buhle.
3 Those are particular, because there is no universal conclusion in tho third. 4 Festino. 5 Baroko.
6 Baroko and Bokardo. 7 In the second and third figures.
CHAP. XL VI.] THE PRIOR ANALYTICS. 171
that the figures are mutually resolvable, appears from what has been said.
Chap. XL VI. — Of the Quality and Signification of the Definite, and Indefinite, and Privative.
There is some difference in the construction or i. Difference in subversion of a problem, whether we suppose the ftate™ent aris-
,, , , . , , . r ,, ing from "not
expressions not to be this particular thing, and to be " and •« to "to be not this particular thing," have the same, tL^ea'^T^ or different signification, e. g. " not to be white," (cf- Herm. 6.) and " to be not white." Now they do not signify the same thing, neither of the expression " to be white," is the nega- tion "to be not white," but, "not to be white;" and the reason of this is as follows. The expression "he is able to walk," is similar to " he is able not to walk," the expression " it is white " to, " it is not white," and " he knows good," to " he knows what is not good." For these, " he knows good," or " he has a knowledge of good," does not at all differ, nei- ther " he is able to walk," and " he has the power of walk- ing ;" wherefore also the opposites, "he is not able to walk," and " he has not the power of walking," (do not differ from each other). If then " he has not the power of walking," signifies the same as "he has the power of not walking," these will be at one and the same time present with the same, for the same person is able to walk, and not to walk, and is cognizant of good, and of what is not good, but affirmation and negation being opposites, are not at the same time present with the same thing.1 Since therefore it is not the same thing " not to know good," and " to know what is not good," nei- ther is it the same thing to be " not good " and " not to be good," since of things having analogy,2 if the one is different the other also differs. Neither is it the same to be " not equal," and "not to be equal,"3 for to the one, namely, " to that which
1 Aristotle demonstrates the difference between infinite affirmation and finite negation by an hypothetical syllogism leading to an absurdity. The reader may find the principle of proper logical affirmation and negation discussed in Whately, b. ii. ch. 2, and Hill, p. 96, et seq.
2 Eandem rationem. — Buhle. Similitude or identity of relation.
3 For "to be not equal " implies at all events that a thing exists, which is affirmation, but "not to be equal" may be nothing, which is pure negation. Hence, as Taylor remarks, Aristotle infers that " not every
172 Aristotle's organon. [book i.
is not equal," something is subjected, and this is the unequal, but to the other there is nothing subjected, wherefore " not every thing is equal or unequal," but " every thing is equal or not equal." Besides this expression, " it is not white wood," and this, " not is white wood," are not present toge- ther at the same time, for if it is "wood not white," it will be wood ; but " what is not white wood " is not of necessity "wood," so that it is clear that of "it is good" the negation is not "it is not good." If then of every one thing either the affirm- ation or negation is true, if there is not negation, it is evident that there will in some way be affirmation, but of every affirm- ation there is negation, and hence of this * the negation is, "it is not not good." They have this order indeed with respect 2. order of af- to eacn other: let to be good be A, not to be rirmation and good B, to be not good C under B, not to be not good D under A. With every individual then either A or B will be present, and (each) with nothing which is the same and C or D with every individual,2 and with nothing which is the same, and with whatever C is present, B must necessarily be present with every individual, for if it is true to say that " a thing is not white," it is also true to say that " not it is white," for a thing cannot at one and the same time be white and not white, or be wood not white and be white wood, so that unless there is affirmation, negation will be present. — C however is not always (consequent) to B, for in short, what is not wood will not be white wood, on the contrary, with whatever A is present D also is present with „ c every individual, for either C or D will be pre-
sent. As however "to be not white"* and "to be white," f cannot possibly co-subsist, D will be present, for of what is white we may truly say, that it is not not white, yet A is not predicated of every D, for, in short, we can- not truly predicate A of what is not wood, namely, to assert that it is white wood, so that D will be true, and A will not be true, namely, that it is white wood. It appears also, that A and C are present with nothing identical, though B and D may be present with the same.
thing" is equal or unequal, because that which is not is neither equai nor unequal ; but that " every thing " is equal or is not equal," because this is contradiction.
1 " It is not good : " — affirmative. 2 Taylor omits this clause.
CHAP. XL VI.]
THE PRIOR ANALYTICS.
173
Privatives also subsist similarly to this position „ _ ,
. , ., i /• i ii» 3- Relation be-
with respect to attributes,1 lor let equal be A, not tween (& aT„- equal B, unequal C, not unequal D. In many ^Tind'attri- things also, with some of which the same thing is butes (kut^o- present and not with others, the negative may be p similarly true, that, " not all things are white," or " that not each thing is white ; " but, " that each thing is not white," or, " that all things are not white," is false. So also of this affirmation, " every animal is white," the negation is not, "every animal is not white," for both are false, but this, " not every animal is white." Since however it is clear that " is not white," signifies something different from " not is white," and that one is affirmation and the other negation, it is also clear that there is not the same mode of demonstrating each, for example,2 " whatever is an animal is not white," or " happens not to be white ;" and that we may truly say, "it is not white," for this is " to be not white." Still there is the same mode as to it is true to say it is white or not white, for both are demonstrated constructively* through * KaTa<TKeVaa- the first figure, since the word "true" is similarly T«*ac, "con-
... n structivc,
arranged with " is," for of the assertion " it is Averr. " con- true to say it is white," the negation is not, " it is Buhk'^' true to say it is not white," but " it is not true to ' T»e differ- say it is white." But if it is true to say, "whatever is a man is a3 musician, or is not4 a musician," we must assume that " whatever is an in"the"mo<ie oi animal is either a musician or is not a musician,"5 demonstratIon and it Avill be demonstrated, but that " whatever + v***™™-
..,,., , , TiKus, "de-
ls a man is not a musician, is shown negatively J structure."
according to the three modes6 stated. Averrois.
In short, when A and B are so, as that they 5. Relative
cannot be simultaneously in the same thing, but provt-d^n'cer-
one of them is necessarily present to every indi- tain eases-
enceof the cha- racter of asser- tion shown by the difference
1 Karriyopiai— predicamenta. Averrois. The word must here be under- stood as opposed to privation in the sense of " habits," not as a species of quality, as it is considered in the Categor. eh. 8.
'* We cannot demonstrate the two assertions given, in the same way.
3 An universal tiniie affirmative.
* An universal indefinite affirmative.
5 This is the major premise, to which if the minor, animal," is added, the syllogism will be in Barbara.
' Viz. Celarent, Cesare, Camestres.
every man is an
174 Aristotle's organon. [book i.
vidual, and again C and D likewise, lut A follows C and does not reciprocate, D will also follow B, and will not reciprocate, and A and D may be with the same thing, but B and C cannot. In the first place then, it appears from this that D is consequent to B, for since one of C D is necessarily present with every individual, but with what B is present C cannot be, because it introduces with itself A, but A and B cannot consist with the same, D is evidently a consequent. Again, since C does not reciprocate with A, but C or D is present with every, it happens that A and D will be with the same thing, but B and C cannot, because A is consequent to
C, for an impossibility results,1 wherefore it appears plain that neither does B reciprocate with D, because it would hap- pen that A is present together with D.2
6. Fallacy Sometimes also it occurs that we are deceived
arising from Dy sucn an arrangement of terms, because of our
not assuming J .o . „ , .
opposites pro- not taking opposites rightly, one of which must perly- necessarily be with every individual, as if A and B
cannot be simultaneously with the same, but it is necessary that the one should be with what the other is not, and again C and D in like manner, but A is consequent to every C ; for B will hap- pen necessarily to be with that with which D is, which is false. For let the negative of A B which is F be assumed, and again the negative of C D, and let it be H, it is necessary then, that either A or F should be with every individual, since either af- firmation or negation must be present. Again also, either C or H, for they are affirmation and negation, and A is by hy- pothesis present with every thing with which C is, so that H will also be present with whatever F is. Again, since of F B, one is with every individual, and so also one of H D, and H is consequent to F, B will also be consequent to D, for this we know. If then A is consequent to C, B will also follow
D, but this is false, since the sequence was the reverse in things so subsisting, for it is not perhaps necessary that either A or F should be with every individual, neither F nor B, for F is not the negative of A, since of " good" the negation is " not good," and " it is not good" is not the same with " it is neither good nor not good." It is the same also of C D, for the as- sumed negatives are two.
' i. e. A and B would co-subsist.
2 Because A cannot be present with B.
CHAP. I.] THE PRIOR ANALYTICS. 175
BOOK II ,
Chap. I. — Recapitulation. — Of the Conclusions of certain
Syllogisms.
In how many figures, through what kind and i. Reference to number of propositions, also when and how a syl- observations, logism is produced, we have therefore now ex- Universal syl-
,°. r , . , , logisms infer
plained ; moreover, what points both the con- many conciu- structor and subverter of a syllogism should slons' regard, as well as how we should investigate a proposed sub- ject after every method ; further, in what manner we should assume the principles of each question. Since, 2. so also do however, some syllogisms are universal, but particular af-
' ii-ii • formative, but
others particular, all the universal always con- not the nega- clude a greater number of things, yet of the par- tive Particular- ticular, those which are affirmative many things, but the negative one conclusion only. For other propositions are con- verted, but the negative is not converted, but the conclusion is something of somewhat ; hence other syllogisms conclude a majority of things, for example, if A is shown to be with every or with a certain B, B must also necessarily be with a certain A, and if A is shown to be with no B, B will also be with no A, and this is different from the former. If however A is not with a cer- tain B, B need not be not present with a certain A, for it possibly may be with every A.1 This then is the common „ ^.„
> ii • i i ^- D'flerence
cause or all syllogisms, both universal and par- between uni- ticular ; we may however speak differently of fir^and'tiiose universals, for as to whatever things are under ofthesesond the middle, or under the conclusion, of all there will be the same syllogism, if some are placed in the middle, but others in the conclusion,2 as, if A B is a conclusion through C, it is necessary that A should be predicated of whatever is
1 As if A -were " man ; " a " certain animal," a certain B ; and animal, B ; therefore though " man" is not present with " a certain animal," (e. g. "a lion,") yet "animal " is with every "man."
2 Hence three conclusions, he means, may be drawn from the same syllogism, one of the minor extreme, another of what is under the minor and the third of what is the subject of the middle.
176 Aristotle's obganon. [book ii.
under B or C, for if D is in the whole of B, but B in the whole of A, D will also be in the whole of A. Again, if E is in the whole of C, and C is in A, E will also be in the whole of A, and in like manner if the syllogism be negative ; but in the second figure it will be only possible to form a syllogism of that which is under the conclusion. As, if A is with no B, but is with every C, the conclusion will be that B is with no C ; if therefore D is under C, it is clear that B is not with it, but that it is not with things under A, does not appear by the syllogism, though it will not be with E, if it is under A. But it has been shown by the syllogism that B is with no C, but it was as- sumed without demonstration1 that it is not with A, wherefore n does not result by the syllogisms that B is not with E. Nevertheless in particular syllogisms of things under the con- clusion, there is no necessity incident, for a syllogism is not • ^P6ra<r^.) Produced,2 when this* is assumed as particular,
JT4re 'n Ist but there wil1 be of> a11 tIlings under the middle, yet not by that syllogism, e. g. if A is with every B, but B with a certain C, there will be no syllogism of what is placed under C, but there will be of what is under B, yet not through the antecedent syllogism. Similarly also in the case of the other figures, for there will be no conclusion of what is under the conclusion, but there will be of the other, yet not through that syllogism ; in the same manner, as in universals, from an undemonstrated proposition, things under the middle were shown, wherefore either there will not be a conclusion there,3 or there will be in these also.4
Chap. II. — On a true Conclusion deduced from false Premises in the
first Figure.
tnuhlrfeLuy It is tnerefore possible that the propositions may
of propositions, be true, through which a syllogism arises, also
byThV^ncfu- that tne7 may be false> also that one may be true
sion. and the other false ; but the conclusion must of
1 A being assumed of no B, B is in a manner assumed of no A, be- cause a proposition universal negative reciprocates.
a Because in the 2nd figure both propositions affirm ; hence nothing is concluded.
3 In universal syllogisms.
4 In particular. For the recognition of the indirect modes, in this chapter, by Aristotle, see Mans?!, p. 66, and 74, note.
CHAP. II.] THE PRIOR ANALYTICS. 177
necessity be either true or false. From true propositions then we cannot infer a falsity, but from false premises
we may infer the truth, except that not the why* *T""»non°X*
but the mere that (is inferred), since there is not propter quid
a syllogism of the why from false premises, and Averr. (kill's
for what reason shall be told hereafter.1 Logic' p- 287->
First then, that we cannot infer the false from
true premises, appears from this : if when A is, it fn^h^ue
is necessary that B should be, when B is not it from false pre-
is necessary that A is not, if therefore A is true, thefeW^rom
B is necessarily true, or the same thing: (A) would *rue Prt;m;s,es-
J a • Prool — (Vide
at one and the same time be and not be,2 which Aidrich.genera! is impossible. Neither must it be thought, be- ^l^?tsyll°' cause one term, A, is taken, that from one certain thing existing, it will happen that something will result from necessity, since this is not possible, for what results from necessity is the conclusion, and the fewest things through which this arises are three terms, but two in- tervals and propositions. If then it is true that with whatever B is A also is, and that with whatever C is B is, it is necessary that with whatever C is A also is, and this cannot be false, for else the same thing would exist and not exist at the same time. Wherefore A is laid down as one thing, the two propositions being co-assumed. It is the same also in negatives, for we cannot show the false from what are true ; but from false propositions we may collect the truth,3 either when both premises are false, or one only, and this not indifferently, but the minor, if it comprehend the whole false,4 but if the whole is not assumed to be false, the true may be collected from either.f Now let A be sumed fell?, with the whole of C, but with no B, nor B with C,
1 In ch. 2 of 1st book, Post Anal.
- Because it is true by hypothesis, but B being denied true, A cannot be true.
3 See the general rules of syllogism in Aldrich, and Hill's Logic. Hereafter Aristotle expounds this more fully ; he means that a true con- clusion may always be inferred in the first figure, unless the major is wholly false, and the minor true.
* By this expression he means, as he explains further on, an universal proposition, contrary to the true, as " no man is an animal." An universal contradictory to the true is of course a particular false proposition, (vide table of opposition, ) and a proposition is said to be false in part, when what is partly true and partly false, is affirmed, or denied, universally.
w
178 aristotle's organon. [book ii.
and this may happen to be the case, as ankaal is with no stone,
nor stone present with any man, if then A is assumed present
with every B, and B with every C, A will be with every C,
so that from propositions both false, the conclusion
* Example (1.) ... , r . L . • 1 *
will be true, since every man is an animal.* So also a negative conclusion (is attained), for neither A may be assumed, nor B present with any C, but let A be with every B, for example, as if, the same terms being taken, man was placed in the middle, for neither animal nor man is with any stone, but animal is
4 Man *
X Aniniai. with every man. Wherefore if with whatf it jis , v present universally, it is assumed to be present with
§ In the major. 1 J\ . 5
none,§ but with what it is not present, we assume II in the minor. t^at -j. -g present -with every individual, || from
s Example (2.) both these false premises, there will be a true con • 4 clusion.^f The same may be shown if each pre-
mise is assumed partly false, but if only one is admitted false, if the major is wholly false, as A B, there will not be a true conclusion, but if B C, (the minor is wholly 3. instance of false,) there will be (a true conclusion). Now I afaise propo- mean by a proposition wholly false that which is contrary (to the true), as if that was assumed pre- sent with every, which is present with none, or that present with none, which is present with every. For let A be with no B, but B with every C, if then we take the proposition B
Ex. 1. Every stone is an animal B A
Every man is a stone Ex. 3. Every animai is a stone
Every man is an animal. C B
Ex. 2. No man is an animal Every man is an animal
Every stone is a man C A
. • . No stone is an animal. . " . Every man is a stone.
B A
Ex. 4. Every thing white is an animal C B
Every swan is white C A
. • . Every swan is an animal.
B A
Ex. 5. Nothing white is an animal C B
All snow is white C A
. " . No snow is an animal.
chap, n.]
THE PRIOR ANALYTICS.
179
* Example (3.)
5.
C as true, but the whole of A B as false, and that A is with every B, it is impossible for the conclusion to be true, for it was present with no C, since A was present with none of what B was present with, but B was with every C*
In like manner also the conclusion will be false, if A is with every B, and B with every C, and the proposition B C is assumed true, but A B wholly false, and that A is present with no individual with which B is, for A will be with every C, since with whatever B is, A also is, but B is with every C. It is clear then, that, the major premise beingassumed wholly false, whether it be affirmative or negative, but the other pre- mise being true, there is not a true conclusion ; if however the whole is not assumed false, there will be. For if A is with every C, but with a cer- tain B, and B is with every C ; e. g. animal with every swan, but with a certain whiteness, and w like- ness with every swan, if A is assumed present with every B, and B with every C, A will also be truly present with every C, since every swan is an animal, "j"
So also if A B be negative, for A concurs with a certain B, but with no C, and B with every C, as animal with something white, but with no whiteness with all snow ; if then A is assumed present with no B, but B with every C, A will be present t Example (5 ) with no C. ~\.
If however the proposition A B were assumed 5 If the major wholly true, but B C wholly false, there will be a is true wholly,
. 11 • l ,i • * n i • but the minor
true syllogism,1 as nothing prevents A irom being wholly false, with every B and every C, and yet B with no C, as ^conclusion is the case with species of the same genus, which
4. When the major is wholly false, but the minor is true, the conclusion is false ; but when the whole is not false, the conclusion is true. Affirmative.
t Example (4.) 2. Negative.
snow, and
1 Here is another instance of " syllogism " being employed in its pure sense, equivalent to " conclusion," frequently it signifies the propositional arrangement necessarily inferring the conclusion.
B A
Ex. 6. Every horse is an animal C B
Every man is a horse C A
. '. Every man is an animal.
B A
Ex. 7. No music is an animal C ' B
All medicine is music C A
. • . No medicine is an animal.
N 2
180 aristotle's organon. [book ii.
are not subaltern, for animal concurs both with horse and man. but horse with no man ; if therefore A is assumed pre- 1 Affirmative. sent w^n eveiT B, and B with every C, the con- clusion will be true, though the whole proposition B C is false.* It will be the same, if the propo- sition A B is negative. For it will happen that A will be neither with any B, nor with any C, and that B is with no C, as genus to those species which are from another genus, for animal neither concurs with music nor with medicine, nor music with medicine : if then A is assumed present with no j . B, but B with every C, the conclusion will be true.f Now if the proposition B C is not wholly but partially false, even thus the conclusion will be true. For nothing prevents A from concurring with the whole of B, and the whole of C, and B with a certain C, as genus with species and difference, thus animal is with every man and with every pedestrian, but man concurs with something, and not with every thing pedestrian : if then A is assumed pre- , „ . ,„ , sent with every B, and B with every C, A will also be present with every u,| which will be true.
B A
Ex. 8. Every man is an animal
C B
Every pedestrian thing is a man B A
. • . Every pedestrian thing is an animal.
B A
Ex. 9. No prudence is an animal
C B
All contemplative knowledge is prudence C A
. • . No contemplative knowledge is an animal.
B A
Ex. 10. All snow is an animal C B
Something white is snow C A
. • . Something white is an animal.
B A
Ex. 11> No man is an animal
C B
Something white is a man
C A
. • , Something white is not an animal.
CHAP. II.] THE PRIOR ANALYTICS. 181
The same will occur if the proposition A B be 2 Negaive negative. For A may happen to be neither with any B, nor with any C, yet B with a certain C, as genus with the species and difference which are from another genus. Thus animal is neither present with any prudence nor with any thing contemplative, but prudence is with something contemplative ; if then A is assumed present with no B, but B with every C, A will be with no C, which will . Example(9 } be true.*
In particular syllogisms however, when the whole of the major premise is false, but the other lars with ama. true, the conclusion may be true ; also when the ^^y^"1 a major A B is partly false, but B C (the minor) there may he wholly true ; and when A B the major is true, ^rnue conclu' but the particular false, also when both are false. For there is nothing to prevent A from concurring with no B, but with a certain C, and also to prevent B from being present with a certain C, as animal is with no } Affirmative. snow, but is with something white, and snow with something white. If then snow is taken as the middle, and animal as the first term, and if A is assumed present with the whole of B, but B with a certain C, the whole proposition A B will be false, but B C true, also the conclu- f Examp]e(10 } sion will be true.j
It will happen also the same, if the proposition A B is ne- gative, since A may possibly be with the whole of B, and not with a certain C, but B may be with a certain C. 2 Neg8tive Thus animal is with every man, but is not conse- quent to something white, but man is present with something white ; hence if man be placed as the middle term, and A is assumed present with no B, but B with a certain C, the con- clusion will be true, though the whole proposition ^ Example(11>) A B is false.!
If again the proposition A B be partly false,1 7. if the major
1 Taylor and Buhle insert, " when B C is true," which is omitted by Waitz and Averrois.
B A
Ex. 12. Every thing beautiful is an animal C B
Something great is beautiful C A
. • . Something great is an animal.
182 Aristotle's organon. [book n.
is partly false, the conclusion will be true. For nothing hinders the conclusion j± from concurring with B, and with a certain C,
will be true. , t» p , . ° . , • r-i i ,
and Jb troni being with a certain b ; thus animal may be with something beautiful, and with something great,1 , ._ .. and beauty also may be with something great. If
1. Affirmative. . . J J ° to
then A is taken as present with every B, and B
with a certain C, the proposition A B will be partly false ;
but B C will be true, and the conclusion will
* Example (12.) . o,
be true.*
2. Negative. Likewise if the proposition A B is negative,
for there will be the same terms, and placed in the same manner for demonstration. f minor~JfariseUe' Again, if A B be true, but B C false, the conclusion will be true, since nothing prevents A from being with the whole of B, and with a certain C, and B from being with no C. Thus animal is with every swan, and with something black, but a swan with nothing black ; hence, if A is assumed present with every B, and B with a cer- + _ : ... . tain C, the conclusion will be true, though B C
t Example (14.) . ' 'to
is false. J
B A
Ex. 13. Nothing beautiful is an animal C B
Something great is beautiful
C A
. • . Something great is not an animal. 1 i. e. to prove a true conclusion from premises, one partly false, and the other true.
B A
Ex. 14. Every swan is an animal C B
Something black is a swan C A
. ' . Something black is an animal. B A
Ex. 15. No number is an animal C B
Something white is number
C A
. ' . Something white is not an animal. B A
Ex. 16. Every thing white is an animal C B
Something black is white B A
. ' . Something black is an animal.
CHAP. II.] THE PRIOR AXALYTICS. 183
Likewise if the proposition A B be taken as 4. Maju: nega- negative, for A may be with no B, and may not be tive" with a certain C, yet B may be with no C. Thus genus may be present with species, which belongs to another genus, and with an accident, to its own species, for animal indeed concurs with no number, and is with something white, but number is with nothing white. If then number be placed as the mid- dle, and A is assumed present with no B, but B with a certain C, A will not be with a certain C, which would be true, and the proposition A B is true, but B C
n 1 # * Example (15.)
Also if A B is partly false, and the proposition minorwhoiiyV B C is also false, the conclusion will be true, for false- nothing prevents A from being present with a certain B, and also a certain C, but B with no C, as if B should be contrary to C, and both accidents of the same genus, for animal is with a certain white thing, and with a certain black thing, but white is with nothing black. If then A is assumed present with every B, and B with a certain C, the con-
. . .Ju , ' , t Example (16.)
elusion will be true.j
Likewise if the proposition A B is taken nega- 6 Ne ative tively, for there are the same terms, and they will be similarly placed for demonstration. J ' t Example (1 7.)
If also both are false, the conclusion will be 7 Both false true, since A may be with no B, but yet with a
1 To prove a true conclusion may be drawn from false premises.
B A
Ex. 17. Nothing white is an animal C B
Something black is white
C A
. • . Something black is not an animal. B A
I5x. IS. Every number is an animal C B
Something white is number C A
• . Something white is an animal.
B A
Ex 19. No swan is an animal
C B
Something black is a swan
C A
. • . Something black is not an arums!.
184 ARISTOTLE'S ORGANON. [BOOK II.
certain C, but B with no C, as genus with species of another genus, and with an accident of its own species, for animal is with no number, but with something white, and number with nothing white. If then A is assumed present with every B, and B with a certain C, the conclusion indeed will
* Example (18.) . , .. , , . . .,,„„,.«
be true, while both the premises will be false.* tiveIaJ°r "ega" Likewise if A B is negative, for nothing pre- vents A from being with the whole of B, and from not being with a certain C, and B from being with no C, thus animal is with every swan, but is not with something black, swan however is with nothing black. Wherefore, if A is assumed present with no B, but B with a certain C, A .„ . ,.„, is not with a certain C, and the conclusion will
t Example (19.) , . , . '
be true, but the premises false.y1
Chap. Ill — The same in the middle Figure.
i in this In tlie middle figure it is altogether possible to
figure we ma; infer truth from false premises, whether both are fromSmisTs, ass"med wholly false, or one partly, or one true, either one or but the other wholly false, whichever of them is partian/false' place(l false, or whether both are partly false, or
one is simply true, but the other partly false, or one is whclly false, but the other partly true, and as well in i. universais. universal as in particular syllogisms. For if A
is with noB but with every C, as animal is with no stone but with every horse, if the propositions are placed con- trariwise, and A is assumed present with every B, but with
no C, from premises wholly false, the conclusion
xampie (i.) w^\ be true j Likewise if A is with every B but
§ Example (2.) with no C, for the syllogism will be the same.§ *
1 Vide Waitz, vol. i. pp. 483 and 487.
B A B A
Ex. 1. Every stone is an animal Ex. 2. No horse is an animal C A C A
No horse is an animal Every stone is an animal
C B C B
. • . No horse is a stone. . ■ . No stone is a horse.
2 One of these syllogisms is in Cesare, but the other in Camestres : yet both are similar in respect of being produced by the same terms ; proving the truth from false premises, and deducing almost the same conclusion.
CnAP. Ill/ THE PRIOR ANALYTICS. 185
Again, if the one is wholly false, but the other 2 0ne whol]y wholly true, since nothing prevents A from being false, the other with every B and with every C, but B with no C, as genus with species not subaltern, for animal is with every horse and with every man, and no man is a horse. If then it is assumed to be with every individual of the one, but with none of the other, the one proposition will be wholly false, but the other wholly true, and the conclu- sion will be true to whichever proposition the * Example (3.) negative is added.1* Also if the one is partly 3 one partly false, but the other wholly true, for A may possibly false- be with a certain B and with every C, but B with no C, as ani- mal is with something white, but with every crow, and white- ness with no crow. If then A is assumed to be present with no B, but with the whole of C, the proposition A B will be partly false, but A C wholly true, and the conclusion t Example (4.) will be true, f Likewise when the negative is 4. Minor or transposed,2 since the demonstration is by the negative.
1 i. e. whether the major or minor premise is negative.
B A B A
Ex. 3. Every horse is an animal No horse is an animal
C A C A
No man is an animal Every man is an animal
C B C B
. • . No man is a horse. . ' . No man is a horse.
B A
Ex. 4. Nothing white is an animal C A
Every crow is an animal C B
. ' . No crow is white.
* If the minor premise denies.
B A B A
Ex. 5. Every crow is an animal Ex. 6. Every thing white is an animal C A C A
Nothing white is an animal No pitch is an animal
C B C B
. • . Nothing white is a crow. . ■ . No pitch is white.
B A
Ex. 7. Every thing white is an animal C A
Nothing black is an animal C B
. • . Nothing black is white.
186 Aristotle's organon. [book ii.
• Example (5). same terms.* Also if the affirmative premise is
5. Affirmative partly false, but the negative wholly true, for no-
thing prevents A being present with a certain B, but not present with the whole of C, and B being present with no C, as animal is with something white, but with no pitch, and whiteness with no pitch. Hence if A is assumed present with the whole of B, but with no C, A B is partly false, but A C t Example (6.) wholly true, also the conclusion will be true.f
6. Eoth partly Also if both propositions are partly false, the con-
clusion will be true, since A may concur with a cer-
B A
Ex. 8. Nothing white is can animal C A
Every thing black is an animal C B
. • . Nothing black is white.
B A
Ex. 9. No man is an animal
C A
Something white is an animal C B
. * . Something white is not a man.
B A
Ex. 10. Every thing inanimate is an animal C A
Something white is not an animal C B
. " . Something white is not inanimate. B A
Ex. 11. No number is an animal
C A
Something inanimate is an animal C B
. * . Something inanimate is not number. B A
Ex. 12. Every man is an animal
C A
Something pedestrian is not an animal C B
. • . Something pedestrian is not a man.
B A
Ex. 13. Every science is an animal C A
A certain man is not an animal C B
• • . A certain man is not science
CHAP. III.] THE PRIOR ANALYTICS. 187
tain B, and with a certain C, but B with no C, as animal may be with something white, and with something black, but white- ness with nothing black. If then A is assumed present with every B, but with no C, both premises are partly false, but the conclusion will be true.* Likewise * ExamPle(7-) when the negative istransposedbythesameterms.f t Example (8.)
This is evident also as to particular syllogisms, since nothing hinders A from being with every
B, but with a certain C, and B from not being with a certain
C, as animal is with every man, and with something white, yet man may not concur with something white. If then A is assumed present with no B, but with a certain C, 1. Major nega- the universal premise will be wholly false, but the tive' particular true, and the conclusion true.} Like- * Example (9.) wise if the proposition A B is taken affirmative, affirmative for A may be with no B, and may not be with a
certain C,§ and B not present with a certain omitted by C ; thus animal is with nothing inanimate, but Ta>'lor- with something white, and the inanimate will not be present with something white. If then A is assumed present with every B, but not present with a certain C, the universal pre- mise A B will be wholly false, but A C true, and the con- clusion true. || Also if the universal be taken true, y Example (io.) but the particular false, since nothing prevents A 3. Univ. true, from being neither consequent to any B nor to par any C, and B from not being with a certain C, as animal is consequent to no number, and to nothing inanimate, and num- ber is not consequent to a certain inanimate thing. If then A is assumed present with no B, but with a certain C, the con- clusion will be true, also the universal proposition, but the particular will be false.^f Likewise if the uni- am versal proposition be taken affirmatively, since A may be with the whole of B and with the whole of C, yet B not be consequent to a certain C, as genus to species and difference, for animal is consequent to every man, and to the whole of what is pedestrian, but man is not (consequent) to every pedestrian. Hence if A is assumed present with the whole of B, but not with a certain C, the universal pro- position will be true, but the particular false, and _ , , ,
, , . l • Example; 12.,
the conclusion true.
188 Aristotle's organon. [book ii.
Moreover it is evident that from premises both 5. case of both fajge there will be a true conclusion, if A happens to be present with the whole of B and of C, but B to be not consequent to a certain C, for if A is assumed present with no B, but with a certain C, both propositions are false, but the conclusion will be true. In like manner when the universal premise is affirmative, but the particular negative, since A may follow no B, but every C, and B may not be present with a certain C, as animal is consequent to no science, but to every man, but science to no man. If then A is assumed present with the whole of B, and not conse- quent to a certain C, the premises will be false, xam but the conclusion will be true.*
Chap. IV. — Similar Observations upon a true Conclusion from false Premises in the third Figure.
There will also be a conclusion from false pre- gameaTwith mises in the last figure, as well when both are the preceding fa]se an(j either partly false or one wholly true,
tiffurcs. ■ * wf *
but the other false, or when one is partly false, and the other wholly true, or vice versa, in fact in as many ways as it is possible to change the propositions. For there is nothing to prevent either A or B being present with any C, l. Both univ. but yet A may be with a certain B ; * thus neither affirm. man, nor pedestrian, is consequent to any thing in-
1 Taylor has made a mistake here both in the letters and in this and the succeeding syllogistic example. I have followed Waitz, Buhle, Averrois, and Bekker; for the general rules to which these chapters refer, the reader may find the subject fully treated in Whately and Hill.
C A
Ex. 1. Every thing inanimate is a man. C B
Every thing inanimate is pedestrian B A
. ' . Something pedestrian is a man. C A
Ex. 2. No swan is an animal C B
Every swan is black
B A
. * . Something black is not an animal.
CHAP. IV.] THE PRIOR ANALYTICS. 189
animate, yet man consists with something pedestrian. If then A and B are assumed present with every C, the propositions indeed will be wholly false, but the conclusion * Example (i.) true.* Likewise also if one premise is negative, 2. onenega- but the other affirmative, for B possibly is present tive with no C but A with every C, and A may not be with a certain
B. Thus blackness consists with no swan, but animal with every swan, and animal is not present with every thing black. Hence, if B is assumed present with every C, but A with no
C, A will not be present with a certain B, and the conclusion will be true, but the premises false. f If, how- t Example (2.) ever, each is partly false, there will be a true con- 3. One partly elusion, for nothing prevents A and B being pre- false'
sent with a certain C, and A with a certain B, as whiteness and beauty are consistent with a certain animal, and white- ness is with something beautiful, if then it is laid down that A and B are with every C, the premises will indeed be partly false, but the conclusion true.J Likewise if A C j Example (3.) is taken as negative, for nothing prevents A not consisting with a certain C, but B consisting with *■ Nesative»-
C A
Ex. 3. Every animal is white C B
Every animal is beautiful B A
. * . Something beautiful is white.
C A
Ex. 4. No animal is white G B
No animal is beautiful
B A
. ' . Something beautiful is not white.
C A
Ex. 5. No swan is an animal C B
Every swan is white
B A
. • . Something white is not an animaL
C A
Ex. 6. No swan is black
C B
Every swan is inanimate
B A
. ' . Something inanimate is not black.
190 amstotle's org anon. [book n.
a certain C, and A not consisting with every B as whiteness is not present with a certain animal, but beauty is with some one, and whiteness is not with every thing beautiful, so that if A is assumed present with no C, but B with every C, both premises will be partly false, but the conclusion will be » Example (4.) true-* Likewise, if one premise be assumed 5. one wholly wholly false, but the other wholly true, for both false, the other A and B may follow every C, but A not be with
a certain B, as animal and whiteness follow every swan, yet animal is not with every thing white. These terms therefore being laid down, if B be assumed present with the whole of C, but A not with the whole of it, B C will be wholly
true, and A C wholly false, and the conclusion will
t Example (5.) be ^ j g() ^ .f fi Q .g ^ ^ A Q ^^ ^
6- there are the same terms for demonstration, black,
t Example (6.) swan, inanimate.1 J Also even if both premises r. Both affirm. are assumed affirmative, since nothing prevents B following every C, but A not wholly being pre- sent with it, also A may be with a certain B, as animal is
1 i. e. to deduce a true conclusion from false premises. C A
Ex. 7. Every swan is black C B
Every swan is an animal B A
. " . Some animal is black.
C A
Ex. 8. Every swan is an animal C B
Every swan is black
B A
. • . Something black is an animal. C A
Ex. 9. Every man is beautiful C B
Every man is a biped B A
. • . Some biped is beautiful.
C A
Ex. 10. Every man is a biped C B
Every man is beautiful
B a
Something beautiful is a biped.
CHAP. IV.] THE PRIOR ANALYTICS. 191
with every swan, black with no swan, and black with a cer- tain animal. Hence if A and B are assumed present with every C, B C will be wbolly true, but A C wholly false, and the conclusion will be true.* Similarly, again, if . Example c ) A C is assumed true, for the demonstration will be through the same terms.j Again, if one is f ExamPIe (»•) wholly true, but the other partly false, since B may be with every C, but A with a certain C, also A with a certain B, as biped is with every man, but beauty not with every man, and beauty with a certain biped. If then A and B are assumed present with the whole of C, the proposition B C is wholly true, but A C partly false, the conclusion will also be true.| Likewise, if A C is assumed true, and B j Example (9.) C partly false, for by transposition of the same 8. terms,1 there will be a demonstration^ Again, if §Exampie(io.) one is negative and the other affirmative, for since B may possibly be with the whole of C, but A with a certain C, when the terms are thus, A will not be with every B. If B is as- sumed present with the whole of C, but A with none, the negative is partly false, but the other wholly true, the con- clusion will also be true. Moreover, since it has been shown that A being present with no 0, but B with a certain C, it is possible that A may not be with a certain B, it is clear that when A C is wholly true, but B C partly false, the conclusion may be true, for if A is assumed present with no C, but B with every C, A C is wholly true, but B C partly false.
Nevertheless, it appears that there will be alto- gether a true conclusion by false premises, in the foUowt^same case also of particular syllogisms. For the same TXi}e' '• e- those
, , ii • with one uni-
terms must be taken, as when the premises were versa] and one universal, namely, in affirmative propositions, af- n^SeCUlarpre" Urinative terms, but in negative propositions, nega- tive terms, for there is no difference2 whether when a thing consists with no individual, we assume it present with every,3 or being present with a certain one, we assume it present uni-
1 In these two last examples, the greater and less extremes change places, yet a true conclusion is deduced.
3 i. e. things assumed in particular, do not differ from the same things assumed in universal syllogisms.
1 i. e. entirely false.
192 aristotle's organox. [book 11.
„ ,, versally,1 as far as regards the setting out of the
3. Alsonega- J ' ° . ° .
thes. terms \l the like also happens in negatives. We
ciuswnlsT'lse see tnen tnat ^ tne conclusion is false, those things
there must be from which the reasoning proceeds, must either
or inoreDof the all or some of them be false ; but when it (the
premises— but conclusion) is true, that there is no necessity,
this does not ' '. . . J
hold good vice either that a certain thing, or that all things, ofthta.ReaS°n should be true; but that it is possible, when nothing in the syllogism is true, the conclusion should, nevertheless, be true, yet not of necessity. The reason of this however is, that when two things3 so sub- sist with relation to each other, that the existence of the one necessarily follows from that of the other, if the one4 does not exist, neither will the other be,5 but if it6 exists that it is not necessary that the other7 should be. If however the same thing8 exists, and does not exist, it is impossible that there should of necessity be the same (consequent);9 I mean, as if A being white, B should necessarily be great, and A not be- ing white, that B is necessarily great, for when this thing A being white, it is necessary that this thing B should be great, but B being great, C is not white, if A is white, it is neces- sary that C should not be white. Also when there are two things,10 if one is,11 the other 12 must necessarily be, but this not
1 i. e. partly false.
2 That is, the terms being proposed, it may be shown, that we can de- duce a true inference from false premises.
3 i. e. antecedent and consequent. * The consequent.
5 The antecedent. It is valid to argue from the subversion of the con- sequent, the subversion of the antecedent ; thus if man is, animal is, but animal is not, therefore man is not.
6 The consequent.
7 The antecedent. It is not necessary that this should exist, because an inference of the existence of the antecedent from that of the conse- quent is invalid.
8 The antecedent.
9 Because we cannot collect the consequent from the affirmation or negation of the antecedent; as, if man is, animal is; and if man is not, animal is.
10 That is, two subject terms, as A and B. He now enunciates that an argument from the negative of the consequent to the negative of the ante- cedent is valid. Buhle and Waitz read this passage differently to Taylor, by the insertion of the letter merely.
11 That is, the antecedent. ,2 The consequent.
CHAP. V.j THE PRIOR ANALYTICS. 193
existing, it is necessary that A* should not be, „ (Illud , thus B not being great, it is impossible that A Buhie. i. e.the should be white.
But if* when A is not white, it is necessary that B should be great, it will necessarily happen that B not being great, B itself is great, which is impossible. For if B is not great, A will not be necessarily white, and if A not being white, B should be great, it results, as through three
r* \ *i Z-CTl- 4. \ •<■ ■ * + t Example (11.;
(terms), that it B is not great, it is great. j
Chap. V. — Of Demonstration in a Circle, in the first Figure.1
The demonstration of things in a circle, and from _ . . each other, is by the conclusion, and by taking this kind of de- one proposition converse in predication, to con- "^^'X- elude the other, which Ave had taken in a former syllogism. As if it were recpiired to show that A is with every 0, we should have proved it through B ;2 again,3 if a person should show that A is with B, assuming A present with C, but C with B, and A with B ; first, on the contrary, he as- sumed B present with C. Or if it is necessary to demonstrate that B is with C,4 if he should have taken A (as predicated ) of C, which was the conclusion,5 but B to be present with A, for it was first assumed6 conversely, that A was with B. It is not however possible in any other manner to demonstrale them from each other, for whether another middle7 is taken, there will not be (a demonstration) in a circle, since nothing is assumed of the same,8 or whether something of these (is as- sumed), it is necessai-y that one alone9 should (be taken), for
Ex. 11. If A is not white B is great
If B is not great A is not white . ' . If B is not great it is great.
1 Vide Mansel's Logic, on this kind of demonstration, pp. 103 — 105 8 The first syllogism, ABC.
3 The second, A C B, in which the major of the first proposition is proved.
4 i. e. the minor proposition of the first syllogism.
* In the first syllogism. 6 In the first syllogism. 7 i. e. different from ABC, the original terms.
s Of the premises in the former syllogism.
* Of the premises of the first syllogism.
D
194 Aristotle's organon. [book n
if botli l there will be the same conclusion, when stratioiTcrfthis we need another. In those terms then which are kind not tmiy not converted, a syllogism is produced from one
made, except - -,•'.,. n x .-,
through con- undemonstrated proposition, tor we cannot demon- and1henlbyS' strate by this term, that the third is with the mid- assumption die, or the middle with the first, but in those which cesso,'C'°oniy. are converted we may demonstrate all by each other, as if A B and C reciprocate ; for A C can be demonstrated by the middle,2 B ; again,3 A B (the major) through the conclusion, and through the proposition B C, (the minor) being converted ; likewise 4 also B C the minor through the conclusion, and the proposition A B con- ofthee2nd verted. We must however demonstrate the pro- syiiogism. position C B,* and B A,f for we use these alone tVJet'hsilo-01, undemonstrated, if then B is taken as present gism. with every C,J and C with every A, there will
tThesthsyiio- De a syllogism of B in respect to A.§ Again, if § i.e. that Bis C is assumed present with every A, and A with with a. every B,|] it is necessary that C should be present
giIm?CA Is"0" with eveiT B. in both5 syllogisms indeed, the pro- position C A is taken undemonstrated, for the others were demonstrated. Wherefore if we should show this, they will all have been shown by each other, gfcmf cb aU° I*" then C is assumed present with every B,^[ and B with every A, both propositions are taken de- monstrated, and C is necessarily present with A, hence it is clear that in convertible propositions alone, demonstrations may be formed in a circle, and through each other, but in others as we have said before,6 it occurs also in these 7 that
1 Premises in the first syllogism
2 The first syllogism of a circle, ABC.
3 The second syllogism, ACB. 4 The sixth syllogism, B A C.
5 i. e. in the fifth and third.
6 One proposition is not demonstrated in a circle.
7 i. e. in the 3rd, 4th, and 5th, in which the converse propositions are proved. It must be remembered that a circle consists of six syllogisms, the others flowing from the first : of these, the 2nd proves the major, and the 6th the minor of the first, but both assume the conclusion of the first, to which the 2nd adds the converse minor, and the 6th the con- verse major of the first : hence the 2nd and 6th prove directly the pro- positions of the first, but assume two converse propositions, which have also to be proved to make the circle complete. This is done by the third
CHAP. V.] THE PRIOR ANALYTICS. 19o
we use the same thing demonstrated for the pur- * The major of
pose of a demonstration. For C is demonstrated *l \he minor of
of B,* and B of A,f assuming C to be predicated 4th.
of A, J but C is demonstrated of A § by these pro- 3rd. e major
positions, II so that we use the conclusion ' for de- •> J,nJ fhelt^>-
1 V1 II C B and B
monstration. a.
In negative syllogisms a demonstration through each other is produced thus : let B be with every negatives! C, but A present with no B, the conclusion that A is with no C. If then it is again necessary to conclude that A is with no B, which we took before, A will be with no C, but C with every B, for thus the proposition becomes con- verted. But if it is necessary to conclude that B is with C, the proposition A B must no longer be similarly .
converted, tor it is the same proposition, i that B is with no A, and that A is with no B, but we must assume that B is present with every one of which A is present with none. Let A be present with no C, which was the con- clusion, but let B2 be assumed present with every of which A is present with none, therefore B must necessarily be present with every C, so that each of the assertions which are three becomes a conclusion, and this is to demonstrate in a circle, namely, assuming the conclusion and one premise converse to infer the other.3 Now in particular . T
. , . r 4. In particu-
syllogisms we cannot demonstrate universal pro- lars the major position through others, but we can the particular, stratedlbut the and that we cannot demonstrate universal is evi- minor is. dent, for the universal is shown by universals, . but the conclusion is not universal, and we must demonstrate from the conclusion, and from the other proposi- tion. Besides, there is no syllogism produced at all when the proposition is converted, since both premises become particular.
and fifth syllogisms, the major of the 3rd and the minor of the 5th being identical, as well as the latter being the converse conclusion of the first, proved by the 4th. Thus a circle may be divided into two parts, of which the conclusion of the 1st, 2nd, and 6th are direct, but those of the 3rd, 4th, and 5th are converse.
1 Of the 4th, i. e. in order to prove the propositions of the same fourth.
2 Omitted by Taylor. 3 Vide Whately and Hill.
Ex. 1. Every B is A Some C is B . • . Some G is A. o 2
196 aristoxle's organon. [book ii.
But we can demonstrate a particular proposition, for let A be 2 demonstrated of a certain C through B, if then
B is taken as present with every A, and the con- clusion remains, B will be present with a certain C, for the , „ , first figure is produced, and A will be the middle.*
* Example (1.) ■= V„ . ' . .
JNevertheless it the syllogism is negative, we can- not demonstrate the universal proposition for the reason ad- duced before, but a particular one cannot be demonstrated, if A B is similarly converted as in universals, but we may show it by assumption,1 as that A is not present with something, but that B is, since otherwise there is no syllogism from the particular proposition being negative.
Chap. VI. — Of the same in the second Figure.
In the second figure we cannot prove the affirm-
1. In uni- .. . ., . t -. ,
versais of the ative in this mode, but we may the negative ; the .second figure affirmative therefore is not demonstrated, because
an affirmative . . . '
proposition is there are not both propositions affirmative, for "trated?011" the conclusion is negative, but the affirmative is
demonstrated from propositions both affirmative, the negative however is thus demonstrated. Let A be with every B, but with no C, the conclusion B is with no C, if then B is assumed present with every A, it is necessary that A should be present with no C, for there is the second figure, the middle is B. But if A B be taken negative, and the other
proposition affirmative, there will be the first I'atfvUeYshe ne~ figure, for C is present with every A, but B with
no C, wherefore neither is B present with any A, nor A with B, through the conclusion then and one pro- position a syllogism is not produced, but when another pro- position is assumed there will be a syllogism. But if the 3. in partieu- syllogism is not universal, the universal proposi- lars the parti- tion2 is not demonstrated for the reason we have
(.mar proposi- . _ „
tion alone is given before,"* but the particular4 is demonstrated
1 That is, hypothetically. As regards the concluding sentence of this chapter, 1 have followed Bekker, Buhle, and Taylor, in preference toWaitz and Averrois, since though I favour the grammatical construction of the tw; latter, the sense of the context is against them. 2 The major.
3 Because the conclusion being assumed, and the minor of Festino or Baroko, both propositions are particular, hence there is no conclusioo.
4 The minor.
CUAP. VII.] THE PRIOR ANALYTICS. 197
when the universal is affirmative. For let A be demonstrated with every B, but not with every C, the conclu- versaiisaffirm- sion that B is not with a certain C, if then B is ative- assumed present with every A, but not with every C, A will not be with a certain C, the middle is B. But if the universal is negative, the proposition A C will not be de- 2 monstrated, A B being converted, for it will hap- pen either that both 1 or that one2 proposition will be negative; so that there will not be a syllogism. Still in the same man- ner there will be a demonstration, as in the case of universals, if A is assumed present with a certain one, with which B is not present.
Chap. VII. — Of the same in the third Figure.
In the third figure, when both propositions are L In this assumed universal, we cannot demonstrate reci- figure, when
. i-i ii i • Dotn proposi-
procally, for the universal is shown through uni- tions are uni- versals, but the conclusion in this figure is always JJ^SSto! particular, so that it is clear that in short we can- tion in a circle. not demonstrate an universal proposition by this 2^ There wm figure. Still if one be universal and the other tion where the particular, there will be at one time and not at JJ**" jj™j;e another (a reciprocal demonstration) ; when then major particu- both propositions are taken affirmative, and the universal belongs to the less extreme, there will be, but when to the other,3 there will not be. For let A be with every C, but B with a certain (C), the conclusion A B, if then C is assumed present with every A, C has been shown to be with a certain B, but B has not been shown to be with a certain C. But it is necessary if C is with a certain B, that B should be with a certain C, but it is not the same thing, for this to be with that, and that with this, but it must be as- sumed that if this is present with a certain that, that also is with a certain this, and from this assumption there is no longer a syllogism from the conclusion and the other proposition. If
1 If the conclusion is assumed and the major premise.
2 If a negative conclusion is assumed, with a minor affirmative.
3 When the major is universal and the minor particular there will not be a trae circle, because from the conclusion and the major premise the minor is not proved.
198 Aristotle's organon. [book it.
however B is with every C, but A with a certain C, it will be possible to demonstrate A C, when C is assumed present with every B, but A with a certain (B). For if C is with every B, but A with a certain B, A must necessarily be with a certain C, the middle is B. And when one is affirmative, but the other negative, and the affirmatives affirmative universal, the1 other will be demon- universal there strated ; for let B be with every C, but A not be uoneo"°therpar- with a certain (C), the conclusion is, that A is not ticuiar nega- vvith a certain B. If then C be assumed besides
tive. . , _ . -ii
present with every B, A must necessarily not be .4. Not when vv^itli a certain C, the middle is B. But when the
the 116ff3.tlV6 IS
universal (ex- negative is universal, the other is not demon- ception). strated, unless as in former cases, if it should be
assumed that the other is present with some individual, of what this is present with none, as if A is with no C, but B with a certain C, the conclusion is, that A is not with a certain B. If then C should be assumed present with some individual of that with every one of which A is not present, it is necessary that C should be with a certain B. We cannot however in any other way, converting the universal proposition, demon- strate the other, for there will by no means be a syllogism.2
It appears then, that in the first figure there is tion of the pre- a reciprocal demonstration effected through the ceding chap- third and through the first figure, for when the conclusion is affirmative, it is through the first, but when it is negative through the last,3 for it is assumed * The predi- that with what this * is present with none, the cate- other f is present with every individual. In the
t The subject. mj^ji_e flgUre however, the syllogism being uni-
1 The particular negative.
2 Thus in Ferison, the minor, being I, cannot be demonstrated in a circle, the conclusion and major being negative, except by converting both these into affirmative. In the cases of the particular modes of the third figure, where there is an universal minor, i. e. Disamis and Bokardo, there may be a perfectly circular demonstration, but not in those which have the major universal, as Datisi and Ferison.
3 Aristotle does not mean the third figure of categoricals, because in the syllogisms mentioned by him, there are a negative minor and an uni- versal conclusion, contrary to the rules of the third figure. He intends therefore an hypothetical syllogism, wherein there are two predicates and one subject, as in the third figure.
CHAP. VIII.] THE PRIOR ANALYTICS. 199
versal, (the demonstration) is through it and through the first figure,1 and when it is particular, both through it and through the last.2 In the third all are through it, but it is also clear that in the third and in the middle the syllogisms, which are not produced through them, either are not according to a circular demonstration, or are imperfect.
Chap. VIII. — Of Conversion of Syllogisms in the first Figure. Conversion is by transposition of the conclusion
J r . , , ±. . .1. Definition of
to produce a syllogism, either that the major is conversion of not with the middle, or this (the middle) is not with gSJ^j. the last (the minor term).3 For it is necessary when the conclusion is converted, and one proposition re- mains, that the other should be subverted, for if this (pro- position) will be, the conclusion will also be.4 2 Differerice But there is a difference whether we convert the whether this is conclusion contradictorily or contrarily, for there dictoriiy or con- is not the same syllogism, whichever way the ^Sjfc'tiolte- conclusion is converted, and this will appear from tween these what follows. But I mean to be opposed (con- shown- tradictorily) between, to every individual and not to every individual, and to a certain one and not to a certain one, and contrarily being present with every and being present with none, and with a certain one, not with a certain } one.5 For let A be demonstrated of C, through the middle B ; if then A is assumed present with no C, but with every B, B will be with no C, and if A is with no C, but B with every C, A will not be with every B, and not altogether with none, for the universal was not concluded through the last figure. In a word, we cannot subvert universally the major
1 For the major of Cesare is proved in Celarent.
- For the minor of Ferison is proved hypothetically. See above.
3 The minor term is here called to rtXivraiov, lower down in this chapter it is called to ta\aTov. By transposition of the conclusion, is intended the change of it into its contradictory or contrary, when a pro- position is enunciated, to which the other proposition is added, and thus a new syllogism in subverting the former is produced. Vide Whately and Hill's Logic.
4 This has been shown above, that we cannot infer falsity from true premises ; if then we admit the conclusion to be false, and take its op- posite, one proposition must be false.
200 Aristotle's organon. [book it
premise by conversion, for it is always subverted through the third figure, but we must assume both propositions to the minor term, likewise also if the syllogism is negative. For let A be shown through B to be present with no C, where- fore if A is assumed present with every C,1 but with no B, B will be with no C, and if A and B are with every C, A will be with a certain B, but it was present with none.2
If however the conclusion is converted contra- dictorily, the (other) syllogisms also will be con- tradictory,3 and not universal, for one premise is particular, so that the conclusion will be particular. For let the syllo- gism be affirmative, and be thus converted, hence if A is not with every C, but with every B, B will not be with every C, and if A is not with every C, but B with every C, A will not be with every B. Likewise, if the syllogism be e aren ' negative,* for if A is with a certain C,4 but with t universally. no B, B will not be with a certain C, and net simply f with no C, and if A is with a certain C,5 and B with every C, as was assumed at first,0 A will be with a certain B.
3. inparticu- ^n particular syllogisms, when the conclusion is
lars, of the first converted con tradictorilv, both propositions are sub-
figure whsn the
conclusion is verted, but when contrarily, neither of them ; for it trTdktoniy0"" no longer happens, as with universals, that through both proposi- failure of the conclusion7 by conversion, a subver-
tions are sub- • ■ j j • 'j.i. 1 ,_ •, a
verted, if con- S10n 1S produced, since neither can we subvert its
lraD!Ty'neither' at an- For let A be demonstrated of a certain C,$
if therefore A is assumed present with no C,9 but
B with a certain C, A will not be with a certain B,10 and if A
1 i. e. by converse of the conclusion and assumption of the minor.
2 By hypothesis in the major premise of Celarent.
3 In their opposition, for they will prove a particular conclusion contra- dicting the previously assumed universal proposition.
4 The subversion of the minor in Ferison.
5 The subversion of the major in Disamis. * In the minor proposition of Celarent.
' iWuTTovros tov ovfi7rtpa(jfiaTog, deficiente conclusione. Buhle. This expression signifies the change from an universal to a particular in the conclusion, because in the latter case it comprehends fewer things.
8 Because there is no syllogism from particular premises.
9 The subversion of the minor in Camestres — while the major of the first syllogism is retained.
10 The contradictory of the major will be concluded.
CHAP. IX. J THE PRIOR ANALYTICS. 201
is with no C, but with every B, B will be with no C,1 so that both propositions are subverted. If however the con- elusion be converted contrarily, neither (is sub- verted), for if A is not with a certain C, but with every B, B will not be with a certain C, but the original proposition is not yet subverted,* for it may be present with a » Viz the mj_ certain one, and not present with a certain one. nor premise of Of the universal proposition A B there is not any syllogism at all,2 for if A is not with a certain C, but is with a certain B, neither premise is universal. So also if the syllo- gism be negative, for if A should be assumed present with every C, both are subverted, but if with a certain C, neither ;• the demonstration however is the same.
Chap. IX. — Of Co)iversion of Syllogisms in the second Figure.
Ix the second figure we cannot subvert the major premise contrarily, whichever way the conversion versais we can- is made, since the conclusion will always be in the not infer th1
' 1 contrary to the
third figure, but there was not in this figure an major premise, universal syllogism. The other proposition in- ^ ^ntTadic- deed we shall subvert similarly to the conversion, tory— the mi-
I, . M i ./» ,v • t nor dependent
mean by similarly, it the conversion is made upon the as-
contrarily (we shall subvert it contrarily), but if sumption of the
t •! i t • -n i a a i conclusion.
contradictorily by contradiction, tor let A6 be with every B and with no C, the conclusion B C, if then B is assumed4 present with every C, and the proposition A B remains, A will be with every C, for there is the first figure. If however B is 5 with every C, but A with no C, A 9 is not with every B, the last figure. If then B C (the conclusion) be converted contradictorily, A B may be de- monstrated similarly,6 and A C contradictorily. For if B is with a certain C,7 but A with no C, A will not be present, with a certain B ; again, if B 8 is with a certain C, but A
1 That is, by assuming a contradictory conclusion of the first syllo- gism, and retaining the major premise of the same, a conclusion will be drawn, contradictory of the minor.
2 In which the major premise of Darii is subverted.
3 This is inCamesires. 4 Barbara subverting the minor of Camestres. i Felapton subverting the major of Camestres.
8 i. e. subverted by a contrary.
7 Darii subverting the minor. 8 Ferison subverting the major.
202 aristotle's organon. [book ii.
with every B, A is with a certain C, so that there is a syllo-
3 gism produced contradictorily.1 In like manner
it can be shown, if the premises are vice versa,2
lar^ifthe con ^ut ^ tne syn°gism is particular, the conclusion trar'yofthe being converted contrarily, neither premise is as"umeSd\nei- subverted, as neither was it in the first figure, (if ther proposi- however the conclusion is) contradictorily (con- vened ; if the verted), both (are subverted). For let A be as- Do"hrareCtory' sumed present with no B, but with a (certain) C,3 the conclusion B C ; if then B is assumed present with a certain C, and A B remains, the conclusion will be that A is not present with a certain C, but the original would not be subverted, for it may and may not be present with a certain individual. Again, if B is with a certain C, and A with' a certain C, there will not be a syllogism, for neither of the assumed premises is universal, wherefore A B is not sub- verted. If however the conversion is made contradictorily, both are subverted, since if B is with every C, but A with no B, A is with no C, it was however present with a certain (C).3 Again, if B is with every C, but A with a certain C, A will be with a certain B, and there is the same demonstration, if the universal proposition be affirmative.
Chap. X. — Of the same in the third Figure.
1 in this figure, *N tne tn*r<i &%nre> when the conclusion is con- if the contrary' verted contrarily, neither premise is subverted,
sion^ass'um- according to any of the Syllogisms, but When COn- ed, neither tradictorily, both are in all the modes. For let ver^d.VuUf A be shown to be with a certain B, and let C be tory^bo'th"3'0" taken as the middle, and the premises be universal : if then A is assumed not present with a certain B, but B with every C, there is no syllogism of A and C,4
1. universal. nor if" A is not Present witn a certain B, but with
every C, will there be a syllogism of B and C.5
There will also be a similar demonstration, if the premises
1 Because Darii proves a contradictory conclusion to the minor, and Ferison a contradictory conclusion to the major — of the same Camestres.
2 That is, if the major is negative, but the minor affirmative, hence a syllogism produced in Cesare.
3 A was assumed present with a certain C, in the minor of Festino.
* Because the major is particular. 5 Because the major is particular.
CHAP. X.] THE PRIOR ANALYTICS. 203
are not universal, for either both must be particular by con- version, or the universal be joined to the minor, but thus there was not a syllogism neither in the first nor in the middle figure. If however they are converted contra- , dictorily, both propositions are subverted ; for if A is with no B, but B with every C, A will be with no C ; again, if A is with no B, but with every C, B will be with no C. In like manner if one proposition is not uni- versal ; since if A is with no B, but B with a certain C, A will not be with a certain C, but if A is with no B, but with every C, B will be present with no C. So also if the syllogism be negative, for let A be shown not pre- sent with a certain B, and let the affirmative proposition be B C, but the negative A C, for thus there was a syllogism ; when then the proposition is taken contrary to the conclusion, there will not be a syllogism. For if A were with a certain B, but B with every C, there was not a syllogism # of A and C,*1 nor if A were with a certain B, t>. i. Anai.'pr! but with no C was there a syllogism of B and C,t + Vide ch- v-
hi Anal Pr
so that the propositions are not subverted. When
however the contradictory (of the conclusion is
assumed) they are subverted. For if A is with
every B, and B with C, A will be with every C, * camestres.
but it wa3 with none.2 Again if A $ is with every
B, but with no C, B will be with no (J, but it was with every C.3
There is a similar demonstration also, if the pro- 2. particulars
positions are not universal^ for A C II becomes the same.
. . " . § Ferison
universal negative, but the other, ^f particular af- u The major firmative. If then A is with every B, but B with PJ0'';
/ ' IT The minor
a certain C, A happens to a certain C, but it was pr with none ;4 again, if A is with every B, but with no * Ca™estres- C,* B is with no C, but if A is with a certain B, and B with a certain C, there is no syllogism,5 nor if A is with a certain B, but with no C, (will there thus be a syllogism):0 . „,.
,v , , . i . j. r t The contra-
^^^nce in that way,j but not in this,| the pro- dictory. positions are subverted. I The contrary.
1 Because the major is particular,
8 So .assumed in the major proposition of Felapton.
3 In the minor of Felapton.
* In the major of Ferison. s Because of part, premises.
6 Because of the part, major.
204 aristotle's org anon. [book ii.
From what has been said then it seems clear tioifeCai"tUla" how, when the conclusion is converted, a syllogism arises in each figure, both when contrarily and when contradictorily to the proposition, and that in the first figure syllogisms are produced through the middle and the last, and the minor premise is always subverted through the middle (figure), but the major by the last (figure) : in the se- cond figure, however, through the first and the last, and the minor premise (is) always (subverted) through the first figure, but the major through the last : but in the third (figure) through the first and through the middle, and the major pre- mise is always (subverted) through the first, but the minor premise through the middle (figure). What therefore con- version is, and how it is effected in each figure, also what syllogism is produced, has been shown.
Chap. XI. — Of Deduction to the Impossible in the first Figure.
1 Howsyiio- -A- syllogism through the impossible is shown,
gism iia -rpv when the contradiction of the conclusion is laid
shown,°and its down, and another proposition is assumed, and it
distinction js produced in all the figures, for it is like conver-
from conver- *■ °
sion (aur<- sion except that it differs insomuch as that it is
oTpo<pn)- converted indeed, when a syllogism has been
made, and both propositions have been assumed, but it is de- duced to the impossible, when the opposite is not previously acknowledged but is manifestly true. Now the terms subsist similarly ! in both, the assumption also of both is the same, as for instance, if A is present with every B, but the middle is C, if A is supposed present with every or with no B, but with every C, which was true, it is necessary that C should be with no or not with every B. But this is impossible, so that the supposition is false, wherefore the opposite 2 is true. It is a similar case with other figures, for whatever are capable of conversion, are also capable of the syllogism per impossibile. 2. The univer- All other problems then are demonstrated the fi^t'figure tnrough the impossible in all the figures, but the not demonstra- universal affirmative is demonstrated in the mid-
1 That is to say, both in the converse syllogism and in that per impos- sibile. z The contradictory.
CHAP. XI.~| THE PRIOR ANALYTICS. 205
-i
die, and in the third, but is not in the first. For Me per impo;- let A be supposed not present with every B, or slbUe- present with no B, and let the other proposition be assumed from either part, whether C is present with every A, or B with every D, for thus there will be the first figure. If then A is supposed not present with every B, there is no syllo- gism,1 from whichever part the proposition is assumed, but if (it is supposed that A is present with) no (B), when the pro- position B D is assumed, there will indeed be a syllogism of the false, but the thing proposed is not demonstrated. For if A is with no B, but B with every D, A will be with no D, but let this be impossible, therefore it is false that A is with no B. If however it is false that it is present with no B, it does not follow that it is true that it is present with every B. But if C A is assumed, there is no syllogism,2 neither when A is supposed not present with every B, so that it is manifest that the being present with every, is not demonstrated in the first figure per impossibile. But to be present with a certain one, and with none, and not with every is de- 3 Butthepar monstrated, for let A be supposed present with affir. and univ. no B, but let B be assumed to be present with demonstrated, every or with a certain C, therefore is it neces- ^h™ tne c°n-
i iiii -i -i tradictory of
sary that A should be with no or not with every the conclusion C, but this is impossible, for let this be true and isassumed- manifest, that A is with every C, so that if this is false, it is necessary that A should be with a certain B. But if one proposition should be assumed to A,3 there will not be a syllogism,4 neither when the contrary to the conclusion is supposed as not to be with a certain one, wherefore it appears that the contradictory must be supposed. Again, let A be sup- posed present with a certain B, and C assumed present with every A, then it is necessary that C should be with a certain B, but let this be impossible, hence the hypothesis is false, and if this be the case, that A is present with no B is true.
1 Because of a particular nega. prem. being inadmissible in the first fig. - Because from the hypothesis being negative it eainioc be the minor in the first fig.
3 So that it becomes the major.
4 Because the negative hypothesis becomes the minor prem. contrary to the rule.
206 Aristotle's okganon. "book n.
In like manner, if C A is assumed negative ; if however the proposition be assumed to B, there will not be a syllogism, but if the contrary be supposed, there will be a syllogism, and the impossibile (demonstration), but what was proposed will not be proved. For let A be supposed present with every B, and let C be assumed present with every A, then it is neces- sary that C should be with every B, but this is impossible, so that it is false that A is with every B, but it is not yet neces- sary that if it is not present with every, it is present with no B. The same will happen also if the other proposition 1 is assumed to B, for there will be a syllogism, and the impossible (will be proved), but the hypothesis is not subverted, so that the contradictory must be supposed. In order however to prove that A is not present with every B, it must be supposed 4 Ms the ar Presenfc with every B, for if A is present with neg. is demon- every B, and C with every A, C will be with tneatsudb'-coUnt-lf every B. so that if this impossible, the hypothesis trary to the is false. In the same manner, if the other proposi- assumed, what tion is assumed to B,2 also if C A is negative in ruabvPertedSed 'S *^e same way> f°r tnus there is a syllogism, but if the negative be applied to B, there is no demon- stration. If however it should be supposed not present with every, but with some one, there is no demonstration that it is not present with every, but that it is present with none, for if A is with a certain B, but C with every A, C will be with a certain B, if then this is impossible it is false that A is present with a certain B, so that it is true that it is present with none. This however being demonstrated, what is true is subverted besides, for A was present with a certain B, and with a cer- tain one was not present. Moreover, the impossibile does not result from the hypothesis, for it would be false, since we cannot conclude the false from the true, but now it is true, for A is with a certain B, so that it must not be supposed pre- sent with a certain, but with every B. The like also will occur, if we should show that A is not present with a certain B, since if it is the same thing not to be with a certain indi- vidual, and to be not with every, there is the same demon- stration of both.
1 A proposition evidently true.
2 If the true proposition becomes the minor.
CHAP. XII.] THE PRIOR ANALYTICS. 207
It appears then, that not the contrary, but the
\.r , i • 11 11 • i »• Summary
contradictory must be supposed in all syllogisms,1 and reason of for thus there will be a necessary (consequence), su^p'tiJn.88" and a probable axiom,2 for if of every thing af- firmation or negation (is true), when it is shown that negation is not, affirmation must necessarily be true. Again, except it is admitted that affirmation is true, it is fitting to admit nega- tion ; but it is in neither way fitting to admit the contrary, for neither, if the being present with no one is false, is the being present with every one necessarily true, nor is it probable that if the one is false the other is true.
It is palpable, therefore, that in the first figure, all other problems are demonstrated through the impossible ; but that the universal affirmative is not demonstrated.
Chap. XII. — Of the same in the second Figure. In the middle, however, and last figure, this3 also
*-' In the second
is demonstrated. For let A be supposed not pre- figure a is sent with every B, but let A be supposed present K£*g£ with every C. therefore if it is not present with contradictory is every B, but is with every C, C is not with every "omra"^!* B, but this is impossible, for let it be manifest that C is with every B, wherefore what was supposed is false, and the being present with every individual is true. If how- ever the contrary be supposed, there will be a syllogism, and the impossible, yet the proposition is not demonstrated. For if A is present with no B, but with every C, C will % be with no B, but this is impossible, hence that A
1 Leading to the impossible. Taylor gives rise to much confusion, by using the word opposite as antithetical to contrary, instead of the word contradictory.
2 aliwfia tvSoKov— dignitas probabilis, Averr.— axioma rationi con- sentaneum, Buhle ; the latter notes, that Aristotle refers to the principle, that of two contradictories, one is true and the other false, from which it follows that when the contradictory of the first conclusion is proved false, the original conclusion itself is proved true. As to the words them- selves, it may be sufficient to remark, that dKidifJ-ara are the original pre- mises, from which demonstration proceeds, and are a branch of ^ the Koiva'i 'Ap\ai ; and that taken purely, per se, Aristotle regards to. tvc6$a as among the elements of syllogism, some of wliich are necessary. See also Waitz, vol. i. p. 505.
3 An universal affirmative.
208 aristotle's orgaxox. [book ii
is with no B is false. Still it does not follow, that if this is
false, the being present with every B is true, but when A is
with a certain B, let A be supposed present with
no B, but with every C, therefore it is necessary
that C should be with no B, so that if this is impossible A must
necessarily be present with a certain B. Still
if it* is supposed not present with a certain
one,j" there will be the same ' as in the first figure.
Again, let A be supposed pi'esent with a certain B, but let it
be with no C, it is necessarv then that C should not be with
a certain B, but it was with every, so that the supposition is
false, A then will be with no B. When however A
is not with every B, let it be supposed present with
every B, but with no C, therefore it is necessary that C should
be with no B, and this is impossible, wherefore it is true that
A is not with every B. Evidently then all syllogisms are
produced through the middle figure.2
Chap. XIII. — Of the same in the third Figure.
1 in this figure Through the last figure also, (it will be con- both affirma- eluded) in a similar way. For let A be supposed tives are de-ga" not present with a certain B, but C present with monstrabie per every B, A then is not with a certain C, and if
absurdum. .... .,,..„, ,
this is impossible, it is raise that A is not with a certain B, wherefore that it is present with every B is true. If, again, it should be supposed present with none, there will be a syllogism, and the impossible, but the proposition is not proved, for if the contrary is supposed there will be the same3 as in the former (syllogisms). But in order to con- clude that it is present with a certain one, this hypothesis must be assumed, for if A is with no B, but C with a certain B, A will not be with every C, if then this is false, it is true that A is with a certain B. But when A is with no B, let it be supposed present with a certain one, and let C be assumed present with every B, wherefore it is necessary that A should be with a certain C, but it was with no C, so that it is false that A is with a certain B. If however A is supposed
1 The proposition will not be so much confirmed as subverted, for if O is false, A is true, and vice versa. - By a deduction to an absurdity.
3 A will not be demonstrated universal, I ut particular.
CHAP, XIV."| THE PRIOR ANALYTICS: 209
present with every B, the proposition is not demonstrated,1 but in order to its not being present with every, this hypothesis must be taken.2 For if A is with every B, and C with a cer- tain B, A is with a certain C, but this was not so, hence it is false that it is with every one, and if thus, it is true that it is not with every B, and if it is supposed present with a cer- tain B, there will be the same things as in the syllogisms above mentioned.
It appears then that in all syllogisms through the impossible the contradictory must be supposed, t2i-0n.ecapitula" and it is apparent that in the middle figure the affirmative is in a certain way3 demonstrated, and the universal in the last figure.
Chap. XIV. — Of the difference beticeen the Ostensive, and the Deduction to the Impossible.*
A DEMONSTRATION to the impossible differs from i. Difference
an ostensive, in that it admits what it wishes to |£SSSti2ta? subvert, leading to an acknowledged falsehood, and that per but the ostensive commences from confessed imP0Sslblle- theses. Both therefore assume two allowed propositions, but the one 5 assumes those from which the syllogism is formed, and the other0 one of these, and the contradictory of the con- clusion. In the one case* also the conclusion need not be known, nor previously assumed that sive it is, or that it is not, but in the other it is neces- sary7 (previously to assume) that it is not ; it is of no conse- quence however whether the conclusion is affirmative or
1 Because if A is with every B is false, that A is with no B is not im- mediately true, but only the particular negative is true.
2 A, i. e. the hypothesis of being universally present.
3 By a deduction to an absurdity.
4 Compare Prior Anal. i. 23; Hessey'sLogicalTables.No. 4 ; Whately's Treatise on Rhetoric, part i. c. 3 ; Rhetoric, xi. 22. It is clear from the remark in the text, that the demonstration per impossibile is one kind of the hypothetical syllogism, the object of which is to prove the truth of a problem, by inferring a falsity from its contradiction being assumed. (Vide An. i. 23, and 29; also Waitz, vol. i. p. 430.) The reader will find llie question fully discussed in note G, Appendix to Mitchell's Logic.
5 The ostensive. 6 The per impossibile.
7 i. e. we must assume the contradictory of the concision, to be proved.
v
210 Aristotle's org anon. [book ii.
negative, but it will happen the same about both.1 New whatever is concluded ostensively can also be proved per im- possibile, and what is concluded per impossibile may be shown ostensively through the same terms, but not in the same figures. For when the syllogism2 is in the first figure,3 the
monst'ratld p« truth wil1 be in tne middle, or in the last, the ne-
absurdum in gative indeed in the middle, but the affirmative
is'prored inthe i° the last. When however the syllogism is in
second osten- the middle figure,4 the truth will be in the first in
tiively, if the n i , , \ , , ,, ...
problem be ne- all the problems, but when the syllogism is in the
fh^thirdflgire last' the truth wil1 be in tne first and in the mid" if it be affirm- die, affirmatives in the first, but negatives in the
l/^barii. middle. For let it be demonstrated through the
first figure* that A is present with no, or not with
every B, the hypothesis then was that A is with a certain B,
but C was assumed present with every A, but with no B, for
thus there was a syllogism, and also the impossible. But
this is the middle figure, if C is with every A, but with no B,
and it is evident from these that A is with no B. Likewise if it
2 t Barbara bas been demonstrated to be not with every, j- for
the hypothesis is that it is with every, but C was
assumed present with every A, but not with every B. Also
in a similar manner if C A were assumed negative, for thus
also there is the middle figure.! . Again, let A be
Festino. shown present with a certain B,§ the hypothesis
rent.InCela tnen ls> tnat ** 1S Present >vith none, but B was assumed to be with every C, and A to be with
every or with a certain C, for thus (the conclusion) will be
5 ii Dara ti impossible, but this is the last figure, if A and B || are with every C. From these then it appears
that A must necessarily be with a certain B, and similarly if
B or A is assumed present with a certain C.
« n Baroko Again, ^et ^ De shown in the middle figure^"
that A is with every B, then the hypothesis was
that A is not with every B, but A was assumed present with
1 The conclusion is called negative when it is false, whether it affirms cr denies, hence if it affirm a falsity, it is said "not to be," and when it denies a truth, it is equally said " not to be." Waitz omits " not" in the same figures ; I read with Bekker, Buhle, and Taylor.
2 Per impossibile. 3 The thing proposed will be proved. — Taylor.
4 Sometimes also in the 3rd, in fact what Arist. here states are the prin- cipal modes of demonstration, and are not tc be too generally assumed.
CHAP. XIV.] THE PRIOR ANALYTICS. 211
every C, and C with every B, for thus there will be the im- possible. And this is the first figure,* if A is 7 » Barbara with every C, and C with every B. Likewise if it is demonstrated to be present with a certain one,f 8" + Caraestres- for the hypothesis was that A was with no B, but A was as- sumed present with every C, and C with a certain B, but if the syllogism J should be negative,1 the hypothesis 9 + Festino in. was that A is with a certain B, for A was assumed ferring the im- to be with no C, and C with every B, so that v°bS1 e' there is the first figure. Also if in like manner the syllo- gism § is not universal, but A is demonstrated not to be with a certain B,|| for the hypothesis was sibtie. imp°s that A is with every B, but A was assumed present 10- U in cesare. with no C. and C with a certain B, for thus there _ . is the first figure.^
Again, in the third figure,* let A be shown to . _, „ , , be with every B, therefore the hypothesis was that A is not with every B, but C has been assumed to be with every B, and A with every C, for thus there will be the impossible, but this is the first figure.^ Likewise also, if the demonstration is in a certain thing,2 J for the hypothesis would be that A is with no B, + but C has been assumed present with a certain B, and A with every C, but if the syllogism is negative, § the by- pothesis is that A is with a certain B, but C has been assumed present with no A, but with every B, and this is the middle figure. In like manner also,3 if the demonstra- tion is not || universal, since the hypothesis will be that A is with every B, and C has been as- n dtlS1- sumed present with no A, but with a certain B, « Festino and this is the middle figure.^
It is evident then that we may demonstrate 3. what is de- each of the problems through the same terms, both "^"rdumls'so ostensively4 and through the impossible, and in also ostensive-
1 If it should prove a conclusion in E, which contradicts the minor of Festino.
2 This will prove a conclusion in I.
3 If the syllogism per impossible in Datisi should prove O.
4 Buhle, Bekker, and Taylor insert " and through the impossible," which Waitz omits. It may be remarked, that though in some cases the demon- stration per impossibile is advantageous, yet that it is more open to fallacy, especially to tliat of "a non-causa pro causa," a deception
p 2
212 Aristotle's org anon, [book n.
iy, and vice like manner it will be possible when the syllo- vers5- gisms are ostensive, to deduce to the impossible in
the assumed terms when the proposition is taken contradic- tory to the conclusion. For the same syllogisms arise as those through conversion, so that we have forthwith figures through which each (problem) will be (concluded). It is clear then that every problem is demonstrated by both modes, (viz.) by the impossible and ostensively, and we cannot possibly separ- ate the one from the other.
Chap. XV. — Of the Method of concluding from Opposites in tJie
several Figures.
In what figure then we may, and in what we may Jus°flguTesVari not' syllogize from opposite propositions1 will be from which a manifest thus, and I say that opposite propositions duciWeTrom are according to diction four, as for instance (to opposite pro- ^g present) with every (is opposed) to (to be pre- latter («ara tij» sent) with none ; and (to be present) with every kinii1,°(cfrr t0 (t0 be present) not with every ; and (to be pre- Herm. ?,) but sent) with a certain one to (to be present with) «"u.,,Tot" three, no one ; and (to be present with) a certain one to
(to be present) not with a certain one ; in truth however they are three, for (to be present) with a certain one
which is very frequent in dialectical disputation when the opponent is a.sked to grant certain premises. Vide the 17th ch. of this book, also Rhet. ii. 24.
1 avriicufiivai irporaaHQ, is an expression sometimes limited to con- tradictories, the Kara n)v Xsfiv, opposition is properly subcontrary : that of subalterns is not recognised by Aristotle {inra\\r]Koi) ; the laws of this last are first given by Apuleius de Dogmate Plat. lib. iii. anonymously ; also by Marcian Capella. Vide Whately's and Hill's Logic. Taylor, from his extreme fondness for the expression 'opposites," certainly does not " what is dark in this, il'.bmine, ncr what is low, raise and support ."
Ex. 1. Every science is excellent No science is excellent • • . No science is science.
Ex. 2. Every science is excellent
No medicine (a certain science) is excellent . • . No medicine (a certain science) is science.
Ex. 3. No science is opinion
All medicine (a certain science) is opinion . • . No medicine (a certain science) is science.
CHAP. XV.] THE PRIOR ANALYTICS. 213
is opposed to (being present) not with a certain one accord- ing to expression only. But of these I call such contraries as are universal, viz. the being present with every, and (the being present) with none, as for instance, that every science is excellent to no science is excellent, but I call the others contradictories.
In the first figure then there is no syllogism 2. No conciu- frora contradictory propositions, neither affirma- s!°n f™ .°,Ppo"
J * r _ sites of either
tive nor negative : not affirmative, because it kind in the is necessary that both propositions should be rs gure' affirmative, but affirmation and negation are contradictories : nor negative, because contradictories affirm and deny the same thing of the same.* but the middle in the first
* \riHp Aid-
figure is not predicated of both (extremes), but rich's logic, ch. one thing is denied of it, and it is predicated of Eiln'ch^s1*' another ; these propositions however are not con- tradictory.
But in the middle figure it is possible to pro- 3 Butfrom duce a syllogism both from contradictories and both in the . from contraries, for let A be good, but science B and C ; if then any one assumed that every science is excel- lent, and also that no science is, A will be with every B, and with no C, so that B will be with no C, no science there- fore t is science. It will be the same also, if, , _, . ,, .
. ., . . ,, ' ' + Example (I.)
having assumed that every science is excellent, it should be assumed that medicine is not excellent, for A is with every B, but with no C, so that a certain science will not be science, t Likewise if A is with every C, but with + „ , ... .
-d 1 -d • • r* J- • A • • * Example (2)
no B, and B is science, U medicine, A opinion, for assuming that no science is opinion, a person would have assumed a certain science to be opinion. § This1 Exam . however differs from the former2 in the conver- sion of the terms, for before the affirmative was joined to B,3 but now it is to C. || Also in a similar manner, if Thg one premise is not universal, for it is always the middle which is predicated negatively of the one and affirma- tively of the other. Hence it happens that contradictories are
1 Cesare. 2 Camestres.
3 That is, in Camestres the major of course was affirmative, the minor negative.
214 aristotle's organon. [book ii.
concluded, yet not always, nor entirely, but when those which * i. e. the ex- are under the middle * so subsist as either to be tremes, being the same, or as a whole to a part : l otherwise it middle1 in 2nd is impossible, for the propositions will by no means figure. De either contrary or contradictory,
r .v .v.- ^ In the third figure there will never be an af-
4. In the third . •, ° „ . . . c
no affirmative firmative syllogism trom opposite propositions, tor is deduced. the reason alleged in the first figure ; but there will be a negative, both when the terms are and are not uni- versal. For let science be B and C, and medicine A, if then a person assumes that all medicine is science, and that no medicine is science, he would assume B present with every A, and C with no A, so that a certain science will + Example (4.) ^ be gcience.j. Likewise, if the proposition A
B is not taken as universal, for if a certain medicine is science, and again no medicine is science, it results that a certain sci- ence is not science.} But the propositions are " xampe(j- contrary, the terms being universally taken,2 if however one of them is particular,3 they are contradictory.
We must however understand that it is possible thus to as- sume opposites as we have said, that every science is good, and again, that no science is good, or that a certain science is not good, which does not usually lie concealed. It is also possible to conclude either (of the opposites), through other interrogations, or as we have observed in the viii°ch. i°.° Topics, § to assume it. Since however the op- 5. opposition positions of affirmations are three, it results that six-fold. we may taj,e 0pp0S;tes m six Ways, either with
every and with none, or with every and not with every indi- vidual, or with a certain and with no one ; and to convert
1 As genus to species — thus science is related to medicine.
Ex. 4. No medicine is science All medicine is science . • . A certain science is not science. A B
Ex. 5. A certain medicine is not science. A C
All medicine is science
C B
. * . A certain science is not science. » In Felapton. 3 In Bokardo.
CHAP. XV. j
THE PRIOR ANALYTICS.
21,
this in the terms, thus A (may be) with every B but with no C, or with every C and with no B, or with the whole of the one, but not with the whole of the other ; and again, we may convert this as to the terms. It will be the same also in the third figure, so that it is clear in how many ways and in what figures it is possible for a syllogism to arise through op- posite propositions.
But it is also manifest that we may infer a true conclusion from false premises, as we have ob- served* before, but from opposites we cannot, for a syllogism always arises contrary to the fact, as if a thing is good, (the conclusion will be,) that it i>ie from such is not good, or if it is an animal, that it is not an Pr°P°sitions- animal, because the syllogism is from contradiction, and the subject terms are either the same, or the one is a whole,f but the other a part.} It appears also evident, that in paralogisms l there is nothing to prevent a contradiction of the hypothesis arising, as if a thing is an odd number, that it is not odd, for from opposite propositions there was a con- trary syllogism ; if then one assumes such, there will be a contradiction of the hypothesis. We must under- stand, however, that we cannot so conclude contraries from one syllogism, as that the conclusion may be that what is not good is good, or any thing of this kind, unless such a pro- position is immediately assumed,2 as that every animal is white and not white, and that man is an animal.3 But we must either presume contradiction,4 as that all science is opinion,5 and is not opinion, and afterwards assume that medicine is a sci- ence indeed, but is no opinion, just as Elenchi6 are produced, or (conclude) from two syllo-
* Vide this t-ook, chapters 2, 3, and 4.
6. No true con- clusion deduei-
■f Genus. X Species.
7. From con- tradictories a contradiction to the assump- tion is inferred.
8. To infer con- tradiction in the conclusion, we must have contradiction in the premises. (Vide Whately, b.ii. c. 2 and 3.)
1 All reasoning from opposites is faulty, because one proposition is necessarily false.
2 A proposition opposed.
3 The minor ; the conclusion will be, man is white and not white.
4 That is, at firsi suppose an axiom :ontradictory of subsequent con- clusion, e- g- all science is opinion.
5 This clause is omitted by Waitz, it is the conclusion contradicting the hypothesis.
6 In the '20th chapter of this book, an Elenchus is denned to be a syllo- gism of contradiction, or (b. i. c. 1, Soph. Elun.) "a syllogism with con-
216 aristotle's . organon. [book ii.
gisms.1 Wherefore, that the things assumed should really be contrary, is impossible in any other way than this, as was be- fore observed.
tentiis syiio- Chap. XVI. — Of the " Petitio Principii" or
gisticis. (Aver- Begging the Question? *
rois.)
1. what the -po \ye„ anci assume the original (question) con-
" petitio pnn- ° P . . . ,
cipii " is — t6 sists, (to take the genus ot it,) in not demon - *}■'?*# a>Tei<>- strating the proposition, and this happens in many ways, whether a person does not conclude at all, or whether he does so through things more unknown, or equally unknown, or whether (he concludes) what is prior through what is pos- t vide Post. terior ; for demonstration is from things more An. b. i. ch. 2, creditable and prior, t Now of these there is no
10 32 ...
begging the question from the beginning, but since some things are naturally adapted to be known through them- selves, and some through other things, (for principles3 are + „ . . known through themselves, but what are under
I Conclusions. . » '
principles! through other things,) when a person
2. How this fai- endeavours to demonstrate by itself what cannot be sT/mirfLo^c' known by itself, then he begs the original question, p. 331, et seq. ' It is possible however to do this so as immediately
to take the thing proposed for granted, and it is
tradiction of the conclusion," " proprie syllogismus est adversarium re- darguens, confirmando scil. quod illius sententiae contradicat." Aldrich. It is well observed by Dr. Hessey, that the iXeytcTiicbv ti>6vfi)]fia of the Rhetoric seems to include the two processes, rj tig rb dSvv. d-rvayiiiyi) and avWoyig. Sid tov dfivv., An. Pr. i. 38, and to correspond to the tig to advv. ayovaa dnoSei^ig, An. Post. i. 26. Vide Hessey's Tables, 4, llhet. ii. 22, and ii. 24.
1 Proving affirmation in one, and negation in the other. This takes place when one of the premises (whether true or false) is either plainly equivalent to the conclusion, or depends on that for its own reception. The most plausible form of this fallacy is arguing in a circle, (vide supra,) and the greater the circle, the harder to detect. Whately, b. iii. sect. 4. Aristotle enumerates five kinds of it, these however do not concur with those given by Aldrich in his Fallacies extra dictionem. As to the identity of the syllogism with a petitio principii, see Mansel's Logic, Appendix, note D. Conf. Top. 8 ; also Pacius upon this chap.
3 These precede all demonstration : for their relative position refer to note p. 81 ; also Meta. v. 1, x. 7, vi. 4, and Sir W. Hamilton Reid'a Works, p. 16.
CHAP. XVI.] THE PRIOR ANALYTICS. 21"
also possible, that passing to other things which are naturally adapted to be demonstrated by that (which was to be investi- gated), to demonstrate by these the original proposition ; as if a person should demonstrate A through B, and B through C, while C was naturally adapted to be proved through A- for it happens that those who thus syllogize, prove 2 Exam . A by itself. This they do,1 who fancy that they given of ma- describe parallel lines, for they deceive themselves thematicians by assuming such things as they cannot demonstrate unless they are parallel. Hence it occurs to those who thus syllo- gize to say that each thing is, if it is, and thus every thine will be known through itself, which is impossible. If then a man, when it is not proved that A is with C, and likewise with B, begs that A may be admitted present with B, it is not yet evident whether he begs the original proposition, but that he does not prove it is clear, for what is similarly doubtful is not the principle of demonstration. If however B so subsists in reference to C as to be the same,2 or that they are evidently convertible, or that one is present with the other,3 then he begs 4. the original question. For that A is with B, may # . be shown through them, if they are converted, the minor, and but now4 this prevents5 it, yet not the mode ; if through c.B however it should do this,* it would produce 5. + Beg the what has been mentioned before,f and a conver- iuestlon- sion would be made through three terms.6 In like manner if any one should take B to be present with C, whilst it is equally doubtful if he assumes A also (present with C), he
1 Those beg the question who endeavour to show that certain lines are parallel because they never meet, for they ought to prove that equi-dis- tant lines do not meet ; so that it is tantamount merely to saying that lines are equi-distant because they are equi -distant, and they prove the same thing by the same, and beg the question.
2 The same in reality, as a vestment and a garment. Taylor.
3 B predicated of C, as genus of spec'es.
* i. e. when this is done, viz. B predicated thus of C.
5 That is, B being of wider extension than A, prevents the demonstrat- ing A of B through C, though the syllogistic mode does not prevent conversion taking place, but rather favours it, since it is Parbara, wherein alone a perfect circle is produced by this kind of conversion.
8 Not always really three, but sometimes one term is assumed f ji two, and therefore in one respect there are three terms.
213 aristotle's organon. [book ii.
does not yet beg the question, but he does not prove it. If however A and B should be the same, or should be converted, or A should follow B, he begs the question from the beginning for the same reason, for what the petitio principii can effect we have shown before, viz. to demonstrate a thing by itself which is not of itself manifest.
If then the petitio principii is to prove by it- may occur in self what is not of itself manifest, this is not to andVrdfiKures prove, since both what is demonstrated and that but in the case by which the person demonstrates are alike du- tive^yiiJ^sm bious, either ' because the same things are assumed by the 3rd and present with the same thing, or the same thing with the same things ;2 in the middle figure, and also in the third, the original question may be the ob- jects of petition, but in the affirmative syllogism, in the third and first figure.3 Negatively when the same things are absent from the same, and both propositions are not alike,4 (there is the same result also in the middle figure,) because of the non- conversion of the terms in negative syllogisms.5 A petitio principii however occurs in demonstrations, as to things which thus exist in truth, but in dialectics as to those (which so sub- sist) according to opinion.
1 i. e. when A and B are the same, thus A is' said to be with C in the conclusion, but B with C in the minor, and in Barbara.
2 i. e. when B and C are the same with which in Barbara A is present, the latter being predicated of B in the major, and of C in the con- clusion.
3 Because there is no affirmative syllogism in the 2nd figure.
4 A petitio principii can only occur in an affirmative proposition.
5 i. e. the terms of a negative proposition, being different in significa- tion, cannot be converted, which would be necessary if a petitio principii could occur in an affirmative proposition. For whenever this fallacy occurs in the other proposition, the subject and attribute should be iden- tical, or nearly so. After all, it must be remembered that the Pet. Prin. is a material, and non-logical, not a formal fallacy.
CHAP. XVII.1 THE PRIOR ANALYTICS. 219
Chap. XVII. — A Consideration of the Syllogism, in which it is argued, that the false does not happen — " an account of £/«'»,'' vapa tovto ovpfiaivtiv, to \ptvfioc.1
That the false does not happen on account of this , This h (which we are accustomed to say frequently in pens in a de-
\. \ « , . n • i j1 duction to the
discussion) occurs hrst in syllogisms leading to impossible, the impossible, when a person contradicts that T'h\c.h is, con".
r ' r Ti- i tradicted not in
which was demonstrated by a deduction to the ostensive de- impossible. For neither will he who does not con- monstratlon- tradict assert that it is not (false) on this account, but that something false was laid down before ;2 nor in the ostensive (proof), since he does not lay down a contradiction. Moreover when any thing is ostensively subverted through n u e osten A B C,* we cannot say that a syllogism is pro- s'veiy through duced not on account of what is laid down, for we then say that is not produced on account of this, when this being subverted, the syllogism is nevertheless completed, which is not the case in ostensive syllogisms, since the thesis being subverted the syllogism which belongs to it will no longer subsist. It is evident then that in syllogisms leading to the impossible, the assertion, " not on account of this," is made, and when the original hypothesis so subsists in refer- ence to the impossible as that both when it is, and when it is not, the impossible will nevertheless occur.
Hence the clearest mode of the false not subsist- „ _.
2. The per-
ing on account of the hypothesis, is when the feet example ot syllogism leading to the impossible 3 does not con- the prop, of join with the hypothesis by its media, as we have which the
_ , syllo consists
observed in the j" Topics. For this is to assume as do not concur. a cause, what is not a cause, as if any one wishing t sop. Eien. to show that the diameter of a square is incom-
1 "Non penes hoc." Averr. — " non per hoc." Waitz. Confer. Sop Elen. v. 11, 29, 1 ; Rhet. ii. 24; Whately, ill. 3 and 4 ; Hill's ed. Aid rich, p. 330.
* Viz. of the propositions anterior to the conclusion. He also who uses an ostensive proof, of course does not adduce a proposition contradictory of what he wishes to prove.
3 Taylor translates this passage somewhat differently, but I prefer the rendering of Buhle. Aristotle joins the Sop. Elen. with the Topics, be- cause the former contain sophistical, as the other dialectic, places.— Note Julius Pacius.
220 aristotle?s organon. fBOOK n.
mensurate with its side should endeavour to prove the argu- ment of Zeno,* that motion has no existence, and * 33P-4Elen' x* to this should deduce the impossible, for the false is by no means whatever connected with what was stated from the first.1 There is however another mode, if the impossible should be connected with the hypothesis, yet it does not happen on account of that, for this may occur, whether we assume the connexion up or down, as if A is placed present with B, B with C, and C with D, but this should be false, that B is with D. For if A being subverted B is neverthe- 3. Another less with C, and C with D, there will not be mode. the false from the primary hypothesis. Or
a°-ain, if a person should take the connexion upward, as if 2 A should be with B, E with A, and F with E,
but it should be false that F is with A, for thus there will be no less the impossible, when the primary hypo- thesis is subverted. It is necessary however to
1. Necessity of . . . .,, . . . » , ,.
connecting the unite the impossible with the terms (assumed) ™P,0Sfubl! from the beginninsr, for thus it will be on account
with the terms o e>'
assumed from of the hypothesis ; f as to a person taking the ■M. e?the im- connexion downward, (it ought to be connected) possible will be with the affirmative term ; for if it is impossible that A should be with D, when A is removed there will no longer be the false. But (the connexion being assumed) in an upward direction, (it should be joined) with the subject, for if F cannot be with B, when B is subverted, there will no longer be the impossible, the same also occurs when the syllogisms are negative.
It appears then that if the impossible is not connected with the original terms, the false does not happen on account of the thesis, or is it that neither thus will the false occur always on account of the hypothesis ? For if A is placed present not with B but with K, and K with C, and this with D, thus also the impossible remains ; and in like manner when we take the terms in an upward direction, so that since the impossible happens whether this is or this is not, it will not be on account
1 That the diameter of a square is not commensurable with its side Upon the argument called Achilles, which Zeno used to support the lead- ing tenet of Parrnenides, viz. the unity of all things; a sophism which after all turns upon the falsity of the major premise. See Plato, Parm. 128, Cousin, Nouv. Frag., and Maiisel, p. 125. Ar. Phys. lib. vi.
CHAP. XVin. XIX.] THE PRIOR ANALYTICS.
221
of the position.* Or if this is not, the false ne- vertheless arises ; it must not be so assumed, as if the impossible will happen from something else being laid down, but when this being subverted, the same impossible is concluded through the re- maining propositions, since perhaps there is no absurdity in inferring the false through several hypotheses, as that parallel lines meet,1 both whether the in ternal angle is greater than the external, or whether a tri angle has more than two right angles.
• i. e. the hy- pothesis.
5. This not
to be employ- ed as if a de- duction to the impossible arises from other terms.
Chap. XVIII. — Of false Reasoning.
False reasoning arises from what is primarily
false. For every syllogism consists of two or
more propositions, if then it consists of two, it is
necessary that one or both of these should be false,
for there would not be a false syllogism from true
propositions.! But if of more than two, as if C book> cnaP-
(is proved) through A B, and these through D E
F G, some one of the above2 is false, and on this account the
reasoning also, since A and B are concluded through them.
Hence through some one of them the conclusion and the false
occur.3
I. False con- clusion arises from error in the primary propositions.
t Vide this
Chap. XIX. — Of the Prevention of a CatasyllogismA
To prevent a syllogistical conclusion being ad- duced against us, we must observe narrowly when (our opponent) questions the argument5 without conclusions, lest the same thing should be twice granted in the propositions, since we know that
1. Rule to pre- vent the ad- vancement of a catasyllogism is to watch against the same term
1 This is a false conclusion from two false hypotheses ; the one, that when a line falls on two parallel lines the internal angle is greater than the external angle ; the other is, if a triangle has three angles greater than two right angles.
2 i. e. D E F G.
3 i. e. the false conclusion C. Vide Aldrich and Huyshe for the rules of syllogism.
4 Kara<rv\\oyiZioOai vox dialcctica, disputatioDum et interrogatiouuin laqueis aliquein irretire. VVaitz.
5 i. e. the propositional matter.
222 Aristotle's organon. £eook ti.
being twice ad- a syllogism is not produced without a middle, but mitted in the the middle is that of which we have frequently spoken. But in what manner it is necessary to observe the middle in regard to each conclusion, is clear from our knowing what kind of thing is proved in each figure, and this will not escape us in consequence of knowing how we sustain the argument.1
Still it is requisite, when we argue, that we and meThod^f should endeavour to conceal that which we direct masking our the respondent to guard against,2 and this will be
design in hi"- °
gument— two done, first, if the conclusions are not pre-syllogized, ingyth°iLeffect Dut are unknown when necessary propositions are
assumed, and again, if a person does not question those things which are proximate, but such as are especially
immediate,* for instance, let it be requisite to con-
*eiysidLogtca.n" clude A of F> and ^t the media be B C D E ; therefore we must question whether A is with B, and again, not whether B is with C, but whether D is with E, and afterwards whether B is with C, and so of the rest. If also the syllogism arises through one middle, we must begin with the middle, for thus especially we may deceive the re- spondent.
Chap. XX. — Of the Elenchus?
•• The e,en- Since however we have when, and from what man- tio) is a syiio- ner of terminal subsistence syllogism is produced, it
1 We shall know the principal conclusion, as being the subject matter of our dispute.
* i. e. if we wish to infer an indefinite conclusion, we should secretly endeavour that our opponent may grant us two propositions, in which the middle is latent ; if however we wish to infer a definite conclusion, we must assume propositions containing the middle from which the con- clusion is inferred mediately and remotely. Taylor, from whom the above note is chiefly taken, appears to have fallen into the same error as Buhle, Boeth, and some of the older interpreters, by reading fiiaa instead of afitaa, which I have followed from Waitz and Averrois, and which the former evidently proves to be the right reading. Vide Waitz, torn. i. p. 521 ; Aver. vol. i. p. 159; Top. 8. Immediate inference is that with which opposition and conversion are connected; mediate pertains to in- duction and syllogism.
3 An tTri\eipt]fia admits of a species of this, which is called airoprjfia The original meaning of IXtyxog is, as Dr. Hessey observes, (Table 4,) the refutation of an actual adversary's position, and so indirectly a con-
CHAP. XXI.] THE PRIOR ANALYTICS.
223
is also clear when there will and will not he an gism of contra-
Elenchus. For all things being granted, or the an- duce°" MchPr°'
swers being arranged alternately, for instance, the there must be
one being negative and the other affirmative, an elen- thoughgthe iat-
chus may be produced, since there was a syllogism te.r ™ay subsist
J r ' . •,.°, without the
when the terms were as well in this as in that former. (Conf. way, so that if what is laid down should be con- s°P-Elen-fi-) trary to the conclusion, it is necessary that an elenchus should be produced, for an elenchus is a syllogism of contradiction. If however nothing is granted, it is impossible that there should be an elenchus, for there was not a syllogism when all the terms are negative, so that there will neither be an elen- chus, for if there is an elenchus, it is necessary there should be a syllogism, but if there is a syllogism, it is not necessary there should be an elenchus. Likewise, if nothing should be universally laid down in the answer,* for the determination of the elenchus and of the syllogism, will be the same.1
* i. e. if the respondent should not con- cede any uni- versal proposi- tion.
Chap. XXI. — Of Deception, as to Supposition — Kara Conf- Uet*-
J . • <■* i 2 lib. vi. and iii.,
TT)V VTroXrjipiv- and de Animfi,
iii. 3, 7.
Sometimes it happens, that as we are deceived in i. This kind of
the position of the terms,! so also deception arises as f0e1<deptlon two"
to opinion, for example, if the same thing happens + vide ch. 33,
to be present with many things primary,3 and a
person should be ignorant of one, and think that it is
present with nothing, but should know the other.
For let A be present with B and with C,
per se, (that is, essentially,) and let these, in like manner, be
with every D ; if then somebody thinks that A is with every
B, and this with every D, but A with no C, and j Through b.
this with every D ; he will have knowledge J * p
and ignorance § of the same thing, || as to the samc.^f n a.
firmation of our own; but, practically, the process of meeting a real or supposed opponent, is the same. Vide Rhet. ii. '22 and 24.
1 The reader will profitably read upon this chapter, Hill's notice and examples of the Elenchus, given at p. 3"22 of his Logic.
* See Hill and Whately on Fallacies.
* So Waitz; Buhle, and Taylor read Trpwrwg; the latter adds, i. e. " without a medium," a meaning which is evidently concurred in by Waitz.
224 aristotle's orgaxox. "book n.
2 Again, if one should be deceived about thosfa
* « waJrw things which are from the same class,1 * as if A is w<tt.«x«<m. with B but th;s w;t]1 q, an(j q w;th T)) an(i
should apprehend A to be with every B, and again with no C, he will at the same time both know and not apprehend its presence. Will he then admit nothing else from these things, than that he does not form an opinion on what he knows ?2 for in some way, he knows that A is with C through t c being a B, just as the particular is known in thef uni- part of B. versal, so that what he somehow knows, he ad-
I i. e. in the ' . . . ' .
first deception, mits he does not conceive at ail, which is lmpos- middhts^nBar- sible. In what, however, we mentioned before,^ bara and Ceia- if the middle is not of the same class, it is impos-
rent, not being ... • i ,i •,• t
subaltern. sible to conceive both propositions, according to
Barbara"^01 °f eacn °f the media,3 as if A were with every B, § H Major of but with no C,|| and both these with every D.^f irVhe minor of For it happens that the major proposition assumes both- a contrary, either simply or partially,4 for if with
every thing with which B is present a person thinks A is present, but knows that B is with D, he also will know that A is with D. Hence, if, again, he thinks that A is with nothing with which C is, he will not think that A is with any thing with which B is, but that he who thinks that it is with every thing with which B is, should again think that it is not with something with which B is, is either simply or partially contrary. Thus however it is impossible to think, still nothing prevents (our assuming) one proposition according to each (mid- dle),5 * or both according to one, as that A is with every B, and B with D, and again, A with no C. For a de- ception of this kind resembles that by which we are deceived about particulars, as if A is with every B, but B with every C, A will be with every C.6 If then a man knows that A is
' Taylor says, " co-ordinatum ; " Waitz, " ex eadem serie." It is clear, that subalterns are intended.
2 For in the major of Celarent, he assumes no C is A, whereas he knows, as will be shown, that C is A.
3 That is, he cannot, at one and the same time, assume both the prop. of Barbara, and both of Celarent.
4 i. e. by reason of D, the subject of both B and C.
5 i. e. one prop, for B, the other for C, as every B is A, no C is A, the minors not being added.
s Vide Post An. i. 1 ; Eth. Nicom. b. vi. c. 3.
CHAP. XXI.] THE PRIOR ANALYTICS. 225
with every thing with which B is, he knows also that it is with C ; still nothing prevents his being ignorant of the ex- istence of C, as if A were two right angles, B a triangle, and C a perceptible triangle.* For a man may think „ Ex le (1 s that C does not exist, knowing that every triangle has two (equal to) right angles, hence he will know and be ignorant of the same thing at once ; for to know 3 Distinction that every triangle has angles equal to two right, between uni-
■ • i -a ■ • . .« • vcrsJil 3.11(1 pflr-
is not a simple thing, j but in one respect arises ticuiar know- from possessing universal science, in another, par- ^j^'jj is „an. ticuiar science. Thus therefore he knows by uni- ceps amw- versal science, that C has angles equal to two right guum" Waitz' angles, but by particular science he does not know it, so that he will not hold contraries. In like manner is the reasoning in the Meno,| that discipline is reminiscence, for it t Meno,(Piat.) never happens that we have a pre-existent know- p- si. Ritter,
, . „ rr . . i • i • i • r vol. n. p. 293.
ledge ol particulars, but together with induction, b . „, „
°. , . n • i • r. § Cf. Eth. VI. 4.
receive the science ot particulars as it were by recognition ; since some things we immediately know, as (that there are angles) equal to two right angles, if we know that (what we see) is a triangle, and in like manner as to other things.
By universal knowledge then we observe par- 4. our observ- ticulars,1 but we do not know them by an (innate) ation of parti"
B A
Ex. 1 . Every triangle has angles equal to two right angles (known) C B
This is a triangle (unknown)
m?- i_ i ,, ". .,, , S known by universal
. • . Ihis has angles equal to two right angles j unknownJ by particular
knowledge. Vide Post. An. i. 4.
1 It would weary the reader, and far exceed the limits to which, ne- cessarily, we confine our remarks, to enter fully into the analysis of the distinction here drawn. In the Post An. i. 6, the subject is again ntered upon, but for all necessary understanding of the matter, the reader is referred to Sanderson upon Certainty, book iii., and to Mansel's notes upon Syllogism quoad Materiam, artic. Opinio, p. 97, et seq. Al- though we have translated inroXrjipvs, supposition, yet as it approaches nearest to our idea of logical judgment, (see Trendelenburg de Anima, p. 469,) the latter term shows at once, not only the nature, but frequently the causes, of error, (An. Post. i. 6, 8,) which may be individual, that is, con- nected with the person's own constitution of mind or circumstances, and, both as to universals and particulars, partake much of the character of
Q
e
226 aristotle's organon. [book ir.
culaw, derived peculiar knowledge, hence we may be deceived iedge°ofruni°W about them, yet not after a contrary manner, but yersais, a pecu- while possessing the universal, yet are deceived
lisritv noticed.
(Met. book vi. in the particular. It is the same also as to what 9.) Lockers Ess. we have Sp0ken of, for the deception about the vi. 2. middle is not contrary to science about syllogism,
nor the opinion as to each of the middles. Still nothing prevents one who knows that A is with the whole of B, and this again with C, thinking that A is not with C, as he who knows that every mule is barren, and that this (animal) is a mule, may think that this is pregnant ; for he does not know that A is with C 5. a deception from not at the same time surveying each. Hence from knowing jt }s evident that if he knows one (of the proposi-
one prop, and . v r r
being ignorant tions), but is ignorant of the other, he will be de- ceived as to how the universal subsists with refer- ence to the particular sciences. For we know nothing of those things which fall under the senses as existent apart from sense,1 not even if we happen to have perceived it before, un- less in so far as we possess universal and peculiar knowledge,
6 scientific anc^ no* m tna* we energize. For to know is pre- knowiedge is dicated triply, either as to the universal or to tripiyC.ate tne peculiar (knowledge), or as to energizing, so
that to be deceived is likewise in as many ways. Nothing therefore prevents a man both knowing and being de- « i. e. so as not ceived about the same thing, but not in a con- to noid a self- trary manner,* and this happens also to him, who
either. What however Aristotle here means is, that scientific knowledge, or that of particulars, is said of truths deduced from higher truths ; hence to each of these there is a foundation, in universal knowledge (vo&v), viz. we originally begin our speculation wpon them, s£ akrjQwv /cat 7rpa>raiv, or intuitively perceived truths, though these generals will not of themselves suffice to prevent error in particulars, seeing that to each of the last its own peculiar study and examination is appropriately necessary. This is fully borne out by the relative meanings of iiricTiifiri and vovq. The word "innate" we have inserted from Buhle; by a contrary manner is not only meant, as Taylor says, "not in a manner contrary to science," but without holding a contradictory opinion, we may know the general, yet mistake the particular truth. (Cf. Hill's note on Objective and Sub- jective Certainty. Leibnitz de Stylo Nizolii. Sir W. Hamilton Reid's Works, p. 671.)
1 Vide de Anima, lib. ii. 5 and 6. — aioQr\oiQ is perception by the senses, as vovg is the intellectual element. Vide Eth. vi. 1 and 12 ; in the lat- ter, aioQ. is reckoned intuition.
CHAP. XXI.] THE PRIOR ANALYTICS. 22"/
knows each proposition, yet has not considered contradictory before ; ' for thinking that a mule is pregnant, he °Pin,on- has not knowledge in energy* nor again, on ac- * "™t«i(p-
„ . . to„ , it ■ 7e<". " Scien-
count oi opinion/ has he deception, contrary to tiam actu." knowledge, since deception, contrary to universal >i"tle8"./Vlde 'knowledge), is3 syllogism.
Notwithstanding, whoever thinks that the very 7. From a de- being of good is the very being of evil, will ap- ^nd°a person prehend that there is the same essence of good may imagine and of evil ; for let the essence of good be A, and concurs with the essence of evil B ; and again, let the essence its contrary. of good be C. Since then he thinks that B and C are the same, he will also think that C is B ; and again, in a similar manner, that B is A, wherefore that C is A.| E le Far just as if it were true that of what C is predi- cated B is, and of what B is, A is ; it was also true that A is predicated of C ; so too in the case of the verb " to opine." In like manner, as regards the verb " to be," for C and B being the same, and again, B and A, C also is the same as A. Likewise, as regards to opine, is then this necessary,4 if any one should grant the first ? but perhaps that is false,5 that any one should think that the essence of good is the essence of evil, unless accidentally,6 for we may opine this in many ways, but we must consider it better.7
1 i. e. he has not considered both propositions together.
2 i. e. because he thinks the mule parturient.
3 i. e. as Taylor says, it is a deceptive syllogism, which proves no mule barren, because the universals are contrary. The opinion proposed is however particular, because it thinks this particular mule barren.
B A
Ex. 2. He thinks the essence of evil is the essence of good
C B
He thinks the essence of good is the essence of evil C A
. • . He thinks the essence of good is the essence of good.
4 That one who conjointly considers both propositions should hold con- trary opinions, if a person should state the essence of good and of evil to be identical.
s Vide the opinion of Heraclitus, upon the nature of contraries; also Met. books ix. and xiii.
• That is, what is essentially good, for instance, to return a person's property, may be in a certain case bad, as to give a sword to a madman.
1 In the Ethics and Metaphysics.
228 Aristotle's organon. [book n.
Chap. XXII. — On the Conversion of the Extremes in the first
Figure.
1 if the terms When the extremes are converted, the middle connected by a must necessarily be converted with both. For if are converted! A is present with C through B, if it is converted, the middle an(j q js with whatever A is, B also is converted verted with with A,* and with whatever A is present, B also both- is through the middle C, and C is converted with
e major, -g ^ through the middle A. The same will occur with negatives, as if B is with C,1 but A is not with B,2 neither will A be with C, if then B is converted with A, C also will be converted with A. For let B not be with A,3 neither then will C be4 with A, since B was with every C, and if C is converted with B, (the latter) is also converted with A ; for of whatever B is predicated, C also is, and if C is converted with A, B also is con- verted with A, for with whatever B is present, C also is,5 but 3. Themodeof C is not present with what6 A is. This also alone mTative" f *io- DeSms from the conclusion, (but the others not gism, begins similarly,) as in the case of an affirmative syllo- X"sfon,eas0iri gism. Again, if A and B are converted, and C Barbara. and D likewise ; but A or C must necessarily be
present with every individual ; B and D also will so subsist, as that one of them will be present with every individual. For since B is present with whatever A is, and D with what- ever C is, but A or C with every individual, and not both at the same time, it is evident that B or D is with every indi- vidual, and not both of them at the same time ; for two syllo- I omitted by gisms are conjoined. :j: Again, if A or B is with waitz. every individual and C or D, but they are not
2- present at the same time, if A and C are converted
B also and D are converted, since if B is not present with a certain thing with which D is, it is evident that A is present
1 The minor of Celarent. 2 The major of Celarent.
3 The minor of Camestres. 4 The conclusion of Camestres.
s i. e. every B is C, this is the major of Camestres, inferred from the conversion of the minor of Celarent'.
• i. e. no A is C, the minor of Camestres, taken from the conversion of the conclusion of Celarent.
CHAV XXII.] THE PRIOR ANALYTICS. 229
with it. But if A is, C also will be, for they are converted, so that C and D will be present at the same time, but this is impossible ; l as if what is unbegotten is incorruptible, and what is incorruptible unbegotten, it is necessary that what is be- gotten should be corruptible, and the corruptible begotten. But when A is present with the whole of B and C, and is predicated of nothing else, and B also is with every C, it is necessary that A and B should be converted, as since A is predicated of B C alone, but B itself is predicated both of it- self and of C, it is evident that of those things of which A is predicated, of all these B will also be predicated, except of A itself. Again, when A and B are with the whole of C, and C is converted with B, it is necessary that A should be with every B, for since A is with every C, but C with B in conse- quence of reciprocity, A will also be with every B. But when of two opposites A is preferable to B, and 4 caseofeiec- D to C likewise, if A C are more eligible than B tjon of oppo- D, A is preferable to D, in like manner A should be followed and B avoided, since they are opposites, and C (is to be similarly avoided) and D (to be pursued), for these are opposed. If then A is similarly eligible with D, B also is simi- larly to be avoided with C, each (opposite) to each, in like man- ner, what is to be avoided to what is to be pursued. Hence both (are similar) A C with B D, but because (the one are) more (eli- gible than the other they) cannot be similarly (eligible), for (else) B D would be similarly (eligible) (with A C). 5 The r t If however D is preferable to A, B also is less to be good and less avoided than C, for the less is opposed to the less, fo thetesYgood and the greater good and the less evil are prefer- and greater able to the less good and the greater evil, where- fore the whole B D is preferable to A C. Now however this is not the case, hence A is preferable to D, consequently C is less to be avoided than B. If then every lover accord- ing to love chooses A, that is to be in such a condition as to be gratified, and C not to be gratified, rather than be gratified, which is D, and yet not be in a condition to be gratified, which is B, it is evident that A, i. e. to be in a condition to be gratified,
1 He had before shown B to be predicated of D universally, though it does not hence follow that they are convertible unless D is shown to be predicated of B universally ; this is omitted for brevity, as the proof is the same as the other.
230 Aristotle's organon. [book n.
is preferable to being gratified.1 To be loved then is preferable according to love to intercourse, wherefore love is rather the cause of affection than of intercourse, but if it is especially
g The desire (tne cause) °f tnis> this also is the end. Where- of the end, the fore intercourse either, in short, is not or is for the pursuit!6 (Eth? sake of affection, since the other desires and arts b. i. c. 7.) are thus produced.* How therefore terms sub-
» \Vaitz con- . L . ...... ..
eludes the sist as to conversion, also in their being more eli-
chapter here. gibie or m0re to be avoided, has been shown.
Chap. X XIII. — Of Induction.2
1. Not only di- We must now show that not only dialectic and deeicticsyiioa-PO demonstrative syllogisms are produced through gisms, hut also the above-named figures, but that rhetorical are
rhetorical, and , . . . ° . . _
every species of also, and in snort, every kind ot demonstration arTthrough the and ^y every method. ( For we believe all things above-named either through syllogism or from induction!)
Induction, then, and the inductive syllogism is to prove one extreme in the middle through the other,3 as if B is the middle of A C, and we show through C that A is with B, for
1 This confirms the opinion of Plato in the Symposium. The demon- stration is thus ; if of four terms the first is preferable to the 2nd, and the 4th to the third, but the 1st and 3rd together preferable to the 2nd and 4th together, then the 1st is preferable to the 4th, hence to be in a condition adapted to be gratified is preferable to being gratified.
2 Aristotle attributes the discovery of induction and also of definition to Socrates, but the induction of the latter (who exhibited both dialec- tically) comes closer to the " example " of Aristotle. Vide Gorgias 460, also Metaph. xii. 4, 5.
1 i. e. to prove the major term of the middle by the minor. The ex- pression e£ iiraywyriQ ovXk. — used here, does not (as Mansel justly re- marks) denote the syllogism proper, or reasoning from a whole to its parts, but comprehends formal reasoning generally, as in Rhet. ii. 25, Enthymem is spoken of as including example. For induction properly is an inverted syllogism, which argues from the individuals collected to the universal or whole class they constitute, whereas syllogism does just the reverse. Upon the various kinds of induction see Hill's Logic, 229, where some examples are given ; also Mansel's Logic, Appendix note F. Inasmuch as we seldom can enumerate all the individuals of a class, we rarely meet with a specimen of perfect in- duction, but we agree with Whately in believing, that the cause of the opposition of induction to syllogism, arises entirely from the inac- curacy in the use of the word. Vide Whately, Log. b. iv. c. i. 1. Even however the distinction between perfect and imperfect induction is extra-
CHAP. XXIII.] THE PRIOIl ANALYTICS.
231
thus we make inductions. Thus let A be long- lived, B void of bile, C every thing long-lived, as man, horse, mule ; A then * is present with the whole of C, for every thing void of bile is long- lived, but Bf also, or that which is void of bile, is present with every C, if then C is converted with B,| and does not exceed the middle, it is necessary that A should be with B. For it has been before shown,1 that when any two things are present with the same thing, and the extreme is convertible with one of them, that the other predicate will also be present with that which is converted We must however consider C as composed of all singulars, for induction is produced through § all. A syllogism of this kind however is of the first, and immediate proposition ; for of those which have a middle, the syllogism is through the mid- dle, but of those where there is not (a middle) it proved without is by induction.2 In some way also induction is opposed to syllogism, for the latter demonstrates the extreme II of the third through the middle, but the former the extreme of the middle through the third. % To nature therefore the syllogism pro- duced through the middle is prior or more known, but to us that by induction is more evident.3
logical. The reader may profitably consult on this subject the Edinburgh Review, No. 115, p. '229; Bacon, Nov. Orga. lib. 2, Aph. x. ; Sir W. Hamilton lieid's Works, p. 712. The word tiraywyri, or induction, is clearly taken from the Socratic accumulation of instances, serving as antecedents to establish the requisite conclusion. Confer. Cicero de In- ventione i. 32.
1 In the preceding ch.
C A
Ex. 1. Every man, horse, mule, is long-lived B C
Whatever is void of bile is man. horse, mule B A
. ' . Whatever is void of bile is long-lived.
* Vide Aldrich's Logic upon the second species of demonstration, v. 5, 1 ; also remarks made before upon the use of the terms mediate and im- mediate.
* Some things are more known to nature, but others more known to us. Vide Post. An. i. 1, 2 ; Pliny, b. i. z. 1 ; Metaph. b. ii. c. 1. Com-
2. Induction is proving the major term of the middle by the minor.
* The major of the induction . in the 3rd figure.
t The minor o/ the induction.
I A reduction to the 1st figure.
§ Example (1.)
3. Induction is occurrent in those demon- strations, which are
|| i. e. the major.
f The minor.
■
230
Aristotle's organon.
[book If.
is prefercle to being gratified.1 To be loved then is preferable accordin to love to intercourse, wherefore love ia rather the cause ofiffection than of intercourse, but if it is especially „,, A . (the cause) of this, this also is the end. Where-
The desr V ' .',.,. . c ,
fore intercourse either, in short, is not or is tor the sake of affection, since the other desires and arts are thus produced.* How therefore terms sub- sist as to conversion, also in their being more eli- gible or more to be avoided, has been shown.
6
of the end, e incentive tae pursuit, (h. b. i. c. 7.) * Waitz cot eludes the chapter hen
Chap. XXIEL— Of Induction.
1. Not only, alectic and a- deictic syllo- gisms, hut a> rhetorical, ai every specieif demonstrate are through e above-name, figures.
We must now show that not only dialectic and demonstrative syllogisms are~"prbducedthrough the above-named figures, but that rhetorical are also, and in short, every kind of demonstration and by every method. ( For we believe all things either through syllogism or from induction^ Induction, then, and the inductive syllogism is to prove onextreme in the middle through the other,3 as if B is the middle oA C, and we show through C that A is with B, for
1 This cifirms the opinion of Plato in the Symposium. The demon- stration isius; if of four terms the first is preferable to the '2nd, and the 4th toie third, but the 1st and 3rd together preferable to the 2nd and 4th tather, then the 1st is preferable to the 4th, hence to be in a condition ;apted to be gratified is preferable to being gratified.
a Aristoj attributes the discovery of induction and also of definition to Socratebut the induction of the latter (who exhibited both dialec- tically) coes closer to the " example " of Aristotle. Vide Gorgias 460, also Metap xii. 4, 5.
* i. e. torove the major term of the middle by the minor. The ex- pression {£7rayu>yrjc ffvW. — used here, does not (as Mansel justly re- marks) diote the syllogism proper, or reasoning from a whole to its parts, but jmprehends formal reasoning generally, as in Rhet. ii. 25, Enthymerris spoken of as including example. For induction properly is an invesd syllogism, which argues from the individuals collected to the unersal or whole class they constitute, whereas syllogism does just b reverse. Upon the various kinds of induction see Hill's Logic, 221 where some examples are given ; also Mansel's Logic, Appendix ote F. Inasmuch as we seldom can enumerate • individuals)f a class, we rarely meet with a snaoMMB duction, b we agree with Whately in beljj the opposiln of induction to syllogism, arij curacy in e use of the word. Vide WhaU however tl distinction between perfect ap-
m
m
sc
gtf
$sr*
m
m~
y ■ IMF -
H
!<
f J jj-^j
*****
.. ..
.■=..1 Ittifc
Mifl
- > *•
...-■ n
CHAP. XXIII.] THE PRIOK ANALYTICS. 231
thus we make inductions. Thus let A be long- lived, B void of bile, C every thing long-lived, asJroVlnKlT " man, horse, mule; A then* is present with themaJ"rtenn °' whole of C, for every thing void of bile is long-tile minor''. y lived, but Bf also, or that which is void of bile,* The major of is present with every C, if then C is converted* ulea^'0" " with B,| and does not exceed the middle, it isflf?ure- necessary that A should be with B. For it haStUmVuS0' been before shown,1 that when any two things a reduction are present with the same thing, and the extreme^0,^ lst is convertible with one of them, that the other predicate will also be present with that which i converted. We must however consider C as composed of all singulars, for induction is produced through § all. Xamp e A syllogism of this kind however is of the first,3- induction is
j • t , • . n n i , . . occurrent in
and immediate proposition ; for of those whichthose demon- have a middle, the syllogism is through the mid-^J^0"^ die, but of those where there is not (a middle) itpr»xed witnout is by induction.2 In some way also induction iga mi e" opposed to syllogism, for the latter demonstrates n ie the the extreme || of the third through the middle, buimaJ°r- the former the extreme of the middle through the, The minor third.^f To nature therefore the syllogism pro duced through the middle is prior or more knoxi, but to us that by induction is more evident.3
logical. The reader may profitably consult on this subjecthe Edinburgh Review, No. 115, p. 229; Bacon, Nov. Orga. lib. 2, Ap x. ; Sir W. Hamilton Keid's Works, p. 712. The word kiraywyri, < induction, is clearly taken from the Socratic accumulation of instaiBS, serving as antecedents to establish the requisite conclusion, ventione i. 32.
1 In the preceding ch.
C A
Ex. 1. Every man, horse, mule, is long-lived
B C
Whatever is void of bile is man, horse, mule B A
. ' . WhateT ived.
J Vide »''
1;
i
ConferCicero de In-
1
/
(1
■
■ ■
232 aristotle's organon. [book ii
1. *<„««««.„«., Chap. XXIV.-O/ Example}
or example, is
majo'^/the Example is when the extreme is shown 2 to be middle by a present with the middle through something similar bu^gThe111 to the third,3 but it is necessary to know that the minor. middle is with the third, and the first with what
is similar.4 For example, let A be bad, B to (make war) upon neighbours, C the Athenians against the Thebans, D the Thebans against the Phocians. If then we wish , to show that it is bad to war against the Thebans,
* Example. , • °
we must assume that it is bad to war against neighbours, but the demonstration of this is from similars, as that (the war) by the Thebans against the Phocians (was bad). Since then war against neighbours is bad, but that against the Thebans is against neighbours, it is evidently bad to war against the Thebans, so that it is evident that B is with C, and with D, (since both are to war against neighbours,) and that A is with D, (for the war against the Phocians was not advantageous to the Thebans,) but that A is with B will be
pare also the whole chapter with Rhet. b. i. c. 2, b. ii. c. 23 ; and Ethics, Nic. b. vi. c. 3.
1 Compare Rhet. b. ii. c. 20, 24, and b. iii. c. 1 7. Example differs from induction, 1st, in that the latter proves the universal from a complete enumeration of individuals, whilst example selects single cases; 2nd, Induction stops at the universal, whilst example infers syllogistically a conclusion regarding another individual : in fact, example includes an imperfect (therefore illogical) induction and a syllogism. Sometimes it is called loosely reasoning from analogy, but as logic recognises only formal consequence, neither analogy nor example have any logical force. (Vide Mill's Logic, b. iii. ch.20 ; also Mansel, p. 82.) The distinction is however better drawn by Hill, p. 243, comprehending, 1st, the antecedent, which in induction consists of several singular cases, but in example frequently of only one. 2nd, the conclusion, being universal in induction, but singular in example : he adds as usual various examples. See also Whately, b. iv. ch. 1 and 2. As to the place which irapaStiypa occupies with regard to the relation of the subject matter of a premise to the sub- ject matter of the conclusion, in the consideration of Enthymem, the ex- cellent Tables of Dr. Hessey, 2, Div. 1, and Table 5, give a complete scheme of their position, also the statement of the argument given in the text. It is evident, as Aristotle shows, that example consists of two elements, a quasi inductive syllogism apparently in Fig. 3, and a deductb« syllogism in Fig. 1, so it is assailable in each of these.
* i. e. the major. 3 The minor.
* i. e. with what is similar to the minor.
CHAP. XXV.] THE PRIOR ANALYTICS. 233
shown through D. In the same manner also if the demon- stration of the middle as to the extreme should be through many similars, wherefore it is evident subs'utTas e that example is neither as part to a whole, nor as p,art l,0 part*
A *■ J (air jutpo?
whole to a part, but as part to part,1 when both are ^p"? ««p?r.)
*■ "wherein it
under the same thing,2 but one is known. It differs from in- (example) also differs from induction, because the note abo'veY*16 latter shows from all individuals that the extreme3 is present with the middle, and does not join the syllogism to the extreme, but the former,4 both joins it, and does not de- monstrate from all (individuals).
Chap. XXV. — Of Abduction.* 1. 'Anaywy^
a syllogism
Abduction is when it is evident the first is pre- prem? certain, sent with the middle,0 but it is not evident that and the n}™T
, . , -iii i i • • more credible
the middle is with the last, though it is similarly than the con- credible, or more so, than the conclusion ; more- clusion- over if the media of the last and of the middle be few, for it by all means happens that we shall be nearer to knowledge. For instance, let A be what may be taught, B 2. Moreover science, C justice ; that science then may be taught ^proved bythe is clear, but not whether justice is science. If interposition
1 " Exemplo utemur ut singula demonstremus per singula." — Waitz. A is a whole, B part of A, C D parts of B, when therefore example pro- ceeds from D to C, it proceeds from part to part.
2 As C and D under the same A, but D more than C is known to be under A.
3 i. e. the major A with the middle B, and does not join the syllogism with the minor, in other words, it does not prove A of C.
4 Example proves A of C, and does not demonstrate from all individuals, but only from some of them, under B.
5 This term (anay.) must not be confounded when it occurs alone, with the meaning it bears, in reference to the impossible, for when it is by itself, as here, it signifies a syllogism with a major premise certain, and a minor more probable, or demonstrable, than the conclusion. Aldrich is so far right in using the word '"oblique," as applied to it, (though utterly wrong in limiting its sense only to the " ducens ad im- possible,") in that the word means" a turning oft'," from the immediate point to be proved, to something else on which it may depend, this is the foundation of the meaning it bears here, and the more general acceptation of it as a deduction per impossibile. Syllogistically it holds a place between the demonstration and the dialectic syllogism. Confer. Mansel and Hill's Logic. 6 i. e. when the major is known.
234 ARISTOTLE'S ORGANON. [BOOK II
of few middle therefore B C is equally or more credible than terms. A C,1 it is abduction, for we are nearer know-
• Example (i.) ^e^Se because of our assuming A C, not possess- ing science before.* Or again, if the media of B C should be few, for thus we are nearer knowledge, as 2 if D should be to be squared, E a rectilinear figure, and F a circle, then if, of E F there is only one middle, for a An.epr.ac.tZ24n circle to become equal to a rectilinear figure, t Example (2.; through lunula?, will be a thing near to know- ledge.! But when neither B C is more credible than A C, nor the media fewer, I do not call this abduction, nor when B C is immediate, for such a thing is knowledge.
. _. Chap. XXVI.— Of Objection.3
(Instantia,) a
proposition Objection is a proposition contrary to a propo-
,iontr?iT"v to 'i
proposition, it sition, it differs however from a proposition be-
1 The minor than the conclusion.
B A
Ex. 1. Every science may be taught. — Known.
C [ Equally or more credible than the
All justice is science. \ conclusion.
C A
. • . All justice may be taught. — Unknown.
2 As Taylor remarks, Arist. here refers to the quadrature of the circle by Hippocrates of Chius.
E D
Ex. 2. Every rectilinear figure may be squared. — Known.
p v ( proved through
/ 'A A !
Every circle may become a rectilinear figure. ) ?ne miac}le>
J J ° \i. e. per lunulas.
F D | This is proved through many
Every circle may be squared. \ media.
3 We assail an adversary either by bringing an ivaraaiq to show his conclusion is not proved, or by disproving his conclusion, by an avrtavX- Xoyia/xog, (objection to consequent,) i. e. by proving its contradictory by means of a new middle term. Now "Evorao-tc may either be material, or objection to antecedent, or formal objection to consequent. If material, it may be either Ik tclvtov, Ik tov tvavriov, sk tov u/ioiov Ik jcpio-£a>e, or «k tov Kara do£av : (see by this ch.) the relative position of which the reader will find admirably laid down in Dr. Hessey's Schema Rhetorica, wherefrom this note is chiefly taken. The present ch. causes us chiefly to notice the "Ei>o-racrtc Ik ravrov, and this may be either KaOoXov, or Kara yt'ipoQ. In proving the first we assume as a new middle, a term
CHAP. XXVI.] THE PRIOR ANALYTICS. 235
ca ase objection may be partial, but proposition differs from . cannot be so at all, or not in universal syllo- proposition in gisms. Objection indeed is advanced in two ways, l at U maybe
more extensive, and icaSoXod, as compared with the subject of the original irpoTamg ; in proving the ever. Kara juspoc, we assume as a new middle, a term less extensive than the subject of the original 7rp6ruo-ic. Now A may be assailed by proving its contrary, or contradictory, in Fig. 1, or its contradictory in Fig. 3. E may be assailed by proving its contrary (or contradictory) in Fig. 1, or its contradictory in Fig. 3. Lastly, an affirma- tive proposition (but not a negative) may be assailed by an Enstatic Enthymem, in Fig. 2, but Arist. objects to do so. Conf. upon this ch., Julius Pacius ; Whately on the Nature and Fallacy of Objections ; Anal. Post. i. 12 ; Rhet. ii. 26 ; Waitz, p. 535, in loc. Hermogenes, in his trea- tise upon Invention, does not consider objection in the same respect as Arist. The apparent discrepancy between this chap, and the account of objection in the Rhetoric is noticed by Dr. Hessey, Table 5.
Ex. 1. Proposition.
A B
There is one science of contraries.
Objection. A C
There is not one science of opposites
B C
Contraries are opposites
A B
. ' . There is not one science of contraries.
Ex. 2. Proposition.
A B
There is one science of contraries.
Objection. A C
There is not one science of the known, and of the unkncvn
O B
The known and the unknown are contraries
A B
There is not one science of contraries.
Ex. 3. Proposition.
A B
. • . There is not one science of contraries.
Objection. A C
There is one science of opposites
B C
Contraries are opposites
A B
. * . There is one scien w of contraries.
236
ARISTOTLE S ORGAXON.
[book n.
either xa06\ou or £7t< Mtpor.
atives and negatives.
2. Method of alleging the
t Celarent. X Felapton.
and by two figures ; in two ways, because every objection is either universal or particular, and by two figures, because they are used opposite to the proposition, * i. e. affirm- and opposites * are concluded in the first and third figure alone. When then a person requires it to be admitted that any thing is present with every individual, we object either that it is with none, or that it is not with a certain one, and of these, the being present with none, (is shown) by the first figure,"f but that it is not with a certain one by the last.| For instance, let A be "there is one science, and B contraries ;" when therefore a person advances that there is one science of contraries, it is objected either that there is not the same science of opposites, altogether, but contraries are opposites, so that there is the § Example (i.) grsj. figUre .{j or t]ia^ there is not one science of
the known and of the unknown, and this is the third figure,|| for of C, that is, of the known, and of the unknown, it is true that they are contraries, but that there is one science of them is false.^f Again, in like manner in a negative proposition, for if any one asserts that there is not one science of contraries, we say either that there is the same science of all opposites, or that there is of certain contraries, as of the salubrious, and of the noxious ; that there is therefore (one science) of all things is by the first figure,* but that there is of certain by the third.f In short, in all (disputations) it is necessary that he who universally objects should apply a contradiction of the propositions to the universal,^ as if some one should assert that there is not the same science of all contraries, (the ob- jector) should say, that there is one of opposites. For thus it is necessary that there should be the first figure, since the middle becomes an universal to that
Felapton.
IT Example (2.)
* Barbara.
t Darapti.
t Example (3.) 3. Rule for the
KaOoXov evtrraiTi?.
4. And for that
Proposition the same.
Objection. A C
There is one science of the salubrious and noxious
C B
The salubrious and noxious are contraries A B
• •t There is one science of certain contraries.
CHAP. XXVI.] THE PRIOR ANALYTICS 237
(which was proposed) at first, but he who objects nv0£pe'" Vide
in part (must contradict) that which is universal, § § Subject. of which the proposition is stated, as that there is not the same
science of the known, and the unknown, for the m _ .
contraries are universal with reference, to these.* attributed to
The third figure is also produced, for what is par- uhnek^°™™d
ticularly assumed is the middle, for instance, the universal to
known and the unknown ; as from what we may pa
infer a contrary syllojnstically, from the same we en- 5- ' Objection
j j o *^„ . adduced in the
deavour to urge objections. Wherefore we adduce first and third
then (objections) from these figures only,f for in fieures alone-
these alone opposite syllogisms are constructed, + Hence ^ the
since we cannot conclude affirmatively through the prop, is nega-
middle figure.1 Moreover, even if2 it were (pos- tlon'toit cannot
sible), yet the (objection), in the middle figure Je proper in the
,lJ . / • t \ •/» 2nd figure since
would require more (extensive discussion), as it the objection anyone should not admit A to be present with B, ought t0 affirm- because C is not consequent to it, (B). For this is manifest through other propositions, the objection however must not be diverted to other things, but should forthwith have the other proposition apparent,3 wherefore also from this figure alone there is not a sign.4
We must consider also other objections, as those . _.. „
i> t ■ -i 6- Objections
adduced from the contrary, from the similar, and of other kinds from what is according to opinion,5 also whether vWeenot! i?d' it is possible to assume a particular objection from ?upra ; Rhet. the first, or a negative from the middle figure.
1 In self-defence upon this " vexed place," I am obliged to quote the note of Julius Pacius as corroborative of the sense I have given in the text ; Waitz however in most obscure phraseology comes, as Dr. Hessey remarks, to the same point. The following is from Pacius : " Aristoteles loquens de universali objectione inquit hoc simpliciter ; id est, generaliter in omnibus disputationibus obtinere, ut necesse sit, eum qui universaliter objicit, id est, affert objectionem universalem dirigat contradictionem propositorum, id est, suam objectionem, qure opponitur proposition! ad- versarii ; dirigat (inquam) ad universale, id est in ea objectione sumat terminum universalem, qui attribuatur, subjecto propositionis, ut in exemplo antea dato, sumebamus hunc terminum, dvrtKtifitva qui est universalis, et attribuitur subjecto propositionis, id est ivavrloiq." (Vide Julius Pacius in h. 1. ; also Waitz, p. 536, An. Pr.)
2 i. e. when the prop, is affirmative. 3 i. e. the prop, understood.
* See the following ch.
* Examples of all these are given in Table v., Hessey's Schema Rhet.
238 aristotle's organon. [book ii.
Chap. XXVII. — Of Likeliliood, Sign, and Enthymeme.1
1. E«cjt— con- Likelihood and sign, however, are not the sentaneum ar- samej kut tiie iikeiy js a probable proposition for
1 For writers upon the subjects of this chapter we may refer to the com- mentary of Julius Pacius, (Excerpta,) and Crakanthorpii Logica, lib. v., both annexed to the Schema Rhetorica of Dr. Hessey ; No. 115, in the Edinburgh Review, attributed to Sir W. Hamilton; Mansel's Logic, Ap- pendix, note E. ; Whately's Rhetoric and Buckley's note, Bohn's edi- tion of the Rhetoric, book i. chap. 2. The older writers upon it are Rodolphus Agricola, 1485, Phrissemius, 1523, J. Pacius, Scaynus, 1599, and Majoragius, (1572). We now proceed to the words themselves.
The term Ei'icdc, we prefer, with Sir W. Hamilton, to interpret " likeli- hood" to the other senses given by commentators we have named in the margin, since the former approaches nearer to its Aristotelian definition as a proposition stating a general probability. This indeed is a propo- sition nearly, though not quite, universal, and when employed in an Enthymeme, will form the major premise of a syllogism such as the following :
Most men who envy, hate.
This man envies :
Therefore this man (probably) hates.
Aristotle limits it to contingent matter, and its relation to the conclusion is that of an universal to a particular.
2t}(ielov, on the other hand, in a propositional sense, is a, fact which is known to be an indication, more or less certain, of the truth of some fur- ther statement, whether of a single fact or of a general belief. We say in a propositional sense, for sometimes Ei'koc, ffrjfielov, and tikjx^'iov, are used for the Enthymemes drawn from each; it is, in fact, a singular proposition employed relatively to some other proposition which may be inferred from it, and will form one premise of a syllogism, which may be in either of these figures which Aristotle discusses, having respect in this division to the extent of the so-called middle term, as compared with the other two terms. In the first and second figures it is the minor premise, in the third it seems more naturally to belong to the major. Whately con- siders the tiKoc (or Sioti) of Aristotle to be an a priori argument, which may be employed to account for the fact, whereas the oqfisiov (or on) could not be so employed ; he has however glanced at this point but generally. Aristotle tells us that we may either class rtK/iripiov, as he does in the Rhet. c. 2, as a species of otj/jLiiov, or contradistinguish two crr/fiita— in necessary matter as in the relation of a particular to an uni- versal, or of an universal to a particular, and class the reicfiripiov as a species under a genus. By a reference to Dr. Hessey's Tables the exact position of each in the enthymematic system may be clearly perceived : we may merely add that, as propositions, it is no where stated that a/cef and Sq/itiof may not be combined in the same syllogism, and that much of apparent contradiction between the places in the Analytics and liheto-
CHAP. XXVII.] THE PRIOR ANALYTICS. 23c>
what men know to have generally happened or gumentum,
not, or to be or not to be ; this is a likelihood, BuhieandTay.
for instance, that the envious hate, or that lovers ie"'ande" ver!'-
love : but a sign seems to be a demonstrative pro- similltudo,"
i i i p i i-i Averrois,
position, necessary or probable, tor that which waitz;"proba-
when it exists a thing is, or which when it has "'ifkeUhood!"
happened, before or after, a thing has happened, Sir w. Hamii-
this is a sign of a thing happening or being, babie 'proposi-
Now an Enthymeme is a syllogism from likelihoods |s°"dem^n""ray.
or signs, but a sign is assumed triply in as many tive proposi-
ways as the middle in the figures, for it is either cessary orrpn>-
as in the first, or as in the middle, or as in the bable- . Enthy-
mcnic is 3. svl~
third, as to show that a woman is pregnant be- logism drawn cause she has milk is from the first figure, for the from either oi
ric may be solved by a careful study of the tabular view given by the Doctor, of the consideration of these elements of Enthymeme, first as propositions, next as terms.
In regard to Enthymeme, it is no wonder that difficulties should not vanish, when even the abandonment of the word artXijg, ejected as a gloss by Pacius, and discountenanced by the best MSS. of the old Latin version, is still clung to by some authors. Enthymeme is composed of tiKora, or arjfitla, and without circumscribing our notion of it within the limits absurdly laid down of its etymology by Aldrich, we may conceive it in a general sense as comprehending iriaTiiq of every kind ; and at other times limited to a special kind of syllogism designated rhetorical. Vari- ous senses have been attributed to it by Cicero, Quintilian, and others, but Aristotle in general describes it as one sort of argument on moral matters distinguished carefully as to its principle from example, a collateral sort of argument. In the words of Sir W. Hamilton, " Enthymeme is distin- guished from pure syllogism as a reasoning of peculiar matter from signs and likelihoods ;" whether therefore a premise of it be suppressed or not, an argument agreeing with this description is an Enthymeme. The words cnroSuKTiKi) dvayicaia i] tvSo^og, applied to aijfitlnv as a 7rporafftc, do not relate to the modal character of the proposition in itself, but to its logical validity when the other premise is added, without which addition expressed or understood, there is no Enthymeme at all. Lastly, Zimtlov is called a demonstrative proposition, because it professes to enunciate what is absolutely true, i. e. what Aristotle calls necessary, (Rhet. i. c. 2,) the latter word being used in two senses, 1st, of a premise which states a fact, 2nd, of a consequence which is logically unassailable.
B A
■^-x. 1. Whatever woman has milk is pregnant C B
This woman has milk C A
. . This worr.an is pregnant.
240 Aristotle's organon. [book il
these, cf. middle is to have milk. Let A, be to be preg-
Soph."<Ed.coL nant' B t0 have milk> C a woman.* But that
292 and ii99. wise men are worth y, for Pittacus is a worthy
sumediripty", man, is through the last figure, let A be worthy,
according to £ wise men, C Pittacus. It is true then A and
the number of ^, ,. » , - „. ,
figures. B are predicated ot L, except that they do not as-
* Example (lu sert tne one ! because they know it, but the other (a paralogism.) they assume.f But that a woman is pregnant because she is pale, would be through the middle figure, for since paleness is a consequence of pregnancy, and also attends this woman, they fancy it proved that she is pregnant. Let t Example (3.) A be paleness, to be pregnant B, a woman C.J 3. if one prop, jf then one proposition should be enunciated,
be enunciated, . , *■ \ , „ '
there is only a there is only a sign, but it the other also be Slgn- assumed, there is a syllogism, as for instance that
Pittacus is liberal, for the ambitious are liberal, and Pittacus is ambitious, or again, that the wise are good, for Pittacus is good and also wise. Thus therefore syllogisms are produced,
except indeed that the one in the first figure is in- ube^ru^is'irf- controvertible if it be true, (for it is universal,) controvertible Dut that through the last is controvertible though but notSso in" the conclusion should be true, because the syllo- the last or 2nd jrjsm js not universal nor to the purpose, for if
Pittacus is worthy, it is not necessary that on this account other wise men also should be worthy. But that which is by the middle figure is always and altogether con- § i. e. when trovertible, for there is never a syllogism, when ammPremises tne terms tnus subsist, § for it is not necessary, if
1 Viz. " That Pittacus is a wise man," but they assume the other, viz. " That Pittacus is a worthy man."
C A
Ex. 2. Pittacus is a worthy man C B
Pittacus is a wise man B A
. * . Wise are worthy men.
B A
Ex. 3 Whatever woman is pregnant is pale C A
This woman is pale C B
. , This woman is pregnant.
CHAP. XXVII.] THE PRIOR 4.NALTTICS. 241
she who is pregnant be pale, and this woman be » Bekker and pale, that this woman should be pregnant ; what t^i ^bum" is true therefore will be in all the figures,* but and Avemris, ' they have the above-named differences. "xiix*™.
Either therefore the sign must be thus divided, but of these the middle must be assumed as the l (indipium,°'a proof positive, (for the proof positive they say is syllogism in that which produces knowledge, but the middle is (cf. Quintfuan," especially a thing of this2 kind,) or we must call 8ib,v- c- 9| see- those from the3 extremes, signs, but what is from the middle a proof positive, for that is most probable, and for the most part true, which is through the first figure. We may however form a judgment of the disposition 6 B the ex_ by the body, if a person grants that whatever pas- ample of phy- sions are natural, change at once the body and to^shows "' the soul,4 since perhaps one who has learned music tna* ^sns »-
i ill- i • i • pecially proba-
nas changed his soul in some respect, but this bie belong to passion is not. of those which are natural to us, the lst fisure- but such as angers and desires, which belong to natural emo- tions. If therefore this should be granted, and one thing should be a sign of one (passion), and we are able to lay hold of the peculiar passion and sign of each genus, we shall be able
1 The TtKfiijpiov is a arifiiiov in fig. 1, necessarily conclusive, (vide Rhet. i. c. 2,) derived by Arist. from rsK/xap, a boundary. The argument Sid TtKjii)oiov is logical, but rarely occurs, since its advancement settles the question. He speaks of " the middle, "&c, as referring to the first figure, in which the middle term obtains the middle place. TtK/xtjoia can only be refuted by assailing the premises.
2 Cf. Waitz, Tom. i. p. 538. Biese, i. 227, also ch. 14, book i. Anal. Post.
3 Which are referred to the second or third figure; "quae extrema sunt (ut utrobique subjecti aut utrobique predicati locum habeant,") ea signa diccnda sunt; quod autem e medio (sumtum est) ut partim sub- jecti, partim prredicati vicem gerat indicium dicendum est. Buhle.
4 Cf. Arist. Physio. Eth. ii. c. 1, and 5. Buhle, Anal. i. ch. v. Dan. iii. 19. Gen. xxxi. 2.
" My grief lies all within ;
And those external manners of laments
Are merely shadows to the unseen grief
That swells with silence in my tortured soul.
There lies the substance." — Shaks. Hichd. II.
The same sentiment is met with in our dramatists passim. The acqui- sition of knowledge of course changes the soul ; since, to take a high view, it is the first human element of all reLgiou.
h.
242 Aristotle's organon. [book 11.
r The first to conjecture from nature. For if a peculiar pas- physiognomic sion is inherent in a certain individual genus, as fhat°nhaturaiS fortitude in lions, it is necessary also that there passionchanges should be a certain sign, for it is supposed that
at one time the , . , , , , i< ,, . .., ,
body and soul, they (the body and soul) sympathize with each
Uihere2isdoneat otner» and let this be the having great extremi-
sjgnof one pas- ties, which also is contingent to other, not whole,
that'the proper genera.1 For the sign is thus peculiar, because
passion of each ^he passion is a peculiarity of the whole genus,
species of am- f i»«-i»-i_i 0 °
mai may be and is not the peculiarity or it alone/ as we are known. accustomed to say. The same (sign) then will also
be inherent in another genus, and man will be brave, and some other animal, it will then possess that sign,3 for there was one (sign) of one (passion). If then these things are so, and we can collect such signs in those animals, which have one peculiar passion alone, but each (passion) has its (own) sign, since it is necessary that it should have one, we may be able to conjecture the nature from the bodily frame. But if the whole genus have two peculiarities, as a lion has fortitude and liberality, how shall we know which of those signs that are peculiarly consequent is the sign, if either (passion) ? Shall we say that we may know this, if both are inherent in some- thing else, but not wholly,4 and in what each is not inherent
1 Other species, he means, also have this sign, but it is not possessed by every individual in the species.
2 That is, though it may even happen to every individual, it does not happen to that genus alone. This mere sketch presents the outlines, in comparative anatomy, of the strongest evidence upon which modern phrenologists can rest their claim to credence ; it must be remembered however that the whole case falls, if the identification of the peculiar mark with the passion is not fully proved. Hi-s further question, of how we are to apportion each passion to its own mark, when many are pre- sent in one genus, seems unanswerable : — yet we have presumed even to measure the prominence which marks each passion, (if it does mark it,) and to set one over against the other, e. g. benevolence against destruct- iveness, almost to a hair's breadth !
' Viz. great extremities.
4 i. e. If both passions and both signs are inherent in another genus of animals, yet so as not both to be inherent in all the individuals of that genus ; for instance, both courage and liberality, and their signs, are in horses as well as in lions, but not in all horses, for some are brave and not liberal, others liberal and not brave.
Ex. 4. Whatever has great extremities is brave Every lion has great extremities . ' . Every lion is brave.
CHAP. XXVII.] THE PRIOR ANALYTICS. 243
wholly, when they have the one, they have not the other ; for if a (lion) is brave, but not generous, but has , . e great this * from two signs, it is evident that in a lion extremities. also this is the sign of fortitude. But to form a § Whateyer judgment of the natural disposition by the bodily is inferred in frame, is, for this reason, in the first figure, be- ^J^?nc\ £ cause the middle reciprocates with the major ut figure. term, but exceeds the third, and does not recipro- cate with it ; as for instance, let fortitude be A, great ex- tremities B, and C a lion. Wherefore B is present with every individual with which C is, but with ^ ^ ^^ others* also, and A is with every individual of D*„J^i that with which B is present, and with no more, " man." but is converted, for if it were not, there would ( ExampIe (4.} not be one sign of one (passion).f
Whatever has great extremities is brave Some man has great extremities . • . Some man is brave.
R 1
244 aristotle's organon. [book
THE POSTERIOR ANALYTICS.
BOOK I.
Chap. I. — Upon the Nature of Demonstration.
All doctrine, and all intellectual discipline,1 arise tic discipline from pre-existent knowledge. Now this is evi- from°prevSous dent, if we survey them all, for both mathematical knowledge, sciences are obtained in this manner, and also twofold re" each of the other arts. It is the same also with spect. (Cf. arguments, as well those which result through
Mag. Moral. lib, . . .
i. is, and Eth. syllogisms, as those which are formed through ^u2dej jlb' v< c" induction, for both teach through things pre- viously known, the one assuming as if from those who understood them,2 the other* demonstrat- ing the universal by that which is evident as to the singular. Likewise also do rhetoricians persuade, for they do so either through examples, which is induction, or through enthy- + vide Prior menis, which is syllogism, j"3 It is necessary how- Anai. b. ii. c. ever to possess previous knowledge in a twofold respect ; for with some things we must pre-sup- pose that they are, but with others we must understand what that is which is spoken of; and with others both must be
1 Doctrine and discipline are the same in reality, but differ in relation, being called " doctrine " when applied to teaching, and " discipline " as pertaining to learning. Taylor defines Aiavoia, that power of the soul which reasons scientifically, deriving the principles of its reasoning from intellect : and these principles are axioms and definitions. Comp. Poetic, ch. 6, where the word is applied to a certain part of tragedy. Ethics, b. vi. c. 2. Waitz notices the similarity between the commencement of this ch. and the opening ch. of the Ethics. For the principle stated, consult Hill's Logic, p. 137, and for the word, see Biese, i. p. 89.
2 That is, syllogisms contain propositions, assumed to be known either by demonstration or per se.
3 Vid. lthet. b. i. ch. 2. It was shown (b. ii. ch. 2 4, Anal. Pri.) that example is reduced to a syllogism in the 1st figure, the major prop, of which is proved by an imperfect deduction ; wherefore as the whole force of th« example consists in that induction, it is not undeservedly said to be a certain induction. Tay.or.
C:iAP. I.] THE POSTERIOR ANALYTICS. 245
known, as for instance, (we must pre-assume,) that of every- thing it is true to affirm or deny that it is, but of a triangle, that it signifies so and so, and of the monad (we must know) both, viz. what it signifies and that it is, for each of these is not manifest to us in a similar manner.1 It is possible how ever to know from knowing some things previously,2 and re- ceiving the knowledge of others at the same time, as of things which are contained under universals, and of which a man possesses knowledge.3 For he knew before that every tri- angle has angles equal to two right angles, but that this which is in a semi-circle is a triangle, he knew by induction at the same time. For of some things knowledge is acquired after this manner, nor is the extreme known through the middle, as such things as are singulars, and are not predicated of any subject. Perhaps however we must confess that we possess knowledge after a certain manner before induction or the as- sumption of a syllogism, but in another manner not.4 For what a man is ignorant about its existence at all, how could he know at all that it has two right angles ? But 2. what we it is evident that he thus knows because he knows aUylnoTgener- the universal, but singly he does not know it. aiiywemay
, . -11 -iii i_ • i_ ■ not know sin- Still if this be not admitted, the doubt which is giy, although
mentioned in the Meno* will occur, either he will ^j^6 same
learn nothing, or those things which he knows,5 * Meno, Piato-
1 Quae antequam disciplina ipsa quaecunque nobis tradatur, cognoscere debemus on tariv, axiomata sunt, quae vero cognoscere debemus n to Xiyofitvov tan, definitiones sunt : unde fit ut disciplinam ipsam quarn- cunque, praecede redebeant, axiomata et definitiones.— Nam etsi definitio rei naturam non patefaciat, tamen quam vim habeat nomen quo res signi- ficetur exponit, ut etiam definitio nominalis, quae dicitur utilitatem quandam habeat. Waitz. See also Meditationes de cognitione Veritatis et Ideis : Leibnitz Opera, p. 80, ed. Erdmann.
2 i. e. to prove the principal conclusion, from certain propositions being proved, pro-syllogistically.
3 Learning them not from antecedent knowledge nor pro-syllogistically, but immediately, just as sensibles are known by the senses. Taylor. Compare also Ethics, b. vi. ch. 3, and Whately's Logic.
4 i. e. the conclusion may be known by universal, yet it cannot be by proper or peculiar knowledge ; for instance, in the case below he knows that this triangle has angles equal to two right, because he knows this to be the case universally of a triangle, but he does not know it singly, ab- solutely, and perfectly by proper knowledge.
* The passage in the Meno of Plato is that commencing icai nva roonot
246 Aristotle's organon. lbook i.
nis Opera, Bek- for he must not say, as some endeavour to solve !vrp 32' tom' tne doubt, " Do you know that every duad is an even number or not?" for since if some one says that he does, they would bring forward a certain duad which he did not think existed, as therefore not even ; and they solve the ambiguity, not by saying that he knew every duad to be even, but that he was ignorant as to what they know is a duad. Nevertheless they know that of which they possess and have received the demonstration, but they have received it not of every thing which they know to be a triangle or a number, but of every number and triangle singly, for no pro- position is assumed of such a kind as the number which you know, or the rectilinear figure which you know, but univers- ally. Still there is nothing (I think) to prevent a man who learns, in a certain respect knowing and in a certain respect being ignorant,1 for it is absurd, not that he should in some way know what he learns, but that he should thus know it, as he does when he learns it, and in the same manner.
Chap. II. — Of Knowledge, and Demonstration, and its Elements.
* Soph. Eienc. We think that we know each thing singly, (and xi. l.Metap. not in a sophistical manner,* according to acci- , ' .' ... dent,) when we think that we know the cause on
1. scientific ' „ . . . . . . ...
knowledge is account oi which a thing is, that it is the cause of
wheSnSwed'know tliat tning> and tnat the hatter cannot subsist
the necessary otherwise ; wherefore it is evident that knowledge
tween aching is a thing of this kind, for both those who do not,
Definition118?' anc^ *nose wno do know, fancy, the former, that
Demonstration, they in this manner possess knowledge, but those
vl.1^^)11105' wno know, possess it in reality, so that it is im- possible that a thing of which there is know-
Z,r\ri\aiiQ. The doubt (air6pr)pa) is, that if we can learn nothing, there- fore that nothing is to be investigated, since what we know we need not investigate, and it is vain to search after what we know not, since not knowing the object of our search, we shall be ignorant of it, even when found. Socrates solves this (\vti) by declaring that to discover and to learn, are nothing else than to remember, because the soul, being im- mortal, formerly knew every thing, of which knowledge, becoming ob- livious by being merged in the body, she endeavours to recall knowledge to memory by investigation.
1 Knowing by universal, being ignorant by proper knowledge.
CHAP. II.] THE POSTERIOR ANALYTICS. 247
le<lge simply should subsist ic any other way.1 Whether therefore there is any other mode of knowing we shall tell hereafter, but we say also that we obtain knowledge through demonstration, but I call demonstration a scien- ^ gyiiog qui tific * syllogism, and I mean by scientific that ac- scire facit. cording to which, from our possessing it, we know. If then to know is what we have laid down, it is LSt™' necessary that demonstrative science should be demonstrative from things true, first, immediate, more known than, prior to, and the causes of the conclusion, for thus there will be the appropriate first principles of whatever is demon- strated.2 Now syllogism will subsist even without these, but demonstration will not, since it will not produce knowledge. It is necessary then that they should be true, since we cannot know that which does not subsist, for instance, that the diameter of a square is commensurate with its side. But it must be from things first and indemonstrable, or otherwise a man will not know demonstrable" them, because he does not possess the demonstra- tion of them,3 for to know those things of which there is de- monstration not accidentally is to possess demon- stration. But they must be causes, and more the^ndusfon known, and prior ; causes indeed, because we then know scientifically when we know the cause ; and prior, since they are causes ; previously known also, not only according
1 True science requires, 1st, that the cause of a thing be known, i. e. that the middle term be the cause of the conclusion ; 2nd, that the cause be compared with the effect, so that we know it to be the cause of the conclusion ; 3rd, that we know the conclusion to subsist thus neces- sarily, and that it cannot subsist otherwise. Taylor. Comp. Rhet. i. c. 7. Magna Moralia, i. c. 34. Metap. i. 1, and 10, 3, and 7. Cause and apxq must not be confounded, since the cause precedes the apx*i ; vide Buck- ley's note in Bonn's edition of the Rhetoric quoted above.
2 Vide Hill's Logic, page 289, also Mansel, p. 104, et seq. ; in the ap- pendix note H. of the latter's work, the reader will find the statement of the nature of demonstrative syllogism fully set forth. The words first and immediate, signify that they are not demonstrable by a middle term from any higher truth. The demonstration, " propter quid sit per causam non primam," would only form a subordinate portion of a complex de- monstration. Vide Wall's Log. lib. iii. cap. 22. As post demonstrations depend upon those prior, therefore all are said to be from things first.
3 Either they would be unknown or not be principles, because they might be demonstrated by other things prior to them, ad infinitum. Vide Whately's Logic, b3ok iv.
248 Aristotle's organon. [book i.
to the other mode by understanding (what they more known, in signify), but by knowing that they are.1 More-
spect f°ld re over tney are Prlor and more known in two ways,
for what is prior in nature, is not the same as that which is prior in regard to us, nor what is more known (simply) the same as what is more known to us. Now I call things prior and more known to us, those which are nearer to sense, and things prior and more known simply, those which are
more remote from sense ; and those things are sense.' m most remote * which are especially universal,2 and
those nearest which are singular, and these are mutually opposed. That again is from things first, which is
from peculiar principles,3 and I mean by first, the
5. Immediate. r, . r, r. '. . , , J. . ' „
same thing as the principle, but the principle of demonstration is an immediate proposition, and that is imme- diate to which there is no other prior. Now a of p^opo"i?«o°n. proposition is one part of enunciation, one of one,4 dialectic indeed, which similarly assumes either (part of contradiction), but demonstrative which definitely (assumes) that one (part) is true. Enunciation is either part of contradiction, and contradiction is an opposi- Categories. tionf which has no medium in respect to itself. But that part of contradiction (which declares)
1 Principles are prior in a two-fold respect, they cause a thing to be, and also cause the same to be known. Taylor. Comp. Anal. Post. i. 24. The inquiry into the definition of a thing is identical with that of its cause, with the difference that the cause of attributes is to be sought in their subject, but in the case of substances per se the cause must be sought in themselves only. Cf. Metap. v. 1, 2 ; x. 7, 2.
2 Aristotle here intimates his concurrence with the Platonic theory, that the soul contains in itself essentially the " universal," or true principle of demonstration ; vide the Commentary of Proclus on the Parmenides of Plato, in which he exhibits the priority of universals to singulars, and the method of their reception by the diancetic faculty. Cf. also Ritter and Cousin upon the Old Academy. Arist. Ethics, b. vi. c. 11, and Metap. books i. iv. vi. and xii. (Leip. ed.) If demonstration be from universals prior by nature, it follows, according to Aristotle, that it is alone from forms essentially inherent in the soul, since abstract forms are not naturally prior, because they are universals of a posterior origin.
3 That principles ought to be peculiar to the science, and to what is to be demonstrated, he shows, ch. vii. and ix.
4 One enunciation signifies one thing of one. Vide ch. 8, on Inter- pretation.
CHAP. II.] THE POSTERIOR ANALYTICS. 249
something, of somewhat, is affirmation, and that (which signi- fies) something from somewhat is negation.* Of * Ch 6 on In_ an immediate syllogistic principle, I call that the terpretation. thesis, which it is not possible to demonstrate, nor the^if Tons?- °f is it necessary that he should possess it, who in- dered by Pa- tends to learn any thing ; but what he who intends a^synmymous to learn any thing must necessarily possess, that with «w««- I call an axiom,1 for there are certain things of 5- 0f axiom- this kind, and in denominating these, we are accustomed generally to use this name. But of thesis, that which re- ceives either part of contradiction, as for instance, I mean that a certain thing is, or that it is not, is hypo- thesis, but that which is without this, is definition. ^;s0f hyPothe' For definition is a thesis, since the arithmetician lays down unity to be that which is indivisible, according to quantity, yet it is not hypothesis, since what unity is, and that unity is, are not the same thing.
Notwithstanding, since we must believe in and know a thing from possessing such a syllogism as we call demonstration, and this is, because these are so, of which syllogism consists — it is necessary not only to have a previous knowledge of the first, or all, or some things, but that they should be more known, for that on account of which any thing exists, always exists itself in a greater degree ; for example, that on account of which we love is itself more beloved. Hence if we know and believe on account of things first, we also know and believe those first things in a greater degree, because through them (we know and believe) things posterior. A man however cannot believe more than what he knows, those things which he does not know, nor with respect to which he is better disposed
1 Axioms are common, according to Aristotle, to several classes, but in the case of a single science need only be assumed to an extent com- mensurate with the object-matter of that science. As Mansel well ob- serves, the places in which the axioms are mentioned in connexion with demonstration, have never been satisfactorily explained on the usual scholastic interpretation. I entirely agree with him, that the supposition that axioms are virtually, but not actually, employed in demonstration, and the distinction drawn between immediate propositions and axioms, are equally unfounded ; in fact it subverts Aristotle's own expression. Vide Mansel's Logic, App. 66. Compare also Zabarella in I. An. Post. Cont. 57, 58. Crakanthorpe, Logic, lib. iv. c 1. Aquinas Opusc. 48, de Sy'lo. Dem. cap. 6.
250 aristotle's organon. [book t.
than if he knew.1 This however will happen, unless some one should previously know of those who give credence through demonstration, since it is more necessary to believe either in all or in certain first principles, than in the conclu- sity ofknow?ng sion. It is not only however requisite that he who principles and js to possess knowledge through demonstration, in order to pos- should know in a greater degree first principles, demo'nltrarion7 and believe rather in them than in the thing de- monstrated, but also that nothing else should be more credible or more known to him than the opposites of the principles, from which a syllogism of contra-deception may consist, since it behoves him who possesses knowledge singly to be unchangeable.2
Chap. III. — Refutation of certain opinions as to Science and Demonstration.
i Refutatio ^0 some' because it is necessary that first things of those who should be known, science does not appear to exist,
e'nce'o^cfenct but to others to exist indeed, yet (they think)
there are demonstrations of all things, neither of
which opinions is true or necessary.3 For those who suppose
1 By being better disposed, Aristotle, who is here speaking of demon- strative knowledge, means the intuitive apprehension of intellect. Cf. Waitz and Biese in loc.
2 That is, free from lapsing into error, which he would fall into by not knowing opposites, since he might believe that the opposites to true prin- ciples are true. For the better elucidation of the above chapter, the fol- lowing table of the principles of science is given :
'ApxaL
A
Koivai (t£ wv) "iSiai (irtpi o)
a%iti>fiara Q'eouq
Constituting the original premises from which de- monstration proceeds.
< "~- ; — I-
Opiff/lOl VTTOVEOtlQ
Definitions — real, of Assumptions of the
the subjects — nominal, existence of the
of the attributes. subjects as necessary
to their definition. 3 The argument is as follows : there are, or are not, certain irpaira ; if there are not, but we admit a process ad infinitum, there is no science, since the latter ultimate^ depends on certain irpwra : if there are
CHAP. III.] THE POSTERIOR ANALYTICS. 2.51
that knowledge does not subsist at all, these thir.k that we are to proceed to infinity as if we may not know things subse- quent by things prior, of which there are no first, reasoning rightly, since it is impossible to penetrate infinites.1 And if (they say) we are to stop, and there are principles, these are unknown, since there is no demonstration of them, which alone they say is to know scientifically ; but if it is not possible to know first things, neither can we know either simply or properly things which result from these, but by hypothesis, if these exist. Others however assent with re- 2. Aisoofthose spect to knowledge, for (they assert) that it is who declare all
, , ,, ° . , * ',. things capable
only through demonstration, but that nothing pre- of demonstra- vents there being a demonstration of all things, tlon' for demonstration may be effected in a circle, and (things be proved) from each other. We on the contrary assert, that neither is all science demonstrative, but that the science of things immediate is indemonstrable. And this is evidently necessary, for if it is requisite to know things prior, and from which demonstration subsists, but some time or other there is a stand made at things immediate, these must of necessity be indemonstrable. This therefore we thus assert, . _,. . . ,
. i • * 1 That is, de-
and we say that there is not only science,* but monstrative also a certain principle of science, by which we science- know terms.2 But that it is impossible to demon- jj- We cannot.
. . . f . demonstrate in
strate in a circle simply is evident, since demon- a circle things
" firsts " on the other hand, still there is no science, for the latter being from things prior, there can be nothing prior to " firsts."
1 They are right in saying we cannot know things posterior through the prior, unless the progress of investigation stop at certain " firsts ; " they are wrong in asserting that these firsts cannot be known. Cf. Phy- sics, lib. i. and iii.
2 A certain knowledge antecedent to demonstrative science. The word opoi, here, Pacius mistakes for " simple terms;" it signifies rather, as St. Hilaire observes, " les propositions immediates," i. e. axioms. The fol- lowing is the interpretation by Ammonius of this place. The principle of science is intellect, not our intellect, but that which is divine and above us ; but terms are intelligible and divine forms, which axe called terms in consequence of being the boundaries of all things. For as mul- titude originates from the monad, and is dissolved into the monad, and tens are the boundaries of hundreds, and hundreds of thousands, but the monad is the common boundary of all numbers; thus also with respect to things, we may say that the boundaries of sensibles are the celestial bodies, of the celestial bodies intelligible essences, and of all things in common the first cause. And this may be said in answer to those who
252 Aristotle's organon. [book i.
which do not stration must consist of things prior and more reciprocate. known, as it is impossible that the same should be prior and posterior to the same, unless in a different way, as for instance, some things with reference to us, but others
simply in the manner in which induction makes *y,\ldfv^chatiT known.*" If however this be so, to know simply also Metap. will not be well defined, but it is two-fold,1 or the
other demonstration is not simply so which is pro- 1 1 e. of the (Juced from things more known to us.t Still there
on, seech. 13. ° . I
happens to those who assert there js demonstra- tion in a circle, not only what has now been declared, but that they say nothing else than this is if it is, and in this manner we may easily demonstrate all things. Nevertheless it is evi- dent that this occurs, when three terms are laid down, for to assert that demonstration recurs through many or through few terms, or whether through few or through two, makes no . ,, , difference. For when A existing, B necessarily
4. K xampic . **
is, and from this last C, if A exists C will exist, if then, when A is, it is necessary that B should be, but this existing, A exists, (for this were to demonstrate in a circle,) let A be laid down in the place of C. To say therefore that because B is A is, is equivalent to saying that C is, and this is to say that A existing C is, but C is the same as A, so that it happens that they who assert there is demonstration in a circle, say nothing else than that A is because A is, and thus we may easily demonstrate all things. Neither however is this possible, except in those things which follow each other
as properties : from one thing however being hook^'ch^T laid down, it has been proved % that there will
never necessarily result something else, (I mean by one thing, neither one term, nor one thesis being laid down,) but from two first and least theses, it is possible (to infer necessarily something else), since we may syllogize. If then A is consequent to B and to C, and these to each
subvert demonstration by a procession to infinity, that we not only say there is demonstration, but that things do not proceed to infinity, because there is a certain principle of demonstration by which we know the terms or boundaries of things, when we obtain illumination from thence. Per- haps, however, by a " certain principle of science," Aristotle means our intellect, and by terms, axioms. Cf. Metap. lib. ii. and x.
1 The one from things more known and prior, according to nature ; the other from those more known and prior, according to us.
nnxr. iv.] the postertop analytics. 253
other, and to A, thus indeed it is possible to demonstrate all those things which are required from each other in the first figure, as we have shown in the books on * Anal. Prior, Syllogism.* It has also been shown f that in the book _"• eh- 5- other figures there is either not a syllogism,} or et se'q; c ' ' not one concerning the subjects assumed ;l but it t (circulo.) is by no means possible to demonstrate in a circle Buhle- those which do not reciprocate. Hence, since there are but few such in demonstrations, it is evidently vain and impossi- ble to say, that there is demonstration of things from each other, and that on this account universal demonstration is possible.
Chap. IV. — Upon the terms " every" "per se," and " universal."
Since it is impossible that a thing, of which there is simply science, should have a various subsist- demonstration* ence, it will be also necessary that what we know should pertain to demonstrative science, and demonstrative science is that which we possess from possessing demon- stration, hence a syllogism is a demonstration from neces- sary (propositions). We must comprehend then of what, and what kind (of propositions), demonstrations consist ; but first let us define what we mean by " of every," and " per se," and " universal."
I call that " of every," which is not in a cer- tain thing, and in another certain thing is not, nor t;"on "(feom"* which is at one time, and not at another ; as if nV" animal is predicated of every man, if it is truly said that this is a man, it is true also that he is an animal, and if now the one is true, so also is the other ; and in like manner, if a point is in every line. Here is a proof, for when we are questioned as it were of every, we thus object, either if a thing is not present with a certain individual, or if it is not sometimes. But I call those " per se " which 3. of " To ko.0* are inherent in (the definition of) what a thing ai™>' ' Per
1 Both assumed prop, are not proved, because in the 2nd fig. the con- clusion is negative, wherefore we cannot prove an affirmative prop, in a circle ; and in the 3rd fig. the conclusion is particular, wherefore an uni- Yersal cannot be demonstrated in a circle.
TO kcltu navrot.
254 aristotle's organon. [book i.
is,! as line is in triangle, and point in line, (for Hnean/poTnt. *hft essence of them is from these,* and they are
in the definition explaining what it is:)2 also those things which are inherent in their attributes in the definition declaring what a thing is,3 as the straight and the curved are inherent in a line, and the odd and even in - As 3 5 7 number, and the primaryf and composite,! tne &c ' ' ' equilateral § and the oblong :4 and they are inhe- t As 9, i. e. rent in all these, in the definition declaring what
3, 3, 3, &c. a t^g jS) tnere inciee(i iine) but here number.
number.S(1Uare IQ a similar manner, in other things, I say that
Taylor. such are per se inherent in each, but what are
4. of accidents, in neither way inherent (I call) accidents, as the fcf^Phys°Tib. being musical, or white in an animal. Moreover, lib e\Metap' tnat which is not predicated of any other subject,
as that which walks being something else, is that which walks, and is white, but essence and whatever things signify this particular thing, not being any thing else, are that which they are. Now those which are not predicated of a subject, I call " per se," but those which are so predicated, I call accidents. Again, after another manner, that which on account of itself is present with each thing is " per se," but that which is not on account of itself is an accident ;5 thus it is an accident if while any body was walking it should lighten, for it did not lighten on account of his walking, but we say that it accidentally happened. If, however, a thing is present on account of itself, it is per se, as if any one having his throat
1 Four senses are given of this expression, to KaO' avro: 1. When the predicate is part of the definition of the subject. 2. When the subject is part of the definition of the predicate. 3. When existence is predicated of a substance. 4. When the subject is the external efficient cause of the predicate. In proper demonstration, propositions must be " per se " either in the first or second meaning. Cf. Mansel's Logic, note H. on the Demonstrative Syllogism.
2 Thus a triangle is defined to be a figure contained by three straight lines.
3 As, to use Aristotle's graphic illustration, in the definition of nose, flatness of nose is not employed, but flatness of nose is defined to be a curvature of nose.
4 An oblong number is that which a number produces, not multiplied by itself, but by another number, as six is from twice three. Taylor.
* This relates to the efficient cause.
3HAP. IV.] THE POSTERIOR ANALYTICS. 255
cut should die, and through the wound, because he will die in
consequence of his throat being cut, but it did not accideut-
ally happen that he whose throat was cut died.
Those therefore which are predicated in things recapitulation.
which are simply objects of science per se, so as
to be inherent in the things predicated,* or which * lst mode-
are themselves inherent in subjects,! are on ac- t 2nd mode.
count of themselves, and from necessity, for it
does not happen that they are not inherent either simply or as
opposites, as the straight and the curved in a line, and the
even or odd in number. For a contrary is either
privation or contradiction in the same genus, as contra^.18 a
that is even which is not odd in numbers, so far
as it follows r1 hence if it is requisite to affirm or deny, it is
also necessary that those which are per se should be inherent.
Let then the expressions " of every " and " per 7 se " be thus defined : I call that universal, however, ™ " afT<5,
• t t n »i quatenus lp-
which is both predicated " of every and " per sum," and to se," and so far as the thing is.2 Now it is evident "^eT ex" that whatever are universal are inherent in things necessarily, but the expressions " per se," " and so far as it is," are the same ; as a point and straightness are per se pre- sent in a line, for they are in it, in as far as it is a line, and two right angles in a triangle, so far as it is a triangle, for a triangle is per se equal to two right angles. But universal is then present, when it is demonstrated of any casual and pri- mary thing, as to possess two right angles is not universally inherent in figure, yet it is possible to demonstrate of a figure that it has two right angles, but not of any casual figure, nor does a demonstrator use any casual figure, for a square is in- deed a figure, yet it has not angles equal to two right. But
1 Contraries may, however, be both absent from a subject, as a body may be neither white nor black ; but the even and odd are opposed as contradictories, so that one of them must be present in a subject. Vide Categ. ch. 10. The even is compared to the not odd, because it is neces- sarily consequent to it.
2 As man is risible, because every man is, both " per se " and " qua- tenus ipsum ;" upon the apparent inconsistency of Aristotle in the use of the word KaOuXov, see Waitz, 1. Ana. Post. p. 315. The reader will find some valuable remarks upon the demonstratio potissima, especially in reference to this place, in Mansel's Logic, Appendix, note H., where the example is regularly stated.
256 Aristotle's organon. [book r.
any isosceles has angles equal to two right, yet not primarily, for triangle is prior. Whatever therefore is casually first demonstrated to possess two right angles, or any thing else, in this first is the universal inherent, and the demonstration per se of this is universal, but of other things after a certain manner not per se, neither is it universally present in an isosceles, hut extends farther.
Chap. V. — Of Errors about the primary Universal}
We ought not to be ignorant that frequently error arises, and that what is demonstrated is not primarily universal, in so far as the primarily universal appears to be demonstrated. l. Sources of Now we are deceived by this mistake, when error in effect- either nothing higher can be assumed, except
ing universal , . . . , .
demonstration, the singular or singulars, or when something Example. ejge can ^Q ^gum^ \)Ut jt wants a name in
things differing in species, or when it happens to be as a whole in a part, of which the demonstration is made, for demonstration will happen to particulars, and will be of every individual, yet nevertheless it will not be the demonstration of this first universal. Still I say the demonstration of this first, so far as it is this, when it is of the first universal. If then any one should show that right lines do not meet, it may appear to be (a proper) demonstration of this, because it is in all right lines, yet this is not so, since this does not arise from the lines being thus equal, but so far as they are in some way or other equal. Also if a triangle should be no other than isosceles, so far as isosceles it may appear to be inherent :
1 All universals are gained by abstraction, i. e. by separating the phe- nomena in which a certain number of individuals resemble each other, from those in which they differ ; Locke calls all universals, abstract ideas. Upon generalization as distinguished from abstraction, vide Stewart, Phil, of the Human Mind ; Whately's Logic, Outline of Laws of Thought, p. 44. The causes of the error which a person commits who demonstrates of the inferior as of species, what he ought to demonstrate of the superior as of genus, are four. 1st, When one particular being under universal, we demonstrate the former instead of the latter : 2nd, when we demon- strate of all contained under a proper subject when we seem to do so of the proper subject itself : 3rd, when the particular is demonstrated be- cause the universal has no name : 4th, when we conclude that an universal demonstration of a thing has been given because the demonstration is of every individual. Of. Waitz, p. 387, et sea.
CHAP. V.] THE POSTERIOR ANALYTICS. 257
alternate proportion also, so far as regards numbers and lines and solids and times (as was once shown separately) it is possi- ble at least to be demonstrated of all by one demonstration, but inasmuch as all these, numbers, length, time, are not one deno- minated thing, and differ from each other in species, they were assumed separately. But now the demonstration is universal, for it is not in so far as they are lines or numbers, that it is inherent, but in so far as this thing which they suppose to be universally inherent. For this reason neither if one should demonstrate each several triangle by one or another demon- stration, that each has two right angles, equilateral, the scalene, and the isosceles separately, would he yet know that the triangle (itself) has angles equal to two right, except in a sophistical manner,* nor triangle universally, though there should be no other triangle besides these. For he does not know it so far as it is triangle, nor does he know every triangle, except according to number, but not every, according to species, even if there be no one that he does not know.1 When then does he not know uni- versally, and when knows he simply ? It is clear that if there is the same essence of a triangle, and of an equilateral either of each or of all, he knows, f2 but if there is not the same, but different, and it is inherent so ^ e- UIllvers" far as it is triangle, he does not know.3 Whether however is it inherent, so far as it is triangle, or so far as it is isosceles ? And when, according to this, is it primary ? And of what is the demonstration universally ? It is evident that it then is, when, other things being taken away, it is in- herent in the primary, thus two right angles will be inherent in a brazen isosceles triangle, when the being brazen and the being isosceles are taken away, but not if the figure or bound- ary is taken away, nor if the primary are. But what pri-
1 That is, in number. Triangles are here said to be as many in num- ber as in species.
2 Universally and simply mean nearly the same thing, because when a man knows not sophistieally, i. e. simply, he knows universally, hence Taylor and Buhle insert, the one "universally," the latter " simpliciter," as equivalent in this place.
a That is, by demonstration of a species of triangle, he does not know the universal property as demonstrated of triangle, viz. the possession oi three angles equal to two right.
9
258 Aristotle's organon. [book i
mary ? if indeed triangle (is taken away) ; according to this it is inherent in others, and of this universally is the demon- stration.
Chap. VI. — Demonstration consists of Principles per se ; and of a
necessary Medium}
If then demonstrative science is from necessary tion ftrue de*-" principles, (for what is scientifically known cannot monstration subsist otherwise,) and those which are per se in-
only from ne- »/ ... /n
cessary propo- herent are necessarily so in things, (tor some are sitions. inherent in the definition of what a thing is, but
others are they in the very nature of which the subjects are inherent, of which they are so predicated, that one of opposites is necessarily present,) it is evident that the demonstrative syllogism will consist of certain things of this * i.e. of propo- kin(j * for everv thins; is either thus inherent, or
sitions per se. ' J , »
according to accident, but accidents are not ne- cessary.
Either therefore we must say this, or that demonstration is a necessary thing, if we lay down this principle, and that if de- monstration is given that a thing cannot subsist otherwise, wherefore thef syllogism must be from necessary rnonstrative6 (matter). For it is possible without demonstra- tion to syllogize from what are true, but we can- not do so from things necessary, except by demonstration, for this is now (the essence) of demonstration. An indication also that demonstration is from things necessary is, that we thus object to those who think they de- monstrate that (the conclusion) is not necessary, whether we think that the matter may altogether be otherwise possible, or on account of the argument. Hence too the folly 1 Reply to f those appears, who think they assume princi-
objection. rr ' . . • , , , ■,
pies rightly, if the proposition be probable and true, as the Sophists (assume) that to know is to possess knowledge.2 For it is not the probable or improbable, which
1 If things per se or essential are necessary, and the principles of de- monstration are necessary ; therefore the principles of demonstration are per se. As Taylor observes, by conversion of the major, Aristotle's argu- ment here may become a syllogism in Barbara.
2 It was thus argued by Protagoras : Whoever knows any thing, pos-
CHAP. VI.] THE TOSTERIOR ANALYTICS. 259
is the principle, but that which is primary of the genus about which the demonstration is made, nor is every thing true ap- propriate. But that it is necessary that the syl- 2nd pro(rf logism should consist of necessary things appears also from these ; for if he who cannot assign a # The major reason why a thing is,* when there is a demon- t vide 2nd ct stration, does not possess knowledge,! let A J be * ie minor necessarily predicated of C, but B the medium through which it is demonstrated not of necessity, (in this case) he does not know the cause. For this is not on account of the medium, for the latter may not exist, yet the conclusion is necessary. Besides, if some one does not know, though he now 3 possesses a reason, and is safe, the thing also be- ing preserved, he not having forgotten it, neither did he bo fore know it. But the medium may perish if it is not neces- sary, so that he, being safe, will have a reason, § the thing being preserved, and yet not know it, LnuBuMe! wherefore neither did he know it before.1 But if the medium is not destroyed, yet may possibly perish, that which happens will be possible and contingent, it is impossi- ble however that one so circumstanced should know.2
When therefore the conclusion is from neces- 3. if the con-
, . .. -i. elusion be ne-
sity, there is nothing to prevent the medium Cessary,thePre- through which the demonstration was made from ™^%nu¥wne0n being not necessary, since it is possible to syllogize the latter are so the necessary even from things not necessary, just musw>° neee£ as we may the true from things not true. Still sary. when the medium is from necessity the conclusion is also from necessity, as the true (results) from the true always : for let A be of necessity predicated of B, and this of C, then it is
sesses science : he who possesses science knows what science is : there- fore, he who knows any thing knows what science is.
1 Scientia quam quis habet, non perditur, nisi aut ipse perit ant obliviscitur aut res quam scivit, intent. Waitz. For a general analysis of the argument, see Waitz, page 320, in locum.
J Vide Prior Anal, book ii. chap. 2 — 4. The argument that the me- dium, the source of science as containing the cause, does not perish, though it may do so, and therefore by its remaining that science may be possessed. Aristotle shows to be ineffectual, since they who advance it are compelled to confess that to be possible, viz. that the medium may perish, which is impossible, and hence that we may be ignorant of what we know. By being "so circumstanced," is meant "to Ik- ignorant without ibrgoiful- ness " Ci. Whately's Logic, b. iv. c. ii. sec. 2.
s 2
260 Aristotle's organon. [book i.
necessary that A should be with C. But when the conclu- sion is not necessary, neither possibly can the medium be ne- cessary : for let A be present with C, not of necessity, but let it be with B, and this with C of necessity ; A then will also be of necessity present with C, yet it was not supposed so.1 Since therefore what one knows demonstratively must be in- herent of necessity, we must evidently obtain the demonstra- tion through a necessary medium also, for otherwise, he will neither know why a thing exists, nor that it is necessary for it to exist, but he will either imagine not knowing, if he assumes what is not necessary as if it were necessary,2 or in like manner he will not imagine if he knows that
it is through media, and why it is through the
immediate.*3 Of accidents however which are not per se after the man- ner in which things per se have been defined, there is no de-
1 The necessary relations between premises and conclusion may be considered as four :
1. If the conclusion is necessary, the propositions may be non-neces- sary.
2. If the conclusion is non-necessary, the prop, are non-necessary.
3. If the prop, are necessary, the conclusion is always necessary.
4. If the prop, are non-necessary, the conclusion may be necessary. Granting that the last (number 4.) may be true, yet Aristotle denies that in such a case the person who thus infers demonstrates, because demonstration produces true science, but such a man is ignorant that the conclusion is necessary. Vide also Hill's Logic, p. 285, et seq.
2 Sanderson defines thus : Error est habitus quo mens inclinatur ad assentiendum sine formidine falsitati. Opinio est habitus quo mens in- clinatur ad assentiendum cum formidine alicui proposition! propter proba- bilitatem quam videtur habere. Error, therefore, as Mansel observes, implies certainty of the subject, but not of the object; whilst opinion can- not consist with certainty of the subject, nor yet, strictly, with that of the object. It is of course clear, that what one may scientifically know, another may only think, but to constitute real science two things are necessary : 1. A correct ascertainment of the data from which we are to reason ; 2. Correctness in deduction of conclusions from them. Cf. Whately, b. iv. c. 2, sect. 3. Error, as defined above, comes under the state of mind described in the text bv Aristotle.
3 Cf. Aquinas, Op. 48, cap. 1 ; Occam, Log. p. 3, c. 2. If the premise is not the first cause, though it contains the cause of the conclusion, the syllogism is not Si a/u<rajv, and there is no demonstration : neither if the premise be an effect and not a cause of the conclusion, nor if the pre- mise, though immediate, be a remote cause of it, since in all these cases we know the fact only, but not the cause. Cf. Mansel and Wa'Js Log. 'ib. iii. cap. 22.
CHAP. VII.] THE POSTERIOR ANALYTICS. 261
monstrative science, since it is not possible to de-
' . „ * . , 4. The non-rie-
monstrate the conclusion ot necessity, because cessary, not to accident may possibly not be present, for I speak ^spuuuond in of accident of this kind.1 Still some one may perhaps doubt why we must make such investigations about these things, if it is not necessary that the conclusion should be, for it makes no difference if any one interrogating casual things * 2 should afterwards give the conclusion : , nevertheless we must interrogate not as it (the (cf. Rhetoric, conclusion) were necessary on account of things Jo/phy.ubfiLl interrogated, but because it is necessary for him who asserts these should assert this, and that he should speak truly if the things are truly inherent.
Since, however, whatever are inherent per se .
7 ., . , , . i 5. Necessity of
are necessarily inherent in every genus, and so the minor and
far as each is, it is clear that scientific demonstra- ^0aJ°rb^osi"
tions are of things " per se" inherent, and consist "per se."
of such as these. For accidents are not neces- t An. Post. u.
sary : f wherefore it is not necessary to know the
conclusion why it is, nor if it always is, but not " per se,"3
as, for instance, syllogisms formed from signs.|
For what is " per se " will not be known " perse," J^ £het-
nor why it is, and to know why a thing is, is to
know through cause, wherefore the middle must " per se " be
inherent in the third, and the first in the middle.
Chap. VII. — Tliat we may not demonstrate by passing from one Genus to another.*
It is not therefore possible to demonstrate pass- kdemonltrT in°- from one srenus to another, as, for instance, tion, viz. a de
1 i. e. about common accident— for proper accident is predicated in the second mode per se of a subject. Taylor.
8 Ad veram demonstrationem nihil attinet si quis sumat quae in casu posita, et mutationi obnoxia sint et qua? inde consequantur, declarer. Waitz. The casual, here alluded to, are propositions not belonging to the conclusion.
3 If it always is inherent, i. c. if the propositions be always true.
* Cf. Anal. Post. i. 10. Eth. i. '2. Kcckennann Syst. Log. ni. Tract. 2. cap. 1. Zabarella de Meth. lib. ii. cap. 7. Genus lure signifies the object or materia circa quarn, often, but improperly, called the sub- ject; the species are the subdivisions of the general subject. In the
262 Aristotle's org anon. [book i
monstrated (to demonstrate) a geometrical (problem) by conclusion, ax arithmetic, for there are three things in demon-
10ms, and the . 1 • i •
subject genus, strations, one the demonstrated conclusion, and • Th b ^'1S is that which is per se inherent in a certain concluded of genus.* Another are axioms, but axioms are the subject. ^ey. from which (demonstration is made), the third is the subject genus, whose properties and essential + cf Aquinas accidents demonstration makes manifest. f Now Opusc 48, c it is possible that the things from which demon- stration consists may be the same,| but with those I Videch. 11. wh0ge genus is different, as arithmetic and geo- metry, we cannot adapt an arithmetical demonstration to the accidents of magnitudes, except magnitudes are numbers, and how this is possible to some shall be told here- after. § But arithmetical demonstration always has the genus about which the demonstration (is conversant), and others in like manner, so that it is either simply neces- sary that there should be the same genus, or in a certain re- spect,1 if demonstration is about to be transferred ; but that 2. That the ex- it is otherwise impossible is evident, for the ex- tremes and tremes and the middles must necessarily be of the
media must be . <f
of the same same genus, since it they are not per se, they genus. wjjj ^e accjc|ents Qn this account we cannot by
geometry demonstrate that there is one science of contra- ries, nor that two cubes make one cube,2 neither can any science (demonstrate) what belongs to any science, but such as are so related to each other as to be the one under the other, for instance, optics to geometry, and harmonics to arithmetic. Nor if any thing is inherent in lines not so far as they are lines, nor as they are from proper principles, as if a straight line is the most beautiful of lines, or if it is contrary to circumference, for these things are inherent not by reason of their proper genus, but in so far as they have something common.
demonstrative syllogism, the minor term is the subject; the major, the attribute ; the middle, the cause.
1 Of subaltern sciences, the subject is not entirely the same, as the subject of geometry is a line, but of optics an optical line. Taylor. Vide also Trendelenburg, p. ] 18.
2 That is, geometry cannot teach a method of doubling the cube. Vide Reimer de Duplicatione Cubi. Omnis demonstratio genus suum, non excedere sed in eo consistere debet. Waitz.
CHAP. VIII. IX.] THE POSTERIOR ANALYTICS. 263
Chap. VIII. — Tilings which are subject to Change are incapable of Demonstration per se.
It is also evident that if the propositions of which a syllogism consists are universal, the conclusion of such a demonstration, and in short of the demonstration of itself, must necessarily be perpetual. There is not then either demon-
1. That there
stration, nor in short science of corruptible na- is no demon-
tures, but so as by accident, because there is not finftVo°n "°ere"
universal belonging to it, but sometimes, and after se" of mutable
a certain manner. But when there is such, it is caused the
necessary that one proposition should not be uni- universal being
non-existent.
versal, and that it should be corruptible, cor- ruptible indeed, because the conclusion will be so if the pro- position is so, and not universal, because one of those things of which it is predicated will be, and another will not be,1 hence it is not possible to conclude universally, but that it is now. It is the same in the case of definitions, since definition is either the principle of demonstration, or demonstration, diifei'ing in the position (of the terms), or a certain conclusion of demonstration. The demonstrations and sciences however of things frequently occurrent, as of the eclipse of the moon, evidently always exist, so far as they are such, but so far as they are not always, they are particular,2 and as in an eclipse, so also is it in other things.
C
Chap. IX. — That the Demonstration of a thing ought to proceed from its own appropriate Principles : these last indemonstrable.
Since however it is evident that we cannot de- } That true monstrate each thing except from its own prin- demonstration
1 Hoc quidem (tempore) erit quod asseritur, hoc vero (tempore) non erit. Buhle. I prefer Buhle's translation for its clearness, but have fol- lowed Taylor's on account of its exactness. The science of things sub- ject to change is not simply science, but with the addition of Kara avfi- /3$/3//(coc. Upon the relation of science to its subject matter, see Rhet. book i. oh. 7. Cf. also Rhet. ii. ch. 24. Anal. Prior, i. ch. 13. The subject of science, he expressly says in the Ethics, (b. vi. ch. 4,) has a necessary existence, therefore it is eternal and indestructible.
2 Particular cases, (of eclipses, for instance,) as they are not alf syi tie same, do not fall under demonstration.
264 aristotle's organon. [book r.
only results ciples, if what is to be demonstrated is inherent
appnroprStePtoS in a subject so far as the subject is that (which it
the subject of js^ to have a scientific knowledge of that thing is
the terms must not this, if it should be demonstrated from true,
either be homo- indemonstrable, and immediate (propositions).1
geneous, or • , i -r»
from two ge- .bor we may so demonstrate possibly, as rJryso oneais°contain- did, the quadrature of the circle, since such rea- ed in the other, sonings prove through something common, that which is inherent in another thing, hence these arguments are adapted to other things not of the same genus.2 Wherefore that thing would not be scientifically known, as far as it is such, but from accident, for otherwise the demonstration would not be adapted also to another genus.
We know however each thing not accidentally when we know it according to that, after which it is inherent from * cf Eth b vi principles which are those of that thing, so far ch. 3. as it is that thing ;3* as that a thing has angles
i The possession equal to two ri^ht angles, in which the thing
of three angles ^ , „ , . ° . „= . » „ - . °
equal to two spoken oi j is essentially inherent Irom the pnn-
i'gof triangle. c*ples 0I" tnis thing. J Hence if that§ is essen-
§ ndtiou or tially inherent in what it is inherent, it is neces-
liimhete. ' e sary that the middle should be in the same affinity, ||
II i. e. with the but if not yet it will be as harmonics are proved
extremes, sub- • • i -i • 1 * n i a-l"
ject, and pro- through an arithmetical principle. ouch things perty. however are demonstrated after a similar manner,
1 That is, the propositions must also be appropriate to the subject of demonstration.
3 According to Alexander Aphrodisiensis — Bryso endeavoured to de- monstrate the quadrature of the circle thus : Where the greater and less are found, there also is the equal found, but a square greater and less than a circle is found, therefore a square equal to the circle may also be found. The minor is proved, because a square inscribed in a circle is less, and ctVewmscribed about a circle is greater than the circle, but the de- monstration is founded on a common principle, because the greater, the less, and the equal are found not only in a square and circle, but also in other things. Neither is the major universally true, because a rectilinear angle may be given greater or less than the angle in a semicircle, but one equal to it cannot be given. Vide Euclid Elem. Prop. xvi. b. 3.
3 The examples of Aristotle are principally taken from the Mathe- matics, and the tests of ko.9' clvto and y avro are expressly applied to a geometrical theorem. Mansel. Vide the 4th chap, of this book.
4 That is, by the application of the principle of a superior science, to a problem belonging to a subaltern science, as music is subaltern to arith- metic.
CHAP. IX.] THE POSTERIOR ANALYTICS. 265
yet they differ,1 for that they are, is part of another * r"ferior sci" science,* (for the subject genus is another, J) but \ \. e. differs why they are, is a province of a superior science, g^ySfc,. of which they are the essential qualities. Hence science, from these things also it is apparent that we cannot demon- strate each thing simply, but from its proper principles, and the principles of these % have something t of subaltern common. sciences-
If then this is evident, it is also clear that it 2 That the ap_ is impossible to demonstrate the proper principles propriate prm- of each thing, for they will be the principles of tltagarettfem- all things, and the science of them the mistress of selves incapa-
.D ' . „ _ , . . ,./> ble of demon-
all (sciences):2 for the man has more scientific stration. what
knowledge who knows from superior causes, since 1sscitehneCe_special he knows from prior things when he knows not from effects, but from causes. So that if he knows more, he knows also most, and if that be science, it is also more, and most of all such. Demonstration however is not suitable to another genus, except as we have said, geometrical to me- chanical or optical, and arithmetical to harmonical demon- strations.
Nevertheless it is difficult to know whether a ,
, -• 3. Difficulty of
man possesses knowledge or not, since it is hard deciding whe- to ascertain if we know from the principles of ^J* ^jj1^" each thing or not, which indeed constitutes know- ledge. We think however that we know, if we have got a syllogism from certain primary truths, but it is § . e the con not so, since it is necessary that they § should be elusions with of a kindred nature with the primary. prmcip es.
1 Where the principle is assumed from the same science, or from a superior one, the difference is, that, in the former case, the oti and diori are known ; but in the latter, the Swri is known in the superior, the on in the inferior science.
* Metaphysics. See the third book of Aristotle's treatise on that sub- ject; also Magna Moralia, lib. i. ; Ue Anima, books i. ii. iii.
266 aristotle's orgaston. [book i.
• Cf. Metaph. Chap. X. — Of the Definition and Division of Prin
books v. vi. x
ciples.
1. Definition I call those principles in each genus, the exist- (,lpxa^1)Cthe7r ence of which it is impossible to demonstrate.
as'sum'eT 'e^ Wnat tlien first tnings>t an<l sucn as result from ample. ' these signify, is assumed, but as to principles, we
t vide ch. 2. must assume that they are, but demonstrate the rest, as what unity is, or what the straight and a triangle are ; it is necessary however to assume that unity and magnitude exist, but to demonstrate the other things.1
2 what are tll0se wnicn are employed in demonstrative
peculiar to each sciences, some are peculiar to each science, but wSmmon. others are common, and common according to
analogy, since each is useful, so far as it is in the genus under science. The peculiar indeed are such as, that a line is a thing of this kind, and that the straight is, but the common are, as that if equals be taken from equals the re- mainders are equal. Now each of these is sufficient, so far as it is in the genus, for (a geometrician) will effect the same, though he should not assume of all, but in magnitudes alone, and the arithmetician in respect of numbers2 (alone). 2 liia Proper principles, again, are those which are
assumed to be, and about which science considers whatever are inherent per se, as arithmetic assumes unities, and geometry points and lines, for they assume that these are,
Th m ancl that tiiey are tJlis Partlcular thing. $ But the
that theylre?6 essential properties of these, what each signifies,
arid what they they assume, as arithmetic, what the odd is, or
the even, or a square, or a cube ; and geometry,
1 The above clears Aristotle from the charge unjustly brought against him by Mill, since the former states here the necessity of assuming the existence of the subject, as clearly as the latter asserts it. (Vide Mill's Logic, vol. i.) The principles (e£ wv) from which Aristotle demonstrates are axioms of which he gives a specimen below : " If equals, &c." Vide the table of the principles of science, given before. Cf. also Euclid, b. vi. Prop. 11.
2 The geometrician and arithmetician each assume the principle, only so far as it is analogous to his subject science ; thus the former does not assume every whole to be greater than its part, but that every magnitude is so, and the latter that every whole number is greater than its part. Cf. Wait2 in loc.
CHAP. X.] THE POSTERIOR ANALYTICS. 267
what is not proportionate, or what is to be broken, or to in- cline ; but that they are, they demonstrate through * ; e pril]ci. things common,* and from those which have been P'es. demonstrated.! So also astronomy, for all de- sions. monstrative science is conversant with three ?• ^!l demon-
stration con-
things, those which are laid down as existing, versant with and these are the genus,! (the essential properties ofwhich'we of which the science considers,) and common sometimes may
ncclcct two
things called axioms, from which as primaries % \. e. the siib- they demonstrate ; and thirdly, the affections, § §e properties the signification of each of which the demon- Taylor.— Affec- strator assumes.1 There is nothing however to !!°passiones. e' prevent certain sciences overlooking some of these, Averrois. as if the genus is not supposed to be, if it be manifest2 that it exists, (for it is not similarly manifest that number is, as that the cold and hot are,) and if (the science) does not assume what the affections signify, if they are evident, as neither does it assume what things common signify, (as what it is) to take away equals from equals, because it is known ; nevertheless these things are naturally three, viz. that about which demon- stration is employed, the things demonstrated, and the prin- ciples from which they are.
Neither however hypothesis nor postulate is 4 of the dif. that which it is necessary should exist per se, and ference he- be necessarily seen,|| for demonstration does not w^IV^'and' belong to external speech, but to what is in the ?'2Wak,„ soul,-5 since neither does syllogism. t or it is p. 38, App. always possible to object to external discourse,
Waitz in loc.
1 Vide Trendelenburg Erlaiiteringen, p. 118. For a full enunciation of the statement made here by Aristotle, the reader is referred to Mansel's Logic, p. 109, and Appendices.
2 It is not made the subject of hypothesis, if it is manifest; in other words, it is tacitly assumed.
3 The two kinds of speech were, 1st, Xoyoc 6 t£w, ical Trpo^opiKog, Kai Kara ti)v (pojviiv, i. e. the external, and ('2nd) the internal, 6 taw, icai ivSiaBtroQ, Kal Kara Tr\v ^\iv\i\v. Plut. in Philo. et Damascen. Both Whately and Aldrich regard language as the principal object of logic; the former declares that " if any process of reasoning can take place in the mind without any employment of language, orally or mentally, such a process does not come within the province of the science here treated of." Mansel, on the contrary, considers " the laws of such process, equally with any other, matters of logical investigation." The reader may pro-
268 Aristotle's organon. [book i.
but not always to internal. Whatever things then, being de- monstrable, a man assumes without demonstration, these, if he assumes what appear probable to the learner, he supposes, and this is not an hypothesis simply, but with reference to the learner alone ; but if, there being no inherent opinion, or when a contrary is inherent, the demonstrator assumes, he requires the same thing to be granted to him. And in this hypothesis and postulate differ, for postulate is any thing sub-contrary to the opinion of the learner, which though demonstrable a man assumes, and uses without demonstration. 5. That deflni- Definitions then are not hypotheses, (for they tion is not hy- are not asserted to be or not to be,) but hypothe- ses are in propositions. Now it is only necessary that definitions should be understood, but this is not hypothe- sis, except some one should say that the verb to hear is hypo- thesis. But they are hypotheses, from the existence of which, in that they are, the conclusion is produced. Neither does the geometrician suppose falsities, as some say, who assert, that it is not right to use a false (principle), but that the geometrician does so, when he calls a line a foot long when it is not so, or the line which he describes a straight line when it is not straight. The geometrician indeed concludes nothing from the lines being so and so, as he has said, but concludes those, which are manifested through these (symbols). More- over postulate and every hypothesis are either as a whole or as in a part, but definitions are neither of these.1
fitably compare Locke's Essay, b. iv. 5, 5, and 6, 2 ; also Sanderson. The former's distinction between mental and verbal propositions is well known. The words in the text are only enunciative of oral as con- trasted with mental reasoning, but are not decisive against Whately's opinion. Vide De Anima, b. i. and iii. ; Eth. b. i. c. 13. Dr. Hessey speaks sensibly enough of the " absurdity of maintaining that logic re- gards the accident of the external language, and not the necessity of the internal thought" (p. 4, Intro. Schem. Rhet.). It appears to be, after all, " splitting a straw ; " for such an opinion is not only " absurd," but self-destructive, we never do, because we never can, practically adopt it.
1 Defmitio ab hypothesi eo differt quod nihil edicit de existentia rei quae definitur : nam si quis contendat definitionem, licet non ponat ali- quid esse vel non esse, sed intelligi tantum velit id quod dicat, tamen esse hypothesin, quodcunque auribus percipimus, si quod dictum est in- telleximus, hypothesis dicenda erit. Verum viroOkaiiQ dicuntur quibus positis {pcrwv ovtwv) et ex quibus aliud quid colligitur. Alia causa cur
CIIAP. XI.] THE POSTKRIOK ANALYTICS. 269
Chap. XL — Of certain Common Principles of all Sciences.
That there should then be forms,* or one cer- * nsr,— spe- tain thing besides the many, is not necessary, to cies' Buh,e- the existence of demonstration,1 but it is necessary truly to predicate one thing of the many, for there will not be the uni- versal unless this be so, and if there be not an universal, there will not be a medium, so that neither will there be a demonstration. It is essential then that uo^n^exist there should be one and the same thing, which is without €i&n, not equivocal in respect of many : no demonstra- out an uni- " tion however assumes that it is impossible to af- ^rnsal conceP- firm and deny the same thing at one and the same time, unless it is requisite also thus to demonstrate the conclusion. It is demonstrated however by assuming the first f to be true of the middle, and that it is t i. e. the ma- not true to deny it, but it makes no difference ior Pr°P-
definitio non appellari possit hypothesis in eo est, quod hsec aut uni- versalis est aut particularis, in ilia, vero quod subjectum est aequale esse debet ei quod pradicalur. Waitz. Vide also scheme of principles of science. Cf. Locke's Essay, b. iii. 4, 7. Occam's Logic, part i.
1 The Platonic theory of Idea, to which Aristotle here refers, so highly commended by St. Augustine, is not free from much error, arising from Plato's opinion thai the ideas in man's soul are inherently good. The remark which Aristotle makes in this place, seems chiefly, as Taylor thinks, to prevent the misconception of Plato's theory, by those who imagined his ideas to be corporeally separate from matter, and not incorporeal forms residing in a divine intellect ; but the real case is, that Aristotle elsewhere impugns the doctrine of the idea as not practical. Vide Ethics, lib. i. c. 6, Browne's note, Bohn's edition ; also Metaphysics, lib. xii. De Anima ; Brewer's Ethics ; Ritter, vol. ii. The province of the Platonic dialectic was to investigate the true nature of that connexion, which existed between each thing and the archetypal form or idea which made it what it was, and to awaken the soul to a full remem- brance of what she had known prior to her being imprisoned in the body. Hence, dialectic, with Plato, is the science of the immutable, and takes cognizance of the universal principle ; in fact, is an object identical with the Metaphysics of Aristotle, whereas the dialectic of the latter partook of the essentially practical nature of his mind, and is merely "the art of disputing by question and answer." Cf. Gorgias, Theaitetus, Meno, and the Commentaries of Syrianus, and upon the doctrine of universals, see Locke's Essay, b. iv. ; Stewart, Phil, of Human Mind; Whately's and Mansel's Logics.
270 Aristotle's organon. [book i.
whether we assume the middle to be or not to be, and in a
similar manner also in respect of the third.1 For e major. .^ ^aj. ^e granted * in respect of which it is true to predicate man, even if (some one should think that man is) not man, (the conclusion) will be true, if only it is said that man is an animal, and not that he is not an animal, for + sup lvthe ** w^ ^e true to say that Callias, even if he be minor— caiiias not Callias,f yet is still an animal,! but not that js Thewnciu- * which is n°t an animal. The cause however is, sion. that the first is not only predicated of the middle,
of what is can- but also of something else, in consequence of its of contradic-le DemS common to many, so that neither if the tion in demon- middle be that thing itself, or not that thing, does
it make any difference in respect to the conclu- sion. But the demonstration which leads to the impossible,
assumes that of every thing affirmation or nega- Prior, book ii. tion is true,§ and these | it does not always (as- Tayior.oms ' sume) universally, but so far as is sufficient, and
it is sufficient (which is assumed) in respect of the genus. I mean by the genus, as the genus about which a „ „., person introduces demonstrations, as I have ob-
H Vide ch. 10. x , . „ _-
served betore."| „ All sciences communicate with each other ac-
irion principles cording to common (principles), and I mean by com- c5;inLleveral mon those which men use as demonstrating from these, but not those about which they demonstrate, nor thai which they demonstrate, and dialectic is (common) to all * (Science.) (sciences). If also any one* endeavours to demon- metamh j;.se" strate universally common (principles), as that of vide Metap. every thing it is true to affirm or deny, or that equals b' U1" remain from equals, or others of this kind. Dia-
lectic however does not belong to certain things thus definite, f i. e. it is con- nor to one particular genus ; f for it would not versant with interrogate, since it is impossible for the demon- strator to interrogate, because the same thing is t Pr. An. b. ii. n°t proved from opposites : 2 this however has ch. is. been shown in the treatment of syllogism. t
1 Though the minor should not be assumed both to be and not to be that which it is, nevertheless the conclusion will be right. * Here is a proof of the difference between the iialectic of Plato and
CHAP. XII. ] THE POSTERIOR ANALYTICS.
271
Chap. XII. — Of Syllogistic Interrelation.
If syllogistic interrogation is the same as a pro- j M h
position of contradiction,1 but there are proposi- deciding what
tions in each science, from which the syllogism [J^to'eTch6
which belongs to each consists, there will be a science,
certain scientific interrogation, from which the M ,
„ . * i • , • , . * i. e. the de-
syllogism, which is appropriate to each science, monstrative is drawn. It is clear, then, that not every inter- svll°sism- rogation would be geometrical, or medical, and so of the rest, but from what any thing is demonstrated about which geo- metry is conversant, or which are demonstrated from the same principles as geometry, as optics, and in like man- ner with other sciences. These f also must be pr0ved irTgeo- discussed from geometrical principles and conclu- metry, &c. sions4 but the discussion of principles is not to ciuskmsfrom1 be carried on by the geometrician so far as he is the former be- such ; likewise with other sciences. Neither is to^/subse- eS every one who possesses science to be interrogated i"6"1 demon-
J r . . ° strations.
with every question, nor is every question about each to be answered, but those which are defined about the science. It is evident then that he does well, who disputes with a geometrician thus, so far as he is such, if he demon- strate any thing from these principles, but if not, he will not do well. Again, it is clear that neither does he confute the geometrician except by accident, so that there cannot be a discussion of geometry by those who are ignorant of geometry, since the bad reasoner will escape detection, and it is the same with other sciences.
Since there are geometrical interrogations, are 2. of discover- there also those which are ungeometrical ? and to which each*
that of Aristotle, pointed out above. Moreover the dialectician interro- gates so that his opponent may either affirm or deny, but the demon- strator proves or interrogates in order to make the thing evident from principles better known to his hearer; again, the dialectician may em- ploy affirmation or negation, but the demonstrator has to prove a certain conclusion.
1 Interrogation and proposition are the same in reality, but differ in definition. A proposition is such as, " Every man is an animal;" an interrogation is such as, " Is not every man an animal ? " Taylor.
272 Aristotle's organon. [book l
false syllogism in each science are those ignorant questions Avhich appertains. are 0£ a certain quality1 geometrical? whether also is a syllogism, from ignorance, a syllogism composed from opposites or a paralogism,2 but according to geometry, or from another art, as a musical interrogation is ungeometrical, about
geometry, but to imagine that parallel lines meet subjectTerms6 ^s *n a certain respect geometrical,* and after an- are so. other manner ungeometrical ? t For this ± is two-
false. fold, in the same way as what is without rhythm ;
VometricaT1" an<^ tne one *s ungeometrical because it possesses
not (what is geometrical), as what is without rhythm ; but the other because it possesses it wrongly — and
this ignorance which is from such principles, § is prop°with geo- contrary. || In mathematics however there is not metrical terms. jn jjj-g manner a paralogism, because the middle
II To science. . £ f> ' .
is always two-told,"5 tor (one thing) is predicated of every individual of this, and this again of another every, but the predicate is not called universal ;4 those, nevertheless, it is possible, we may see by common percep- tion,^ but in argument they escape us. Is then every circle a figure ? If any one should delineate it, it is clear. But what, are verses a circle ? They are evidently not so.5
1 Ignorance is two-fold; 1st, From pure negation; 2nd, From a de- praved disposition. Vide chapters 16, 17, and 18; also Eth. b. iii. ch. 1. Cf. Metap. lib. iii.
2 Utrum syllogismus ayEw/xtrpjjroc dicendus est is, qui fiat ex pro- positionibus veritati repugnantibus, sive etiam qui ex propositionibus veris non recte colligat (6 irapaXoyto-^oc) dummodo propositiones ex quibus fiat geometriae sint propria? an syll. qui ex alia doctrina desumtus ad geometriam omnino non pertineat ? Waitz. Aristotle says (after- wards) that certain interrogations, entirely geometrical, are assumed from another art or science, and correspond to the ignorance which is said to be of pure negation, as " Is number even or odd ? " but that there are others which are in a certain respect geometrical, and in a certain respect not, and which are falsely conceived of geometrical points, as " Will not parallel lines meet ? " Cf. Philop. fol. 34.
3 That is, the middle term is twice assumed, viz. in the major and in the minor prop.
4 The majus extremum is universally attributed to the middle term in the major prop, in the first figure, (to which Aristotle refers,) and the middle term is universally attributed to the minor extreme in the minor proposition ; but the expression of universality is not added to the predi- cat?, but to the subject only.
• I read the concluding paragraph according to Waitz's stopping. Am-
CHAP. XII.] THE POSTERIOR ANALYTICS. 2?3
Still it is improper to object to it, if it be an in- ductive proposition ;* tor as neither is that a pro- 1™*™-.. position which is not in respect of many things, 3 When ob (since it will not be in all, but syllogism is from jection ie not uriiversals,) neither, it appears clear, is that an ob- jection, for propositions and objections are the same, as the objection which one adduces, may become either
t Cf ch 4
a demonstrative or a dialectic proposition.1!
It occurs that some argue contrary to syllogism, 4 instance of
from assuming the consequences of both (ex- ajyllogistie
tremes), as Caeneus does,2 that fire is in a mul- Employing J
tiple proportion, because, as he says, both fire and syllogism with
,. . . „ -, -n both prop, af-
this proportion are rapidly generated. But thus firm, in the 2nd there is no syllogism,3 though there will be, if ngure-
totle says, they may be seen by common perception, ( tq vorjcrii,) the verb vosTv being said of self-evident truths, because mathematicians represent these things by diagrams, and therefore if a circle was similarly described, it would be manifest ; KvicXog however signifies both a mathematical figure and a kind of period or verse. Vide Hermo. et Demet.
1 The following is the note of Julius Pacius on Anal. Prior, c. 28, (Pacian Division,) as to the apparently conflicting statement made by Aristotle here. " Discrimen ponit Aristoteles (lib. ii. Prior, cap. 28) inter objectionem et propositionem, id est propositionem illam cui objicitur : alioquin etiam ipsa objectio est propositio, ut dictum fuit in definitione. Discrimen est, quod objectio est universalis, vel particu- laris : propositio vero, si sit pars syllogismi universalis, necessario est universalis. Sensus est propositiones constituentes syllogismum esse universales : everti autem vel per objectiones universales, ut contrarias ; vel per particulares ut contradicentes. Huic sententiae opponitur quod ait Aristoteles, lib. i. Post. cap. 12, par. 11, omnem instantiam esse universalem. Existimo haec loca per distinctionem esse concilianda. Aristoteles in Prior, considerat instantiam sive objectionem quatenus evertit propositionem contrariam ; haec objectio potest esse tarn universa- lis quam particularis. In Poster, autem considerat objectionem quatenus per earn, non solum evertitur propositio adversarii, sed etiam demon- stratio erigitur. Quoniam igitur demonstratio constat ex propositionibus universalibus, etiam haec objectio necessario est universalis." On the con- sideration of the enstatic enthymeme, and of the passages relative to the "Evaraaig, vide Dr. Hessey's Schem. Rhet. Supple. Table 5. Cf. aUo Waitz in loc.
2 Caeneus argued : " That which is increased by multiple proportion is
rapidly increased Fire is rapidly increased . • . Fire is increased by multiple proportion." The last expression means that by every addition it becomes double or triple, etc.
' Because both prop, affirm, in the 2nd fig.
7
2/4 aristotle's o::c:a:;on. [book i.
the multiple is consequent to the most rapid proportion, and the most rapid proportion to fire in motion. Sometimes it does not happen that a conclusion is made from the assump- tions, and sometimes it happens, hut is not perceived : if however it were impossible to demonstrate the true from the * , ^ . rf false, it would be easy to resolve* for (the terms) Prior An. b. u. would be necessarily converted.1 lhus let Ay t Propositions, exist, and this existing, these things also exist J t This conciu- fae existence of which I know, as B, from these know is true, then § I will demonstrate that that || exists. What sionheB?nclU pertain however to mathematics, are rather con- II The proposi- verted, because they take nothing accidental, (and in this they differ from dialectical subjects,) but definitions.
Yet they are increased, not through media, but
5. Mathemati- i it ■ i ._• a j» t> a • ±-
cai demonstra- through additional assumption, as A of r>, this ol
nr vl Thely ^» tn*s agam °f A an& so on to infinity. Also same, by many transversely, as A both of C and of E, as there is
a number so great or even infinite, which is A, an odd number so great B, and an odd number C. A then is (true)
of C, and the even is a number so great D, the ir Example (i). eyen number ig E wherefore A is (true) of E.f
Chap. XIII. — The difference between Science, " that" a thing is,
and " why " it is.
l. A twofold Now there is a difference between knowing:
uiiiGrcncc II tuG
syllogism be that a thing is, and why it is, first in the same
1 Difficilius est ad dijudicandum ex quibus propositionibus coactum sit. quod syllogismus confecit {to dvaXvetv). Waitz. Aristotle means that the truth of the prop, might easily be collected from the truth of the conclusion, for they might be converted.
B A
Ex. 1. Every odd number is finite or infinite C B
Every ternary is an odd number C A
. * . Every ternary is finite or infinite.
D A
Every even number is finite or infinite
E D
Every binary is an even number E A
. * . Every binary is finite or infinite
CHAP. XIII.] THE POSTERIOR ANALYTICS. 275
science, and in this in two ways, the one, if the not through
' . ... ,1 • 3' j. things mime-
syllogism is not formed through things immediate, diate : next, if (since the primary cause is not assumed, but the I^JJJ^L., science of the why has respect to the first cause,) in the same but the other if it is through things immediate science> indeed, yet not through the cause, but through that which is more known of the things, which reciprocate.1 Now nothing prevents that which is not a cause being sometimes more known amongst things which are mutually predicated, so that demonstration shall accrue through this, as that the planets are near, because they do not twinkle. Let C be the planets, B not to twinkle, A to be near, B therefore is truly predi- cated of C, since the planets do not twinkle, A also of B, for what does not twinkle is near, but this * may be * i. e. the two assumed by induction or by sense.2 It is neces- propositions.
1 When the effect immediately follows the cause, the two are said to reciprocate, because one being admitted, the other is necessarily so, though sometimes the effect is more known than the cause, as he says be- low. For the two senses of the word ayaaog, cf. Anal. Post. i. 2, and ii. 19 ; here it signifies a premise immediate, as regards its conclusion, i. e. not requiring the insertion of lower middle terms, to connect its terms with those of the conclusion. On the particular meaning of the word " cause," and in fact in relation to the whole chapter, see Hill's Logic, under " Demonstrationis species." pp. 287, et seq., and Mansel's Logic, 106, Appendix, pp. 63, et seq.
2 The major by induction, because a lamp, gold, etc., when they are near, do not twinkle ; the minor by sense, because we see the planeta fio not twinkle. Taylor.
B A
Ex. 1. Whatever does not twinkle is near C B
The planets do not twinkle C A
. • . The planets are near.
B A
Ex. 2. Whatever is near does not twinkle , C B
The planets are near
C A
. • . The planets do not twinkle.
B A
Ex. 3. What is spherical is thus increased C B
The moon is spherical C K
.' . The m:on is thus increased.
/
276 Aristotle's organon. [book i.
sary then that A should be present with C, so of th^s?!!6 ^hat ^ *s demonstrated that the planets are near.*
This syllogism then is not ef the " why," but of the "that" (a thing is), for the planets are not near because they do not twinkle, but they do not twinkle because they are near. It happens indeed that the one may be proved through the other, and the demonstration will be of the " why," as let C be the planets, B to be near, A not to twinkle, B then is
present with C, so that A "not to twinkle" will |,H(y be with C.t It is also a syllogism of the "why,"
for the first cause was assumed. Again, as they show the moon to be spherical through increments (of light), for if what is thus increased be spherical, and the moon is in- creased, it is evident that the moon is spherical, thus then a
syllogism of the "that" is produced, but if the wmiddiVbe"1 middle is placed contrarily,| there is a syllogism comes the ma- of the " why," for it is not spherical on account of former major the increments, but from being spherical she becomes the receives such increments : let the moon be C, § Example (3.) spherical B, increase A.§ Where again the media 2. Where the do not reciprocate,1 and what is not the cause is reciprocate°the more known, the "that" is indeed demonstrated, on is demon- but not the " why ; " further, where the middle is where the mid- placed externally,2 for in these the demonstration fyepiaceeXdtemal" is of tlie "that," and not of the "why," as the
cause is not assigned. For example, why does not a wall breathe ? because it is not an animal, for if this was the cause of its not breathing, it would be necessary that animal should be the cause of its breathing, since if negation is the cause of a thing not being, affirmation is the cause of its being, thus if the disproportion of hot and cold is the cause of not being well, the proportion of these is the cause of be- ing well. Likewise if affirmation is the cause of being, nega- tion is the cause of not being, but in things which have been thus explained, what has been stated does not occur, for not
1 The cause is the middle, in the demonstration of the " «'%," and the effect is the middle, in the demonstration of the "that." By media not reciprocating, is meant when we reason affirmatively, from the effect to the remote cause ; as, man is risible, therefore he is animal : here we miss the proximate cause, "is rational."
2 i. e. before both extremes, in the 2nd figure, in which demonstration through a remote cause (as he will show) occurs.
CHAP. Xm.l THE POSTERIOR ANALYTICS. 277
every animal respires.1 A syllogism of such a cause is never- theless produced in the middle figure, for example, let A be animal, B to respire, C a wall, A then is present with every B, (for whatever respires is animal,) but with no C, so that neither is B present with any C, wherefore a wall does not respire.* Such causes however resemble things spoken hyperbolically,2 and this is, when we turn aside to speak of the middle, which is more widely extended, as for instance, that saying of Anacharsis, that amongst the Scythians there are no pipers, since neither are there any vines.3
As to the same science then, and the position Anoth ... of the media, these are the differences between a ference be- syllogism of, that a thing is, and of why it is, but JJE'rffflKfci in another respect the why differs from the that, ?nd the 3'°™, because each is beheld in a different science. Now each belonging such are those things which so subsist with re- t0.a dlfferent
o . science.
ference to each other, as that the one is under the other, such as optics with reference to geometry, mechanics to the measurement of solids, harmonics to arithmetic, and celestial phenomena to astronomy. Some of these sciences are almost synonymous, as astronomy is both the mathematical and the nautical; and harmony is both mathematical and
' But only those which have lungs, hence the proximate cause of respiration is not animal, but the possession of lungs, which cause how- ever is not assigned.
B A
Ex. 4. Whatever respires is an animal C A
No wall is an animal C B . • . No wall respires.
2 Remote causes being adduced resemble hyperboles, in that more is said than is requisite, for a remote is of wider extension than a proximate cause.
3 When we leave (the proximate cause) to speak of that middle which is more widely extended than (cause). Taylor. The demonstration of Anacharsis is thus framed in the 2nd figure. There are no pipers where there are no vines, but there are no vines among the Scythians, . " . among the Scythians there are no pipers. Now the successive causes to the first or major premise are, there are no vines because there are no grapes ; no grapes is the cause of no wine ; no wine is the cause of no intoxication; no intoxication cause of no pipers; but these intermediate causes are omitted, and the effect is at once connected with the remote cause.
278
ARISTOTLE S ORGANON.
[book I.
that which belongs to the ear. For here to know Sti that a thing is, is the province of those who ex- beiongs to the ercise the sense, but to know why it is, belongs thel^to the to mathematicians, since these possess the demon- mathematicai, strations of causes, and often are ignorant of the that, as they who contemplating universals, fre- quently are ignorant of singulars from want of observation. But these * are such as being essentially something else J use forms, for mathematics are conversant with forms, since they do not regard one certain subject, for though the geometrical are of a cer- tain subject, yet not so far as they are geometrical are they in a subject.J As optics also to geome- try, so is some other science related to optics, as for example, the science about the rainbow, for to know that it is, appertains to the natural philosopher, but why it is, to the optician either simply or mathematically. Many sciences . . ., ,. also which are not arranged under each other
§ i. e. the oTt m ° ,. .
is known in subsist thus, § for example, medicine with regard to but tneToVi in geometry, for to know that circular wounds heal another. more slowly is the province of the physician, but
why (they do so) of the geometrician.1
* i. e. the su- perior sciences + Essentially different from their subject sciences.
I Cf. Procli. Con. in Euclid Elem.
Chap. XIV. — The first Figure most suitable to Science.
1 Mathemati- Op the figures, the first is especially adapted to cai demonstra- science, for both the mathematical sciences carry
1 Viz. because he knows that the capacity of the circle is the largest of all figures, having equal perimeters, hence the parts of a circular wound coalesce more slowly. For the development of the chapter, the following scheme of demonstration is introduced :
Demonstratio
Quod sit
I
Propter quid sit
Obliqua
per deductionem
ad impossibile
Directa
Per effectum
Per causam remotam
Non potissima per causam
proximam quae non est prima
Potissima per causam proximam et primam.
CHAP. XV.] THE POSTERIOR ANALYTICS. 279
out their demonstrations by this, as arithmetic, tions effected
geometry, optics, and nearly, so to speak, whatso- fig™"egh thls ever sciences investigate the "why," since either
entirely or for the most part, and in most sciences, 2. Also the syi
the syllogism of the why is through this figure, aX^cf. book
Wherefore also, on this account, it will be espe- lnd- ..
. . ' . . . ' . r 3. Also the sci-
cially adapted to science, tor it is the highest pro- ence of roi t»
perty of knowledge to contemplate the " why ; " *■"'"' in the next place, it is possible through this figure alone to
investigate the science of what a thing is; for in the middle figure, there is no affirmative syllogism, but the science of
what a thing is belongs to affirmation,* and in * i. e. the defi-
the last figure, there is an affirmative, but not an nitlon affirnii
universal ; but the what a thing is belongs to ^g^s °0„!r
universals, for man is not a biped animal in a densed by this
certain respect. Moreover this has no need of t j." e. they are
those, but they are condensed f and enlarged % ^^^ the
through this, till we arrive at things immediate : § 1 By prosyiio-
it is evident, then, that the first figure is in the fisime.'inde-
highest degree adapted to scientific knowledge. monstrabie.
Chap. XV. — Of immediate negative Propositions.
As it happened that A was present with B indi- 1. That one vidually, so also it may happen not to be present, sibTy^fbe^nl and I mean by being present with, or not, indi- dividuaiiy pre- vidually, that there is no medium between them, other. Exam- for thus the being present with or not, will not be ples- according to something else. When then either A or B is in a certain whole, || or when both are, it is impos- sible that A should not be primarily present with Pr^rd? ^j™1; B. For let A be in the whole of C, if then B is not in the whole of C, (for it is possible that A may be in a certain whole, but that B may not be in this,) there will be a syllogism^ that A is not present with B, for if C is present with every A, but with no B A will be present with no B. In like manner also, if B is in a cer- tain whole, as for instance, in D, for D is with every B, but A with no D, so that A will be present with no # In Cesare. B by a syllogism.* In the same wayf it can be t in either Ce-
280 aristotle's orgaxon. [book i.
sare or Cames- shown * if both also are in a certain whole, but *rThat a is not *hat *' *s possible that B may not be in the whole with B. in which A is, or again A in which B is, is evi-
dent from those co-ordinations f which do not in- terchange.1 For if none of those, which are in the class A C D, is predicated of any of those in B E F, but A is in the whole of H, which is co-arranged with it, it is evident that B will not be in H, for otherwise the t Example (i.) co_or(iinates woui<i intermingle.}
Likewise also if B is in a certain whole, but if
2
neither is in any whole, and A is not present with L not* a ifin- B, it is necessary that it should not be present demonstrable, individually, § for if there shall be a certain mid- dle, one of them must necessarily be in a certain whole, for there will be a syllogism either in the first, or in the middle figure. If then it is in the first, B will be in a certain whole, (for it is necessary that the proposition in regard to this should be affirmative,) but if in the middle figure either of them || may be (in the whole), for the neSivePin°2nd negative being joined to both,f there is a syllo- figure. gism,* but there will not be when both the pro-
* In 2nd figure. pogitions are negative.
It is manifestly possible then, that one thing may not be individually present with another, also when, and how this may happen, we have shown.
Chap. XVI. — Of Ignorance? according to corrupt position of the Terms, where there are no Media.
+, ci'JSl I2 '•■• The ignorance t which is denominated not ac-
also Eth. b. m. .. ° '.
ch. i. cording to negation, but according to disposition.
1 By co-ordinations, he means the series deduced from each of the ten categories, as substances, body, etc. Now what belongs to one class can- not be arranged in another ; thus body, which is in the category of sub- stance, cannot be in the category of quality.
|
Ex. 1. Substance. H. |
B. |
Quality. |
|
|
Body. A. |
E. |
Colour. |
|
|
Animated. C. |
F. |
Whiteness. |
|
|
Rational. \ -p. Animal. ] |
|||
|
8 Vide Whately; b. in. sec. 15- |
-19 |
. |
CHAP. XVI.] THE POSTERIOR ANALYTICS. 281
is a deception produced through syllogism, and l. Definitian of this happens in two ways, in those things which t?Je'eltv,£nd\ts are primarily present, or not present ; for it hap- kinds. pens either when one simply apprehends the being present, or not being present, or when he obtains this opinion through syllogism : of simple opinion, then, the deception is simple, but of that which is through syllogism, it is manifold. For let A not be present with any B individually, if then A is concluded to be present with B, assuming C as the middle, a person will be deceived through syllogism. Hence it is possible that both propositions may be false, but it is also possible that only one may be so, for if neither A is present with any C, nor C with any B, but each proposition is taken contrary, both will be false. But it may be that C so subsists with reference to A and B, as neither to be under A nor universally (present) with B, for it is impossible that B should be in a certain whole, since it was said that A is not primarily present £xam j with it ; but A need not be universally present affirmative de- with all beings, so that both propositions are false. cePtlon- Nevertheless, we may assume one proposition as true, not either of them casually, but the proposition A C, for the pro- position C B will be always false, because B is in none ; but A C may be (true), for instance, if A is present individually, both with C and B, for when the same thing is primarily pre- dicated of many things, neither will be predicated of neither ; it makes no difference however if it (A) be not individually present with it (C).
The deception then of being present, is by these 3 Negative de- and in this way only, (for there was not a syllo- ception in- gism of being present in another figure,*) but the first and middle deception of not being present with, is in the first ^By^ Anal and middle figure. t Let us first then declare in Prior, b. i. how many ways it occurs in the first, and under omittedbe- what propositional circumstances. It may then cause no uni-
VtTSHlCOTlClll-
happen when both propositions are false, e. g. if sion proved in A is present individually with C and B, for if A ll- should be assumed present with no C, but C with every B, the propositions will be false. But (deception) is possible, when one proposition is false, and either of them casually ; for it is possible that A C may be true, but C B false ; A C true, because A is not present with all beings, but C B false3
262
ARISTOTLE S ORGANON.
("book
because it is impossible tbat C should be with B, with nothing of which A is present ; for otherwise the proposition A C will be no longer true,* at the same time, if both are true, the conclusion also will be true.f But it is also possible that C B may be true, when the other proposition is false, as if B is in C and in A, for onef must ne- cessarily be under the other,§ so that if A should be assumed present with no C, the proposition will be false. || It is clear then, that when one proposition is false, and also when both are, the syllogism will be false. %
In the middle figure, however, it is not possible that both propositions should be wholly false, for when A is present with every B, it will be impossible to assume any thing,* which is present with every individual of the one, but with no individual of the other ; j but we must so assume the propositions that the (middle) may be present with one (extreme), and not be present with the other, if indeed there is to be a syllogism.^ If then, when they are thus assumed, they are false, it is clear that, when taken contrarily, they will subsist vice versa, but this is impossible.1 Still there is nothing to prevent each being partly false, as if C is with A, and with a certain B ; for if it should be assumed present with every A, but with no B, both propositions in- deed would be false, yet not wholly, but partially. The same . go that the will occur when the negative is placed vice versa. § neg. prop, is But it is possible that one proposition, and either major. q£ ^em, may ^e faise> for what is present with
II Because b is every A, will be also with B,|| if then C is as- species of a. sume(j present with the whole of A, but not pre- sent with the whole of B, C A will be true, but the proposi- tion C B false. Again, what is present with no B, will not be present with every A ; for if with A, it would also be with B, but it was not present ; if then C should be assumed pre- sent with the whole of A, but with no B, the proposition C
1 They will be true when the arrangement is such that negation re- sults from affirmation, and affirmation from negation ; but this will be impossible, because when the conclusion is false, the prop, cannot be true.
* Because A is with some C, viz. with B contained un- der C t Vide An. Prior i. ch. 2—4. t A. § C.
|| i.e. partially.
If i. e. the con- clusion will be false.
2. Middle fig.
* Any term. t With every A and no B in Camestres, or with no A and every B in Cesare. t In 2nd figure
CHAP. XVII.] THE POSTERIOR ANALYTICS. 283
B will be true, but the other false.* The same * Either wholly will happen if the negative is transposed,! for °^P^^iially•
u * • • a -li -.1. u • "D -i-\\ tlfthenega-
what is in no A, will neither be in any 13 ; it then tive becomes C is assumed not present with the whole of A, the major' but present with the whole of B, the proposition A C will be true, but the other false.4: Again, also, it is false Who]1 fahe to assume that what is present with every B, is with no A ; for it is necessary, if it is with every B, that it should be also with a certain A ; if then C is assumed pre- sent with every B, but with no A, the proposition C B will be indeed true, but C A false. § Hence, %J^SS^ it is evident that when both propositions are false, and when one only is so, there will be a syllogism deceptive in individuals.1
Chap. XVII. — Continuation of the same with Media.
In those which are not individually present,|| or , syllogism of which are not present, when a syllogism of the the {&}s.e p™-, .
■ ductd in rowli-
false is produced through an appropriate medium, ates, when the
both propositions cannot be false, but only the ^suVfe/a86'
major. But I mean by an appropriate medium, medium.
that through which there is a syllogism of contra- _ .
o J c H i. e. a con-
diction.^ For let A be with B through the me- elusion contra-
dium of C, since then we must take C B as af- jggLfljJ?
firmative, if there is to be a syllogism, it is clear conclusion.
that this will be always true, for it is not con- „
verted.* A C, on the other hand, will be false, changed into a
for when this is converted, a contrary syllogism ne*a,lve-
arises.2 So also if the middle is assumed from another affinity,
as for instance, if D is in the whole of A, and is predicated of
every B, for the proposition D B must necessarily remain,3
but the other proposition must be converted,4 so that the one
(the minor) will be always true, but the other (the major)
always false. Deception also of this kind is almost the same
1 In those cases which have no medium.
2 A syllogism with a conclusion opposite to the true conclusion, and which produces deception opposed to true science.
3 Because the minor in the 1st fig. must continue affirm. * i. e. the major must be changed into a negative.
284 Aristotle's okgaxon. [book i.
2 Case of both as ^a* wnicn *s through an appropriate medium, propositions but if the svllogism should not be through an ap- bemg false. propriate medium,1 when indeed the middle is under A, but is present with no B, it is necessary that both propositions should be false. For the propositions must be assumed contrary to the way in which they subsist, if a syl- logism is to be formed,2 for when they are thus assumed both are false, as if A is with the whole of D, but D present with no B, for when these are converted, there will be a syllogism, and both propositions will be false. When however the me- dium is not under A, for instance, D, A D will be true, but * vide An "^ "^ false, for A D is true, because D was not in Prior, b. i. ch. A, but D B false, because if it were true the con- 2— 4- elusion also would be true,* but it was false.
3 Both prop Through the middle figure however, when de- cannot be ception is produced, it is impossible that both riddle86 in propositions should be wholly false, (for when B figure, when i§ under A, it is possible for nothing to be pre- produced.1S sent with the whole of the one, but with nothing t vide pre- of the other, as has been observed before, f) but ceding chapter. Qne proposition may be false whichever may hap- pen. For if C is with A and with B, if it be assumed pre- sent with A, but not present with B, the proposition A C will be true, but the other false ; again, if C be assumed present with B, but with no A, the proposition C B will be true, but the other false.
4. Affirmative ^ tnen the syllogism of deception be negative,
deception. it has been shown when and through what the
t in Barbara, deception will occur, but if it be affirmative^
when it is through an appropriate medium, it is impossible
§ Affirmative, that both should be false, for C B must necessarily
figure!"* Ut remain, § if there is to be a syllogism, || as was also
1TB From being observed before. Wherefore C A will be always
false. false, for it is this which is converted.^ Likewise
1 When it is through a medium by which a true conclusion cannot be proved : thus, through " brute," it can never be proved that " man is a living being." Taylor.
2 i. e. to form a negative in the 1st figure, (Celarent,) it is necessary in the major prop, that the first be denied of the middle, and in the minor that the middle should be affirmed of the last.
CHAP. XVIII.] THE POSTERIOR ANALYTICS. 285
also, if the middle be taken from another class, as vas ob- served in negative deception, for the proposition D B must of necessity remain, but A D be converted, and the decep- tion is the same as the former. But when it is not through an appropriate medium, if D be under A, this* t indeed will be true, but the other t false, for A
.... . , ' , . ... t Ihe minor.
may possibly be present with many things which are not under each other.1 If however D is not under A, this | will evidently be always false, (for it is as- sumed affirmative,) for D B may be as well true as false, since nothing prevents A being present with no D, but D with every B, as animal with (no) science, but science with (all) music. Again, (nothing prevents) A from being present with no D, and D with no B : it is clear then that when the medium is not under A, both propositions, and either of them, as it may happen, may be false.
In how many ways then, and through what, syllogistic de- ceptions are possible, both in things immediate, and in those which are demonstrated, has been shown.
Chap. XVIII. — Of the Dependence of Universals upon Induction, and of the latter upon Sense.
It is clear, also, that if any sense be deficient, a
• • . .1 Universals
certain science must be also deficient, which we from which de- cannot possess, since we learn either by induction nionstratl°n
, -, r . _T . ■'. . „ proceeds, de-
or by demonstration. JNow demonstration is trom pend upon m- universals, but induction from particulars, it is ida"ter°upone impossible however to investigate universals, ex- sense- (c'f- Eth-
r. ., , . . A. ° , . , . , b. vi. ch. 3;
cept through induction, since things whicii are Rhet. b. i. ch. said to be from abstraction, will be known through 23and b' "' ch' induction;2 if any one desires to make it ap-
1 The expression, present with, must be taken generally, for the being attributed, whether affirmatively or negatively, to many things not un- der each other; thus " brute" is ailirmatively attributed to "quadruped," but negatively to " man ; " but " man " is not subjected to " brute." Taylor.
2 Vide Hill's Logic, and Aldrich de Prnedicab. form.; Whately's Logic, book ii. ch. 5, and book iv. ch. 1. Universals are gained by abstraction, because we separate the points of concord, concomitant with a certain number of individuals, from those points in which they differ, hence Locke calls all universals abstract terms. Properly speaking, abstraction
286 Aristotle's organon. [book i.
parent that some things are present with each genus, although they are not separable, so far as eaeh is such a thing. Never- theless, it is impossible for those who have not sense to make an induction, for sense is conversant with singulars, as the science of them cannot be received, since neither (can it be obtained) from universals without induction, nor through in- duction without sense.
Chap. XIX. — Of the Principles of Demonstration, whether they are
Finite or Infinite.
Every syllogism consists of three terms, and one indeed is able to demonstrate that A is with C from its being present with B, and this last with C, but the other is negative, having one proposition (to the effect) that one certain thing is in another, but the other proposition (to the effect) that it is not with it. Now it is clear, that the same are principles, and what are called hypotheses, since it is necessary to demon- strate by thus assuming these,1 e. g. that A is present with C through B, and again, that A is with B through another me- 1. By those dium, and that B is with C in like manner. By ^aldTaf ft is tnose tnen who syllogize according to opinion only, to be consider- and dialectically, this alone it is clear must be
is the separation of one portion of the attributes co-existing in any object from the rest ; hence, in this sense, Aristotle applies the expression here, rd *£ cKpaipiatojg, to geometrical magnitudes, because the geometer con- siders only the properties of the figure, separating them from those of the material in which it is found. (Cf. An. Post. i. ch. 5.) " Induction," says Taylor, " is so far subservient to the acquisitions of science, as it evocates into energy in the soul, those universals from which demonstra- tion consists. For the universal, which is the proper object of science, is not derived from particulars, since these are infinite, and every induc- tion of them must be limited to a finite number. Hence the perception of the all and the every is only excited, and not produced, by induction." Cf. Trendelen. de An. p. 478. Biese 1. Sententia nostri "loci haec est. Universales propositiones omnes inductione comparantur, quum etiam in iis qua? a sensibus maxime aliena videntur et quae ut mathematica (rd t£ atyatpkcreajc.) cogitatione separantur a materia quacum conjuncta sunt, inductione probentur ea quae de genere, ad quod demonstratio pertineat praedicentur Ka9' avrd et cum ejus natura conjuncta sint. Inductio au- tem iis nititur quag sensibus percipiuntur ; nam res singulares sentiuntur, scientia vero rerum singularium, non datur sine inductione, non datur in- ductio, sine sensu. Waitz. Cf. Metap. b. ii. and vi.; De Anima, b. iii. iv. 1 So that both prop, affirm, or one affirms and the other denies.
CHAP. XIX. ] THE POSTERIOR ANALYTICS. 287
considered, viz. whether the syllogism is produced ed whether the from propositions as probable as possible, so that arist from* pro- if there is in reality a medium between A and B, positions espe- but it does not appear, he who syllogizes through cia ypro this, will have syllogized dialectically. But as to truth, it be- hoves us to make our observations from things inherent : ' it happens thus. Since there is that, which is itself predicated of something else, not according to accident,* but » Cf ch 6 I mean by according to accident, as we say some- times, that that white thing is a man, not similarly saying, that a man is a white thing, for man not being any thing else is white, but it is a white thing, because it happens to a man to be white:2 there are then some such things as are predi- cated per se. Let C be a thing of this kind which is not it- self present with any thing else, but let B be pri- t Immediatelv marily f present with this, without any thing else between. Again, also let E be present in like manner with F, and this with B, is it then necessary that this should stop, or is it possible to proceed to infinity?3 Once more, it' nothing is predicated of A per se, but A is primarily present with H, nothing prior intervening, and H with G, and this with B, is it necessary also that this should stop, or can this likewise go on to infinity?4 Now this so much differs from the former, that the one is, whether whetheTa1"17 it is possible by beginning from a thing of that stated series of
. . • terms proceeds
kind, | which is present with nothing else, but to infinity.
something else present with it, to proceed upward ^ ^j°m a
to infinity ; but the other is, beginning from that
which is itself predicated of another, but nothing predicated
of it, § whether it is possible to proceed to infinity
downward. Besides, when the extremes are finite, |ttribute.eme
is it possible that the media may be infinite ? I
mean, for instance, if A is present with C, but the medium of
them is B, and of B and A there are other media, and of
these again others, whether it is possible or impossible for
these also to proceed to infinity ? To consider this however
1 Whether the propositions are really immediate.
? I read this sentence with Buhle, Bekker, and Waitz.
* So that a first predicate may not be found.
* So that a last subject may not be found.
288
Aristotle's organon.
book T.
is the same as to consider whether demonstra- tions proceed to infinity,* and whether there is demonstration of every thing, f or whether there is a termination (of the extremes) relatively to each other.1
I say also the same in respect of negative syl- logisms and propositions, for instance, whether A is primarily present with no B, or there will be a certain medium with which it was not before present, as if G (is a medium), which is present with every B ; and again, with something else prior to this, as whether (the medium is) H, which is present with every G ; for in these also, either those are infinite with which first they are| present, or the progression stops.
The same thinsr however does not occur in things which are convertible, since in those which are mutually predicated of each other, there is nothing of which first or last a thing is predi- cated;2 for in this respect all things subsist similarly with respect to all, whether those are infinite, which are predi- § The predi- Rated of the same, or whether both § subjects of catesand sub- doubt are infinite, except that the conversion can- ,ec s' not be similarly made ; but the one is as accident,
but the other as predication.3
» Cf. ch. 3. t If so, there are no first principles, for these are inde- monstrable. Cf. Metap. lib. i. and ii.
3. The same as to negatives.
J So Waitz and Bekker ; but Taylor and Buhle read " not present."
4. The doubt does not exist in the case of reciprocals.
1 i. e. whether there may be found a last subject, which is the bound- ary of the progression downward from the first attribute ; and also whe- ther there may be found a first attribute, by which the progression from the last subject upward will be terminated. ITpoc aWrjXa 7npaivta9ai, dicuntur quorum termini medii non infiniti sunt, ut sive uno sive plurilms terminis mediis interjectis major cum minore continua ratiocinatiune connectatur in conclusione. Waitz.
2 In circular proofs, as in the circle itself, there is not a first nor last.
3 Whether the attributes are infinite, in terms convertible, they may become subjects, or whether both attributes and subjects are infmite, the effect is the same, and Aristotle shows that these investigations may be adapted to reciprocals, when one is per se predicated of the other, anc the other from accident. Excluding the last, the inquiry is whether the subjects and predicates which are so per se, are finite or infinite. A thing is attributed from accident, as man to a white thing ; but per se as risibility to a man. Predication therefore is now assumed for attribute per se, as will be shown in chap. 22.
CHAP. XX. XXI.] THE POSTERIOR ANALYTICS.
289
1. Media not infinite where the predica- tions stop— Ex- planation and example.
Chap. XX.— Of Finite Media.
That media cannot be infinite, if the predica- tions, both downward and upward, stop, is evi- dent : I call indeed the predication upward, which tends to the more universal, but the downward that which proceeds to the particular. For if when A is predicated of F, the media are infinite, that is B,* it evidently may be possible that from A in a * a is the high- descending series, one thing may be predicated of p'thptfifte! another to infinity, (for before we arrive at F, there ject, b the me- are infinite media,) and from F in an ascending se- dia" ries, there are infinite (attributes) before we arrive at A. Hence, if these things are impossible,")" it is also impos- sible that there should be infinite media between A and F ; for it does not signify if a man should say that some things of A B FJ so mutually ad- here, as that there is nothing intermediate, but that others cannot be assumed. § For whatever I may assume of B,1 the media with reference to A or to F,|| will either be infinite or not, and it is of no consequence from what the infinites first begin,2 whether directly or not directly, for those which are posterior to them are infinite.
t That there should be infi- nite subjects to A, and infinite attributes to I'/ J So Waitz; Taylor and Eekker, A B ; Buhle, A B C. § Because they are infinite. II The media between B and F, or between B and A.
Chap. XXI. — It is shown that there are no Infinite Media in Negative Demonstration.
It is apparent also, that in negative demonstra- !■ That tliere
.. i . .,, .?. ■, -, . rr. is not an infin
tion the progression will stop, it indeed in athrm- ity of media in
ative it is stopped in both (series), \ for let it be n\X!tration~
impossible to proceed to infinity upward from the proved in the
last,3 (I call the last that which is itself not pre- ft^boS*""
sent with any thing else, but something else ascending and
with it, for instance, F,) or from the first* to the * Predicate.
1 i. e. whatever medium is assumed between A and F ; for the infinite media between A and F are signiiied by the letter B.
- Whether from either (A or F) of the extremes, or from some me- dium. Infinites arc directly or immediately placed from A or from F, but not directly when they arc from some medium.
* That is, in affirmative syllogisms, upward from the last subject.
u
290 ARISTOTLE'S OKGANON. [BOOK I.
last, (I call the first that which is indeed itself predicated of something else, but nothing else of it). If then these things are so, the progression must stop in negation, for the
not being present is demonstrated triply,* since figures16 three either B is present with every individual with
which C is, but A is present with none with which B is. In B C therefore, and always in the other pro- t in the proof position,! it is necessary to proceed to immediates, of the minor, for this proposition is affirmative.1 With regard t A;°thepredi- to the other ^ however it is clear, that if it is not cate of the present with something else prior, for instance,
major. r . .
§ Because in with D, it will be requisite that this (D) should rn1dfid!eUiePhrL be present with every B.§ Also if again it|| is dicateofthe not present with something else prior to D,% it II i. e a. will require that* to be present with every D, so
j As with e. tjiat since the upward progression stops, the downward progression will also stop, and there is immediately will be something first with which it is not pre- demed. sent.f Moreover if B is with every A, but with
no C, A will be with no C ; again, if it is required to show
I viz prop b this,! it is evident, that it may be demonstrated c. either through the superior mode,§ or through
i. e. gure. ^^ Qr through the third, now the first has been 2- spoken of, but the second shall be shown. Thus
indeed it may demonstrate it,2 as, for instance, that D is pre- sent with every B, but with no C, if it is necessary that any
II as D. thing || should be with B,3 and, again, if this^F is * which 'win not Present Wlth C>* something elsef is present be shown. with D, which is not present with C, wherefore f As E* since the perpetually being present with some- thing superior stops, the not being present will also stop. But the third mode was if A indeed is present with every B, but C is not present, C will not be present with every A ;4 again,
1 It is assumed that there is no infinite progression in affirmative prop., because this will be proved in the following chapter.
2 The syllogism in the 2nd fig. will prove B to be predicated of no C.
5 In order that a syllogism may be formed in Camestres ; if, on the other hand, D is predicated of every C, and of no B, it would be in Cesare.
This is a particular prop., in order to effect a syllogism in Bokardo, as Aristotle will shortly prove it in the third figure ; if it were universal in Felapton, it could not be proved in this figure.
CHAP. XXII.] THE POSTEKIOR ANALYTICS. 291
this will be demonstrated either through the above-mentioned modes,* or in a similar manner, f 2nd figure.01 in those modes the progression stops,J but if thus, + Through the it will again be assumed that B is present with 3. E, with every individual of which C is not pre- * Vlde above- sent. ThisS again, also, will be similarly demon- § That c is not strated,|| but since it is supposed that the down- u in the 3rd ward progression stops, C also, which is not ^gTtiat is, a ne- present with,1[ will evidently stop. gative prop.
Nevertheless, it appears plain, that if it should not be de- monstrated in one way, but in all, at one time from the first figure, at another from the second or the third, that thus also the progression will stop, for the ways are finite,* „ but it is necessary that finite things being finitely assumed should be all of them finite.
That in negation then the progression stops, t Taylor and if it does so in affirmation, is clear, f but that it Bunie end must stop in them | is thus manifest to those who iein*afnnna- consider logically.1 tions-
Chap. XXII. — That there are no Infinite Media in Affirmative
Demonstration.
In things predicated therefore as to what a thing j of predica. is, this is clear, for if it is possible to define, or if tions, as to
.1 p ii • 11 i. what a thing
the very nature 01 a thing may be known, but is, there cann, infinites cannot be passed through, it is necessary dftrJrenc^^f3 that those things should be finite which are pre- predication dicated with respect to what a thing is. We pointed out- must however speak universally thus : a white thing we may truly say walks, also that that great thing is wood ; more- over, that the wood is great, and that the man walks, yet there is a difference between speaking in this way and in
1 Aristotle calls those arguments logical which are not derived from the nature of a thing, but analytical are opposed to them, because they re- solve things into their principles ; the one method is, as Waitz says, an accurate demonstration, which depends upon the true principles of the thing itself; the other, that which is satislied with a certain probable ratiocination. Cf. Philop. ; also Biese i. p. 261 ; Waitz in Inc. Cicero (de Finib. i. 7) calls the " logical " that part of philosophy, " quae sit qua}* rendi ac disserendi."
u 2
not
292 akistotle's organon. [book i.
that. For when I say that that white thing is wood, then 1 say that what happens to be white is wood, but what is white is not, as it were, a subject to wood, since neither being white, nor what is a certain white thing, became wood, so that it is not (wood) except from accident. But when I say that the wood is
white, I do not say that something else is white, *hIiVeiseS°me kut ifc happens to that* to be wood, (as when I
say that a musician is white, for then I mean that the man is white, to whom it happens to be a musician,) but wood is the subject which became (white), not being any thing else than what is wood, or a certain piece of wood. If
indeed it is necessary to assign names, let speak- ifs white6 W°°d ing in tais way j- be to predicate, but in that way J j As that which be either by no means to predicate, or to predicate wood. cf. Met. indeed, not simply, but according to accident. lib. v. Phy. lib. ^hat which is predicated is as white, but that of
which it is predicated as wood ; now let it be sup- posed that the predicate is always spoken of what it is predi- cated of simply, and not according to accident, for thus demon- strations demonstrate. Therefore when one thing is predi- cated of one, it will be predicated either in respect of what a thing is, or that it is a quality, or a quantity, or a relative, or an agent, or a patient, or that it is some where, or at some time.
2. Truepredi- Moreover, those which signify substance, sig- cations either nify that the thing of which they are predicated,
define what the * . ° J r . . '
subject is, or is that which it is, or something belonging to it, are accidents, j^j. wiiatever (j0 )10t signify substance, but are
predicated of another subject, which is neither the thing itself, nor something belonging to it, are accidents, as white is pre- dicated of man, since man is neither white, nor any thing which belongs to white, but is perhaps animal, for man is that which is a certain animal. Such as do not signify sub- stance it is necessary should be predicated of a certain sub- ject, and not be something white, which is white, not being any thing else. For, farewell to ideas, for they are mere prattlings,§ and if they exist, are nothing to the subject, since demonstrations are not about such things.1
* Taylor tells us quaintly, " that Aristotle is not serious in the ob-
CHAP. XXII.] THE POSTERIOR ANALYTICS. 293
Again, if this is not a quality of this, and that 2 of this, neither a quality of a quality, it is impos- sible that they should be thus mutually predicated of each other, still they may possibly be truly said, but cannot truly be mutually predicated. For will they be predicated as sub- stance, as being either the genus or the difference of what is predicated ? It has been shown that these will not be infinite, neither in a descending nor in an ascending progression, as for instance, man is a biped, this an animal, this something else ; neither can animal be predicated of man, this of Callias, this of something else,* in respect to what a thing * L e in an in_ is. For we may define the whole of this to be finite series. Cf.
J . ,» . . •■ Phys. lib. iii.
substance, but we cannot penetrate infinites by + Hence they perception, f wherefore neither are there infinites are incapable upwards or downwards, for we cannot define that of definitlon- of which infinites are predicated. They will not indeed be mutually predicated of each other as genera, for genus would be a part itself, neither will quality nor any of the other cate- gories be (mutually) predicated, except by accident, for all these are accidents, and are predicated of sub- 3 In either stances. But neither will there be infinites in case there can-
.,_ p ii- i ■ j- not be an jnli-
ascending series,! tor of each thing, that is preen- nite series cated, which signifies either a certain quality, or nha^vr"fofTate-e a certain quantity, or something of this kind, or gory. those which are in the substance, but these are not D!rfnfinite finite, and the genera of the categories are finite, accidents. since (a category) is either quality, or quantity, or relation, or action, or passion, or where, or when. One thing is however supposed to be predicated of one,§ but those not § ;. e. prop0Si. to be mutually predicated which do not signify J^y'ifjj1^1 what a thing is, since all these are accidents, but theconjunction some are per se, others after a different manner, ofattnbutes- and we say all these are predicated of a certain subject,
jections which he urges against Plato's theory of ideas ; for that demon- stration cannot exist (from the testimony of Aristotle himself) unless the existence of ideas be admitted conformahly to the doctrine of Plato," in total opposition to what is stated in the 1 1 th chap. What Aristotle means is, that ideas, even if they exist, are of little use to effect demonstration, because the latter cannot subsist unless there be iv Kara ttoWuiv; but since ideas subsist per se, (xwqhsto. ttrnv,) they cannot be predicated ol others. Vide also Metap. lib. ix. (x.) and lib. xii (xiii.) ed. Leipaic.
294 Aristotle's organon. ["book i
L
but that accident is not a certain subject, for we do not as- sume any thing of this kind to be, which not being any thing else, is said to be what it is said to be, but we say that it is predicated of something else, and certain other things of another thing.1 Neither then can one thing be predicated of one (infinitely) upwards, nor downwards, for those of which accidents are predicated, are such as are contained in the sub- stance of each thing, but these are not infinite. ject Je SrS1d" Both these indeed and accidents are ascending, t i.e. immedi- and both are not infinite, wherefore it is neces- ^Asc. sary that there should be something* of which
§ As b. primarily f something J is predicated, and some-
catt ^s3 A^^'" tninS else § °f tnis> als° that this Should Stop,
ir Prior to b. and that there should be something II which is is nothing prior neither predicated of another prior thing, % nor to a. another prior thing of it.*
This then is said to be one mode of demon- that amedlate stration, but there is another besides, if there is proposition a demonstration of those of which certain things are previously predicated, but of what there is demonstration, it is not possible to be better affected towards them than to know them, nor can we know without demon- stration.2 Still if thisf becomes known through lionhe °onc U these,! but these we do not know, nor are better I The pre- affected towards them than if we knew them, neither shall we obtain scientific knowledge of that which becomes known through these. If then it is pos- sible to know any thing simply through demonstration, and s cf Prior An not fr°m certain things, nor from hypothesis, § it ii. ch. is. is necessary that the intermediate predications
5. if there is should stop ; for if they do not stop, but there is predication, always something above what is assumed, there demonstration -ii ^ demonstration of all things, so that if
cannot exist. . . in
we cannot pass through infinites, we shall not know by demonstration those things of which there is de- monstration. If then we are not better affected towards them than if we knew them, it will be impossible to know
1 As whiteness of a swan, blackness of a crow.
2 To first principles (indemonstrable) we are better affected than if we knew them through demonstration, as was shown in ch. 2.
CHAP. XXII.] THE POSTERIOR ANALYTICS.
295
any thing by demonstration simply, but by hy- * if the pro-
i • ^c. i positions arc
pothesis.* ' true
Logically then from these things a person may believe about what has been said, but analyti- pTOVed Analyti- cally2 it is more concisely manifest thus, that caiiy from the
, J ..... J ,. . , nature of those
there cannot be infinite predicates in clemonstra- things which tive sciences, the subject -of the present treatise, aTeH ,Pr?djcated either in an ascending or descending series, ror demonstration is of such things as are essentially present with things, essentially in two ways, both such as are in them in respect of what a thing is, and those in which the things themselves are inherent in respect of what a thing is, thus the odd in number which indeed is inherent in number, but number itself is inherent in the definition of it,f again also, multitude or the divisible is inherent odd.eofthe in the definition of number. Still neither of these can be infinites, nor as the odd is predicated of number, for again there will be something else in the odd,$ j e. g. inequai- in which S bein"; inherent, II (the odd) would be »ty- , _, „ .
o <i /\\ \ / £ In the denni-
inherent, and if this be so, number will be first tion of which.
inherent in those things which are inherent in it. jjdd- e- in tlle
If then such infinites cannot be inherent in the f cf. Met. As
one.^F neither will there be infinites in ascend- the finite can-
• o -ii • l n l 1 1 not contain
ing series. Still it is necessary that all should infinity. be inherent in the first,* for example, in number, * Thus .thet
. , , . i ■« • third is in the
and number m them,j so that they will recipro- second, and the cate, but not be more widely extensive. Neither s^"d m thc are those infinite which are inherent in the defi- t in their de- nition of a thing,:}: for if they were, we could not ("ctMetap. define, so that if all predicates are predicated per lib- ix- (*•>• se, and these are not infinite, things in an upward progression will stop, wherefore also those which descend.
1 Jam si vera scientia demonstratione comparari potest, quae neces- sario vera sit, ut non pendeat ex aliis conditionibus quibuscunque, quae et esse possint, et non esse, terminorum mediorum, quibus demonstratio utitur, numerus non erit inlinitus : nam si esset, et omnia demonstrari possent, et, quia infinitam demonstrationem periicere non liceret, quedam demonstrari non possent, ut demonstratio non efficeret veram scientiam, sed hypotheticam, h. e. non cogeretur quod demonstrator ex proposition- ibus certis, sed ex propositionibus quae, quamquam ipsee demonstrari de- berent, tamen pro certis sumtae essent. Waitz. By hypothesis, he alludes to what is not self-evidently certain, but is assumed to be BO.
2 From the principles and essence of demonstration. Vide supra.
296
ARISTOTLE S ORGANON.
[BOOK I.
6. That there is not infinity of media.
* Vide ch. 3
If then this be so, those also which are between the two terms will be always finite, but if this be the case, it is cl°ar now that there must neces- arily be principles of demonstrations, and that there is vn: demonstration of all things, as we observed in tin beginning,* certain persons assert. For if there be principles, neither are all things demonstrable, nor can we pro- gress to infinity, since that either of these should be, is nothing else than that there is no proposition immediate and indivisible, but that all things are divisible, since what is demonstrated + The middle. *s demonstrated from the term f being inwardly introduced, and not from its being (outwardly) as- sumed.]: l Wherefore if this § may possibly proceed to infinity, the media between two terms || might also possibly be infinite, but this is impossible, if i. e. between predications upwards and downwards stop, and attribute of the that they do stop, has been logically shown before, first prop. an(j analytically now.
X Extrinsecus definitio. Buhle.
§ The demon- stration of pro positions.
I, Case where no common ground of in- herency sub- sists. 11 As C of D.
• Some term in common predicated of C and D.
t Viz. triangle.
% i. e. triangle.
§ Viz. scalene, isosceles, etc.
Chap. XXIII. — Certain Corollaries.
From what has been shown it appears plain that if one and the same thing is inherent in two, for instance, A in C and in D, when one is not pre- dicated of the other, If either not at all or not uni- versally, then it is not always inherent according to something common.* Thus to the isosceles and to the scalene triangle, the possession of an- gles equal to two right, is inherent according to something common, f for it is inherent so far as each is a certain figure,]: and not so far as it is something else.§ This however is not always the case, for let B be that according to which A is
1 Being assumed between the subject and attribute of the prop, to be proved. Thus the middle term is assumed in the first figure, in which it is subjected to the attribute, i. e. to the greater extreme, and is attributed to the subject, i. e. to the less extreme. Taylor. By the middle being inwardly introduced, he means that in order to demonstrate A B, A must be predicated of C, and C of B, but A of B, and B of C. Upon the above chap., compare Metap. lib. iii. iv. vi. ix. xiii. ; Eth. book i. ch. 6; De Amm. b. iii. Vide also Hill's Logic, de Definitione, and Whately's Logic, b. h. ch 5, and b. iii. sec. 10.
CHAP. XXIII.] THE POSTERIOR ANALYTICS. 297
inherent in C D. then it is evident1 that B is also inherent in C, and in D, according to something else com- . As E mon * and that alsot according to something else.i t e is -nc so that between two terms. § infinite terms may t As f. be inserted, but this is impossible. II It is not § Viz. between
1 ! 1 • 1 T 1 1 B alld C> 0r B
then necessary that the same thing should always and d. be inherent in many, according to something com- " A lde ch- 22- mon, since indeed there will be immediate propositions ; it is moreover requisite that the terms should be in the same genus, and from the same individuals, since that which is common will be of those which are essentially inherent, for it is im- possible to transfer things which are demonstrated
J. .? «- H Vide ch. 6.
irom one genus to another.!
But it is also manifest that when A is with B, 2 Cases of if there is a certain middle, we may show that B positional de- is with A, and the elements of this* are these and wnen a certain whatever are media, for immediate propositions, "j.!^1,""1 Is either all of them, or those which are universal, • oi the con- are elements.2 Yet if there is not (a medium) clusion B is A- there is no longer demonstration, but this is the way to prin- ciples.! In like manner, if A is not with B, if + To first prin. there is either a middle, or something prior to cipies. which it | is not present, § there is a dcmonstra- + soWaitzar.i tion,3 but if not, there is no demonstration, but a ?e£ker- principle, and there are as many elements as terms, || for the propositions of these are the prin- " VithB. cipies of demonstration. As also there are certain indemon strable principles, that this is that, and that this is present with that, so there are also that this is not that, and that this is not
1 Because if a thing is inherent in two things, it is inherent mediately. Taylor.
2 Immediate particular propositions are not the principles of demon- strations, but of inductions. Upon the use of the word oroix^a, by Aris- totle, cf. Ammonius upon Catego. ch. 12; also Biese i. p. 381, note 5, Trendelenburg Platonis de Ideis. In the Topics, as Waitz observes, he uses aroixt'ia as synonymous with to7toi, for certain universal arguments, from which, with some appearance of truth, a thing may be either proved or refuted. Top. lib. iv. ch. 1, etc. The sense here, of elements, seems most suggestive of their meaning, viz. that of certain principles of dis- putation, which when provided, enable us rightly to conduct an argument.
3 If there is a certain middle (C) through which A is proved not pre- sent with B, A will iirst be denied of C in the major premise, and alter* wards of B in the conclusion; thus a syllogism will result in Cclareiil : No C is A, every B is C ; therefore no B is A.
298 aristotle's organox. [book &
present with that, so that there will be some principles that a thing is, hut others that it is not. Still when it is required to
* As that a is demonstrate,* that which is first predicated of B with b. must be assumed ; let this be C, and let A, in like ifn bSES™ manner» (be predicated) of this ; f by always pro- t The middle ceeding thus> ' there is never a proposition ex- d. ternally, nor is that J which is present with A assumed in the demonstration, but the middle is always con- 3. what posi- Sensed till they become indivisible and one.2 They tion the con- are one indeed when the immediate is produced.
necting term j . • i,
should occupy and one proposition simply, an immediate one,
uvewd ™£- an.d as in other things the principle is simple, but tiveproposi- this is not the same every where, but in weight it is a minor, in melody a demi-semi-quaver,3 and something else in another thing, thus in syllogism, "the one" is an immediate proposition, but in demonstration and science § Cf. An. Post. Jt is intuition. §4 In syllogisms then, which de- ii. ch. 19, and monstrate the being inherent, nothing falls beyond l, 2," ands." ' (the middle), but in negatives here,|| nothing falls •Ir s^u medium external of that which ought to be inherent,5^ as non sumitur if A is not present with B through C. For if C Buhie.U,n; ■ Is present with every B,* but A with no C,f and
* The minor if, again, it should be requisite to show that A is trThe major, "with no C,| we must assume the medium of A
* The conclu- and C, and thus we must always proceed.6 If
1 By assuming a new term, as predicate of the minor, and subject of the major.
3 Until we arrive at an indemonstrable and immediate proposition.
3 Aiearig. The least perceptible sound we have therefore expressed it ; by its closest representative in music.
4 For we know principles by " vovg." Cf. de Anim. iii. ch. 4—6, ubi cf. Trende., Biese. and Rassow. I have translated the word " intuition," agreeing as I do with Professor Browne, (vide Ethics, b. vi. ch. 6, Bohn's edition,) that no other word conveys with the same exactitude Aris- totle's own definition of it in the Magna Moralia (i. 35), 'O vovq lari irspi Tag cipxaq twv votjtujv icai tuiv ovtwv, »; fiev yap iiriarrj/in raiv fttr a.TroSti^iu>Q ovTixii' iariv, apa S' ap\ai avanooiiKToi.
5 Thus Waitz, Buhle, and Bekker. Taylor evidently reads, o, Sh, //?/ virapxiiv, an amendment which Waitz approves in his note, and so do I, for the conclusion of the syllogism is of course negative; the meaning is, that a middle term is never assumed, which is predicated of the major extreme, since the major is that in which the conclusion is negatively predicated of the minor.
b Assume a middle term which does not fall externally to the major extreme, in order to demonstrate the negative proposition.
CHAP. XXIV.] THE POSTERIOR ANALYTICS. 299
however it should be required to show* that D is sion of the pro- not with E, because C is with every D,f but with *yin°camestres. no, or not with every E.t the medium will never f £he major.
,. ,, , -r< i i • p • -i i • n t Tne minor.
tall external to E, and tins § is with what it need § e.
not be present.1 As to the third mode,| it will II The 3rd
never proceed external to that from which, nor gure" which it is necessary to deny.2
Chap. XXIV. — The superiority of Universal to Particular Demonstration proved.
As one demonstration is universal, but another 1. The ques- particular, one also affirmative, but the other ne- tlon stated- gative, it is questioned which is preferable, likewise also about what is called direct demonstration, and that which leads to the impossible. Let us first then consider the uni- versal and the particular, and having explained this, speak of what is called direct demonstration, and that to the impossible.
Perhaps then to some considering the matter 2. Reasons in this way, the particular may appear the better, **y particular
Qcnioiist rstion
for if that demonstration is preferable, by which may appear we obtain better knowledge, for this is the excel- el,£lble- lence of demonstration, but we know each thing better when we know it per se, than when through something else, (as we know Coriscus is a musician, when we know that Coriscus is a musician rather than when we know that a man is a musi- cian, and likewise in other things,) but the universal demon- strates because a tiling is something else, not because it is that which it is, as that an isosceles triangle (has two right angles), not because it is isosceles, but because it is a triangle,) but the particular demonstrates because a thing is what it is, if then the demonstration per se is preferable, and the particular is such rather than the universal, particular demonstration would be the better. Besides, if the universal is nothing else than
1 It is the subject of the negative conclusion, of which D is denied.
2 A middle will never be assumed ahove the greater or less extreme, nor be predicated of either, because in the 3rd figure the middle term is always the subject of both premises. As Taylor remarks, in the whole of this chapter, the middle is said to fall external to the extreme, when it changes its situation ; so that if it was before the subject of the major extreme, afterwards in the pro-syllogism, it becomes the predicate of the major.
300 Aristotle's organon. [book i.
t particulars, but demonstration produces opinion
that this thing is something according to which it demonstrates, and that a certain nature of this kind is in things which subsist, (as of triangle besides particular (tri- angles), and of figure besides particular (figures), and of num- ber besides particular (numbers), but the demonstration about being is better than that about non-being, and that through which there is no deception than that through which there is, but universal demonstration is of this sort, (since men pro- ceeding demonstrate as about the analogous,1 as that a thing which is of such a kind as to be neither line nor number, nor solid nor superficies, but something besides these, is analo- gous,) if then this is more universal, but is less conversant with being than particular, and produces false opinion, uni- versal will be inferior to particular demonstration. ■ i. e. the first. First then may we not remark that one of these 3 Reply to the arguments * does not apply more to universal than to particular demonstration ? For if the possession of angles equal to two right angles is inherent, not in respect of isosceles, but of triangle, whoever knows that it is isosceles knows less essentially2 than he who knows that it is triangle. In short, if not so far as it is triangle, he then shows it, there will + Supply— in- not °*e demonstration, but if it is,f whoever knows herent.orisde- a thing so far as it is what it is, knows that thins:
monstrated so , x/> . , . . , . „ . , . °
far as it is tri- more.* It then triangle is of wider extension ricfthat all (than isosceles), and there is the same definition,! species of it are and triangle is not equivocal, and the possession caUed^angie. °^ tw0 angles equal to two right angles is inhe- rent in every triangle, triangle will have such angles, not so far as it is isosceles, but the isosceles will have them, so far as it is triangle. Hence he who knows the uni-
1 They who employ universal demonstration do not keep within the exact limits of demonstration, but appear to go beyond them in the same way as those who reason Ik tov dvd \6yov, for if they have demon- strated any thing of lines, body, etc., they apply the proof as equally con- clusive to every thing similar, and thus extend the demonstration unfairly.
2 Minus scit quatenus ipsum (tale est ut habere duos rectos angulos illi insit). Buhle.
3 As Mansel observes, (Appendix, note B,) the office of logic is to contribute to the distinctness of a conception, by an analysis and separate exposition of the different parts contained within it. The mind, like the sky, has its nebula?, which the telescope of logic may resolve into their component stars.
CHAP. XXIV.] THE POSTERIOR ANALYTICS. 301
versal, knows more in regard to the being inherent than he who knows particularly, hence too the universal is better than the particular demonstration. Moreover if there is one certain definition, and no equivocation, the universal will not subsist less, but rather more than certain par- ticulars, inasmuch as in the former there are things incorrupt- ible, but particulars are more corruptible.1 Besides, there is no necessity that wre should apprehend this (universal) to be something besides these (particulars), because it shows one thing, no more than in others which do not signify substance, but quality, or relation, or action, but if a person thinks thus, it is the hearer, and not demonstration, which is to blame.2 Again, if demonstration is a syllogism, showing universal the cause and the why, the universal indeed is aione is cogni- rather causal, for that with which any thing is ^Therefore6' essentially present, is itself a cause to itself,* but n,lore causal, the universal is the first, f therefore the universal 5 ; Eth. vi. 3. is cause. Wherefore the (universal) demonstra- i^'in^iiich'a tion is better, since it rather partakes of the cause property is per and the why, besides up to this we investigate the se m erent' why, and we think that then we know it, when this is be- coming, or is, not because something else (is), for thus there is the end and the last boundary. For example, on what ac- count did he come ? that he might receive money, but this that he might pay his debts, this that he might not act unjustly, and thus proceeding, when it is no longer on account of some- thing else, nor for the sake of another thing, then we say that he came, and that it is, and that it becomes on account of this as the end, and that then we especially know why he came. If then the same occurs, as to all causes and inquiries into the why, but as to things which are so causes as that for the sake
1 So Waitz, who has this note, " Notiones universales, si unitatem quandam exprimunt et si alius earum est usus quam ut orationem am- biguam faciant, quum singula quae illis subjecta sint pereant, illse yero non corrumpantur, etiam rectius ipsac existero dicentur quam ra dro/ia." Cf. Metap. lib. ii. (iii.), v. (vi.), vi. (vii.), ix. (x.),and xi. (xii.), Leipsic ; Phys. lib. iii. and viii. ; also Crakanthorpe's Logic, lib. ii., and upon this chapter generally, Aquinas in Periherm. sect. i.
2 That is, if a man thinks that universal is something besides particu- lars. By universal here, he means, that which is " co-ordinated " with the many, and which when abstracted out of the many by the mir.U, produces the universal, which is of posterior origin. Taylor.
S02 Aristotle's organox. "book i.
* (AHquid sit of which,* we thus especially know, in other BuWet-) things also we then chiefly know, when this no
longer subsists because another thing does.1 When therefore we know that the external angles are equal to four right angles, because it is isosceles, the inquiry yet remains, why because isosceles, because it is a triangle, and this be- cause it is a rectilinear figure. But if it is this no longer on account of something else, then we pre-eminently know, then
also universally, wherefore the universal is better. "noVper"6 Again, by how much more things are according aiiud,"but to the particular, do they fall into infinites, but
the universal tends to the simple and the finite, so far indeed as they are infinite, they are not subjects of science, but so far as they are finite they may be known, wherefore so far as they are universal, are they more objects
of scientific knowledge, than so far as they are
?"„YIi",l?rsa-l particular. Universals however are more demon- tend totnesim- r m
pie and finite, strable, and of things more demonstrable is there
m"reescientific. pre-eminent demonstration, for relatives are at
t i. e. if one is one an(l the same time more,f whence the uni-
more, the other Versal is better, since it is demonstration pre-
is more. . , _ ; - , . r
eminently. Besides, that demonstration is prefer- able, according to which this and something else are known, to that, by which this alone is known, now he who has the uni- versal knows also the particular, but the latter does not know the universal, wherefore even thus the universal will be more
eligible. Again, as follows : it is possible rather closer in de- to demonstrate the universal, because a person thenprinciXt0 demonstrates through a medium which is nearer
to the principle, but what is immediate is the nearest and this is the principle ; if then that demonstration which is from the principle is more accurate than that which is not from the principle, the demonstration which is in a greater degree from the principle, is more accurate than that which is from it in a less degree. Now the more universal is of this kind, wherefore the universal will be the better, as if it were required to demonstrate A of D, and the media should be B C, but B the higher wherefore the demonstration
c
through this is more universal.
"O
1 A verbose exemplification of the terse truism of Swift, that " we un- ravel sciences, as we do old stockings, by beginning at the foot."
CHAP. XXV.] THE POSTERIOR 4.XALYriCS.
303
Some of the above arguments are logical, it is chiefly clear however that the universal is more excellent, because when of two propositions we have that which is the prior,* we also in a certain degree know and possess in capacity that which is posterior ; thus if a man knows that every tri- angle has angles equal to two right, he also in a certain respect knows in capacity that an isosceles triangle has angles equal to two right, even if know that the isosceles is a triangle,"]" but he who has this proposition by no means knows the uni- versal, neither in capacity nor in energy. The universal proposition also is intuitively intelligible, but the particular ends in sense.1 J
7. The uni- versal is above all superior, in that it compre- hends the par- ticular, and is more intel- lectual. * The uni- versal proposi- tion.
he does not
t The particu- lar proposition.
t An. Post ii. ch. 19.
Chap. XXV. — TJte Superiority of Affirmative to Negative Demonstration proved.
That universal is better than particular demon- j That the de-
stration, let so much be alleged, but that the af- monstration
firmative is preferable to the negative, will be through" fewer
evident from this. Let that demonstration be postulates, etc.,
, . -, p i • i • e c is, "caetens pa-
better, castens paribus, § which consists ot iewer ribus," the bet- postulates, or hypotheses, or propositions. For if ex'arifpTel^'nd5' they2 are similarly known, quicker knowledge applied to af- will be obtained through these, which is more §Asitmaybe eligible. The reason however of this proposition, from unknown that that which consists of fewer is better, uni- versally is this ; for if the media are similarly known, but things prior are more known, let the demonstration be through the media of B C D, that A is present with E, but through F G, that A is present with E.3 That A is present with D, and that A is present with E subsists similarly,! but y Each is the that A is with D, is prior and more known than conclusion. that A is with E, for that if is demonstrated it viz. a e.
1 Cf. de An. iii. 6 ; Metaph. ix. 1 ; and upon the conception of uni- versal notions, Reid's Works, Hamilton's ed. ; Mill's Logic; Whately's Rhet. ; Trende. Biese i. p. 327, note 4; Rassow, p. 72.
1 Viz. the propositions of both demonstrations.
3 B C and F G are the same, but they are called B C, so far as they form parts of the syllogism concluding A E ; and they are called V li, so far as they belong to the syllogisir I D.
304
ARISTOTLE S OKGANON.
[book
• s. e. A D.
+ i. e. both af- firmatives and negatives. X Affirmative.
2. The nega- tive requires the affirmative, but the latter does not need the former. § Vide Pr. An. i. ch. 7 and 24. || That nega- tion is proved by affirmation. IT By pro-syllo- gisms.
through this,* and that is more credible through which (a thing is demonstrated). Also the de- monstration which is through fewer things is therefore better, ceteris paribus ; both f then are demonstrated through three terms, and two propositions, but the one assumes that something is,J and the other, that something is and is not,1 hence through a greater number of things (the demonstration is made) so that it is the worse.
Moreover since it has been shown impossible for a syllogism to be produced with both propo- sitions negative,§ but that one must of necessity be such (negative), and the other that a thing is present with, (that is affirmative,) we must in ad- dition to this assume this, [| for it is necessary that affirmative (propositions) when the demonstration is increased,^ should become more, but it is im- possible that the negatives should be more than one in every syllogism. For let A be present with nothing of those with which B is, but B be present with every C, if indeed, again, it should be necessary to increase both propo- * To prove sitions,* a middle must be introduced.2 Of A B them by pro- ti,en iet tne middle be D, but of B C let the mid- die be E, E then is evidently affirmative,-!- but D firmed of E,and is affirmative indeed of B, yet is placed negatively E of c- as regards A, since it is necessary that D should
be present with every B, but A with no D ; there is then one negative proposition, viz. A D.J The same mode also subsists in other syllogisms, for the middle of affirmative terms is always affirmative in re- spect of both (extremes), § but in the case of a negative (syllogism), the middle must be neces- sarily negative in respect to one of the two,|| so there is one proposition of this kind,^[ but the others are affirmative. If then that is more known and credible through which a thing is demon- strated, but the negative is shown through the
X The major.
§ Subject of the major, and predicate of the minor — both affirmatively. || Of the major extreme to which it is sub- ject in the T>:ajor prem. *fi The major is negative.
1 Because of negative demonstration, one premise affirms, but the other denies.
2 This is done when a pro-syllogism is constructed in the 1st figure, because here alone the middle term occupies the middle place. .
CHAP. XXVI.] THE POSTERIOR ANALYTICS. 305
affirmative, and the latter not through the former, this, since it is prior, more known, and more credible, will be better. Again, since the principle of syllogism is an universal imme- diate proposition, but the universal proposition in an ostensive (demonstration) is affirmative, but in a negative is negative, and since the affirmative is prior to, and more known than, the negative, for negation is known through affirmation, and at' tirmation is prior, just as being is prior to not be- 3. Affirmative ing, therefore the principle of affirmative is better comes nearer
., 1 f • 1 -i t tnan negative
than that or negative demonstration, but that to the nature of
which uses better principles is better. Moreover aPnnciPle-
it partakes more of the nature of principle,* * upxoedca-
since without affirmative there is no negative T£pa' demonstration.1
Chap. XXVI. — The Superiority of the same to Demonstration ad impossibile proved."
Since affirmative is better than negative de- 1. Thediffer- monstration, it is evidently also better than that exan$e7be- y which leads to the impossible,! it is necessary *ween direct
1 '.' J demonstration
however to know what the difference between and that which them is. Let A then be present with no B, but sUarcdsum^ ab" let B be with every C, wherefore it is necessary t vide infra. that A should be with no C, (the terms) then being thus as- sumed, the negative proposition proving that A is not present with C will be ostensive. The demonstration however to the impossible is as follows : if it is required to show that A is not present with B it must be assumed present,;}: also j in order to a that B is with C so that it will happen that A is right syllogism with C. Let this however be known and ac- '" b lgulc knowledged impossible, then it is impossible that A should be with B ; if then B is acknowledged present with C, it is im-
1 An affirmative partakes more of the nature of principle than a nega- tive demonstration, because the minor prem. of a negat. is proved through an affirmative.
2 Vide Hill's and Mansel's Logic, article Demonstration ; alsoWhately, App. I. xi., upon "Impossibility," and Rhetoric, part i. ch. 3, see. 7. The tig to afiovarov dyovaa anofittZtg here, seems to correspond with the tXtyriKov ivOvprifia of the Rhetoric, upon which sec Dr. Hessey's Schera. Khet. Table 4. CI', also Anal. Pr. 1. 22 and 38; Khet. ti. 22—24 and 30 ; iii. 17, 13.
T
306 Aristotle's okganox. [book i.
possible that A should be with B. The terms then indeed
* in theosten- are similarly arranged,* but it makes a difference
she as in the which negative proposition is more known, viz.
impossi i e. wjietjier tjiat ^ js not presenj; -vvith B, or that A
is not present with C. When then the conclusion is more known that it is not, there is a demonstration to the impos- t The negation si°le produced, but when that which f is in the that a is not syllogism (is more known) the demonstration is ostensive. Naturally, however, that A is not pre- sent with B is prior to A is not present with C, for those things are prior to the conclusion, from which the conclusion (is collected), and that A is not with C is the conclusion, but that A is not with B is that from which the conclusion is de- rived. For neither if a certain thing happens to be subverted, is this the conclusion, but those (the premises) from which (the conclusion is derived). That indeed from which (it is on- ro osi m^erred) ls a syllogism, which may so subsist as tion"is tPor°theS1 either J a whole to a part, or as a part to a tohapSnhe!e whole>§ b.ut the propositions A C and A B do not the major as to thus subsist with regard to each other. If then § A™'™ major tnat demonstration which is from things more f s'ai™ f'd known and prior be superior, but both are credi- monstrative ble from something not existing, yet the one from
iTlKa- the Prior' the other from what is" posterior, nega- tive. 2nd, tive demonstration will in short be better, than
Adgabsurdum.' taat to the impossible, so that as affirmative de- ll Than nega- monstration is better than this,|| it is also evidently tive- better than that leading to the impossible.
Chap. XXVII. — Upon the Nature of more Accurate Science}
l. That one sci- One science is more accurate than, and prior to, subtieSa™drac- anotnei'> both the science that a tiling is, and the curate than same why it is, but not separately that it is, than the science of why it is, also that which is not of a subject2 than that which is of a subject, for instance, arith-
1 Cf. ch. 13; Plato, Phileb. ; Rhet. b. i. ch. 7. In the last place, he says that the precedence of one science over another is dependent upon the higher elevation of its subject matter. Met. lib. i. and x.
2 Not conversant with a material subject, as arithmetic, which is con- versant with number. Taylor.
CHAP. XXVIII. XXIX.] THE POSTERIOR ANALYTICS. 307
metic then harmonic science, and that which consists of fewer things than that which is from addition, as arithmetic than geometry. I mean by " from addition," as unity is a sub- stance without position, but a point is substance with posi- tion,1 this is from addition.
Chap. XXVIII. — What constitutes one, and what different
Sciences.
One science is that which is of one genus of those 1. whatever
things which are composed of first (principles), min!tratlddC"
and are the parts or affections of these per se;2 from principles
, .*.,.«. n ,-t i of a common
but a science is different trom another, whose genus, these
principles are neither from the same things, nor ^„£^™
one from the other.3 A token of this is when ture of diverse
any one arrives at things indemonstrable, for it is sciences-
necessary* that they should be in the same genus * if it is one
with those that are demonstrated ; it is also a science- sign of this when things demonstrated through them are in the same genus and are cognate.
Chaf. XXIX. — That there may be several Demonstrations of the
same thing.
There may possibly be many demonstrations of J^^mon- the same thing, not only when one assumes an strabie in many
1 A point was defined by the Pythagoreans, unity with position : ct*. Categ. ch. 6 ; Procl. in Euc. Elem. lib. ii. Oso-tv txliv dicuntur ea quorum partes simul intuemur ac si oculis subjectae essent; quae dum fluunt, manent et quorum quasi imagines ita animo representantur, ut qua? praeterierint mente repeti possint simul cum iis, quae praesto suit. Waitz, in Cat. cap. 6.
8 Thus natural productions, though they possess their own propel principles, are ultimately composed of the first and common principles, matter and form : these last constitute the parts of body, but body and soul the parts of animal. Also in the sciences we must consider the sub- jects of them, their parts, and their proper affections.
J Thai is, their principles neither issue from a common source, nor are so intermingled that the one may be derived from the other: thus phy- sics and arithmetic are different sciences, but the science of motion and of the heavens are not entirely different Vide Physics.
x 2
308 Aristotle's organon. [book i.
modes, both un-continued medium from the same class,* as if when the raid- q j) an(j jo (were assumed) of A B, j" but also from fmmX^ame, another (series).1 Thus, let A be to be changed, ferentVnuf D to be movedJ B to be delighted, and again G * when one is to be tranquillized. It is true then to predicate the other.10 D of B and A of D, for whoever is delighted is t The concin- moved, and what is moved is changed : again, it is
true to predicate A of G, and G of B, for every one who is delighted is tranquillized, and he who is tran- quillized is changed. Wherefore there is a syllogism through different media,2 and not from the same class, yet not so that
neither is predicated of neither medium, since it
I DandG. -g necessary that both it should be present with § b. something § which is the same. We must also
II Through how consider in how many ways|| there may be a syl- many media. i0a-ism of the same thing through the other figures.
Chap. XXX. — That there is no Science of the Fortuitous.3
1. This class There is no science through demonstration of does not come tjiat which is fortuitous, since the fortuitous is pur subjects10!- neither as necessary nor as for the most part, but demonstration. tnat wnicn is produced besides these, and demon- stration is of one of these. For every syllogism is through premises, either necessary, or through those which are for the most part (true), and if indeed the propositions are necessary, the conclusion also is necessary ; but if for the most part (true), the conclusion also is of the same character. Hence if the fortuitous is neither as for the most part nor necessary, there cannot be demonstration of it.
n Vide Ethics, Chap. XXXI. — That toe do not possess Scientific b. vi. ch. 2 Knowledge through Sensation.^
and 3.
i. The percep- Neither is it possible to have scientific know- tion of the led"-e through sensation, for although there is
1 That is, it is possible to effect this when the one is not subaltern to the other, as it may be shown that man is an essence if we take biped as a medium, or walking, or disputing, for these are not from the same class as the former.
2 That is, D and G, media, the same conclusion A B is proved. * Cf. Meiap. lib. v. (vi.).
CHAP. XXXI.] THE POSTERIOR AXALYT1CS. 309
sensible perception of such a thing as this, ana senses is not not of this particular thing,* yet it is necessary *CNececert£e to have a sensible perception of this particular hujus rei.
.,. , , r i i -o , .. • • • Buhle.
thing, and some where and now. Uut it is impossi- ble sensibly to perceive the universal and in all things, for it is not this particular thing, nor now, otherwise it would not be universal, since we call the universal that which is always and every where. Since then demonstrations are universal, but these cannot be perceived by sense, it is plain that neither can scientific be possessed through sense. In fact, it is clear, that even if we could perceive by sense that a triangle has angles equal to two right, we should require demonstration, and not, as some say, know this scientifically, for it is necessary sensibly to perceive the singular, but science is from the knowledge of the universal.! Where- j+ibc^ *net]' fore also if we were above the moon, and saw the earth opposite, we should not know the cause of an eclipse (of the moon). For we should perceive that it is eclipsed, but in short should not perceive ichy, since there would not be a sensible perception of the universal. Nevertheless, from observing this frequently to happen, by investigation of the universal, we should obtain demonstration, for the universal is manifest from many singulars, but is valuable, because it discloses the cause, wherefore the universal (knowledge) about such things, of which there is another cause, is more honour- able than the senses and apprehension : about first j cf. An. Post, principles however there is another reason. J2 »■ ch- 9-
1 Aristotle intends to show that sense is not science ; otherwise since sense apprehends qualities, as sounds, etc., it may seem that sense and science are the same; but the fact is, that though they are employed about the same things, yet they are not so after the same manner, for sense apprehends particularly, but science universally. Moreover the perception of the senses is limited by time and place, but science, or uni- versal knowledge, is not so restricted, so that the ascertainment of the universal is beyond the scope of sensuous perception. Cf. Physics; De Animu, lib. ii. and iii. ; Metap. lib. i. ch. 1 ; Magna Moral, lib. i. 34, and Moral. Eud. lib. v. c. 3.
2 The nearest approach to simple apprehension is t) twv atiaipirwi' voiiaiQ, but voi)oiq is variously used, and in its widest sense will embrace all the logical operations. Mansel. See also Reid's Works, pp. 242, 692. Waitz observes upon the passage, " Quare in iis quorum causa aliunde suspensa est, cognitio quam maxime universalis potior est omni alia, quae vel ex sensuum affectione gignatur vel ex cognitione sola originem ha- beat: eorum vero quae non aliunde probantur, quippe quibus nitatur
310 Aristotle's organon. [book i.
It is clearly then impossible to possess scien- Lreha?egcer- tific knowledge of any thing demonstrable by tain things un- sensible perception, unless some one should affirm rtedeficfen^ that sensible perception is this, to possess science of sensible per- through demonstration. There are indeed certain
problems which are referred to the deficiency of our sensible perception,1 for some if we should see them we should not investigate, not as knowing from seeing, but as possessing the universal from seeing. For instance, if we saw glass perforated, and the light passed through it, it would be
also manifest why it illuminates in consequence giaPss!Ce °f of our seeing separately in each,* and at the same + pieces. time perceiving that it is thus with all.f
(Cf. An. Post. Chap. XXXIL— On the Difference of Principles ac- i- i. 10.) cording to the Diversity of Syllogisms.
i. Theimpos- That there should be the same principles of all sibiiity of prin- syllogisms is impossible, first (this will be seen) syi'iogisms'be- by those who consider logically. For some syl- ing identical, logisms are true, others false, since it is possible to conclude the true from the false, yet this but rarely happens, for instance, if A is truly predicated of C, but the middle B is false, for neither is A present with B nor B with , ,, . C.t If however the media of these propositions
I Example 1.) + _ , „, , „ , «, , x x
are assumed, they will be false,2 because every false conclusion is from false principles, but the true from true principles, and the false and the true are different. Next, neither are the false (deduced) from the same (princi- ples) with themselves, for they are false and contrary to each
omnis ratiocinatio, alia ratio est : haec enim mente ipsa intuemur et quasi amplectimur.
1 Philoponus observes that Aristotle added this observation lest any discrepancy should appear to exist between what he has stated here and at chapter 18. Philop. Schol.
B A
Ex. 1 . Every stone is an animal C B
Every man is a stone C A
• . Every man is an animal. * i. e. the propositions of the prosyllogisms, if the former are to be proved by the latter.
CHAP. XXXII.] THE POSTERIOR ANALYTICS. 311
other, and cannot be simultaneous, for instance, it is impossible that justice should be injustice or timidity, that man should be a horse or an ox, or that the equal should be greater or less. From these positions indeed (we may prove it) « j e that thus,* since neither are there the same principles there are not of all the true (conclusions), for the principles of CiPi|s 0feaunn many are different in genus, and are not suitable, things- as units do not suit points, for the former have not position, but the latter have it. At least it is necessary to adapt (either) to media or from above or below, or to have some terms within but others without.1 f Nor can t The ex- there possibly be certain common principles from jremes. (Syi-
m. */ *■ i loErismum )
which all things may be demonstrated : I mean Buhie. by common as to affirm or to deny every thing, for 2- the genera of beings are different, and some are present with quantities, but others with qualities alone, with which there is demonstration through the common. Again, principles are not much fewer than conclusions, for the propositions are principles, but the propositions subsist when a term is either assumed or introduced. Moreover, conclusions are infinite, but terms finite ; besides, some principles are from necessity, but others contingent.
To those therefore who thus consider, it will be 2. Reply to ob- impossible that there should be the same finite Jjjj mutakln principles when the conclusions are infinite, but identity. if any one should reason in some other way, for instance, that these are the principles of geometry, but these of reckoning,:}: and these of medicine, what is this 1 \o-r,ouwv, statement other than that there are principles of J^tayfor9" the sciences ? § but to say that there are the same and Buhie. principles because they are the same with them- principFe^oV" selves is ridiculous.il for thus all things become the several sci- the same. Still neither is to demonstrate any n Because no- thing from all things to investigate whether there f^itedf™ are the same principles of all, since this would be
1 That is, if principles are to be accommodated to another science, we must so arrange the terms as that the demonstrations may be formed either in the 1st figure, wherein the middle term holds the middle place; or in the '2nd figure, where it occupies the hist place, and is above both the extremes ; or in the 3rd figure, where it holds the last place under each extreme. Moreover, some must be formed in the first, but otherg in the second or third figure.
312 Aristotle's organon. [book i
* i. e. Mathe- very silly. For neither does this happen in evi- matk-s. dent disciplines,* nor is it possible in analysis,1
since immediate propositions are principles, and another con- . go that he elusion arises, when an immediate proposition is assumes the assumed. f If however any one should say that the many^onciu- firs* immediate propositions are the same princi- sions- pies, there is one in each genus, but it" it is nei-
ther possible that any thing can be demonstrated as it ought to be from all (principles), nor that they should be so different, as that there should be different ones of each science, it re- mains that the principles of all are the same in
sPecfes.iffer " genus't but that from different principles differ- ent sciences (are demonstrated). Now this is § ch. 7. evidently impossible, for it has been shown S that
3 Principles . ^
(c,px.ai) two- the principles are different in genus of those fold, i£ <Sv and things which are generically different, for princi- ples are two-fold, viz. from which and about which, those indeed from which are common,2 but those about uhich are peculiar, for instance, number and magnitude.
Vid. Ethics, Chap. XXXIII. — Upon the Difference beticeen Science vi.ch. 3, a."* b. iii. ch. 2.
b'vi-ch-3'and and Opinio^. ||
l. science is The object of scientific knowledge and science rublfs^ ' ai (itself) differs from the object of opinion, and from through things opinion, because science is universal, and subsists
necessary: m- • f ' . '
teiiecttheprin- through things necessary, and what is necessary cipie of science. cannot subsist otherwise than it does : some things however are true, and subsist, yet may possibly subsist otherwise. It is evident then that science is not conversant with these, (for else things which are capable of subsisting other- wise, could not possibly subsist otherwise). Yet
IT See Ethics, b. .,/ ... „ r.K J .. , ,' T ..
vi ch. 2 and 3, neither is intellect! conversant with such, (for I call Bohn"s'editteS' inte^ect tne principle of science,3) nor indemon- * vnox^is. strable science, and this is the notion * of an imme-
1 If any one were to analyze the different sciences into their principles, he would not be able to analyze them into the same, but into different principles.
2 As axioms, see ch. 10; also table of the principles of science. Cf. Sanderson's Logic, b. iii. ch. 11 ; Mill's Logic, vol. i. p. 197; Metap. v. and vi.
3 Because of our cognizance of axioms by it
CHAP. XXXIII.] THE POSTERIOR ANALYTICS. 313
diate proposition. But intellect, science, and opi- See Mansel's nion, and what is asserted through these, are true, n°t^c' p' 5' wherefore it remains that opinion is conversant with the true or false, which yet may have a various subsist- ence, but this is the notion of an immediate and not neces- sary proposition. This also agrees with what . .
J r K. , ., . . . . , , : ., 2. opinion con-
appears, lor both opinion is unstable, and its na- versant with
ture is of this kind,1 besides, no one thinks that thenon-neces- he opines, but that he knows, when he thinks it impossible for a thing to subsist otherwise than it does, but when he thinks that it is indeed thus, yet that nothing hinders* it being otherwise, then he thinks that he opines ; * so waitz, opinion as it were being conversant with a thing and'Huhie^1"1 of this kind, but science with what is necessary. KuXuei.
How then is it possible f to opine and know + Taylor and the same thing', and why will opinion not be sci- B_ulllf inser!
b' m J r _ _ on — " non li-
ence, if a person admits that every thing which cet," "it is not he knows he may opine ? for both he who knows waitzandBek- and he who opines will follow through media till keromitit.
, ... , . , • n .1 n 3- Solution of
they come to things immediate, so that if the former an inquirywhy
knows, he also who opines knows. For as it oBiifio'n^a.8*68
is possible to opine that a thing is, so likewise not be science.
why it is, and this is the medium. Or \ if he so "shaiFwesay."
conceives things which cannot subsist otherwise, Taylor, waitz
.„. iii if..- i i i-i , omits, but Bek-
as it he had the definitions through which the ker retains the demonstrations are framed, he will not opine, but iuestlon- know ; but if that they are true, yet that these are not pre- sent with them essentially, and according to form, he will opine and not know truly both the that and the why, if in- deed he should opine through things immediate ; but if not
1 In fact, as Aldrich observes, " ei (opinioni) nulla competit certitudo sed in ipsa sui ratiune includit ibrmidinem oppositi : sunt opinioni tamen gradus quidam ad certitudincin." For the most admirable example of all the vacillation of opinion from surmise to certainty, and of the desire for that full knowledge and assurance which after all will crush the heart, " the doom it dreads, yet dwells upon," see Shakspeare's Othello, passim, but especially act iii. scene 3 :
" Oth. By the world, I think my wife be honest ; and think she is not ; I think that thou art just ; and think thou art not; I'll have some proof."
See also Butler's Analogy, Introduction on Probable Evidence. Cf. Top. i. 1 ; Aldrich, Whately, Sanderson's and Hill's Logic, in verb.
314 Aristotle's organon. [book i.
through the immediate, he will only opine that they are. Still opinion and science are not altogether conversant with the same thing, but as both the true and the false opinion are in a manner about the same thing, thus also science and opinion are conversant with the same.1 For as some say that true and false opinion are of the same ; absurd consequences
follow both in other respects, and also that he iH.ch.^etb' who opines falsely does not opine.2 * Now since
the same thing is stated in several ways, in one way there may be, and in another there cannot be (a true and false opinion of the same). For to opine truly that the diameter of a square is commensurate with its side, is ab- surd, but because the diameter about which there are (con- trary) opinions is the same thing, thus also they are of the same thing, but the essence of each according to the definition is not the same.3 In like manner also knowledge and opinion are conversant with the same thing, for the former is so con- versant with animal as that it is impossible animal should not exist, but the latter so as that it may possibly not exist, as if the one should be conversant with that which is man essen- tially, but the other with man indeed, yet not with what is t But accident- man essentially ;f for it is the same thing, that is, ally' man, but not the same as to the manner.
4. We cannot, From these then it is clearly impossible to opine at one and the an(j know the same thing at the same time, for
same time, . ° '
know, and otherwise at one and the same time a man might opme" have a notion that the same thing could and could
not subsist otherwise, which is impossible. In different (men) indeed each (of these) may be possible about the same thing,
1 Science is however distinguished from opinion, by the certainty of its subject : error also consists with certainty of the subject, but opinion cannot consist with it. Vide Mansel's note, p. 102 ; Sanderson's defini- tions. Cf. also Anal. Post. i. 6. The whole subject is well discussed by Hill (Logic, p. 275, et seq.), and upon the distinction of the dialectic and demonstrative syllogism, as enuuciative of opinion and science, the reader will find some valuable remarks in Mansel, and Crakanthorpe's Logic. Cf. Top. i. 1.
2 He here glances at the opinion entertained by Protagoras and the sophists, who asserted that truth and falsehood were only in opinion, and that if every opinion is true, false opinion is not opinion.
3 From the thing being considered in two ways, there are two essences of the thing, and the diameter is assumed in true opinion in one way, and in false opinion in another. Taylor.
CHAP. XXXIV.] THE POSTERIOR ANALYTICS. 315
as we have said,* but in the same (man) it is im- , vide Aidrich possible even thus, since he would have a notion in-verb. •• opi- at the same time, for instance, that man is essen- tially animal, (for this it is to be impossible not to be an animal,) and is not essentially an animal, for this it is to be possible not to be an animal.
For the rest, how it is necessary to distinguish between dis- course and intellect, and science and art, and prudence and wisdom, belongs rather partly to the physical, and partly to the ethical theory.1
Chap. XXXIV.— Of Sagacity. + t Cf. Ethics,
J J * ' b. vi. ch. 9
Sagacity is a certain happy extempore conjee- j Definition
ture of the middle term, as if a man perceiving of sagacity.
that the moon always has that part lustrous which ££££& x'pola
is towards the sun, should straightway understand To;; uiao" : in"
StiillCtS
why this occurs, viz. because it is illuminated by
the sun, or seeing a man talking to a rich person, should know
that it is in order to borrow money of him, or that persons
are friends, because they are enemies of the same
man ; for he who perceives the extremes^ knows \^\ eonclu"
all the middle causes. Let to be lustrous in the
part toward the sun be A, to be illuminated by the sun B,
the moon C. Wherefore B to be illuminated by the sun is
present with the moon C, but A to be lustrous in the part
turned towards that by which it is illuminated is present
with B, hence also A is present with C through
t. r r ° § Example ,1.)
1 Cf. Biese, vol. i. p. 89, 327 ; Hamilton's Reid, p. 768. Atdvoia. is the progress of the intuitive intellect (vovg) in investigating truth, and is perhaps best rendered here " discourse," though the latter applies both to it and to Xoyicr/ioc. Upon these terms, cf. Mansel's note, pp. 4 — 6, and upon the powers or energies themselves, see Ethics, b. vi., Bonn's edition, and De Anima.
B A
Ex. 1. Whatever is illuminated by the sun shines in the part towards the sun
C B
The moon is illuminated by the sun C A
• . Tie moon shines in the part towards the sun.
316
Aristotle's org anon.
book n.
BOOK II.
Chap. I. — That the subjects of Scientific Investigation are four.
I. Subjects of investigation : the that ; the why; the if; and the what. A thing is to
OTf TO, OiOTi, el ZoTIV, T* €<TTtv.
Instances.
The subjects of investigation are equal in num- ber to the things which we scientifically know ; but we investigate four things ; that a thing is, why it is, if it is, ivhat it is. For when we in- quire whether it is this, or that, having reference to a number (as whether the sun is eclipsed or not) we investigate the that, and a sign of this is that when we have found that it is eclipsed we desist from our in- quiries, and if we knew from the first that it is eclipsed, we do not inquire whether it is so. But when we know the that, we investigate the why, for instance, when we know that directing there is an eclipse, and there is an earthquake, we inquire why there is an eclipse, and an earth- quake. These things indeed we investigate thus,* but some after another manner, f for instance, if there is, or is not, a centaur or a God. I say if there is or is not, simply,1 and not if it is white When however we know that a thins-
our attention tomanythings. t Simply con- sidering one thing.
X Bekker and Waitz end here : Taylor
and Buhle add or not. the opening
sentence of the is, we inquire what it is, tor instance, what God, next chapter. 0r what man is. J
Chap. II. — That all Investigation has reference to the Discovery of
the Middle Term.
I. The former The things then which we investigate, and which Hom "mayl be having discovered we know, are such and so reduced to two, many, but when we inquire the that or if a thing
' Vide Trendelen. Elem. Log. p. 74. By simply, he means an inves- tigation into the mere existence of the thing, but when an inquiry as to the ™ on is made, then it becomes a question of the quality. Upon the ar- gument of this whole book, see Kuhn's work, Hal. 1844 ; we may remark that the question or to lyrov^vov here, has a more extensive application than what Aldrich assigns to it, since two of the questiones scibiles, " an sit," and "quid self," cannot in all cases be determined syllogistically. Cf. ch. 3, of this book. See aiso Mansel's Appendix, note B.
CHAP. II. J THE POSTERIOR ANALYTICS. 317
is simply, then we inquire whether there is a concerning the medium of it or not, but when knowing, either ^ere^te'oiie1 that it is, or if it is, either in part or simply,1 we and what it is. again investigate why it is, or what it is, then we inquire what the middle is. But I mean by the that if it is in a part and simply, in a part indeed (as) is the moon eclipsed or increased ? for in such things we inquire if a thing is or is not ; but simply (as) if there is a moon or not, or if night is or net.* In all these inquiries it occurs that we * a question of investigate either if there is a middle or what the the whole, not middle is, for the cause is the middle, and this is 2, The middle investigated in all things. Is there then an 1S that wh'th
O . .0 ...... expresses the
eclipse r is there a certain cause or not r atter this, cause why the when we know that there is, we inquire what "ated'of the"11" this is. Fur the cause of a thing not being this or minor. that, but simply substance, or not simply, but something of those which subsist per se, or accidentally, is the middle. I mean by what is simply (substance) the subject, as the moon, or the earth, or the sun, or a triangle, but by a certain thing, (as) an eclipse, equality, inequality f if it is in the middle or not.| For in all these it is evident that Jhfangksl/a what a thing is and toll)/ it is are the same ; what triangle.
v «j • .• » v 1 , j 4l X Refeiring to
is an eclipse r a privation ot light tram the moon the earth, as in through the interposition of the earth. Why is the centre of
= r ... i- j a the spheres.
there an eclipse, or why is the moon eclipsed r because its light fails through the interposition of the earth.2 What is symphony? a ratio of numbers in sharp and flat. Why does the sharp accord with the flat ? because the sharp and flat have the ratio of numbers. Do then the sharp and flat accord?- is there then a ratio of them in numbers? as- suming that there is, what then is the ratio ?
That the inquiry is of the middle those things prove whose middle falls within the cognizance of fnv^tigtt'e the the senses, since we inquire when we have not a middle, if the sensible perception, as of an eclipse, whether it is and its1 cause,
or not. But if we were above the moon we should fl" within the . , . n , . . , , , cognizance ot
not inquire neither it, nor why, but it would be our senses. immediately evident, as from sensible perception {^t^o'asn we should also obtain knowledge of the universal ;
1 In part that it is, or simply if it is.
- Upon the reduction ol this demonstration to syllogistic form, see Aquinas Opusc. 3s, and Crakanthorpe Loir. lib. iv. cap. 1.
S18 Aristotle's organon. [book 11.
for sense (vould show us) that the earth is now opposed, for it would be evident that there is now an fibC£ Metap' eclipse, and from this there would arise the uni- versal. ' * As therefore we say, the knowledge of the Awhat is the same as the knowledge of the why, and,vthis is either1 simply, and not somewhat of things inherent, ^of it is of things inherent, as that there are two right angles or that it is greater or less.
Chap. III. — Upon the Difference between Demonstration and
Definition.
That all investigations then are an inquiry of the middle is evident, but let us show how tohat a thing is, is demon- strated, and what is the method of training up a thing to its ,. , . i, principles,2! also what a definition is, and of what e. avahiaew subjects doubting first about these. But let the commencement of the future (doubts) be that which is most appropriate to the following discussion, since , w perhaps a man might doubt whether it is possible
1. We cannot r , r ° , . , ,.r
know by defi- to know the same thing, and according to the subjecfcapabie same D7 definition and demonstration, or whether of demonstra- it is impossible? For definition seems to be of what a thing is, but every thing (which signifies) what a thing is, is universal and affirmative, but some syllo- gisms are negative, others not universal ; for instance, all those in the second figure are negative, but those in the third not universal. Next, neither is there definition of all affirmatives in the first figure, as that every triangle has angles equal to two right angles ; the reason of this is, because to know
1 By sensible perception that of the universal is produced.
- That is, how definition is reduced to demonstration, for every de- finition is either the principle or the conclusion of demonstration, or it alone differs from demonstration in the position of terms, as was shown in ch. 8, of the preceding book. Taylor. Upon the subject of this chapter, and the subsequent ones, the reader is referred to the truly valuable remarks in Mansel's Appendix, note B., which want of room prevents my fully quoting, and justice to the excellent treatment the author has shown of his subject, forbids me to abridge. In many cases I have been compelled to give only references, where otherwise I would have entered into greater detail. The student will do well also to con- sult Rassow, Aristot. de notionis def. doctr., and Crakanthorpe's Logic. Cf. also Top. i. 5 and 6, 4 and 14; Metap. vi. 11 ; De Anima, i. 1.
CHAP. III.] THE POSTERIOR ANALYTICS. 319
scientifically that which is demonstrable, is to possess de- monstration, so that if there is demonstration in regard to things of this kind, there can evidently not be also definition of them, for a person might know by definition without de- monstration, since nothing prevents the possession of it at one and the same time. A sufficient evidence of this is also derived from induction, for we have never known by de- finition, any of those which are inherent per se nor which are accidents ; besides, if definition be a certain indication of sub- stance, it is evident that such things are not substances.
Clearly then, there is not definition of every thing of which there is also demonstration, but nionsTrationaii what, is there then demonstration of every thing those which are of which there is definition or not ? there is one fmition. reason and the same also of this.* For of one *bo>™posed thing, so far as it is one, there is one science, so that if to know that which is demonstrable be to possess demonstration, an impossibility would happen, for he who possesses definition would know scientifically without de- monstration. Besides, the principles of demonstration are definitions, of which it has been shown before, there will not be demonstrations,-!" since either principles will be demonstrable, and principles of principles, and this ch^and1^1 would proceed to infinity, or the first (principles) will be indemonstrable definitions.
Yet if there are not of every thing and the 3. in fact, no- same, may there not be definition and demonstra- thing capable
.. J ... . . „ ... of definition
tion of a certain thing and the same r or is it 1m- admits de- possible ? since there is not demonstration of what monstratlon- there is definition. For definition is of what a thing is, and of substance, but all demonstrations appear to suppose and assume what a thing is, as mathematics, what is unity and what an odd number, and the rest in like manner. More- over every demonstration shows something of somewhat, as that it is, or that it is not, but in definition one thing is not predicated of another, as neither animal of biped, 4. one part of a nor this of animal, nor figure of superficies, for su- definition is
/»••./> c c • a not predicated
perficies is not figure, nor figure superficies. Again, 0f another. it is one thins to show what a thins is, but an- yweHill'a
0 ° Lopic, and
other to show that it is, definition then shows what Whately on a thing is, but demonstration that this thing, either " Definitlon-"
320 Aristotle's organon. [book n.
is or is not of this. Of a different thing indeed there is a dif- ferent demonstration, unless it should be as a certain part of the whole. I say this because the isosceles has been shown (to have angles equal) to two right, if every triangle has been shown (to » The isosceles ^ave them), f°r that is a Part, but this a whole : * being a species these however, that a thing is, and what it is, do to it^a'part not thus subsist in reference to each other, since
to a whole. the one js not a par^ 0f tJje other.
Evidently then there is neither entirely demon- tion.eCapitUla" stration of what there is definition, nor entirely de- finition of what there is demonstration ; hence in t Definition short it is impossible to have both f of the same *£itionTn" tmng? so that it is also evident that definition and
♦ -m. ,.- demonstration will neither be the same, nor the
% The things . , . , , , . ' .
defined and de- one contained in the other, otherwise their sub-
monstrated. jectgi woul(j subsist similarly.|
Chap. IV. — That the Definition of a thing cannot be demonstrated.
1. in order to ^jET then so far these things be matters of doubt,
collect by a syi- but as to what a thing is whether is there, or is
thing is, the there not, a syllogism and a demonstration of it, as
midu!lterm the present discussion supposed ? for a syllogism
ought to ex- r ... n , i ,
press the defi- shows something in respect oi somewhat through mtIon- a medium, but the (definition) what a thing is,
is both peculiar and is predicated in respect of what it is. Th nat Now it is necessary that these should reciprocate : |i of the thing for if A is the property of C, it is evidently alsc wWchttis the that of B, and that of C, so that all § reciprocate nature. with each other. Nevertheless, if A is present
with every B in respect of what it is, and uni- versally B is predicated of every C in respect of what it is, it is also necessary that A should be predicated of C in the ques- tion what it is. Still if some one should assume without this reduplication,2 it will not be necessary that A should be predi- cated of C in the question what a thing is, though A should f in the major, ^e predicated of B^[ in the same question, but not
* intneminor. of those of which B is predicated in this question.*
Now both these | will signify what a thing (C) is,
' to. inro Kti/Atva, h. e. finis ad quem tendit utraque vel id quod utraqua conricere vult. Waitz.
2 That is, simply saying that A is attributed to B, and B tc C.
CHAP. IV. "1 THE POSTERIOR ANALYTICS. 321
wherefore B will also be the definition of C, hence if both signify what a thing is, and what the very nature of it is, there will be the very nature of a thing prior in the middle term. Universally also, if it is possible to show what man is, let C be man, but A what he is, whether biped animal, or any thing else ; in order then that a conclusion should be drawn, A must necessarily be predicated of every B, and of this there will be another middle definition, so that this also will be a definition of a man, wherefore a person assumes what he ought to show, for B also is the definition of a man.
We must however consider it in two proposi- 2. a twofold tions, and in first and immediate (principles), for consideration, what is stated becomes thus especially evident : they there- fore who show what the soul is, or what man or any thing else is, by conversion, beg the question,1 as if a man should assume the soul to be that which is the cause to itself of life,* and that this is number moving itself,f he must necessarily so assume as a postulate that the t The major, soul is number moving itself, as that it is the pf-.de ; Anim-
b. i cfii 4 16.
same thing. For it does not follow if A is con- sequent to B, and this to C, that A will therefore be the definition of the essence of C, but it will be only possible to say that this is true, nor if A is that which is predicated essentially of every B. For the very nature of animal is predicated of the very nature of man, since it is true that whatever exists as man, exists as animal, (just as every man is animal,) yet not so, as for both to be one thing.| t Because one If then a person does not assume this, he will not is genus, the
1 In the minor in fact the terms so reciprocate as to become identical, and the very nature of a thing, and that of which it is the very nature, are the same. The whole argument goes to show that no definition, as such, can be proved, but the endeavour necessarily results in a petitio principii. and the reason is simply because a definition can be predicated essentia1 ly ( f v rip ti tan ) of nothing but that, of which it is the definition ; and sin., to prove a conclusion concerning the essence, the premises must be of th* same character, the assumed middle must be identical with the minor, and the major premise with the conclusion. The argument is used against Xenocrates. Cf. Scholia, p. 242, b. 35. Trendelenburg, de An. p. '273. Kuhn, de Notionis Definitione, p. 11. Mansers Logic, Appendix B. In some passages (Metap. vi. 5, b ; vi. 4, 12) Aristotle declares sub- stances alone capable of definition, but in a wider sense, as used throughout the Post. Anal., the remark is applicable both to substances and attributes
Y
322
ARISTOTLE S OKGANON.
1 BOOK II.
other species. 3. He who proves the de- finition by a syllogism begs tiie question.
tio principii.
conclude that A is the very nature and sub- stance of C, but if he thus assume it, he will assume prior to the conclusion that B is the de- finition of the essence of C. Therefore there has been no demonstration, for he has made a " peti-
Chap. V. — That there is no Conclusion by Divisions proved.
1. That the method by di- vision is in- conclusive. * An. Prior, i. 31.
t The members of division. % The defini- tion to be proved.
§ The admitted premises.
Nevertheless, neither does the method througt divisions infer a conclusion, as we observed in the analysis about figures,* since it is never necessary that when these things exist, f that J should exist, as neither does he demonstrate who forms an in- duction. For the conclusion ought not to inquire nor to exist from being granted, but it necessarily is, when they§ exist, although the respondent does not acknowledge it. Is man (for instance) animal or inanimate,1 if he has assumed him to be an animal, it has net been syllogistically concluded. Again, every ani- mal is either pedestrian or aquatic, he assumes it pedestrian, and that man is that whole animal pedestrian, is not neces- sary from what is said, but he assumes also this. It signifies nothing however, whether he does this in respect of many 2. The same things or few, since it is the same thing ; to those reasoning good therefore who thus proceed, and in what is capa- definUion.8 ° ble of syllogistic conclusion, this use is unsyllo- gistic. For what prevents the whole of this|| being true of man, yet without enunciating what a thing is, or the very nature of it ? Again, what prevents something being added to, or taken away from, or exceeding the essence ? 2
Negligence then happens about these things, but we may avoid it by assuming all things (as granted) in respect of what a thing is, and the first being made a postulate by arranging the order
Pedestrian.
3. A rule ap- plied for divi- sional defini- tion.
1 This is an interrogation of one, investigating a definition by division.
2 That is, that something may be superfluous or defective in the defini- tion. Cf. rules for definition in the common Logics ; also Passow, Arist de Notionis Defin. Doct., Crakanthorpe, and Sanderson, and especially Boethius de Divisione.
CHAP. VI. J THE POSTERIOR ANALYTICS. 323
in division, omitting nothing. This however is requisite, for it is necessary that there should be an individual, . „
? , , . ... ' 4. By constant
yet nevertheless there is not a syllogism, but if so division, when it indicates after another manner. And this is not nitfonTs'^*" at all absurd, since neither perhaps does he who rived ?l- we makes an induction demonstrate, though at the rhVat the fn- same time he renders something manifest, but he dlvidual- who selects definition from division does not state a syllo- gism.1 For as in conclusions without media, if a man state that from such things being granted, this particular thing necessarily exists, it is possible to inquire why, thus also is it in definitions by division. What is man ? A mortal animal, pedestrian, biped, without wings. Why ? according to each addition,'2 for he will state and show by division as he thinks that every one is either mortal or immortal. The whole however of such a sentence is not definition,* * For the defi- wherefore though it should be demonstrated by nifion h!iS t0 be division, yet the definition does not become a it, i.e. a mortal
Syllogism.3 animal.
Chap. VI. — Case of one Proposition defining the Definition itself.
Is it however possible to demonstrate what a 1. it is proved thing is according to substance, but from hvpo- !ihat thT Is no
, P . ^1 demonstration
thesis assuming that the very nature of a thing ofthedefini- in the question what it is, is something of its S?pSjS£2
1 Oil Xiyti 6 fc/tXfyon'. A paronomasia; a definition is said to be selected from division, because not all the members of the division are assumed in the definition, but always from two opposite members, the one is assumed and the other relinquished. Taylor.
2 That is, we may question each part of the definition, which is added successively, e. g. why is man animal ? why mortal? etc. Trap' iica<7T7]p irpoaOcoiv.
3 Syllogism here, as in other places continually, means the conclusion, and, as Waitz remarks, Aristotle would more accurately have written d\\' o ovWoyia/iOQ oi)% opirr/xbg ytverai. Division was a favourite method with Plato, for the demonstration of definitions, but Aristotle considers it only a weak kind of syllogism ; in fact, that its chief use is to test definitions when obtained. Andronicus Rhodius wrote a separate trea- tise on division, and amongst the later Peripatetics, the system was ap- parently held in higher estimation. Cf. Cic. Top. en. 6; Quintil. v. 10; vii. 1 ; Hamilton's Keid ; Trendelen. Elem. and Abelaid Dialectica, ed. Cousin.
Y 2
324 aristotle's organon. [book ii.
defines the de- peculiar principles, and that these alone1 indicate finition itself. -^ substance, and that the whole2 is its peculiar- ity ? for this is its essence. Or again, has a person assumed the very nature of a thing in this also ? for we must neces- sarily demonstrate through a middle term.3 Moreover, as in a syllogism, we do not assume what is to have been syllo- gistically concluded, (for the proposition is either a whole or a part, from which the syllogism consists,) thus neither ought the very nature of a thing to be in a syllogism, but this should be separate from the things which are laid down, and in reply to him who questions whether this has been syllo- gistically concluded or not, we must answer that it is, for this was the syllogism.4 And to him who asserts that the very nature of the thing was not concluded, we must reply that it was, for the very nature of the thing was laid down by us, so that it is necessary that without the definition of syllogism, or of the definition itself, something should be syllogistically inferred.
2 Nor b Also, if a person should demonstrate from hy-
other hypotne- pothesis, for instance, if to be divisible i3 the
ica sy ogism. egsence 0f evji . ^ut 0f a contrary, the essence is
contrary of as many things as possess a contrary ; but good is contrary to evil, and the indivisible to the divisible, then the essence of good is to be indivisible. For here he proves assuming the very nature of a thing, and he assumes it in * Therefore order to demonstrate what is its very nature : *
** be°"S the •
question." cf. let however something be different, since in de-
1 The things assumed as constituting the definition.
2 The composite from many attributes. It may be observed that there are two ways of investigating definition ; one by division, and the other by induction; the first took a wide genus, including the object to be de- fined, and contracted it by the addition of successive differentia?, until we obtain a complex notion, co-extensive with that of which the definition is sought ; this was Plato's favourite method, though rejected by Speusip- pus. Vide Scholia, p. 179, b. xi. The other method was by induction, which consisted in examining the several individuals of which the term to be defined is predicable, and observing what they have in common ; the definition sought, being the one common notion which is thus obtained. Vide Mansel's Logic, Appendix B. ; Locke's Essay, book ii. ch. 23.
3 The medium being the essence, the latter is thus assumed to demon- strate itself.
4 i. e. from the definition of syllogism, it must be shown that the syllo- gism was rightly constructed, and the conclusion properly inferred.
CHAP. VII.] THE POSTERIOR ANALYTICS.
325
monstrations k is assumed that this is predicated of that, yet not that very thing, nor that of which there is the same definition,* and which recipro- cates.! To both however there is the same doubt against him who demonstrates by division, and against the syllogism thus formed, why man will be an animal biped pedestrian,1 but not an ani- mal and pedestrian,}; for from the things assumed, there is no necessity that there should be one predicate, but just as the same man may be both a musician and a grammarian. §
Prior. An. b. ii. ch. 16.
* Equally un- known as the conclusion, t When the proposition can be equally- proved by, as prove the con- clusion. t So that one thing is not proved from these.
§ Cf. Interpre- tation, ch. 11.
Chap. VII. — That what a thing is can neither be known by Demon- stration nor by Definition.
How then will he who defines show the essence , .„ ,„„, .
i. ah inquiry
of a thing, or what it is ? for neither as demon- into the me-
strating from things || which are granted will he ingdetomon."
render it evident that when they exist, it is ne- °blection.s:
cessary that something else^f should be, for de- n The coneiu-
monstration is this, nor as forming an induction Bion"
by singulars which are manifest, that every thing thus subsists,
from nothing * subsisting otherwise ; since he does
not show what a thing is, but that it is, or is not.
What remaining method is there? for he will not
indicate by sense nor by the finger.
Moreover how will he show what it t is ? for it \- „r .
, ' t So Waitz and
is necessary that he also who knows what man is, Rekker. Buhie
or any thing else, should also know that he is,2 % for fead^hat1,
no one knows with respect to non-being that it is, " ™an" is.
but what the definition or the name signifies, as chapte"?* when I say "tragehiphos," it is impossible to
* No indi- vidual.
n
1 So that one thing is produced from these, according to the nature of definition. Cf. on Interpretation, ch. 5.
2 Before we can determine the real definition of any object (n tort) we must of necessity ascertain that it exists (on fori). (Vide next chap- ter.) Now the existence of attributes and that of substances being de- termined in two different ways, there is a corresponding variety in the form of definition, the former being defined by the same cause which served as a middle term to prove their existence, a mode of definition described as frvWoyiVfibg tov Tt tort, HTWOtl fiatyipujv ri}<; AiroCli%lW£ — four causes being recognised by Aristotle (cf. An. Vunt. b. ii. en. 11) : but
326 Aristotle's organon. [book n.
know what tragelaphos is. Moreover, if he should show what a thing is, and that it is, how will he show this in the same sentence ? for both definition and also demonstration manifest one certain thing, but what man is is one thing, and the es- sence of man is another.
We next say that it is necessary to show by not"t^SeSsub-S demonstration every thing, that it is, except it be stance to any substance, but to be, is not SLibstar.ee to any thing, for being is not the genus. There will then be tionof"what" demonstration that it is,* and this the sciences 'tis. now effect. For ivhat a triangle means, the geo-
metrician assumes, but that it is, he demonstrates. What then will he who defines what it is, prove? that it is a ... triangle ? he then who knows what it is by
+ Fecause it is &, .„ . , , , . !
not yet chosen definition, will not know ll it is,j but this IS
to be a triangle. impossible.
4. Error of Evidently then those who define according to
present modes. tbe present methods of definition, do not demon- strate that a thing is, for although those lines be equal which are drawn from the middle, yet why is it the thing de- . drc]e fined ? \ and why is this a circle ? § for we might § wV "is™ he say that there is the same definition of brass. || For circle a figure neitiier do definitions demonstrate that it is possi- lines from the ble for that to be which is asserted, nor that that drnu!mfetrenchee thing is, of which they say there are definitions,1 ll ope.x«Ax™. \yUt it, is always possible to say why.^f rog'ate', why Ys If then he who defines shows either what a this a circle. thing is or what the name signifies, except there is, by no means (an explanation) of what a thing is, definition will be a sentence signifying the same thing as a name, but this is absurd. 2 For in the first place
the definition of substances is determined by the formal cause, in refer- ence to the essential constituents of the general notion, the possession of which entitles the individual to be reckoned under it. Aristotle makes summa genera, and individuals alone indefinite. Locke avers that simple ideas only cannot be defined. Cf. Metap. books vi. and x. ; Locke's Essay, b. iii. 4, 7; Descarte's Princip. i. 10; Occam's Logic, Part I.
1 Definition does not teach that the proposed thing, the essence of which is investigated, exists in the nature of things, nor does it teach that the thing is that, the essence of which the definition unfolds. Taylor.
1 Cf. Top. vi. 4 and 6, 14; Metap. vi. 11; Albert de Praed. Tract, i. : Occam, Part I. eh. 26 ; Whately's Logic, and Aldrich upon nominal and
CHAP. VIII.] THE POSTERIOR ANALYTICS.
327
there would be a definition of non-essences and of non-entities, since it is possible even for non-entities to have a signification. Again, all sentences will be definitions, for we might give a name to any sentence, so that we might all discuss in definitions, and the Iliad would be a definition. Besides, no science would demonstrate that this name signifies this thing, neither there- fore do definitions manifest this.
From these things therefore it appears that neither definition nor syllogism are the same thing, nor are syllogism and definition of the same thing, moreover that definition neither demon- strates nor shows any thing, and that we can know what a thing is neither by definition nor by demonstration.
6. Recapitula- tion. It is proved that we can know '■ quid res sit neither by de- finition nor by demonstration.
Chap. VIII. — Of the logical Syllogism of what a thing is.
Moreover we must consider which of these j QUestion„ things is well, and which is not well asserted, also propounded tor what definition is, and whether there is in a consi eratlon- certain way or by no means a demonstration and definition of what a thing is. Now since it is the same thing as we have said to know what a thing is, and to know the cause where- fore * it is, and the reason of this is, that there is a certain cause, f and this is either the same or another, \ and if it is another, it is either demon- strable or indemonstrable ; if then it is another, and is capable of demonstration,1 it is necessary that the cause should be a medium, and should be de- monstrated in the first figure, for that which is demonstrated is both universal and affirmative. § Now one method will be that which has been now investigated, viz. to demonstrate what a thing is through something else, for of those things which
* uniov TOV T eanv. Cf. ch. 2. t Essentiae rei. I Different from the es- sence of whict it is the cause.
§ i. e. the n? ture of a thing is universally affirmed of that of which it is the nature.
reai definition. It will be found from various places cited, that physical definition was rejected by Aristotle, and that nominal definition is one in which the existence of the objects to which the definition is applicable is not proved; in fact, it is questionable whether the name " nominal defini- tion " is sanctioned by Aristotle (Cf. Trendelen. Elem. 55, upon ch. 10 of this book, and Mansel, Appendix B.
1 If being different from the " what" a thing ia, it can be demonstrated " what" it is.
328
Aristotle's organon.
[book II.
are predicated in respect of what a thing is, it is necessary that the medium should be what it is, lightf defectof and a property in respect of properties, wherefore of two essential natures of the same thing,* it will demonstrate the one,f but not the other.|
That this method then is not demonstration, has been shown before, but it is a logical syllogism of what a thing is, still let us show in what method this is possible, discussing it again from the be- ginning. For as we investigate why a thing is, when we know that it is, but sometimes those become evident at the same time, but it is not possible to know why it is, prior to knowing that " what a thing it is, it is clear that in like manner the very nature andknown?16*1 of a tning> or what it is, cannot be known, with- out knowing that it is, since it is impossible to know what a thing is, when ignorant if it is.§ We sometimes indeed know if it is, accidentally, knowing sometimes something belonging to the thing,1 as thunder we know, because it is a cer- tain sound of the clouds, and an eclipse, because it is a eer"-
• e. g. an eclipse.
t e. g. the op position of the earth.
2. The logical syllogism " de eo, quid sit." The "why" and the " that" sometimes si- multaneously known. The " if" some- times known. Kara avtifie- 3riKor. How
§ Vide last chapter : other- wise the defi- nition will be only nominal.
1 This passage is doubtful : it has nevertheless been used for the de- cision of the question as to whether the class of definitions described as rrjg tov ri ioriv aTroSti^aog avfiirepaapa, is to be regarded as nominal, or as imperfect real definition ; the question is of less importance as Aris- totle elsewhere condemns their use (De Anima ii. 2, 2). The instances he gives here may refer either to the one or the other description. The authorities who hold the first view of the subject are Averroes, Zabarella and St. Hilaire ; those who hold up their pens " on the contrary," are the Greek commentators, Pacius, Rassow, and Kuhn.
B A
That to which the earth is opposed is eclipsed.
B C
The earth is opposed to the moon.
C A
The moon is eclipsed.
Ex. 1.
Ex. 2.
B
What does not produce a shadow when nothing intervenes u
A eclipsed.
C B
The moon does not produce a shadow, &c»
C A
The moon is eclipsed.
CHAP, vm.] THE POSTERIOR ANALYTICS. 329
tain privation of light, and a man, because it is a certain animal, and soul, because it moves itself. As regards then whatever we know accidentally that they are, it is by no means necessary that we should possess any thing by which to know what they are, for neither do we (really) know that they are, and to inquire what a thing is, when we do not know that it is, is to inquire about nothing. In those things however of which we know something, it is easy (to inquire) what they are ; hence as Ave know that a thing is, so also are we disposed to know what it is, now of those things, of whose essential nature we know something, let this be first an example, an eclipse A, the moon C, the opposition of the earth „ _,
t» * m • • i 1 i i • i> Example (1.)
B. lo inquire then whether there is an eclipse or not, is to inquire whether B is or not, but this does not at all differ from the inquiry if there is a reason of it, and if this is, we say that that also is. Or we (inquire) of which con- tradiction there is a reason, whether of possessing, or of not possessing, two right angles, but when we have discovered, we know at the same time, that it is, and why it is, if it is inferred through media ;f but if it is not so in- + SoBekker ferred, we know the that, but not the why. Let Buhie, and C be the moon, A an eclipse, not to be able to w^tz'a»,U
aue-
<JWV.
produce a shadow when the moon is full and nothing is seen interposed between us, B, if then B, that is, not to be able to produce a shadow when there is nothing be- tween us, be present with C, and A, to be eclipsed, present with this, that there is an eclipse, is indeed evident, but why is not yet so, and that there is an eclipse, we indeed know, but what it is we do not know.t Yet as it is clear ^ „ , ,„ .
. . r~. , . \ , . . . 1 Example (2.)
that A is with C, (to inquire) why it is, is to in- vestigate what B is, whether it is the opposition (of the earth), or the turn of the moon, or the extinction of light, but this is the definition of the other extreme, as in those (examples) of A, since an eclipse is the interposition of the earth. What is thunder ? the extinction of fire in a cloud : why does it thunder ? because fire is extinguished in a
B A
Ex. 3. Where there is an extinction of fire there is thunder. C B
In a cloud there is extinction of fire. C A
. ' . In % cloud there is thunder.
330 akistotle's organon. [book n.
cloud. Let C be a cloud, A thunder, B the extinction of
fire, hence B is present with C, that is, with the cloud, for
fire is extinguished in it, but A, sound, is present
* ^"another wittl thiS' and B *S the definition °f A' tlle firSt
prio/cause of extreme ; * if there be again another medium of ofeth°ePearth.0n this "f it will be from the remaining definitions.1
of what a ^e kave snown therefore thus, how what a
thing Z, the™ thing is, is assumed, and becomes known, where- logism "or de-" fore there is neither syllogism nor demonstration monstration, 0f what a thing is, still it will become evident festeVbyTolh. through syllogism, and through demonstration; cf. ch. 3. an(j nence without demonstration it is neither
possible to know what a thing is, of which there is another cause, nor is there demonstration of it, as we have already observed in the doubts.
Chap. IX. — Of certain Natures or Principles incapable of Demonstration.
i. a two-fold Of some things indeed there is a certain other division of cause, but of others there is not, so that it is plain method used that some of them are immediate, and principles, in each. whose existence and what they are, we must sup-
pose, or make manifest after another manner,2 which indeed the arithmetician does, for he both supposes what unity is, and that it is. Of those however which have a medium,3 and of whose essence there is another cause, it is possible, as we have said, to produce a manifestation through demonstration, yet not by demonstrating what they are.
1 Sin autem etiam alius terminus medius inveniri potest per quem co- gatur propositio A B, is quoque una ex reliquis definitionibus notionis A non esse non poterit. Waitz. If what a thing is, may be proved by another what, this last may also be proved by another, so that there will be three causes of an eclipse, of which the 1st proves the 2nd, and the 2nd the 3rd, and if all are joined there will be a perfect definition. Cf. ch. 10.
2 As by induction, or a demonstration of the " that." He shows here that definitions are assumed prior to all demonstration, and are real, in- asmuch as the existence of the objects is assumed with them. The ground of the assumption will vary according to the nature of the object to be defined. Cf. Metap. x. 7.
3 A cause different from themselves.
CHAP. X. THE POSTERIOR ANALYTICS. 331
Chap. X. — Upon Definition and its kinds.
Since definition is said to be a sentence (ex- ] Definition planatory) of what a thing is, it is evident that either explains one definition will be of what a name signifies, or Jjj™16 of a another nominal sentence, as what a thing signi- fies, which is so far as it is a triangle, which when we know that it is, we inquire why it is.1 Still it is difficult thus to assume things, the existence of which we do not know, and the cause ofthis difficulty has been explained before, because neither do we know whether it is or is not, except accidentally. One sentence is indeed in two ways, the one by conjunction, as the Iliad, but the other from signifying one thing of one, not accidentally.
The above-named then is one definition of a 2 0r shows its definition, but the other definition is a sentence <?use. a dis-
. . if- Unction drawn.
showing why a thing is, so -that the iormer signifies, but does not demonstrate, but the lattei will evi- dently be, as it were, a demonstration of what a thing is, dif- fering from demonstration in the position (of the terms). For there is a difference between saying, why does it thunder ? and what is thunder ? for thus a person will answer, because fire is extinguished in the clouds ; but what is thunder ? the sound of fire extinguished in the clouds ; hence there is the same sentence spoken in another manner, and in the one way there is a continued demonstration, but in the other there is a de-
1 Vide Aldrich, Hill's and Whately's Logics upon nominal and real definition. With regard to the expression \oyoe inpog, opo^arwdtjg, (oratio diversa nominalis, Buhle.) Trendelenburg's, (Elementa, 55,) the literal rendering, gives the idea that nominal as well as real defini- tions must be sentences, but Manse] thinks the context seems rather to mean " a definition of the signification of a name, or of another sentence having the force of a name ; " yet on the other hand fairly allows that in this wav the word crtpog " is superfluous," and the example given " un- intelligible." There is no doubt therefore that by Xoyoc ovofiarw^rtq is meant a sentence whose signification, like that of a single noun, is one ; a description which includes all real definitions, of which the example is a specimen. We subjoin the places he refers to : Int. v. "2 ; Metap. vi. 4, and 1'2, and vii. 6; Alex. Scholia, p. 743, a. 31. In the Greek com- mentators \6yog ovofi. is clearly used for nominal definitions : see Philop. Schol. p. 211, b. 31, also Mansel, Appendix B. p. 19. For the differ- ent uses of the word Aoyoc. by Aristotle, as en.jnciative of definition, cf. Waitz upon this chapter.
332 ARISTOTLE S ORG ANON. [BOOK n.
finition. Moreover the definition of thunder is, a sound in the clouds, but this is the conclusion of the de- ckle also8' monstration of what it is; now the definition of Mansei's Logic, things immediate is, the indemonstrable thesis of
page 16, App. * i .
note.) essence.*1
3. Brief sum- One definition then is, an indemonstrable sen- forms~ fdefini *ence (significative) of essence, but another is a tion. syllogism of essence, differing from demonstration t i. e. in in case, j and a third is the conclusion of the de- form, or in the monstration of what a thing is. Wherefore, from position of the wnat we have said, it is evident how there is, and
terms.
how there is not, a demonstration of what a thing is, also of what things there is, and of what there is not ; more- over in how many ways definition is enunciated, and how it demonstrates the essence of a thing, and how it does not ; also of what things there is, and of what there is not, definition ; yet more, how it subsists with respect to demonstration, and how it may, and how it may not be, of the same thing.
Chap. XI. — Of Causes and their Demonstration.
l. Causes of Since we think that we scientifically know, wWcliareaTi'1' wnen we are cognizant of the cause, but causes expressed by are four,2 one indeed as to the essence of a
1 " Of things immediate," such as the definition of a subject. Waitz and Pacius consider Trraxrig and Qeoig synonymous. Upon the kinds of definition referred to here, the reader will find ample information in Mansel's Appendix B., where they are ably and fully discussed.
2 Upon the four causes of things, see Forchhammer Verhandlungen der sechsten, Versammlung deutscher Philoll. und Schulmm. Cassel, 1344, p. 84 — 89. Although Aristotle allows any of the four to be used as a mid- dle term, yet it by no means follows that each may be a definition of the major, for while he has not decidedly expressed his opinion, it is probable that he regarded the formal cause only, as available for defini- tion. For not only has a material cause no place in attributes, but in physical substances (Metap. vii. 4) ; in this chapter he gives a material cause, instanced as a middle term, as in fact identical with the formal. The efficient and final causes seem, as Mansel says, to be excluded, as not being contemporaneous with their effects, so that from the existence ot the one we cannot certainly infer that of the other. Vide Waitz, vol. ii. p. 41 1 ; Trendelenburg, de Anim. p. 355 ; Mansel, App. B. 17. Cf. also next chapter; Metap. books vi., xi., xii., xiii. ; De Anim.i. ; Physic, lib. i. and ii.
CHAP. XI.] THE POSTERIOR ANALYTICS.
333
the middle term.
* TO t* rjv t'ivut
— the formal cause.
t The material cause.
: The efficient cause. § The final. || When one of these is as- sumed for a middle. (Vide note.) IT The middle.
* Vide Euclid, b. iii. prop. 31.
thin": * another that which from certain tilings ex- isting, this necessarily exists, f a third that which first moves something,} and a fourth on account of which a thing (exists) ; § all these are demonstrated through a medium. || For the one that this existing it is necessary that that should be, is not from one proposition being assumed, but from two at the least, but this is, when they have one medium ; this one therefore being assumed,^ there is neces- sarily a conclusion, which is evidently thus : Why is the angle a right one in a semicircle, or from the existence of what, is it right ? * Let then A be a right angle, B the half of two right angles, and the angle in the semicircle C. Hence B is the cause why A the right angle is inherent in C, i. e. in the angle of a semi- circle ; for this angle is equal to A, but C is equal to B, for it is the half of two right angles ; B then being the half of two right angles, A is inherent in C, and this was for the angle in a semicircle to be a right angle. f + Example 0.) This! however is the same as the explanation of *. The concIu-
n i sion.
the essence of a thing, § because definition signifies § Because a this, but the cause of the essence of a thing has samfas Us na- been shown to be the middle. || Why was there a tur,e- Median war with the Athenians ? What was the cause of waging war with the Athenians ? Because the latter with the Eretrians attacked Sardis ; this was the first cause of the movement. Let war then be A, first made the attack B, the Athenians C, B then is present with C, i. e. to have first made the attack is present with the Athenians, but A is also with B, for they make war with the aggressors, A then is present with B, i. e. to wage war is present with the aggressors, but this, B, is present with the Athenians, for they were the aggressors. Wherefore the middle is the cause here, and that which first moves ; but of those things, whose cause is for the sake of some- thing, as, why does he walk ? that he may be well ■ why is a
B A
Ex. 1. Every angle which is the half of two right angles is a right angle
C B
Every angle described in a semicircle is the half of two right angles
C A
. " . Every angle described in a semicircle is a right angle.
334 Aristotle's organox. [book ii.
house built ? that furniture may be preserved ; the one is for the sake of health, but the other for the sake of preservation. Still there is no difference between why is it necessary to walk after supper, and for the sake of what is it necessary ? but let walking after supper be C, the food not to rise B, to be well A. Let then walking after supper be the cause why the food does not rise to the mouth of the stomach, and let this be healthy ; for B, that is, for the food not to rise, appears to be present with walking, C, and with this A, salubrious. What then is the cause that A, which is that for the sake of which (the final cause), is present with C ? B (is the cause), that is, the food not rising, this * how- X Example (2.) ever is as ** were> the definition of it,f for A will § The premises be thus explained.1 1 Why is B present with C? *nExamp"e u"' because to be thus affected is to be well : we must it in final nevertheless change the sentences, & and thus the
causes. , ,° ?3
* Efficient several points will be more clear. || The genera-
tTnttie latter. tions ^ere ^ indeed, and in causes respecting mo-
t The cause, tion,* subsist vice versa, for there f it is necessary
t TnTeffect5.6' that the middle if should be first generated, but
jr The last in here S C, which is the last,|| and that for the sake
ti me, not in P ,■'. . . , "
nature. or which is generated the last.lf
2 The same Possibly indeed the same thing may be for the
thing may sake of something, and from necessity ; for instance, sesTtwocS; wh7 does Mght pass through a lantern? for ne- cessarily that which consists of smaller particles passes through larger pores, if light is produced by transit, also (it does so) on account of something, that we may not fall. If then it possibly may be, is it also possible to be generated ?
1 That is, the healthy will be explained to be that which does not suf- fer the food to rise.
B A
Ex. 2. For the food not to rise in the stomach is healthy C B
Walking after supper does not suffer the food to rise, ettv C A
. ' . Walking after supper is healthy.
A B
Ei. 3. That which is healthy causes the food not to rise C A
Walking after supper is healthy
C B
. * . Walking after supper causes the food not to rise.
CHAP. XII.] THE POSTERIOR ANALYTICS. 335
as if it thunders, fire being extinguished, it is necessary that it should crash and rumble, and, as the Pythagoreans say, for the sake of threatening, that those in Tartarus may be terri- fied. Now there are many things of this kind, 3 Necessity is especially in those which are constituted and con- two-foid; in-
. • stances Cf
sist from nature, for nature produces one thing Rhet. i. 11. for the sake of something* and another from *.?°rthe,sake
. ° ' of the end or
necessity;]" but necessity is two-told, one accord- form.
ing to nature and impulse,! another with violence, of1matter.eSSlty
contrary to impulse ; thus a stone is borne from t opm'j, i. e.
. i .1 i !i i natural im-
necessity both upward and downward, yet not pu]Se. from the same necessity. S In things however § Because it
m descends na-
which are from reason, || some never subsist irom turaiiy, but chance, as a house, or a statue, nor from neces- J1 Artificial06' sity,1 but for the sake of something, whilst others things, are also from fortune, as health and safety.2 ^[ ir cf. Poetics, Especially in those which are capable of a various ch' 9' subsistence, as when the generation of them is not from for- tune, so that there is a good end, on account of which it takes place, and either by nature or by art : from fortune however nothing is produced for the sake of something.
Chap. XII. — Upon the causes of the Present, Past, (Cf. Phys. lib. and Future. iv)
TnE cause of things which are, is the same also 1. identity of as that of things which are generated, which cause- have been generated, and which will be, for the middle is the cause, except that being is the cause to be, what is generated, to those which are generated, what has been, to those which
1 Not from the necessity of matter ; because though there are wood, stones, and cement, yet there is no necessity on that account that there should be a house.
2 " As health," which is either from the medicinal art, or from chance, e. g. when Pheraeus Jason was healed by a dart thrown by an enemy, as Cicero relates in book hi., de Naturft Deorum ; "and safety," which so happens to a ship when it is preserved, either on account of the art and skill of the pilot, or fortuitously. Taylor. Upon necessity, chance, and the principles generally alluded to at the close of this chapter, cf. Phy- sics, book ii. ; Metaph. books iv. v; Rhet. i. 6 (Bohn's ed., where see note) ; also i. 10, and Ethics i. 9. See also Montaigne's Essays, pp. 50 and 105, Hazlitt's ed.
336 Aristotle's organon. [book ii.
have been, and what will be to those that will be. Thus why was there an eclipse ? because the earth was interposed, but an eclipse is generated, because an interposition of the earth is generated, but there will be, because the earth will be, and there is, because it is interposed. What is ice ? Let it be as- sumed to be congealed water ; let water be C, congealed A, the middle cause B, a perfect defect of heat ; B then is pre- sent with C, but with this A, viz. to be congealed,* but ice is generated, when B is generated, it was so, when the latter was so, and it will be, when the latter will be.
2. Causes and Hence that which is thus a cause, and that of simultaneous17 which it is the cause, are generated at one and —an inquiry the same time, when they are generated ; are si- thin grot's?- multaneously when they are ; and in like man- muitaneous. ner? jn respect to the having been, and the will be, generated. In the case of things which are not simul- taneous, are there in a continued time, as it seems to us, dif- ferent causes of different things ? for instance, is another thing having been generated the cause of this thing having been generated, and another thing which will be, the cause that this will be, and of this being, something which was generated before ? the syllogism however is from what was eluded the afterwards generated.! And the principle of these foundation was are those things which have been generated,
laid from the , _ b . , ° . . '
house being wherefore the case is the same as to things 3UTheposte- which are generated. From the prior indeed rior not col- there is no (syllogism), as that this thing was
lected from the P, -, \ •/ o /
prior. atterwards generated, because that thing was
I That because generated, I it is the same also in regard to the
was laid the future. For whether the time be indefinite or
house was definite, § it will not result that because that thing
§ That is, the was truly said to have been generated, this which
tweeruie6 is posterior is truly said to have been generated.
B A
Ex. 1. That, the heat of which fails, is congealed B C
The heat fails of water C A
. . Water is congealed.
CHAP. XII.] THE POSTERIOR ANALYTICS.
337
since in the interval it will be false to say this,1 former and the when already another thing* has been produced. |^ner eenera- The same reasoning also happens to what will be, * The founda- nor because that f was produced, will this | be, as t'°The founda- the middle must be generated at the same time;2 V°.{?nehouse of things that have been that which has been, 4. Medium of the future the future, of what are produced [anfou^with11' that which is produced, of things which are those of which that which is, but of what was generated, and of dium. that which will be, the middle cannot possibly be produced at one and the same time. Moreover neither can the interval § be indefinite, nor definite,3 since it will § Between the be false to assert it in the interval ; 4 but we must past and fu- consider what is connected with it, so that after the having been generated, to be generated may exist in things.5 Or is it evident that what is generated is not connected with what was generated ? for the past does not cohere with what was generated, since they are terms and individuals. As then neither points are mutually connected, those things which have been produced are not so, for both are indivisible ; nor for the same reason does that which is, cohere with that which has been generated, for that which is generated is divisible, but that which has been is indivisible. As a line then is to a point, so is that which is to that which was generated, for infinite things which have been, are inherent in that which is ;|| we must however enunciate these poinVin aline, matters more clearly in the universal discussions about motion. %
Concerning then the manner in which, when there is a successive generation, the middle cause of past and fu-
, . , ,i , <• . ,1 i tures, some
subsists, let so much be assumed, tor in these also principle or it is necessary that the middle and the first should {j**.*™1184 be be immediate, thus A was generated because C was so, but C was after, A before. The principle indeed is
11 Vide Physics, b. vi.
5. In the cases
Vide Waitz on this
1 As that the house was produced.
2 Supply — with that of which it is the medium, chap., vol. ii. p. 411 ; and CI'. An. Prior ii. 5.
3 Supply- -in which we may justly infer, that one will be, because another is.
* Since the future does not exist in that time.
4 So that there may be a continual successive \ reduction.
338 Aristotle's organon. [book ii.
C, because it is nearer to the now, which is the principle of time, but C was generated if D was, hence from D having been, it is necessary that A should have been. The cause how- ever is C, for from D having been, it is necessary that C should have been generated, but C having been, A must of necessity have been produced before. When however we thus assume the middle, will (the process) at any time stop at the immediate, or on account of the infinity will a medium always intervene ? for, as we have stated, what has been ge- nerated is not connected with what has been ; nevertheless we must commence at least from the immediate * and Mediate, Tay- from the first now.1 Likewise with regard to the
BekkeUrhle' ^ " wil1 be'" f°r if [t is trUe t0 Sa7 that D wiU be>
it is necessary that, prior to this, it should be true to say that A will be, the cause however of this is C, for if D will be, prior to it C will be, but if C will be, prior to it A will be. Likewise also in these the division is infinite, for things which will be, are not mutually coherent, but an im- mediate principle must also be assumed in these. It is thus in the case of works, if a house has been built, stones must necessarily have been cut, and formed ; and why this ? because the foundation must of necessity have been laid, if the house was built, but if the foundation was laid, stones must neces- sarily have been prepared before. Again, if there shall be a house, in like manner there will be stones prior to this, still the demonstration is in like manner through a medium, for the foundation will have a prior subsistence. 6. Things ge- Notwithstanding, since we see in things which neratedinacir- are, that there is a certain generation in a circle,!
clp must hjivf ^^
a similar de- this happens when the middle and the extremes fol- monstratum. ]ow each other, for in these there is a reciprocation ; ally. this however was shown in the first treatise,! viz.
ch. 5— 7" also that the conclusions are converted ; § but the case Post. An. b. i. 0f being in a circle is thus. In works it appears § changed into after this manner, when the earth has been moist- prem. ened, vapour is necessarily produced, from the
production of this, there is a cloud, from this last, water, and from the presence of this, the earth is necessarily moistened, this however was the (cause) at first, so that it has come round
1 Compare Waitz upon this place.
CHAP. XIII.] THE POSTERIOR ANALYTICS. 339
in a circle, for any one of these existing, another is, :.nd if that is, another, and from this, the first.
There are some things which are generated i. of things universally, (for always, and in every thing, they S^iy,0* either thus subsist, or are generated,) but others butusuaiiy.the
, » i ,, principles
not always, but for the most part ; thus not every snouid be non- vigorous man has a beard, but this is generally f07tjfea£'osbtut the case, now of such things it is necessary that part true. cf. the medium also should be for the most part ; for Wallls> IU- 2S> if A is universally predicated of B, and this of C universally, it is necessary that A also should be predicated always, and of every C, (for the universal is that which is present with every individual and always,) but it was supposed to be for the most part, wherefore it is necessary that the medium also, B, should be for the most part : hence of those which are for the most part, the principles are immediate, as many as thus subsist for the most part, or are generated.
Chap. XIII. — Upon the Method of investigating Definition.
We have before shown how what a thing is, is attributed to definitions, and in what way there is or is not a demonstra- tion or definition of it, how therefore it is necessary to inves- tigate1 things which are predicated in respect to what a thing is, let us now discuss.
Of those then, which are always present with i. Division of each individual, some have a wider extension, yet ^tension"3'1 are not beyond the genus.* I mean those have a * of the sub- wider extension, as many as are present with Ject' each individual universally, yet also with another thing, thus there is something which is present with every triad, and also with that which is not a triad, as being is present with a triad, but also to that which is not number. Nevertheless the odd is present with every triad, and is of wider extension, for it is with five, but it is not beyond the genus, f for the five is number, and nothing out of num-
i i -».t ii- , j. i e 2. For the at
ber is odd. Now such things we must take so tar tainraentofde-
1 He uses the term Stiqivuv. see also Mansel's note (Appendix B.) in reference to the expressions KaTaaicivaZuv and Z,r\Ttiv as applied se- parately to the two methods of "hunting lor" *ud " testing" the defini- tion, viz. Division and Induction.
z 2
340 ARISTOTLE S ORGANON. [BOOK II.
fnition those to until so many are first assumed, each of which* of whieh'is of is of wider extension,! but all of them together s1onethaXnebut are not °^ greater extent, for it is necessary that an together this should be the substance of a thing.1 For ex- thing to'be 6de- ample, number, the odd is present with every triad, fined the first in both ways, both as not being: mea-
* Taken separ- , , , \ ' . . ° , „
ateiy. sured by number and as not being composed of
t^hingTobe6 numbers.2 Now therefore the triad is this, viz. defined. the first odd number, and the first in this way, for
each of these is present, the one with all odd numbers, but the last also with the dual, yet all of them (together) with none (but the triad). Since however we have ch^f b°°k' shown above,:}: that those things which are predi- cated in respect of what a thing is are necessary, but universals are necessary, but what are thus assumed of a triangle, or any other thing, are assumed in respect to what a thing is, thus from necessity the triad will be these things. That this however is its essence appears from this, since it is neces- sary, unless the very nature of a triad were not this, that this should be a certain genus, either denominated or anonymous. It will be therefore of wider extension than to be with a triad alone, for let the genus be supposed of that kind as to be more widely extended according to power, if then it is present with nothing else than individual triads, this will be the essence of the triad. Let this also be supposed, that an ultimate predi- cation like this of individuals is the essence of each thing, wherefore in like manner, when any thing is thus demon- strated, it will be the essence of that thing, s. Method of Nevertheless it is right when any one is con-
dividing the versant with a certain whole,3 to divide the genus i which can- into the individuals which are first in species, §
1 As some discrepancy has been supposed to exist between this pas- sage and Metap. vi. 12, it may be well to observe that, although in the latter passage he seems to maintain that the last differentia must be co- extensive with the subject, he is there apparently speaking not of the specific difference per se, but of the difference regarded as dividing the genus : this is in fact equivalent to saying, that the whole must be co- extensive, which no one would think of denying. Vide Mansel's Ap- pendix, note B. ; Boethius, Hill, and Whately upon logical definition and decision ; also Waitz's remarks.
2 Because the triad is the first number, the monad being the principle of number, and the dual, a medium between 1 and 3.
3 In investigating the definition of a subaltern species.
CHAP. Xni."| THE POSTERIOR ANALYTICS. 34 1
for instance, number into triad and dual, then to not be divided endeavour thus to assume the definitions of these, mt0 sPecles- as of a straight line, of a circle,1 and of a right angle ; after- wards assuming what the genus is,2 for instance, whether it is quantity or quality, he should investigate the peculiar pas- sions* through common first (principles.)3 For *of the first those which happen to the composites from indi- species, viduals will be evident from the definitions,! be- t of the first cause definition and that which is simple4 are sPecies- the principles of all things, and accidents are essentially pre- sent with simple things alone, but with others according to them. The divisions indeed by differences5 are 4 Differential useful for our progression in this way, but how division useful indeed they demonstrate we have shown before,^ gation of den-' but they would thus be useful only for syllo- "u!on- .
1 .1 • • T • 1 1 V I An' Prl0r '■
gizing what a thing is, and indeed they may ap- ch.3i,and tiiia pear to do nothing, but to assume every thing ^ ' 5" immediately,§ just as if any one assumed from H-e. without the beginning without division. It makes some difference, however, whether what is predicated be so, prior or posterior,6 as for instance, whether we call animal, mild biped, or biped, animal mild, for if every thing consists of two,|| and one certain thing is animal mild, a;ffeerenceand and again from this, and the difference, man or any thing else which is one, consists, we must necessarily make a postulate by division. Besides, thus only is it possible to leave out nothing in the definition, since when the first genus is assumed, if a person takes a certain inferior division,7 every thing will not fall into this ; for instance, not every animal has entire or divided wings, but every animal which is winged, for this is the difference of it,1f but the 'i-e. thedivi- first difference of animal is that into which every Taylor.
1 A circle is first amongst figures, because it is circumscribed by one line, other figures by many lines.
2 In what category the thing defined is contained.
3 Principles common to the first .and remaining lowest species, for the principles of the subaltern are those of the infinia species.
* The defin. of the first simple species. & Specific differences.
• Therefore division is useful for the arrangement of things properly in regard to priority, etc. Cf. Waitz.
7 In winch there is not the peculiarity of genus, but of some lowet species.
342
ARISTOTLE S ORGANON.
[lJOOK II.
animal falls. Likewise in regard to each of the rest, both of * The first di- those genera * which are external to animal, and
vision is to be assumed, t The first di- vision of bird.
I In the defini tion.
5. It is not re- quisite that he who defines should know all other sub- jects from which he dis- tinguishes the tiling defined.
of those which are contained under it, as of bird,f is that into which every bird falls, and of fish that into which every fish falls. Thus proceeding we may know that nothing is omitted, J but other- wise we must omit something, and not know it. It is not at all necessary that he who defines and divides, should know all things that subsist,1 though some say it is impossible to know the dif- ferences of each thing without knowing each ; but it is impossible to know each thing without differences, for that from which this does not dif- fer, is the same with this, but that from which it differs is something else than this. In the first place then this is false, for it is not something else according to every difference, since, there are many differences in things which are the same in species, yet not according to substance, nor per se. Next, when any one fi. a division assumes opposites, and difference, and that every thing falls into this or that, and assumes also that the question is in one part of the two, and knows this, it is of no consequence whether he knows or does not those other things of which the dif- ferences § are predicated. For it is evident that thus proceeding, j| if he should arrive at those of which there is no longer a difference, he will ob- tain the definition of the substance ; but that every thing will fall into division, if there should be opposites of which there is no medium, is not a postulate,^ since every thing must necessarily be in one of them, if in- deed it will be the difference of it.
In order to frame definition by divisions, we must attend to three things, viz. to assume the things predicated in respect of what a thing is ; to arrange these, which shall be first or se- cond ; and that these are all. Now the first of
into opposite members, as of animal into rational and irrational.
§ Rational, etc.
II From genus to species by differences.
5 Not a petitio principii.
7. Three things to be attended to, in division- al definition — how to effect these. Vide Whately, Kill, and Aldrich.
1 We find from the scholia that Aristotle here glances at Speusippus : he proceeds to show that it does not signify tc the proper knowledge of the thing defined, whether a person knows, or does not know, other things in- cluded in either species ; since if he carries on division he will arrive at those which have no difference, and will then have attained the desired definition.
CHAP. Xni.f TIIE POSTERIOR ANALYTICS. 343
these arises from our being able as syllogistically ' y. . to collect accident, that it is inherent,* so to con- took a. ' ' struct through genus.f There will however be a t Topics, book proper arrangement if what is first be assumed, 1V' and this will be if that be taken which is consequent to all, but all not consequent to it ; for there must be something of this kind. This then being taken, there must now be the same method in the things inferior, since the second will be that which is first of the rest, and the third that which is first of the following, for what is superior being taken away, what- ever succeeds will be the first of the others ; there is also similar reasoning in the other cases. Still that all these should be, is clear from assuming what is first in the division, that every animal is either this or that,| but this is * e ratj0nai inherent ; § and again the difference of this whole ' or irrational, but that of the last 2 there is no longer any differ- e" g" ra lona ' ence, or immediately with the last difference 3 this || n Being as- does not differ in species from the whole:4 for it sumed- is clear that neither more (than is necessary) is added, for every thing has been assumed in reference to what a 8 The gum. thing is, nor is any thing deficient, for it would mum genus be either genus or difference. Both the first then definition. is genus, and this assumed together with differ- J Essential.
0 * o * Aninia.1 ra-
ences, but all the differences are contained, for tionai, mortal, there is no longer any posterior difference.^" +laE*s'entiaiiy Otherwise the last* would differ in species, this from the whole
, , , , vfl. 1 animal, ration-
however has been shown not to dmer.j ai, mortai.
Still we must investigate, looking to those which Metnod t0 are similar and do not differ, first (considering) what be applied in that is which is the same in all these, then again veral^pedeT in other things which are in the same genus with with some-
, , , . , .-, , ,-, thingcommon.
them, and which are among themselves the same
in species, but different from those. Yet when in these that is
1 Subdivision of rational animal into mortal, immortal, etc.
2 As of mortal rational animal.
3 This may be some accidental difference, e. g. " black," united to the last, as animal rational mortal black.
* That is, from animal rational mortal, but as it does not differ from it essentially, the last accidental difference (black) ought not to be admit- ted. He uses the term to trvvoXov, when the definition is composed of the genua and its differences. Of. Wait/., Boethius, and Keckermann'8 Lyst. Log. Mm. lib. i. cap. 17. Wallis, Log.
344 Aristotle's organon. [book ii.
assumed which all have the same, and in others similarly, we must consider in the things assumed whether it is the same, until we arrive at one reason, for this will be the definition of the thing. Yet if we do not arrive at one, but at two or more, it is evident that the question will not be one, but * ue-raXoiWa. many> f°r instance, I mean if we should inquire cf. Eth. Nic. what magnanimity * is, we must consider in the
iv. 3 and 4, and n . • • i
shaks. corioia- cases ot certain magnanimous persons, whom we nus, passim. know what one thing they all possess, so far as they are such. Thus if Alcibiades is magnanimous, or Achilles, or Ajax, what one thing have they all? intolerance
t Alcibiades °^ msultj f°r one °f them fought,1 f another sulked,2 another slew himself.:): Again, in other instances, as in that of Lysander or Socrates. If then (it is common to these) to behave in the same manner, in prosperity and adversity, taking these two, I consider what indifference with regard to fortune, and what impatience under insult possess in common ; if they have nothing there will be two species of magnanimity.
Every definition is nevertheless universal, for daily universal the physician does not prescribe what is whole- to°be defined some f°r a certain eye, but defines what is fit for every eye, or for the species. The singular however is easier to define than the universal, wherefore we must pass from singulars to universals, for equivocations lie more con- cealed in universals, than in things without a difference. But as in demonstrations the power of syllogizing must necessarily « videi • i ^e inherent, so also perspicuity must be in de- ruies for defini- finitions,§ and there will be this, if through things tion m Aidncn. wj1jc}1 are singularly enunciated, what is in each genus be separately defined ; as with the similar, not every similar, but that which is in colours and in figures, and the
1 Alcibiades, to revenge the preference given by his countrymen to Lysias, revolted to Lacedeemon, and brought war on his country.
2 Achilles, for Briseis. The reader may smile at the graphic term used here for s/xijvio-tv, as descriptive of the "angry boy" in the Iliad, but will confess that its use is warranted, both verbally, by Johnson, and circumstantially, by Shakspeare (Troilus and Cressida). Upon the freaks and follies of Ajax, see the speech of Thersites in the same play, act iii. scene 3, and Sophocles (Ajax) passim. Zell observes that mag- nanimity was a conspicuous element in Aristotle's own character: upon Christian magnanimity, see St. Paul's Epistles.
CHAP. XIV.l THE POSTERIOR ANALYTICS. 345
sharp that which is in voice, and so to proceed to what is common, taking care that equivocation does not « Because of occur. But if it is not right to use metaphors in l^f^edefi- disputation, we must clearly not define by meta- nition is some- phors,* nor by those things which are spoken by JftJ l™^0/.' metaphor, otherwise it will be necessary to use sion. (cf
r. . ,. , Waitz, vol. il.
metaphors in disputation, j P. 420 )
Chap. XIV.— Rules for Problems* t Cf. An. Prior
J T 1. 4, and 1. 2G ;
also Topics i. 4,
Now that we may have problems, we must select and i. 11. sections and divisions, and thus select, the com- \ Needofdiyi-
_ ,. . ' , c , sion for rightly
mon genus of all being supposed, as lor example, appropriating if animals were the subjects of consideration, (we ^h'sdeVce. must first consider,) what kind of things are pre- sent with every animal.1 When these have been taken, we must again see what kind of things are consequent to every first individual of the rest,2 thus if this is a bird, what things follow every bird, and so always that which is nearest,3 for we shall evidently now be able to say why things are present, which are consequent to those under what is common, as why they are present with man or horse.4 Let then animal be A, B things consequent to every animal, C D E certain animals, why then B is present with D is evident, for it is present through A : in a similar manner with the rest, and
„*=,., , • c § Example (1.)
in others there is always the same reasoning. §
1 For the word problem and its uses, see Alexander Scholia, p. 150, b. 40. What he means here, is that we ascertain the questions or pro- blems to be discussed in every system, by the use of proper divisions and sections, (which Aristotle assumes l'or the same thing,) and by proceed- ing from universals to singulars. Vide Biese i. p. 314.
2 Of the first species.
3 To the first species, which is next to the proposed genus. Taylor.
4 i. e. the properties of animal.
A B
Ex. 1. Every animal is sentient D A
Every horse is an animal D B
. • . Every horse is sentient. The proof may be applied in the same manner to every species f animal.
346
Aristotle's organon.
[book II.
Now then we speak according to presented common names,1* but we must not only consider in these, but also assume if any thing else should be seen to be common, afterwards consider to what things this is consequent, and the quality of the things consequent to this,2 as those consequent to having horns are the possession of a rough muscular lining to the stomach, and the not having teeth in both jaws. Moreover to what things the possession of horns is consequent, for it will be evident why what has been mentioned f is present with them, J for it will be so in consequence of their possessing horns.
There is yet another mode of selection by anal- ogy^ since it is impossible to assume one and the same thing, which it is necessary to call sepium, spine, and bone, there are also things consequent to these, as if there were one certain nature of this kind.3
* Synonyms. 2. Also of in- vestigating that which is inherent in the singulars as something common.
t Viz. to have teeth in one jaw only, etc. J With the spe- cies of horned animals.
3. Selection jcaTu to ava~ \oyov. § i. e. to as- sume a com- mon analogous thing.
Chap. XV. — Of Identical Problems.
l. Problems are Some problems are the same from having the same haTeeithM'tne medium, f°r instance, because all things are an same middle antiperistasis,4 but of these some are the same in
1 Cf. Top. i. 5; Categ. ch. 1. Synonyms are not allowed to be real definitions, in the proper sense, by Aristotle, though admitted to be optica ; as nominal definitions, they are recognised by Alexander on Metaph. vi. 4, p. 442, Bonitz ed., but the genuineness of this portion of the commentary has been questioned. Vide Mansel's Logic on Definition.
2 We must not only use this method in things synonymous, and in- vestigate the common generic properties, and afterwards the specific pecu- liarities, but if there be any thing common without a name, yet we must assume it, in order to investigate its properties, and afterwards to con- sider to what species it is attributed, and the quality of the things which are consequent to the anonymous genus.
3 The instances given are analogous, because there is the same relation of the sepium in a particular kind of fish ; of the spine in fish gener- ally, and of bone in quadrupeds. He means that from a certain analogy, which is expressive of some common nature in things, we may ascertain what is common to various individuals. Cf. Scholia, p. 42, a. 37, 47.
4 Quod omnia fiant quia contraria qualitas cerminus instat. Buhle. Compressio undique circumfusa. Scap. Theoph. de Caus. pi. 1, 2. The
CHAP. XVI. 1 THE POSTERIOR ANALYTICS. 347
genus, which have differences from belonging to term, ore/ other things, or from subsisting differently, e. g. *s subjected"^ why is there an echo, or why is there a reflection, the oper- and why a rainbow ? for all these are the same problem in genus, (for all are reflection,) but they differ in species.1 Other problems differ from the medium being contained under another medium, as why does the Nile have a greater flow during the fall of the month ? 2 because the fall of the month is more winterly : but why is the fall more winterly ? because the moon fails, for thus do these subsist towards each other.
Chap. XVI.— Of Causes and Effects.
Some one may perhaps doubt concerning cause difficuUy— the* and that of which it is the cause, whether when middle tenn the effect is inherent, the cause also is inherent, ^pres/the^ as if the leaves fall from a tree, or there is an cause of the in- eclipse, will there also be the cause of the eclipse, Aidrich's Lor., or of the fall of the leaves ? As if the cause of Jj^^Sg this, is the having broad leaves, but of an eclipse Log.) the interposition of the earth, for if this be not so, something else will be the cause of these, and if the cause is present, at the same time the effect will be, thus if the earth be interposed, there is an eclipse, or if a tree have broad leaves, it sheds them. But if this be so, they would be simultaneous, and de- monstrated through each other, for let the leaves to fall be A, the having broad leaves B, and a vine C, if then A is present with B, (for whatever has broad leaves sheds them,) but B is present with C, for every vine has broad leaves, A is present with C, and every vine sheds its leaves, but the cause is B,
word signifies the effect produced from a thing being surrounded by its contrary. Thus why is hail produced ? Because the cold is contracted by the surrounding heat. Why are subterranean places cold in summer and hot in winter ? Because in winter the heat is contracted on account of the surrounding cold, and in summer the cold, on account of the sur- rounding heat. Taylor. Cf. Physic, b. iv. v. vi. ; also Lucretius.
1 Reflection of the air produces the echo ; of the figure in the mirror produces the image ; of the sun's rays produces the rainbow.
* During the fall of the month there is more rain ; hence the Nile rises, and there is more rain during the decrease of the moon, because -when her light fails, she more powerfully excites humid bodies. Taylor. Ci. also Herod, lib. ii. c. 19 — 25.
348 Aristotle's org axon. [book it.
• ei m ^ie middle.* We may also show that the vine has broad leaves, from its shedding them, for if D be what has broad leaves, E to shed the leaf, F a vine, E then is present with F, (for every vine sheds its leaf,) but D with E, (for every thing which sheds its leaf, has broad leaves,) every vine then has broad leaves, the cause is, its . shedding them, j* Nevertheless if they cannot be the cause of each other, (since cause is prior to that of which it is the cause,) the cause of an eclipse indeed is the interposition of the earth, but an eclipse is not the cause of the earth interposing. If then the demonstration by cause (shows) why a thing is, but that which is not through cause, that it is, one knows1 indeed that the earth is inter- posed, but why it is, he does not know.2 Yet that an eclipse is not the cause of the interposition, but this of an eclipse, is plain, since in the definition of an eclipse, the in- terposition of the earth is inherent, so that evidently that is known through this,3 but not this through that.4
2 There is ^*r may tnere be many causes of one thing ?
only one cause for if the same tiling may be predicated of many slmeethi"ids>the primary, let A be present with B a first, and from which it with C another first, and these with D E, A then will be present with D E, but the cause why it is with D will be B, and C the cause why it is with E, hence from the existence of the cause there is necessarily the ex-
B A
Ex. 1. Whatever consists of broad leaves sheds its leaves C B
Every vine consists of broad leaves C A
. ' . Every vine sheds its leaves.
E D
Ex. 2. Whatever sheds its leaves has broad leaves F E
Every vine sheds its leaves F D
. • . Every vine has broad leaves.
1 i. e. he who through an eclipse proves the interposition of the earth.
2 That is, one kind of knowledge (that of the on) is empirical, but the other (that of the Siori) is scientific. Cf. Ethic. Nic. b. i. c. 5.
* The eclipse is proved through the interposition of the earth.
* Cause is not truly proved through effect, because the true demonstra- tion is of the " why," but. demonstration from effect is of the " that."
CHAP. XVII.] THE POSTERIOR ANALYTICS. 349
istence of the thing, but when the thing exists, it is not ne- cessary that every cause should exist, still some cause indeed, yet not every cause. Or if the problem is always universal, is the cause also a certain whole, and that of which it is the cause universal ? ' as to shed the leaf is present definitely with a certain whole,* though there should be species
°. ii- » i_ • i_ ^r genus.
of it,2 and with these universally, 1. e. either with plants or with such plants.f Hence in these, the t e_ g plants medium and that of which it is the cause must with broad be equal, and reciprocate,3 for instance, why do the trees shed their leaves? if indeed through the concre- tion of moisture, whether the tree casts its leaf, there must of necessity be concretion, or whether there is concretion not in any thing indiscriminately, but in a tree, the latter must necessarily shed its leaf.
Chap. XVII. —Extension of the same subject.
Whether however may there not be possibly the i. If the same
same cause of the same thing4 in all things,5 but ^ESSf™*
a different one, or is this impossible? or shall we except there is
say it cannot happen, if it is demonstrated per se deinMiftratfon,
and not by a sign or accident?6 for the middle is it must be
the definition of the extreme,7 but if it is not thus, thesame cause.
(shall we say that) it is possible?8 We may g^gg^.
however consider that of which9 and to which10 cai, the middle
1 " Universal " is here used in the same sense as in ch. iv. of the pre- ceding book, when a property is predicated of every subject and prima- rily, so as to reciprocate with it. Cf. Waitz, vol. ii. 424.
2 The property may be in the several species as in the genus, but its presence in the latter does not prevent its predication of the former.
3 Reciprocals are called equals because they are identical in quantity.
4 Property — which in the demonstration is the major extreme.
s In subjects which are the minor extremes— by cause understand, the middle term. • Cf. Anal. Pr. ch. xxvii. and Waitz, p. 425, vol. ii.
7 Of the major, see below.
8 That if it is not demonstrated per se, but from accident, there may be many causes.
8 The property.
10 The subject, it is possible to consider these from accident, just as if a grammarian was proved visible, because man is visible. Taylor.
350 Aristotle's okganon. [book ii.
term wm be jt [s t]ie cause foy accident, still they do not ap- Post. i. 13. pear to be problems,1 but if not, the medium will subsist similarly,2 if indeed they are equivocal, the medium will be equivocal, if however as in genus3 the medium will be similar. For instance, why is there alternate proportion ? for there is a different cause in lines, and in numbers, and
the same (medium) so far as they are lines, is differ- samemedium ent,* but so far as it has an increase of the same quoad num- kind,f it is the same, the like also occurs in all t Muitipiica- things. There is indeed a different cause in a ciid'bookv.Eu* different subject, why colour is similar to colour,
and figure to figure, for the similar in these is . T . equivocal, for heret perhaps it is to have the
I In figures. .* ' + i f
sides analogous, and the angles equal, but in co- lours it consists in there being one sense (of their perception) or something else of the kind. Things however analogically the same, will have also the same medium by analogy, and this . i e the mid- ^s so fr°m cause, § and that of which, || and to die. which % it is the cause following each other ; but
extreme.aJ°r by assuming each singly,* that of which it is the it The minor cause is more widely extended, as for the exter-
extreme*
* The several nal angles to be equal to four, is of wider exten- nimorS °f the S10n t'ian triangle or square, but equal f in all, for t with the ge- whatever have external angles equal to four right, "eTheyUrecT- will also have the medium similarly. J The me- procate. dium however is the definition of the first ex-
treme,4 wherefore all sciences are produced by definition, thus § Magis com- t° shed the leaf, is at the same time consequent to mune est. the vine, and exceeds, §5 and to the fig tree, and exceeds, yet does not exceed all (plants), but is
1 Because problems ought to be ''per se," not from accident.
2 To the extremes. 3 They are synonymous.
4 Vide Mansel, Appendices B. and H., and cf. upon the method of in- terpretation to be used here, Anal. Post. i. 4, and i. 5. Aristotle intends by the middle being the definition of the major extreme, that it is so of the property which is demonstrated. For instance, why does it thunder ? or why is there a noise in a cloud ? because fire is extinguished. What is thunder? An extinction of fire in a cloud : here the medium is the definition of the major extreme, thunder, and not of the less, that is, of a cloud.
5 Vide Waitz, vol. ii. p. 426-7, and the Port Royal Logic, p. i. ch. vi., also Mansel, App. A.
C:iAP. XVII.] THE POSTERIOR ANALYTICS. 3.51
equal to them. If then you take the first middle1 2. The major it is the definition of shedding the leaf, for the (S°tj**£ first will be the middle of one of them, because nor in extent, all are such,2 next the middle of this* is, that sap oughT to ex- is congealed, or something else of the sort, but c?^d l,he indi"
o ' ° viduals com-
what is it to shed the leaf ? it is for the sap to be prehended. congealed, at the junction of the seed. of ^pianfhav-
In figures, to those who investigate the conse- inR broa(i
^ leaves
quence of the cause, and of what it is the cause, we may explain the matter thus : let A be present with every B, and B with every D, but more extensively, B then will be universal to D, I call that universal which _
, . . , , , ., . . t Cum latius
does not reciprocate, y but that the first universal, sit. Buhie.
with which each singular does not reciprocate, fs' p/edlcated'of
but all together reciprocate, and are of similar ex- things differing
tension. B then is the cause why A is present canb^demon-
with D, wherefore it is necessary that A should seated by di-
verse roiclul&
be more widely extended than B, for if not, why terms. will this J be rather the cause than that?§ If jB then A is present with all those of E, all those § a. will be some one thing different from B,|| for if not, how will it be possible to say that A is present with every thing with which E is, but E not with every thing with which A is ? for why will there not be a certain cause as there is why A is present with all D ? wherefore will all those of E be one thing ? We must consider this, and let
1 The first universal subject in which the property is inherent — e. g. a plant with broad leaves, in which the falling oft' of leaves is present.
2 i. e. The universal subject will be the cause of the leaves falling, as to the vine, fig tree, &c. because all vines and fig trees are plants with broad leaves. Vide Biese i. p. 317.
B A
Ex. 1. Whatever is without bile is long-lived D B
Every quadruped is without bile D A
' . Every quadruped is long-lived.
C A
Every animal of a dry complexion is long-lived
E C
Every bird is an animal of a dry complexion E A
. • . Evert bird is long-lived.
352
ARISTOTLE S ORGANON.
[book IT.
» As B and C.
t Of the same property as of A.
I D and E dif- fer in species.
§ i. e. an inde- monstrable proposition. || Example (1.) IT Each under the other.
there be C, hence there may be many causes* of the same thing, f but not to the same in spe- cies,! for instance, the cause why quadrupeds are long-lived, is their not having bile, but why birds live long, their being of a dry complexion, or something else : if however they do not arrive immediately at an individual, § and there is not one medium only, but many, || the causes also are many.^f
Chap. XVIII. — Observation upon Cause to Singulars.
» As to D. 1. The middle term ought to be the nearest to the singular to which it is cause, t As B. I A. S In D.
|| Example (1.)
Which of the media is the cause to singulars,* whether that which belongs to the first universal, or that to the singular ? Evidently the nearest to the singular to which it is cause.1 For this is the cause why the first, j" under the universal,^ is inherent,^ C is the cause that B is inherent in D, hence C is the cause why A is inherent in D, but B is the cause why it is in C, yet to this it- self is the cause.2 II
Chap. XIX. — Upon the Method and Habit necessary to the ascer- tainment of Principles.
Concerning syllogism then and demonstration, what either of them is, and how it is produced, is clear, and at the same f Taylor and time a°out demonstrative science, for it is the Buhie ar.-nex same : % 3 but about principles, how they become
1 The medium is to be assumed, proximate to the subject rather than to the property. Habet et Aid™ suos gradus, quia potest esse causa proxima quae non est prima h. e. per se nota et indemonstrabilis : cujus idco praefertur, evidentia, quia (contra quam cetera) sua luce est conspi- cua, et nihil indiget aliena. Quare, quae hanc adhibet causam demon- strate, et habetur et nominatur " potissima." Aldrich. Cf. also Whately and Hill.
2 As the puration of bile is the cause to itself of longevity. Taylor.
Ex. 1. Whatever is without bile is long-lived
Every quadruped is without bile
. • . Every quadruped is long-lived : but
Every horse is a quadruped . '. Every horse is long-lived. 8 The methods of explaining demonstration and demonstrative science
CHAP. XIX.] THE POSTERIOR ANALYTICS.
353
known, and what is the habit which recognises them, is manifest hence to those who have pre- viously doubted it.
That it is then impossible to have scientific Knowledge through demonstration, without a knowledge of first immediate principles, has been elucidated before,1 still some one may doubt the knowledge of immediate principles, both whether it is the same or not the same,* also whether there is a science of each or not,f or a science of one, but a different kind (of science) of another, and whether non-inherent habits are ingenerated,| or when inherent are latent.2 If then, indeed, we possess them,§ it is absurd, for it happens that it (the principle) escapes those who have a more accurate knowledge than demonstration,3 but if not having them before, we acquire them, how can we know and learn without pre-existent knowledge ? for this is impossible, as we said also in the case of demonstration. It is evident then, that they || can neither be possessed, nor ingenerated in the ignorant, and in those who
are identical therefore sometimes, as in this chapter, demonstration is assumed for demonstrative science.
1 Vide book i. eh. 2. We have already noticed the two senses in which (ifitffog is used by Aristotle ; here it is applied to a proposition not proved by any higher middle term ; i. e. an axiomatic principle, which con- stitutes the first premise of a demonstration: cf. An. Post. i. 2. In An. Post. i. 13, it is applied to a premise immediate as to its conclusion. Vide Mansel ; Aldrich, p. 104, note.
2 As in infants. Aristotle considered the mind as a piece of blank paper, on which nothing was written but natural inclination (ro irtQvKoc). One difference between disposition (Siadtcng) and habit (eK'Q), drawn in the Categories and de Anima, (vide marginal references,) consists in considering habit more lasting than disposition, the former applying to the virtues, etc., the latter to heat, cold, health, etc., which last undergo more rapid mutation. The relation between Svvafiig, ivepytia, and t'Eic, given by Aspasius, as quoted by Michelet, is as follows : Facultas a natura insita jam est potentia qua;dam, sed nondum nobis ut loquimur potentia, cujus ex ipso vigore operatio profluat ; banc demum potentiam philoso- phus habitum vocat.
3 That is, the thing which is known, or the possession of the principle itself, is concealed from children, who having (suppose) a knowledge of axioms, possess thereby a knowledge more accurate than demonstration. Cf. Waitz.
2 A
this sentence to the preceding chapter. Bek ker and Waitz as here.
1. Of the ne- cessity and me- thod of obtain- ing principles of science — cer- tain questions relative to ha- bits solved. • With a knowledge of the conclusion, t i. e. of the principle and of the conclusion, t i. e. are ac- quired. Cf. Eth. Nic. lib. ii. ch. 1, 3, 5, and lib. iii. 5 ; also see Categ. ch. vi., and de Anima, ii. 1, and ii. 5. § i. e. by na- ture.
II The habit of principles.
354
Aristotle's organon.
[book n.
have no habit, wherefore it is necessary to possess a certain power, yet not such an one as shall be more excellent ac- cording to accuracy than these. Now this ap- pears inherent in all animals, for they have an innate power, which they call sensible percep- tion,* but sense being inherent in some animals, a permanency of the sensible object is engen- 5, et seq. ; iii. i . <Jered, but in others it is not engendered.! Those,
t As insects.
vide Tren- therefore, wherein the sensible object does not re- main, either altogether or about those things which do not remain, such have no knowledge with- out sensible perception, but others when they per- ceive, retain one certain thing in the soul.J Now since there are many of this kind, a certain differ- ence exists, so that with some, reason is produced from the permanency § of such things,]) but in others it is not.^f From sense, therefore, as we say, memory is produced, but from repeated re- membrance of the same thing, we get experience, for many remembrances in number constitute one experience. From experience, however, or from every universal being at rest in the soul,* that one besides the many, which in all of them is one and the same, the principle of art and science science'from arises, if indeed it is conversant with generation,! of art, but if with being, of science.1 Neither, therefore, are definite habits inherent, J nor are they produced from other habits more known, but from sensible perception, as when a flight occurs in battle, if one soldier makes a stand,
another stands, and then another, until the fight is restored.
2. Animals pos- sess sensible perception. * alff#i7<Tic. Cf. Eth. b. vi. ch. 2 and 11 ; de Anima, b. ii. 5
delen. de An p. 170, 174.
I So Taylor and Buhle ; but Waitz and Bekker read
£T1. Cf.
Brundisius. § Waitz and Bekker read
UOprKi but
Taylor and Buhle, ui/^utit H As in men. V As in brutes
• i. e. remain- ing.
T With things perishable. 3. In what way we arrive at a certain art
singulars sub- jected to the senses. X i. e. the habits by which princi- ples are known.
1 Cf. Trendelenb. c. i. p. 137 ; Aldrich, Hill, and Mansel upon In- duction and Method ; Zabarella upon the last ; and Whately upon the Province of Reasoning. The " methodus inventionis " can only be a process of inference, for no arrangement of parts is possible before they have been discovered, the discovery of general principles from individual objects of sense, if limited to the inferential process itself, will be induc- tion. The term, however, is sometimes extended so as to include the preliminary accumulation of individuals : in this under sense it will em- brace the successive steps given by Aristotle here, of ai(x8t]<TiG pvin$y, ifiTTEipia, iTraywyij. Mansel. Vide also Poetic, ch. xvi. ; De Anim. Proem. 167.
CHAP. XIX.] THE POSTERIOR ANALYTICS. 355
But the soul has such a state of being, as enables . So as to re- it to suffer this,* what, however, we have before tain many sue. said, but not clearly, let us again explain. When one thing without difference abides, there is (then) first, uni- versal in the soul,1 (for the singular indeed is perceived by sense, but sense is of the universal, as of man, t In these but not of the man Callias,) again, in these f it "^stssP£ stops, till individuals | and universals stop,§2 as Taylor!0" such a kind of animal, until animal,|| and in ^"^ 1"' this^T again (it stops) after a similar manner.* Buhie. ' It is manifest then that primary things become jj l^piy^*" necessarily known to us by induction, for thus permanent in sensible perception produces the universal. But u Animal, since, of those habits which are about intellect, *hmTg"|sse°™e~ by which we ascertain truth, some are always permanent in true, but others admit the false, as opinion, and '^iv°nUg>as reasoning,3 but science, and intellect, are alwaj's true, and no other kind of knowledge, except intellect, is more accurate than science, but the principles of demon- strations are more known, and all science is connected with reason, there could not be a science of principles : but since .nothing can be more true than science except intellect,
1 That is, the first universal notion, or that which remains of those several things which are perceived by tha senses, and which do not specifically differ. From first universal notions, another is formed, com- prehending those things which the severai singulars have in common, until summa genera are arrived at. The universal, of course, is equally and without difference found in many particulars.
* The universals are so called (a/iepri) because they are inherent in singulars, not partially, but wholly, every where totally present with their participants : thus the whole of animal is in one man.
1 Of the powers of the soul, some are irrational and disobedient t.i reason, as the nutritive, others are capable of being obedient to rea- son, as anger and desire. But other powers of the soul are rational ; and of the rational, some are always true, as intellect and science, others are sometimes true, as opinion and Xoyic/xoc, i. e. reasoning about practical and political affairs, and things generable and corruptible, which are in a perpetual flux, and are subject to infinite mutations. For in- tellect, properly so called, is that power or summit of the soul which energizes about things that possess an invariable sameness of subsistence. Taylor. Vide also Trendelenb.de An. iii. c. 4 — 6; Biese i. p. 327 ; Rassow, p. 73. And cf. Eth. Nic. b. i. c. 13, Bonn's ed., where see Browne's note ; Poetics, c. 16: Magna Moral, i. 31; and Eudem. Ti. et lib. v. c. 3, et seq.
S56 Aristotle's organon. [book 11.
intellect will belong to principles, and to those who consider from these it is evident also, that as demonstration is not the principle of demonstra- tion, so neither is science the principle of science. If then we have no other true genus (of habit) besides science, intellect will be the principle of • science : it will also be the principle (of the know- the principle, but all this subsists similarly with every thing.
4. Intelle:t alone conver- sant with, and itself the prin- ciple of science AiJ science through de- monstration knows the ob- jects of science
ledge) of respect to
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