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Full text of "Analysis of Mr. Mill's System of Logic"


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LONDON : ^1/ 









The author's aim has been to produce such a con- 
densation of the original work as may recall its con- 
tents to those who have read it, and may serve those 
who are now reading it in the place of a full body of 
marginal notes. Mr. Mill's conclusions on the true 
province and method of Logic have a high substan- 
tive value, independent even of the arguments and 
illustrations by which they are supported; and these 
conclusions may be adequately, and, it is believed, with 
much practical utility, embodied in an epitome. The 
processes of reasoning on which they depend, can, 
on the other hand, be represented in outline only. 
But it is hoped that the substance of every paragraph, 
necessary for the due comprehension of the several 


Bteps by which the results have been reached, will be 
here found at all events suggested. 

The author may be allowed to add, that Mr. Mill, 
before publication, expressed a favourable opinion of 
the manner in which the work had been executed. 
Without such commendation the volume would hardly 
have been offered to the public. 

London : Dec, 21, 1865. 



Introduction . . . , X 




I. On the Necessity of commencing with an Analysis of 

Language in Logic 3 

II. Names 3 

lU. The Things denoted by Names 7 

rV. Propositions 17 

V. The Import of Propositions 19 

VI. Propositions merely Verbal 24 

Vn. The Nature of Classification, and the Fiye Predicables 26 

Vin. Definition 30 



L Inference, or Eeasoning in General . . . .35 

n. Eatiocination, or Syllogism 86 

III. The Functions and Logical Value of the Syllogism . 39 

rV. Trains of Reasoning, and Deductive Sciences . . 43 

V. & VI. Demonstration and Necessary Truths . . .46 

• •• 





L Preliminaiy Observations on Induction in general . 63 
II. Inductions improperly so called . . . .54 

in. The ground of Induction 57 

IV. Laws of Nature 58 

V. The Law of TJniyersal Causation . . . .60 

VI. The Composition of Causes 66 

VII. Observation and Experiment 67 

VIII. & Note to IX. The Four Methods of Experimental 

Enquiry , . 69 

X. Plurality of Causes, and intermixture of Effects . 73 

XI. The Deductive Method 76 

Xn. & XIII. The Explanation and Examples of the Ex- 
planation of Laws of Nature . . . .77 
XIV. The Limits to the E^lanation <^ Laws of Nature ; 

and Hypotheses 79 

XV. Progressive Effects, and continued Action of 

Causes 81 

XVI. Empirical Laws .83 

XVn. Chance, and its Elimination 85 

XVni. The Calculation of Chances 87 

XIX. The Extension of Derivative Laws to Adjacent Cases . 89 

XX. Analogy 91 

XXI. The Evidence of the Law of Universal Causation . 92 
XXII. Uniformities of Coexistence not dependent on Causa- 
tion 94 

XXIII. Approximate Generalisations, and Probable Evidence 96 

XXIV. The remaining Lawi of Natuxe 99 

XXV. The grounds of Disbelief 103 



I. Observation and Description 107 

II. Abstraction, or the Formation of Conceptions . .108 



III. Naming as Subsidiary to Induction . . . .111 
IV.' The Eequisites of a Philosophical Language, and the 

Principles of Definition 112 

Y. The Natural History of the Variation in the Meaning 

of Terms 115 

VI. Terminology and Nomenclature . . . .117 

Vn. Classification, as Subsidiary to Induction . . .121 

VIII. Classification by Series 124 



I. Fallacies in general 127 

II. Classification of Fallacies 128 

III. Fallacies of Simple Inspection; or, 4 priori Fallacies 130 

IV. Fallacies of Observation 134 

V. Fallacies of Generalisation 137 

VI. Fallacies of Eatiocination 141 

VII. Fallacies of Confusion 143 



I. Introductory Eemarks 148 

II. Liberty and Necessity . . . . . .148 

III. There is, or may be, a Science of Human Nature . 150 

IV. The Laws of Mind 161 

V. Ethology, or the Science of the Formation of Cha- 
racter 153 

VL General Considerations on the Social Science . 155 

VII. The Chemical, or Experimental, Method in the Social 

Science 156 

VIIL The Geometrical, or Abstract Method . . . 157 
IX. The Physical, or Concrete Deductive Method . .158 
X. The Inverse Deductive, or Historical Method . .161 
XI. The Logic of Practice, or Art ; including Morality 

and Policy 165 





No adequate definition is possible till the properties 
of the thing to be defined are known. Previously 
we can define only the scope of the inquiry. Now, 
Logic has been considered as both the science of 
reasoning, i.e. the analysis of the mental process 
when we reason, and the art of reasoning, i.e. the 
rules for the process. The term reasoning, how- 
ever, is not wide enough. Reasoning means either 
syllogising, or (and this is its truer sense) the draw- 
ing inferences from assertions already admitted. But 
the Aristotelian or Scholastic logicians included in 
Logic terms and propositions, and the Port Koyal 
logicians spoke of it as equivalent to the art of think- 
ing. Even popularly, accuracy of classification, and 
the extent of command over premisses, are thought 
clearer signs of logical powers than accuracy of de- 
duction. On the other hand, the definition of logic 
as a ^ science treating of the operations of the un- 
derstanding in the search of truth,' though wide 
enough, would err through including truths known 
from intuition ; for, though doubtless many seeming 
intuitions are processes of inference, questions as to 



what facts are real intuitions belong to Metaphysics^ 
not to Logic. 

Logic is the science, not of Belief, but of Proof, or 
Evidence. Almost all knowledge being matter of in- 
ference, the fields of Logic and of Knowledge coincide ; 
but the two differ in so far that Logic does not find 
evidence, but only judges of it. All science is com- 
posed of data, and conclusions thence : Logic shows 
what relations must subsist between them. All in- 
ferential knowledge is true or not, according as the 
laws of Logic have been obeyed or not. Logic is 
Bacon's Ara Artium, the science of sciences. Grenius 
^ sometimes employs laws unconsciously ; but only 
genius : as a rule, the advances of a science have been 
ever found to be preceded by a fuller knowledge of 
the laws of Logic applicable to it. Logic, then, may 
be described as the science of the operations of the' 
understanding which aid in the estimation of evi- 
dence. It includes not only the process of proceeding 
from the known to the unknown, but, as auxiliary 
thereto. Naming, Definition, and Classification. Con- 
ception, Memory, and other like faculties, are not 
treated by it ; but it presupposes them. Our object, 
therefore, must be to analyse the process of inference 
and the subsidiary operations, besides'framing canons 
to test any given evidence. We need not, however, 
carry the analysis beyond what is necessary for the 
practical uses of Logic ; for one step in analysis is 
good without a second, and our purpose is simply to 
see the difference between good and ill processes of 
inference. Minuter analysis befits Metaphysics; 
though even that science, when stepping beyond the 
interrogation of our consciousness, or rather of our 
memory, is, as all other sciences, amenable to Logic. 






The fact of Logic being a portion of the art of 
tiinking, and of thought's chief instrument being 
words, is one reason why we must first inquire into 
the right use of words. But further, the import of 
propositions cannot really be examined apart from 
that of words; and (since whatever can be an object 
of belief assumes the form of a proposition, and in 
propositions all truth and error lie) this is a para- 
mount reason why we must, as a preliminary, con- 
sider the import of names, the neglecting which, and 
confining ourselves to things, would indeed be to 
discard all past experience. The right method is, to 
take men's classifications of things as shown by names, 
correcting them as we proceed. 



HoBBES*s assertion that a name is a sign, not of a 
thing, but of our conception of it, is untrue (unless 
he merely mean that the conception, and not the 
thing itself, is imparted to the hearer) ; for we intend 

B 2 


by a name, not only to make men conceive what we 
conceive, but to inform them what we believe as to 
the things themselves. 

Names may be divided according to five principles 
of classification. The first way of dividing them is 
into General (not as equivalent to Collective) and 
Individual names ; the aecondy into Concrete, i.e. the 
names of objects, and Abstract, i.e. the names of 
attributes (though Locke improperly extends the 
term to all names gained by abstraction, that is, to 
all general names). An abstract name is sometimes 
general, e.g. colour, and sometimes singular, e.g. 
milk-whiteness. It may be objected to calling attri- 
butes abstract, that also concrete adjectives, e.g. 
white, are attributes. But a word is the name of 
the things of which it can be predicated. Hence, 
white is the name of all things so coloured, given 
indeed because of the quality, but really the name of 
the thing, and no more the name of the quality than 
are names generally, since every one of them, if it 
signifies anything at all, must imply an attribute. 

The third division is into Connotative and Non- 
connotative (the latter being wrongly called Abso- 
lute). By connotative are meant, not (as Mr. James 
Mill explains it) words which, pointing directly to 
one thing, tacitly refer to another, but words which 
denote a subject and imply an attribute ; while non- 
connotativea sigmfy a subject only, or attribute only. 
All concrete general names are connotative. They 
are also called denominative^ because the subject de- 
noted receives a common name (e.g snow is named 
white) from the attribute connoted. Even some ab- 
stracts are connotative, for attributes may have attri- 


butes ascribed to them, and a word which denotes 
attributes may connote an attribute of them; e.g. 
fault connotes hurtftdness. Proper names, on the 
other hand, though concrete, are not connotative. 
They are merely distinguishing marks, given perhaps 
originally for a reason, but, when once given, inde- 
pendent of it, since the reason is proved to be no 
part of the sense of the word by the fact that the 
name is still used when the reason is forgotten. But 
other individual names are connotative. Some of 
these, viz. those connoting some attribute or some set 
of attributes possessed by one object only, e.g. Sun, 
God, are really general names, though happening to 
be predicable only of a single object. But there are 
also real connotative individual names, part of whose 
meaning is, that there exists only one individual with 
the connoted attribute, e.g. The first Emperor, The 
father of Socrates ; and it is so with many-worded 
names, made up of a general name limited by other 
words, e.g. The present Prime Minister of England. 
In short, the meaning of all names, which have any 
meaning, resides, not in what they denote, but in what 
they connote. There perpetually, however, arises a 
difl&culty of deciding how much they do connote, 
that is, what diiBFerence in the object would make a 
difference in the name. This vagueness comes from 
our learning the connotation, through a rude gene- 
ralisation and analysis, from the objects denoted. 
Thus, men use a name without any precise reference 
to a definite set of attributes, applying it to new 
objects on accoimt of superficial resemblance, so that 
at length all common meaning disappears. Even 
scientific writers, from ignorance, or from the aversion 


which men at large feel to the use of new names, often 
force old terms to express an ever-growing number of 
distinctions. But every concrete general name should 
be given a definite connotation with the least possible 
change in the denotation ; and this is what is aimed at 
in every definition of a general name already in use. 
But we must not confound the use of names of inde- 
terminate connotation, which is so great an evil, with 
the employment, necessitated by the paucity of names 
as compared with the demand, of the same words 
with different connotations in different relations. 

K fourth division of names is into Positive and 
Negative. When the positive is connotative, so is 
the corresponding negative, for the non-possession of 
an attribute is itself an attribute. Names negative 
in form, e.g. unpleasant, are often really positive ; 
and others, e.g. idle, sober, though seemingly positive, 
are really negative. Privatives are names which are 
equivalent each to a positive and a negative name 
taken together. They connote both the absence of 
certain attributes, and the presence of others, whence 
the presence of the defaulting ones might have been 
expected. Thus, blind would be applied only to a 
non-seeing member of a seeing class. 

The Jifth division is into Relative and (that we may 
economise the term Absolute for an occasion when 
none other is available) Non-relative names. Corre- 
latives, when concrete, are of course connotative. A 
relation arises from two individuals being concerned 
in the same series of facts, so that the signification of 
neither name can be explained except by mentioning 
another : and any two correlatives connote, not the 
same attribute indeed, but just this series of facts, 
which is exactly the same in both cases. 


Some make a sixth division, viz. Univocals, i.e, 
names predicated of different individuals in the same 
sense, and jiEquivocals, i.e. names predicated of differ- 
ent individuals in different senses. But these are not 
two kinds of names, but only two modes of using 
them ; for an aequivocal name is two names acciden- 
tally coinciding in sound. An intermediate case is 
that of a name used analogically or metaphorically, 
that is, in two senses, one its primary, the other its 
secondary sense. The not perceiving that such a 
word is really two has produced many fallacies. 



Logic is the theory of Proof, and everything prov- 
able can be exhibited as a proposition, propositions 
alone being objects of belief. Therefore, the import 
of propositions, that is, the import of predication, 
must be ascertained. But, as to make a proposition, 
i.e. to predicate, is to assert one thing of another 
thing^ the way to learn the import of predication is, 
by discovering what are the thi/ngs signified by 
names which are capable of being subject or predi- 
cate. It was with this object that Aristotle formed 
his Categories, i.e. an attempted enumeration of all 
nameable things by the summa genera or highest 
predicates, one or other of which must, he asserted, 
be predicable of everything. His, however, is a rude 
catalogue, without philosophical analysis of the 
rationale even of familiar distinctions. For instance. 


his Eelation properly includes Action, Passivity, 
and Local Situation, and also the two categories of 
Position TTori and ttoO, while the difference between 
TTov and KslaSai is only verbal, and l^^*^ ^^ ^^^ ^ 
summum genus at all. Besides— only substantives 
and attributes being there considered — there is no 
category for sensation and other mental states, since, 
though these may rightly be placed, so far as they 
express their relation, if active, to their objects, if 
passive to their causes, in the Categories of Actio and 
Passio, the things, viz., the mental states, do not 
belong there. 

The absence of a well-defined concrete name 
answering to the abstract eodstence^ is one great ob- 
stacle to renewing Aristotle's attempt. The words 
used for the purpose commonly denote substances 
only, though attributes and feelings are equally ex- 
istences. Even being is inadequate, since it denotes 
only some existences, being used by custom as sy- 
nonymous with substance, both material and spiritual. 
That is, it is applied to what excites feelings and has 
attributes, but not to feelings and attributes them- 
selves ; and if we called extension, virtue, &c., beings, 
we should be accused of believing in the Platonic 
self-existing ideas, or Epicurus's sensible forms — in 
short, of deeming attributes substances. To fill this 
gap, the abstract, entity, was made into a concrete, 
equivalent to being. Yet even entity implies, though 
not so much as being, the notion of substance. In 
fact, every word originally connoting simply exist- 
ence, gradually enlarges its connotation to mean 
separate existence, i.e. existence freed from the con- 
dition of belonging to a substance, so as to exclude 


attribute and feelings. Since, then, all the terms 
are ambiguous, that among them (and the same 
principle applies to terms generally) will be employed 
here which seems on each occasion to be lemt am- 
biguous : and terms will be used even in improper 
senses, when these by familiar association convey the 
proper meaning. 

Nameable tkmga are — I. Feelings or States of 
Consciousness. — A feeling, being anything of which 
the mind is conscious, is synonymous with state of 
consciousness. It is commonly confined to the sen- 
sations and emotions, or to the emotions alone ; but 
it is properly a genus, having for species, Sensation, 
Emotion, Thought, and Volition. By thought is 
meant all that we are internally conscious of when we 
think ; e.g. the idea of the sim, and not the sun itself, 
is a thought ; and so, not even an imaginary thing 
like a ghost, but only the idea of it, is a thought. In 
like manner, a sensation diflfers both from the object 
causing it, and the attribute ascribed to the object. 
Yet language (except in the case of the sensations of 
hearing) has seldom provided the sensations with 
separate names ; so that we have to name the sensa- 
tion from the object or the attribute exciting it, 
though we might conceive the sensation to exist, 
though it never actually does, without an exciting 
cause. Again, another distinction has to be attended 
to, viz. the diflference between the sensation and the 
state of the bodily organs, which is the physical 
agency producing it. This distinction escapes notice 
partly by reason of the division ^of the feelings into 
bodily and mental. But really there is no such di- 
vision, even sensations being states of the sentient 

B 3 


mind, and not of the body. The diflference, in fact, 
between sensations, thoughts, and emotions, is only in 
the different agency producing the feeling ; it being, 
in the case of the sensations, a bodily, and, for the 
other two, a mental state. Some suppose, after the 
sensation, in which, they say, the mind is passive, a 
distinct active process called perception, which is the 
direct recognition of an external object, as the cause of 
the sensation. Probably, perceptions are simply cases 
of belief claiming to be intuitive, i.e. free of external 
evidence. But, at any rate, any question as to their 
nature is irrelevant to an inquiry like the present, viz. 
how we get the non-original part of our knowledge. 
And so also is the distinction in German metaphysics, 
between the mind's cLcta and its passive states. Enough 
for us now that they are all states of the mind. 

II. Substances. — Logicians think they have defined 
substance and attribute, when they have shown merely 
what difference the use of them respectively makes in 
the grammar of a sentence. They say an attribute 
must be an attribute of something, but that a sub- 
stance is self-existent (being followed, if a relative, by 
o/, not qv^ substance, but qiia the relation). But 
this of, as distinguishing attributes, itself needs ex- 
planation : besides, we can no more conceive a sub- 
stance independent of attributes, than an attribute 
independent of a substance. Metaphysicians go deeper 
into the distinction than logicians. Substances, most 
of them say, are either bodies or minds ; and, of these, 
a body is the external cause to which we ascribe sen- 
sations. Berkeley and the Idealists, however, deny that 
there exists any cause of sensations (except, indeed, a 
First Cause). They argue that the whole of our notion 


of a body consists of a number of our own or others' 
sensations occurring together habitually (so that, the 
thought of one being associated with the thought of 
the others, we get what Hartley and Locke call a 
complex idea). They deny that a residuum would 
remain if all the attributes were pared off; for that, 
though the sensations are bound together by a law, 
the existence of a substratum is but one of many 
forms of mentally reah'sing the connection. And 
they ask how it is, — sinoe so long as the sensations 
occurred in the old order, we should not miss such a 
substratum^ supposing it to have once existed and to 
have perished — that we can know it exists even now ? 
Their opponents used formerly to reply, that the uni- 
form order of sensations implies an external cause 
determining the law of the order ; and that the attri- 
butes inhere in this external cause or substratum, 
viz. matter. But at last it was seen that the exist- 
ence of matter could not be proved by extrinsic 
evidence; consequently, now the answer to the 
idealist argument simply is, that the belief in an 
external cause of sensations is universal, and as in- 
tuitive as our knowledge of sensations themselves. 
Even Kant allows this (notwithstanding his belief in 
the existence of a miiverse of things in themselves, 
i.e. Noiimena, as contrasted with the mental repre- 
sentation of them, where the sensations, he thinks, 
furnish the matter, and the laws of the mind, the 
form). Brown even traced up to the sensations of 
touch, combined with the sensations seated in the 
muscular frame, those very properties, viz., extension 
and figure, which Eeid referred to as proving that 
some qualities must exist, not in the sensations, but 


in the things themselves, since they cannot possibly be 
copies of any impression on the senses. We have, in 
truth, no right to consider a thing's sensible qualities 
akin to its nature, unless we suppose an absurdity, 
viz. that a cause must, as such, resemble its effects. 
In any case, the question whether Ontology be a 
possible science, concerns, not Logic, but the nature 
and laws of intuitive knowledge. And the question 
as to the nature of Mind is as out of place here as 
that about Body. As body is the unknown exciting 
cause of sensations, so mind, the other kind of sub- 
stance, is the unknown recipient both of the sensa- 
tions and of all the other feelings. Though I call a 
something my self y as distinct from the series of feelings, 
the ' thread of consciousness,' yet this self shows itself 
only through its capacity of feeling or being con- 
scious ; and I can, with my present faculties, conceive 
the gaining no new information but about as yet un- 
known faculties of feeling. In short, as body is the 
unsentient cause of all feelings, so mind is the sentient 
subject (in the Grerman sense) of them, viz. that 
which feels them. About this inner nature we know 
nothing, and Logic cares nothing. 

III. Attributes. — Qualities are the first class of 
attributes. Now, if we know nothing about bodies 
but the sensations they excite, we can mean nothing 
by the attributes of bodies but sensations. Against 
this it has been urged that, though we know nothing 
of sensible objects except the sensations, the quality 
which we ascribe on the ground of the sensation may 
yet be a real hidden power or quality in the object, 
of which the sensation is only the evidence. Seem- 
ingly, this doctrine arises only from the tendency to 


suppose that there must be two different things to 
answer to two names when not quite synonymous. 
Quality and sensation are probably names for the 
same thing viewed in different lights. The doctrine 
of an entity per se, called quality, is a relic of the 
scholastic occult causes; the only intelligible cause 
of sensation being the presence of the assemblage of 
phenomena, called the object Why the presence of 
the object causes the sensation, we know not; and, 
granting an occult cause, we are still in the dark as 
to how that produces the effect. However, the ques- 
tion belongs to metaphysics ; and it suits this doc- 
trine, as well as the opposed one, to say that a quality 
has for its foundation a sensation. 

Eolations form the second class of attributes. In 
all cases of relation there exists some fact into which 
the relatives enter as parties concerned ; and this is 
the fundamentum relationis. Whenever two things 
are involved in some one fact, we may ascribe to them 
a relation grounded on it, however general the fact 
may be. As, then, a quality is an attribute based on 
the fact of a sensation, so a relation is an attribute 
based on a fact into which two objects enter jointly. 
This fact in both is always composed entirely of states 
of consciousness ; and this, whether it be complicated, 
as in many legal relations, or simple, as in the rela- 
tions expressed by antecedent and consequent and by 
simultaneous, where the fact consists merely of the 
two things so related, since the consciousness either 
of the succession or of the simultaneousness of the two 
sensations which represent the things, is a feeling not 
added to, but involved in them^ being a condition 
under which we must suppose things. And so, like- 


wise, with the relations of likeness and unlikeness. 
The feeling of these sometimes cannot be analysed, 
when the fiindamentum relationis is, as in the case 
of two simple sensations, e.g. two sensations of white, 
only the two sensations themselves, the consequent 
feeling of their resemblance being, like that of their 
succession or simultaneousness, apparently involved 
in the sensations themselves. Sometimes, again, the 
likeness or unlikeness is complex, and therefore caii 
be analysed into simpler cases. In any case, likeness 
or unlikeness must resolve itself into likeness or un- 
likeness between states of our own or some other 
mind ; and this, whether the feeling of the resem- 
blance or dissimilarity relate to bodies or to attri- 
butes, since the former we know only through the 
sensations they are supposed to excite, and the latter 
through the sensations on which they are grounded. 
And so, again, when we say that two relations are 
alike (one of the many senses of analogy), we simply 
assert resemblance between the facts constituting the 
two fundamenta relationis. Several relations, called 
by different names, are really cases of resemblance. 
Thus, equality, i.e. the exact resemblance existing 
between things in respect of their quantity, is often 
called identity. 

The third species of attributes is Quantity. The 
assertion of likeness or unlikeness in quantity, as in 
quality, is always founded on a likeness or unlikeness 
in the sensations excited. What the difference is all 
who have bad the sensations know, but it cannot be 
explained to those who never had them. 

In fine, all the attributes classed under Quality and 
Quantity are the powers bodies have of exciting certain 


sensations. So, Eelation generally is but the power 
which an object has of joiiiing its correlative in pro- 
ducing the series of sensations, which is the only sign 
of the existence of the fact on which they both are 
grounded. The relations of succession and simul- 
taneousness, indeed, are not baeed on any fact (i.e. 
any feeling) distinct from the related objects. But 
these relations are themselves states of consciousness ; 
resemblance, for example, being nothing but our 
feeling of resemblance : at least, we ascribe these re- 
lations to objects or attributes simply because they 
hold between the feelings which the objects excite 
and on which the attributes are grounded. And as 
with the attributes of bodies, so also those of minds 
are grounded on states of consciousness. Considered 
in itself, we can predicate of a mind only the series 
of its own feelings : e.g. by devout we mean that the 
feelings implied in that word form an oft-recurring 
part of the series of feelings filling up the sentient 
existence of that mind. Again, attributes may be 
ascribed to a mind as to a body, as grounded on the 
thoughts or emotions (not the sensations, for only 
bodies excite them) which it excites in others : e.g. 
when we call a character admirable, we mean that it 
causes feelings in us of admiration. Sometimes, 
under one word really two attributes are predicated, 
one a state of the mind, the other of other minds 
affected by thinking of it: e.g. He is generous. 
Sometimes, even bodies have the attribute of pro- 
ducing an emotion : e.g. That statue is beautiful. 

The general result is, that there are three chief 
kinds of nameable things : — I. Feelings distinct from 
the objects exciting and the organs supposed to con- 


vey them, and divisible into four classes, perceptions 
being only a particular case of belief, which is itself 
a sort of thought, while actions are only volitions 
followed by an effect. 2. Substances, i.e. the unknown 
cause and the unknown recipient of our sensations. 
3, Attributes, subdivisible into Quality, Eelation, 
Quantity. Of these (a) qualities, like substances, are 
known only by the states of consciousness which they 
excite, and on which they are based, and by which 
alone, though they are treated as a distinct class, they 
can be described. ()8) Eelations also, with four ex- 
ceptions, are based on some fact, i.e. a series of states 
of consciousness. (7) Quantity is, in the same way, 
based on our sensations. In short, all attributes are 
only our sensations and other feelings, or something 
involved in them. We may, then, classify nameable 
things thus: — 1, Feelings; 2, Minds; 3, Bodies, 
together with the properties whereby they are popu-- 
larly (though the evidence is very deficient) supposed 
to excite sensations; 4, the relations of Succession 
and Coexistence, Likeness and Unlikeness, which 
subsist really only between states of consciousness. 

These four classes are a substitute for Aristotle's 
abortive Categories. As they comprise all nameable 
things, every fact is made up of them or some of 
them; those that are called subjective facts being 
composed wholly of feelings as such, and the objective 
facts, though composed wholly or partly of substances 
and attributes, being groimded on corresponding 
subjective facts. 




The copula is a mere sign of predication, though it 
is often confounded with to be^ the verb of existence 
(and that not merely by Greeks, but even by moderns, 
whose larger experience how one word in one language 
often answers to several in another, should have 
saved them from thinking that things with a common 
name must have a common nature). The first divi- 
sion of propositions is into Affirmative and Negative, 
the copula in the latter being is not Hobbes and 
others, by joining the not to the predicate, made the 
latter what they call a negative name. But as a 
negative name is one expressing the absence of an 
attribute, we thus in fact merely deny its presence, 
and therefore the affirmative guise these thinkers give 
to negative propositions is only a fiction. Again, 
vnodal propositions cannot be reduced to the com- 
mon form by joining the modality to the predicate, 
and turning, e.g. The sun did rise, into. The sun is a 
thing having risen ; for the past time is not a par- 
ticular kind of rising, and it affects not the predicate, 
but the predication, i.e. the applicability of the 
predicate to the subject. There are, however, certain 
cases in which the qualification may be detached 
from the copula ; e.g. in such expressions as, may 6e, 
is perhaps; for, then we really do not mean to 
assert anything about the fact, but only about the 
state of our mind about it, so that it is not the pre- 
dication which is affected : e.g. Caesar may be dead, 


may properly be rendered, I am not sure that he is 

The second division is into Simple and Complex. 
Several propositions joined by a conjunction do not 
make a complex proposition. The conjunction, so 
far from making the two one, adds another, as being 
an abbreviation generally of an additional proposi- 
tion : e.g. and is an abbreviation of one additional 
proposition, viz. We must think of the two together ; 
while but is an abbreviation of two additional pro- 
positions, viz. We must think of them together, and we 
must recollect there is a contrast between them. 
But hypothetical propositions, i.e. both disjunctives 
and conditionals, are true complex propositions, 
since with several terms they contain but a single 
assertion. Thus, in. If the Koran comes from God, 
Mahomet is God's prophet, we do not assert the truth 
of either of the simple propositions therein contained 
(viz. the Koran comes from God, and Mahomet is 
God's prophet), but only the inferribility of one 
from the other. The only difference, then, between 
a hypothetical and a categorical proposition, is that 
the former is always an assertion about an assertion 
(though some catogoricals are so likewise ; e.g. That 
the whole is greater than its parts, is an axiom). 
Their conspicuous place in treatises on Logic arises 
from this attribute which they predicate of a propo- 
sition (for a proposition, like other things, has attri- 
butes), viz. its being an inference from something 
else, being, with reference to Logic, its chief attribute. 

The third common division is into Universal, Par- 
ticular, Indefinite, and Singular. A proposition 
whose subject is an individual name, even if not a 


proper name, is singular, e.g. The founder of Eome 
was killed. In particular propositions, if the part 
of the class meant by the some were specified, the 
proposition would become either singular, or uni- 
versal with a different subject including all the part. 
Indefinite in Logic is a solecism like doubtful gender 
in grammar, for the speaker must mean to make 
either a particular or a universal assertion. 



The object of an inquiry into the nature of propo- 
sitions must be to analyse, either, 1, the state of 
mind called belief, or 2, what is believed. Philo- 
sophers have usually, but wrongly, thought the for- 
mer, i.e. an analysis of the act of judgment, the chief 
duty of Logic, considering a proposition to consist in 
the denying or affirming one idea of another. True, 
we must have the two ideas in the mind together, in 
order to believe the assertion about the two things ; 
but so we must also in order to disbelieve it. True 
also, that besides the putting the ideas together, there 
may be a mental process ; but this has nothing to do 
with the import of propositions, since they are as- 
sertions about things, i.e. facts of external nature, not 
about the ideas of them, i.e. facts in our mental 
histQry. Logic has suffered from stress being laid 
on the relation between the ideas rather than the 
phenomena, nature thus coming to be studied by 
logicians second-hand, that is to say, as represented 


in our minds. Our present object, therefore, must 
be to investigate judgments, not judgment, and to 
inquire what it is which we assert when we make a 

Hobbes (though he certainly often shows his belief 
that all propositions are not merely about the mean- 
ing of words, and that general names are given to 
things on account of their attributes) declares that 
what we assert, is our belief that the subject and 
predicate are names of the same thing. This is, 
indeed, a property of all true propositions, and the 
only one true of all. But it is not the scientific 
definition of propositions ; for though the mere collo- 
cation which' makes a proposition a proposition, 
signifies only this, yet that /ottti, combined with 
other matter y conveys much more meaning. Hobbes's 
principle accounts fully only for propositions where 
both terms are proper names. He applied it to 
others, through attending, like all nominalists, to the 
denotation, and not the connotation of words, holding 
them to be, like proper names, mere marks put 
upon individuals. But when saying that, e.g. 
Socrates is wise, is a true proposition, because of the 
conformity of import between the terms, he should 
have asked himself why Socrates and wise are names 
of the same person. He ought to have seen that 
they are given to the same person, not because of 
the intention of the maker of each word, but from 
the resemblance of their connotation, since a word 
means properly certain attributes, and, only second- 
arily, objects denoted by it. What we really assert, 
therefore, in a proposition, is, that where we find 
certain attributes, we shall find a certain other one. 


which is a question not of the meaning of names, but 
of the laws of nature. 

Another theory virtually identical with Hobbes's, 
is that commonly received, which makes predication 
consist in referring things to a cldss ; that is (since 
a class is only an indefinite number of individuals 
denoted by a general name), in viewing them as 
some of those to be called by that general name. 
This view is the basis of the dictum de omni et 
nullo^ on which is supposed to rest the validity of all 
reasoning. Such a theory is an example of varspov 
irpoTspov : it explains the cause by the effect, since 
the predicate cannot be known for a class name 
which includes the subject, till several propositions 
having it for predicate have been first assented to. 
This doctrine seems to suppose all individuals to 
have been made into parcels, with the common name 
outside ; so that, to know if a general name can be 
predicated correctly of the subject, we need only 
search the roll so entitled. But the truth is, that 
general names are marks put, not upon definite 
objects, but upon collections of objects ever fluctuat- 
ing. We may frame a class without knowing a 
single individual belonging to it : the individual is 
placed in the class because the proposition is true ; 
the proposition is not made true by the individual 
being placed there. 

Analysis of different propositions shows what is 
the real import of propositions not simply verbal. 
Thus, we find that even a proposition with a proper 
name for subject, means to assert that an individual 
thing has the attributes connoted by the predicate, 
the name being thought of only as means for giving 


information of a physical fact. This is still more the 
case in propositions with connotative subjects. In 
these the denoted objects are indicated by some of 
their attributes, and the assertion really is, that the 
predicate's set of attributes constantly accompanies 
the subject's set. But as every attribute is grounded 
on some fact or phenomenon, a proposition, when 
asserting the attendance of one or some attributes 
OIL others, really asserts simply the attendance of 
one phenomenon on another ; e.g. When we say Man 
is mortal, we mean that where certain physical and 
moral facts called humanity are found, there also 
will be found the physical and moral facts called death. 
But analysis shows that propositions assert other 
things besides (although this is indeed their ordinary 
import) this coexistence or sequoDce of two pheno- 
mena, viz. two states of consciousness. Assertions in 
propositions about those unknowable entities {noil- 
m&ria) which are the hidden causes of phenomena, 
are made, indeed, only in virtue of the knowable 
'phenomena. Still, such propositions do, besides 
asserting the sequence or coexistence of the pheno- 
mena, assert further the existence of the noiimena ; 
and, moreover, in affirming the existence of a noti- 
menon, which is an unknowable cause^ they assert 
causation also. Lastly, propositions sometimes as- 
sert resemblance between two phenomena. It is not 
true that, as some contend, every proposition whose 
predicate is a general name affirms resemblance to 
the other members of the class; for such proposi- 
tions generally assert only the possession by the 
subject of certain common peculiarities; and the 
assertion would be true though there were no mem- 


bers of the class besides those denoted by the subject. 
Nevertheless, resemblance alone is sometimes predi- 
cated. Thus, when individuals are put into a class 
as belonging to it, not absolutely, but rather than 
to any other, the assertion is, not that they have the 
attributes connoted, but that they resemble those 
having them more than they do other objects. So, 
again, only resemblance is predicated, when, though 
the predicate is a class name, the class is based on 
general imanalysable resemblance. The classes in 
question are those of the simple feelings ; the names 
of feelings being, like all concrete general names, 
connotative, but' only of a mere resemblance. 

In short, one of five things, via Existence, Coex - 
istence (or, to be more particular. Order in Place), 
Sequence (or, more particularly. Order in Time, which 
comprises also the mere fact of Coexistence), Causa- 
tion, and Eesemblance, is asserted or denied in every 
proposition. This division is an exhaustive classifi- 
cation with respect to all things that can be believed. 
Although only propositions with concrete terms have 
been spoken of, it is equally the fact that, in propo- 
sitions with an abstract term or terms, we predicate 
one of these same five things. Tliere cannot be any 
difference in the import of these two classes of pro- 
positions, since there is none in the import of their 
terms, for the real signification of a concrete term 
resides in its connotation (so that in a concrete pro- 
position we reallypredicate an attribute), and what the 
concrete term connotes forms the whole sense of the 
abstract. Thus, all propositions with abstract terms 
can be turned into equivalent ones with concrete, the 
new terms being either the names which connote 


the attributes, or names of the facts which are the 
fundamenta of the attributes : e.g. ThoughtlessneBS 
is danger, is equivalent to, Thoughtless actions (the 
fuTidamentum) are dangerous. 

Finally, as these ^ve are the only things affirmable, 
80 are they the only things deniable. 



The object of Logic is to find how propositions are 
to be proved. As preliminary to this, it has been 
already shown that the Conceptualist view of propo- 
sitions, viz. that they assert a relation between two 
ideas, and the Nominalist, that they assert agreement 
or disagreement between the meanings of two names, 
are both wrong as general theories : for that generally 
the import of propositions is, to affirm or deny re- 
specting a phenomenon, or its hidden source, one 
of five kinds of facts. There is, however, a class of 
propositions which relate not to matter of fact, but to 
the meaning of names, and which, therefore, as names 
and their meanings are arbitrary, admit not of truth 
or falsity, but only of agreement or disagreement with 
usage. These verbal propositions are not only those 
in which both terms are proper names, but also some, 
viz. essential propositions, thought to be more closely 
related to things than any others. The Aristotelians' 
belief that objects are made what they are called by 
the inherence of a certain general substance in the 
individuals which get from it all their essential pro- 


perties, prevented even Porphyry (though more 
reasonable than the mediaeval EeaKsts) from seeing 
that the only diflFerence between altering a non- 
essential (or accidental) property, which, he says, 
makes the thing aXXoioPy and altering an essen- 
tial one, which makes it aWo (i.e. a different thing), 
is, that the latter change makes the object change 
its name. But even when it was no longer believed 
that there are real entities answering to general 
terms, the doctrine based upon it, viz. that a thing's 
essence is that without which the thing could neither 
be, nor be conceived to be, was still generally held, 
tiU Locke convinced most thinkers that the supposed 
essences of classes are simply the significations of 
their names. Yet even Locke supposed that, though 
the essences of classes are tiominal, individuals have 
real essences, which, though unknown, are the causes 
of their sensible properties. 

An accidental proposition (i.e. in which a property 
not connoted by the subject is predicated of it) 
tacitly asserts the existence of a thing corresponding 
to the subject ; otherwise, such a proposition, as it 
does not explain the name, would assert nothing at 
all. But an essential proposition (i.e. in which a 
property connoted by the subject is predicated of it) 
is identical. The only use of such propositions is to 
define words by unfolding the meaning involved in a 
name. When, as in mathematics, impoitant conse- 
quences seem to follow from them, such really follow 
from the tacit assumption, through the ambiguity of 
the copula, of the real existence of the object named. 

Accidental propositions include, 1, those with a 
proper name for subject, since an individual has no 



essence (althougli the schoolmen, and rightly, accord- 
ing to their view of genera and species* as entities 
inhering in the individuals, attributed to the indi- 
vidual the essence of his class) ; and, 2, all general 
or particular propositions in which the predicate 
connotes any attribute not connoted by the subject. 
Accidental propositions may be called real ; they add 
to our knowledge. Their import may be expressed 
(according as the attention is directed mainly, either 
to what the proposition means, or to the way in 
which it is to be used), either, by the formula : The 
attributes of the subject are always (or never) 
accompanied by those signified by the predicate; 
or, by the formula : The attributes of the subject are 
evidence, or a mark, of the presence of those of the 
predicate. For the purposes of reasoning, since pro- 
positions enter into that^ not as ultimate results, but 
as means for establishing other propositions, the 
latter formula is preferable. 




It is merely an accident when general names are 
names of classes of real objects: e.g. The \mity of 
God, in the Christian sense, and the non-existence of 
the things called dragons, do not prevent those 
names being general names. The using a name to 
connote attributes, turns the things, whether real 
or imaginary, into a class. But, in predicating 
the name, we predicate only the attributes ; and even 


when a name (as, e.g. those in Cuvier's system) is 
introduced as a means of grouping certain objects to- 
gether, and not, as usually, as a means of predication, 
it still signifies nothing but the possession of certain 

Classification (as resulting from the use of general 
language) is the subject of the Aristotelians' Five 
Predicables, viz. Oenus, Species^ Differentia^ Pro-- 
priurriy Accidens. These are a division of general 
names, not based on a distinction in their meaning, 
i.e. in the attributes connoted, but on a distinction in 
the class denoted. They express, not the meaning of 
the predicate itself, but its relation (a varying one) to 
the subject. Commonly, the names of any two classes 
(or, popularly, the classes themselves), one of which 
includes all the other and more, are called respectively 
genus and species. But the Aristotelians, i.e. the 
schoolmen, meant by differences in kind {genere or 
specie) something which was in its nature (and not 
merely with reference to the connotation of the 
name) distinct from differences in the accidents. 
Now, it is the fact that, though a fresh class may be 
founded on the smallest distinction in attributes, yet 
that some classes have, to separate them from other 
classes, no common attributes except those connoted 
by the name, while others have innumerable common 
qualities (from which we have to select a few samples 
for connotation) not referrible to a common source. 
The ends of language and of classification would be 
subverted if the latter (not if the former) sorts of 
difference were disregarded. Now, it was these only 
that the Aristotelians called Jdiids {genera or species), 
holding differences made up of certain and definite 

c 2 


properties to be differenced in the acddents of things. 
In conformity with this distinction — and it is a true 
one — any class^ e.g. negro as opposed to white man, 
may, according as physiology shall show the differences 
to be infinite or finite, be discovered to be a distinct 
hind or species (though not according to the natu- 
ralist's construction of spedeSy as including all de- 
scended from the same stock), or merely a subdivision 
of the kind or species, Man. Among kinds, a genua 
is a class divisible into other kinds, though it may 
be itself a species in reference to higher genera; that 
virhich is not so divisible, is an individual's proodTnate 
kind or vafima species {species prcedicahilis and also 
subjicibilis), whose common properties must include 
all the common properties of every other real kind 
to which the individual can be referred. 

The Aristotelians said that the differentia must be 
of the essence of the subject. They vaguely imder- 
Btood, indeed, by the essence of a thing, that which 
makes it the kind of thing that it is. But, as a kind 
is such from innumerable qualities not flowing from 
a common source, logicians selected the qualities 
which make the thing be what it is called, and termed 
these the essence, not merely of the species, but, in 
the case of the infima species, of the individual also. 
Hence, the distinction between the predicables. 
Differentia, Proprium, and Accidens, is founded, not 
on the nature of things, but on the connotation of 
names. The specific difference is that which must 
be added to the connotation of the genus to com- 
plete the connotation of the species, A species may 
have various differences, according to the principle 
of the particular classification. A kind, and not 


merely a class, may be founded on any one of these, 
if there be a host of properties behind, of which this 
one is the index, and not the source. Sometimes 
a name has a technical as well as an ordinary con- 
notation (e.g. the name Man, in the Linnaean 
system, connotes a certain number of incisor and 
canine teeth, instead of its usual connotation of 
rationality and a certain general form); and then 
the word is in fact ambiguous, i.e. two names. 
O&iius and Differentia are said to be of the essence ; 
that is, the properties signified by them are connoted 
by the name denoting the species. But both pro- 
prium and accidens are said to be predicated of the 
species accidentally. A proprium of the species, 
however, is predicated of the species necessarily 
being an attribute, not indeed connoted by the name, 
but following from an attribute connoted by it. It 
follows, either by way of demonstration as a con- 
clusion from premisses, or by way of causation as 
effect from cause; but, in either case, necessarily. 
Inseparable accidents, on the other hand, are attri- 
butes universal, so far as we know, to the species 
(e.g. blackness to crows), but not necessary \ i.e. 
neither involved in the meaning of the name of the 
species, nor following from attributes which are. 
Separable accidents do not belong to all, or if to all, 
not at all times (e.g. the fact of being bom, to man), 
and sometimes are not constant even in the same 
individual (e.g. to be hot or cold) 




A DEFINITION is a proposition declaring either the 
special or the ordinary meaning, i.e. in the case of 
connotative names, the connotation, of a word. This 
may be effected by stating directly the attributes con- 
noted ; but it is more usual to predicate of the sub- 
ject of definition one name of synonymous, or several 
which, when combined, are of equivalent, connotation. 
So that, a definition of a name being thus generally 
the sum total of the essential propositions which 
could be framed with that name for subject, is really, 
as Condillac says, an analysis. Even when a name 
connotes only a single attribute, it (and also the 
corresponding abstract name itself) can yet be de- 
fined (in this sense of being analysed or resolved into 
its elements) by declaring the connotation of that 
attribute, whether, if it be a union of several attri- 
butes (e.g. Humanity), by enumerating them, or, if 
only one (e.g. Eloquence), by dissecting the fact which 
is its foundation. Even when the fact which is the 
foundation of the attribute is a simple feeling, and 
therefore incapable of analysis, still, if the simple 
feeling have a name, the attribute and the object 
possessing it may be defined by reference to the fact : 
e.g. a white object is definable as one exciting the 
sensation of white ; and whiteness, as the power of 
exciting that sensation. The only names, abstract 
or concrete, incapable of analysis, and therefore of 
definition, are proper names, as having no meaning, 
and also the names of the simple feelings themselves. 


since these can be explained only by the resemblance 
of the feelings to former feelings called by the same 
or by an exactly synonymous name, which conse- 
quently equally needs definition. 

Though the only accurate definition is one de- 
claring aU the facts involved in the name, i.e. its 
connotation, men are usually satisfied with anything 
which will serve as an index to its denotation, so as 
to guard them from applying it inconsistently. This 
was the object of logicians when they laid down that 
a species must be defined per genua et diferentiam, 
meaning by the differentia one attribute included in 
the essence, i.e. in the connotation. And, in fact, 
one attribute, e.g. in defining man, Eationality 
(Swift's Houyhnhms having not been as yet dis- 
covered) often does sufficiently mark out the objects 
denoted. But, besides that a definition of this kind 
ought, in order to be complete, to be per genus et 
differentiaSf i.e. by all the connoted attributes not 
implied in the name of the genua, still, even if all 
were given, a aummum genua could not be so de- 
fined, since it has no superior genus. And for merely 
marking out the objects denoted. Description, in 
which none of the connoted attributes are given, 
answers as well as logicians' so-called eaaential defi- 
nition. In Description, any one or a combination of 
attributes may be given, the object being to make it 
exactly coextensive with the name, so as to be pre- 
dicable pf the same things. Such a description may 
be turned into an essential definition by a change of 
the connotation (not the denotation) of the name; 
and, in fact, thus are manufactured almost all 
scientific definitions, which, being landmarks of 


classificatioD, and not meant to declare the meaning 
of the name (though, in fact, they do declare it in 
its new use), are ever being modified (as is the 
definition of a science itself) with the advance of 
knowledge. Thus, a technical definition helps to 
expound the artificial classification from which it 
grows; but ordinary definition cannot expound, as 
the Aristotelians fancied it could, the natural classi- 
fication of things, i.e. explain their division into 
kinds f and the relations among the kinds : for the 
properties of every kind are innumerable, and all 
that definition can do is to state the connotation of 
the name. 

Both these two modes, viz. the essential but in- 
complete Definition, and the accidental, or Descrip- 
tion, are imperfect ; but the Realists' distinction be- 
tween definition of names and of things is quite 
erroneous. Their doctrine is now exploded; but 
many propositions consistent with it alone (e.g. that 
the science of geometry is deduced from definitions) 
have been retained by Nominalists, such as Hobbes. 
Beally a definition, as such, cannot explain a thing's 
nature, being merely an identical proposition ex- 
plaining the meaning of a word. But definitions of 
names kTiown to be names of really existing objects^ 
as in geometry, include two propositions, one a defi- 
nition and another a postulate. The latter affirms 
the existence of a thing answering to the name. The 
science is based on the postulates (whether they rest 
on intuition or proof), for the demonstration appeals 
to them alone, and not on the definitions, which in- 
deed might, though at some cost of brevity, be dis- 
pensed with entirely. It has been argued that, at 


any rate, definitions are premisses of science^ provided 
they give such meanings to terms as suit existing 
things : but even so, the inference would obviously 
be from the existence, not of the name which means, 
but of the thing which has the properties. 

One reason for the belief that demonstrative truths 
follow from the definitions, not from the postulates, 
was because the postulates are never quite triie 
(though in reality so much of them is true as is 
true of the conclusions). Philosophers, therefore, 
searching for something more accurately true, sur- 
mised that definitions must be statements and an- 
alyses, neither of words nor of things, as such, but of 
ideas; and they supposed the subject-matter of all 
demonstrative sciences to be abstractions of the 
mind. But even allowing this (though, in fact, the 
mind cannot so abstract one property, e.g. length, 
from all others; it only attends to the one exclu- 
sively), yet the conclusions would still follow, not 
from the mere definitions, but from the postulates of 
the real existence of the ideas. 

Definitions, in short, are of names, not things: 
yet they are not therefore arbitrary ; and to deter- 
mine what should be the meaning of a term, it is 
often necessary to look at the objects. The obscu- 
rity as to the connotation arises through the objects 
being named before the attributes (though it is from 
the latter that the concrete general terms get their 
meamng), and through the same name being popu- 
larly applied to different objects on the ground of 
genei'al resemblance, without any distinct perception 
of their common qualities, especially when these are 
complex. The philosopher, indeed, uses general 


names with a definite connotation ; but philosophers 
do not make language — it grows : so that, by degrees, 
the same name often ceases to connote even general 
resemblance. The object in remodelling language 
is to discover if the things denoted have common 
qualities, i.e. if they form a class ; and, if they do 
not, to form one artificially for them. A language's 
rude classifications often serve, when retouched, for 
philosophy. The transitions in signification, which 
often go on till the different members of the group 
seem to connote nought in common, indicate, at any 
rate, a striking resemblance among the objects de- 
noted, and are frequently an index to a real connec- 
tion ; so that arguments turning apparently on the 
double meaning of a term, may perhaps depend on 
the connection of two ideas. To ascertain the link 
of connection, and to procure for the name a distinct 
connotation, the resemblances of things must be con- 
sidered. Till the name has got a distinct connota- 
tion, it cannot be defined. The philosopher chooses 
for his connotation of the name the attributes most 
important, either directly, or as the differentiae leading 
to the most interesting propria. The enquiry into 
the more hidden agreement on which these obvious 
agreements depend, often itself arises imder the guise 
of enquiries into the definition of a name. 

BOOK n. 




The preceding book treated, not of the proper subject 
of logic, viz. the nature of proof, but of assertion. 
Assertions (as, e.g, definitions) which relate to the 
meaning of words, are, since thxxt is arbitrary, in- 
capable of truth or falsehood, and therefore of proof 
or disproof. But there are assertions which are sub- 
jects for proof or disproof, viz. the propositions (the 
real, and not the verbal) whose subject is some fact of 
consciousness, or its hidden cause, about which is pre- 
dicated, in the affirmative or negative, one of five 
things, viz. existence, order in place, order in time, 
causation, resemblance: in which, in short, it is 
asserted, that some given subject does or does not 
possess some attribute, or that two attributes, or sets 
of attributes, do or do not (constantly or occasionally) 

A proposition not believed on its own evidence, 
but inferred from another, is said to be provM ; and 
this process of inferring, whether syllogistically or not, 
is reasoning. But whenever, as in the deduction of 
a particular from a imiversal, or, in Conversion, the 
assertion in the new proposition is the same as the 

36 BEAS0NIN6. 

whole or part of the assertion in the original propo- 
sition, the inference is only apparent ; and such pro- 
cesses, however useful for cultivating a habit of 
detecting quickly the concealed identity of assertions, 
are not reasoning. 

Eeasoning, or Inference, properly so called, is, 1, 
Induction, when a proposition is inferred from another, 
which, whether particular or general, is less general 
than itself; 2, Katiocination, or Syllogism, when a 
proposition is inferred from others equally or more 
general ; 3, a kind which falls under neither of these 
descriptions, yet is the basis of both. 



The syllogistic figures are determined by the position 
of the middle term. There are four, or, if the fourth 
be classed under the first, three. But syllogisms in 
the other figures can be reduced to the first by con- 
version. Such reduction may not indeed be neces- 
sary, for different arguments are suited to different 
figures; the first figure, says Lambert, being best 
adapted to the discovery or proof of the properties of 
things ; the second, of the distinctions between things ; 
the third, of instances and exceptions ; the fourth, to 
the discovery or exclusion of the different species of 
a genus. Still, as the premisses of the first figure, 
got by reduction, are really the same as the original 
ones, and as the only alignments of great scientific 
importance, viz. those in which the conclusion is a 
universal afiirmative, can be proved in the first figure 


alone, it is best to hold that the two elementary 
forms of the first figure are the universal types, the 
one in affirmatives, the other in negatives, of aU 
correct ratiocination. 

The dictum de omni et nullo, viz. that whatever 
can be affirmed or denied of a class can be affirmed 
or denied of everything included in the class, which 
is a true account generalised of the constituent parts 
of the syllogism in the first figure, was thought the 
basis of the syllogistic theory. The fact is, that 
when universals were supposed to have an independent 
objective existence, this dictum stated a supposed 
law, viz. that the substantia secunda formed part of 
the properties of each individual substance bearing 
the name. But, now that we know that a class or 
universal is nothing but the individuals in the class, 
the dictum is nothing but the identical proposition, 
that whatever is true of certain objects is true ol 
each of them, and, to mean anything, must be con- 
sidered, not as an axiom, but as a circuitous defini- 
tion of the word daas. 

It was the attempt to combine the nominalist view 
of the signification of general terms with the reten- 
tion of the dictum as the basis of all reasoning, that 
led to the self-contradictory theories disguised under 
the ultra-nominalism of Hobbes and Gondillac, the 
ontology of the later Kantians, and (in a less degree) 
the abstract ideas of Locke. It was fancied that the 
process of inferring new truths was only the substi- 
tution of one arbitrary sign for another ; and Gon- 
dillac even described science as une langue him 
fai^. But language merely enables us to remember 
and impart our thoughts; it strengthens, like an 


artificial memory, our power of thought, and is 
thought's powerful instrument, but not its exclusive 
subject If, indeed, propositions in a syllogism did 
nothing but refer something to or exclude it from a 
class, then certainly syllogisms might have the dictum 
for their basis, and import only that the classification 
is consistent with itself. But such is not the primary 
object of propositions (and it is on this account, as 
well as because men will never be persuaded in com • 
mon discourse to quantify the predicate, that Mr. 
De Morgan's or Sir William Hamilton's quantifica- 
tion of the predicate is a device of little value). What 
is asserted in every proposition which conveys real 
knowledge, is a fact dependent, not on artificial 
classification, but on the laws of nature; and as 
ratiocination is a mode of gaining real knowledge, 
the principle or law of all syllogisms, with proposi- 
tions not purely verbal, must be, for affirmative 
syllogisms, that; Things coexisting with the same 
thing coexist with one another ; and for negative, 
that ; A thing coexisting with another, with which a 
third thing does not coexist, does not coexist with 
that third thing. But if (see supra, p. 26) propo- 
sitions (and, of course, all combinations of them) be 
regarded, not speculatively, as portions of our know- 
ledge of nature, but as memoranda for practical 
guidance, to enable us, when we know that a thing 
has one of two attributes, to infer it has the other, 
these two axioms may be translated into one, viz. 
Whatever has any mark has that which it is a mark 
of; or, if both premisses are universal. Whatever is 
a mark of any mark, is a mark of that of which this 
last is a mark. - 





The question is, whether the syllogistic process is 
one of inference, i.e. a process from the known to the 
unknown. Its assailants say, and truly, that in every 
syllogism, considered as an argument to prove the 
conclusion, there is a petitio pHndpii; and Dr. 
Whately's defence of it, that its object is to unfoid 
assertions wrapped up and implied (i.e. in fact, 
asserted unconsciously) in those with which we set 
out, represents it as a sort of trap. Yet, though no 
reasoning from generals to particulars can, as such, 
prove anything, the conclusion is sl bond fide infer- 
ence, though not an inference from the general pro- 
position. The general proposition (i.e. in the first 
figure, the major premiss) contains not only a record 
of many particular facts which we have observed or 
inferred, but also instructions for making inferences 
in unforeseen cases. Thus the inference is completed 
in the major premiss; and the rest of the syllogism 
serves only to decipher, as it were, our own notes. 

Dr. Whately fails to make out that syllogising, i.e. 
reasoning from generals to particulars, is the only 
mode of reasoning. No additional evidence is gained 
by interpolating a general proposition, and therefore 
we may, if we please, reason directly from the indi- 
vidual cases, since it is on these alone that the 
general proposition, if made, would rest. Indeed, 
thus are in fact di'awn, as well the inferences of 


children and savages, and of animals (which latter 
having no signs, can frame no general propositions), 
as even those drawn by grown men generally, from 
personal experience, and particularly the inferences 
of men of high practical genius, who, not having 
been trained to generalise, can apply, but not state, 
their principles of action. Even when we have 
general propositions we need not use them. Thus 
Dugald Stewart showed that the axioms need not be 
expressly adverted to in order to make good the 
demonstrations in Euclid; though he held, incon- 
sistently, that the definitions must be. All general 
propositions, whether called axioms, or definitions, 
or laws of nature, are merely abridged statements of 
the particular facts, which, as occasion arises, we 
either think we may proceed on as proved, or intend 
to assume. 

In short, all inference is from particulars to parti- 
culars; and general propositions are both registers 
or memoranda of such former inferences, and also 
short formulae for making more. The major premiss 
is such a formula ; and the conclusion is an inference 
drawn, not from, but according to that formula. 
The actual premisses are the particular facts whence 
the general proposition was collected inductively; 
and the syllogistic rules are to guide us in reading 
the register, so as to ascertain what it was that we 
formerly thought might be inferred from those facts. 
Even where ratiocination is independent of induction, 
as, when we accept from a man of science the doctrine 
that all A is B ; or from a legislator, the law that all 
men shall do this or that, the operation of drawing 
thence any particular conclusion is a process, not of 


inference, but of interpretation. In fact, whether 
the premisses are given by authority, or derived from 
our own (or predecessors') observation, the object is 
always simply to interpret, by reference to certain 
marks, an intention, whether that of the propounder 
of the principle or enactment, or that which we or 
our predecessors had when we framed the general 
proposition, so that we may draw no inferences 
that were not vntended to be drawn. We assent to 
the conclusion in a syllogism on account of its con- 
sistency with what we interpret to have been the in- 
tention of the framer of the major premiss, and not, 
as Dr. Whately held, because the supposition of a 
false conclusion from th6 premisses involves a con- 
tradiction, since, in fact, the denial, e.g. that an 
individual now living will die, is not in terms con- 
tradictory to the assertion that his ancestors and their 
contemporaries (to which the general proposition, as 
a record of facts, really amounts) have all died. 

But the syllogistic form, though the process of 
inference, which there always is when a syllogism is 
used, lies not in this form, but in the act of general- 
isation, is yet a great collateral security for the 
correctness of that generalisation. When all possible 
inferences from a given set of particulars are thrown 
into one general expression (and, if the particulars 
support one inference, they always will support an 
indefinite number), we are more likely both to feel 
the need of weighing carefully the suflSciency of the 
experience, and also, through seeing that the general 
proposition would equally support some conclusion 
which we know to be false, to detect any defect in 
the evidence, which, from bias or negligence, we 


might otherwise have overlooked. But the syllogistic 
form, besides being useful (and, when the validity of 
the reasoning is doubtful, even indispensable) for 
verifying arguments, has the acknowledged merit of 
all general language, that it enables us to make an 
induction once for all. We can, indeed, and in simple 
cases habitually do, reason straight from particulars ; 
but in cases at all complicated, all but the most saga- 
cious of men, and they also, unless their experience 
readily supplied them with parallel instances, would 
be as helpless as the brutes. The only counter- 
balancing danger is, that general inferences from 
insufficient premisses may become hardened into 
general maxims, and escape being confronted with 
the particulars. 

The major premiss is not really part of the argu- 
ment. Brown saw that there would be a petUio 
prmdpii if it were. He, therefore, contended that 
the conclusion in reasoning follows from the minor 
premiss alone, thus suppressing the appeal to ex- 
perience. He argued, that to reason is merely to 
ansdyse our general notions or abstract ideas, and 
that, provided that the relation between the two 
ideas, e,g. of man and of mortal, has been first per- 
ceived, we can evolve the one directly from the other. 
But (to waive the error that a proposition relates to 
ideas instead of things), besides that this proviso is 
itself a surrender of the doctrine that an argument 
consists simply of the minor and the conclusion, the 
perception of the relation between two ideas, one of 
which is not implied in the name of the other, must 
obviously be the result, not of analysis, but of ex- 
perience. In fact, both the minor premiss, and also 


the expression of our former experience, must both 
be present in our reasonings, or the conclusion will 
not follow. Thus, it appears that the imiversal type 
of the reasoning process is: Certain individuals 
possess (as I or others have observed) a given attri- 
bute ; An individual resembles the former in certain 
other attributes : Therefore (the conclusion, however, 
not being conclusive from its form, as is the conclu- 
sion in a syllogism, but requiring to be sanctioned 
by the canons of induction) he resembles them also 
in the given attribute. But, though this, and not 
the syllogistic, is the universal type of reasoning, yet 
the syllogistic process is a useful test of inferences. 
It is expedient, firat^ to ascertain generally what 
attributes are marks of a certain other attribute, so 
as, subsequently, to have to consider, secondly^ only 
whether any given individuals have those former 
marks. Every process, then, by which anything is 
inferred respecting an unobserved case, we will con- 
sider to consist of both these last-mentioned pro- 
cesses. Both are equally induction; but the name 
may be conveniently confined to the process of estab- 
lishing the general formula, while the interpretation 
of thia will be called * Deduction.' 



The minor premiss always asserts a resemblance 
between a new case and cases previously known. 
When this resemblance is not obvious to the senses, 


or ascertainable at once by direct observation, but is 
itself matter of inference, the conclusion is the result 
of a train of reasoning. However, even then the 
conclusion is really the result of induction, the only 
difference being that there are two or more induc- 
tions instead of one. The inference is still from par- 
ticulars to particulars, though drawn in conformity, 
not to one, but to several formulae. This need of 
several formulae arises merely from the fact that the 
marks by which we perceive that an inference can be 
drawn (and of which marks the formulae are records) 
happen to be recognisable, not directly, but only 
through the medium of other marks, which were, by 
a previous induction, collected to be marks of them. 
All reasoning, then, is induction : but the diffi- 
culties in sciences often lie (as, e.g. in geometry, 
where the inductions are the simple ones of which 
the axioms and a few definitions are the formulae) 
not at all in the inductions, but only in the forma- 
tion of trains of reasoning to prove the minors ; that 
is, in so combining a few simple inductions as to 
bring a new case, by means of one induction within 
which it evidently falls, within others in which it 
cannot be directly seen to be included. In propor- 
tion as this is more or less completely effected (that 
is, in proportion as we are able to discover marks of 
marks), a science, though always remaining induc- 
tive, tends to become also deductive^ and, to the same 
extent, to cease to be one of the eayperirnental 
sciences, in which, as still in chemistry, though no 
longer in mechanics, optics, hydrostatics, acoustics, 
thermology, and astronomy, each generalisation rests 
on a special induction, and the reasonings consist 
but of one step eiich 


An experimental science may become deductive 
by the mere progress of experiment. The mere 
connecting together of a few detached generalisations, 
or even the discovery of a great generalisation work- 
ing only in a limited sphere, as, e.g. the doctrine of 
chemical equivalents, does not make a science deduc- 
tive as a whole ; but a science is thus transformed 
when some comprehensive induction is discovered 
connecting hosts of formerly isolated inductions, as, 
e.g. when Newton showed that the motions of all the 
bodies in the solar system (though each motion had 
been separately inferred and from separate marks) 
are all marks of one like movement. Sciences have 
become deductive usually through its being shown, 
either by deduction or by direct experiment, that the 
varieties of some phenomenon in them uniformly 
attend upon those of a better known phenomenon, 
e.g. e^very variety of sound, on a distinct variety of 
oscillatory motion. The science of number has been 
the grand agent in thus making sciences deductive. 
The truths of numbers are, indeed, aflBrmable of all 
things only in respect of their quantity ; but since 
the variations of quality in various classes of phe- 
nomena have (e.g. in mechanics and in astronomy) 
been found to correspond regularly to variations of 
quantity in the same or some other phenomena, every 
mathematical formula applicable to quantities so 
varying becomes a mark of a corresponding general 
truth respecting the accompanying variations in 
quality ; and as the science of quantity is, so far as a 
science can be, quite deductive, the theory of that 
special kind of qualities becomes so likewise. It 
was thus that Descartes and Clairaut made geometry. 


which was already partially deductive, still more so, 
by pointing out the correspondence between geo- 
metrical and algebraical properties. 



All sciences are based on induction ; yet some, e.g, 
mathematics, and commonly also those branches of 
natural philosophy whicji have been made deductive 
through mathematics, are called Exact Sciences, and 
systems of Necessary Truth. Now, their necessity, 
and even their alleged certainty, are illusions. For 
the conclusions, e.g. of geometry, flow only seemingly 
from the definitions (since from definitions, as such, 
only propositions about the meaning of words can be 
deduced) : really, they flow from an implied assump- 
tion of the existence of real things corresponding to 
the definitions. But, besides that the existence of 
such things is not actual or possible consistently with 
the constitution of the earth, neither can they even 
be conceived as existing. In fact, geometrical points, 
lines, circles, and squares, are simply copies of those 
in nature, to a part alone of which we choose to attend ; 
and the definitions are merely some of our first 
generalisations about these natural objects, which 
being, though equally true of all, not exactly true 
of any one, must, actually, when extended to cases 
where the error would be appreciable (e.g. to lines 
of perceptible breadth), be corrected by the joining 
to them of new propositions about the aberration. 
The exact correspondence, then, between the facts 


and those first principles of geometry which are in- 
volved in the so-called definitions^ is a fiction, and 
is merely supposed. Geometry has, indeed (what 
Dugald Stewart did not perceive), some first prin- 
ciples which are true without any mixture of hypo- 
thesis, viz, the axioms, as well those which are 
indemonstrable (e.g. Two straight lines cannot enclose 
a space) as also the demonstrable ones ; and so have 
all sciences some exactly true general propositions : 
e,g. Mechanics has the first law of motion. But, 
generally, the necessity of the conclusions in geometry 
consists only in their following necessarily from cer- 
tain hypotheses^ for which same reason the ancients 
styled the conclusions of all deductive sciences neces^ 
sary. That the hypotheses, which form part of the 
premisses of geometry, must, as Dr. Whewell says, 
not be arbitrary — ^that is, that in their positive part 
they are observed facts, and only in their negative 
part hypothetical — ^happens simply because our aim 
in geometry is to deduce conclusions which may be 
true of real objects : for, when our object in reasoning 
is not to investigate, but to illustrate truths, arbitrary 
hypotheses (e.g. the operation of British political 
principles in Utopia) are quite legitimate. 

The ground of our belief in axioms is a disputed 
point, and one which, through the belief arising 
too early to be traced by the believer's own recol- 
lection, or by other persons' observation, cannot 
be settled by reference to actual dates. The axioms 
are really only generalisations from experience 
Dr. Whewell, however, and others think that, though 
suggested, they are not proved by experience, 
and that their truth is recognised a priori by the 

48 REA80NI19Q. 

constitution of the mind as soon as the meaning of 
the proposition is understood. But this assumption 
of an d 'priori recognition is gratuitous. It has 
never been shown that there is anything in the facts 
inconsistent with the view that the recognition of 
the truth of the axioms, however exceptionally com- 
plete and instant, originates simply in experience, 
equally with the recognition of ordinary physical 
generalisations. Thus, that we see a property of 
geometrical forms to be true, without inspection of 
the material forms, is fully explained by the capacity 
of geometrical forms of being painted in the imagi- 
nation with a distinctness equal to reality, and by 
the fact that experience has informed us of that 
capacity; so that a conclusion on the faith of the 
imaginary forms is really an induction from observa- 
tion. Then, again, there is nothing inconsistent with 
the theory that we learn by experience the truth of 
the axioms, in the fact that they are conceived by 
the mind as universally and necessarily true, that is, 
that we cannot figure them to ourselves as being 
false. Our capacity or incapacity of conceiving ^ 
depends on our associations. Educated minds can 
break up their associations more easily than the un- 
educated ; but even the former not entirely at will, 
even when, as is proved later, they are erroneous. 
The Greeks, from ignorance of foreign languages, 
believed in an inherent connection between names 
and things. Even Newton imagined the existence 
of a subtle ether between the sun and bodies on 
which it acts, because, like his rivals the Cartesians, 
he could not conceive a body acting where it is not. 
Indeed, inconceivableness depends so completely on 


the accident of our mental habits^ that it is the 
essence of scientific triumphs to make the contraries 
of once inconceivable views themselves appear incon- 
ceivable. For instance, suppositions opposed even to 
laws so recently discovered as those of chemical com- 
position appear to Dr. Whewell himself to be incon- 
ceivable. What wonder, then, that an acquired 
incapacity -should be mistaken for a natural one, 
when not merely (as in. the attempt to conceive 
space or time as finite) does experience afi'ord no 
model on which to shape an opposed conception, but 
when, as in geometry, we are unable even to call up 
the geometrical ideas (which, being impressions of 
form, exactly resemble, as has been already remarked, 
their prototypes), e.g. of two straight lines, in order 
to try to conceive them inclosing a space, without, 
by the very act, repeating tjhe scientific experiment 
which establishes the contrary. 

Since, then, the axioms and the misnamed defi- 
Xiitions are but inductions from, experience, and since 
the definitions are only hypothetically true, the 
deductive or demonstrative sciences-rof which these 
axioms and definitions form together the first prin- 
ciples — must really be themselves inductive and 
hypothetical. Indeed, it is to the fact that the 
results are thus only conditionally true, that the 
necessity and certainty ascribed to demonstration 
are due. 

It is so even with the Science of Number, i.e. 
arithmetic and algebra. But here the truth has been 
hidden through the errors of two opposite schools ; 
for while many held the truths in thi£^ science to be 
d priori, others paradoxically considered them to 



be merely verbal, and every process to be simply a 
succession of changes in terminology, by which 
equivalent expressions are substituted one for an- 
other. The excuse for such a theory as this latter 
was, that in arithmetic and algebra we carry no ideas 
with us (not even, as in a geometrical demonstration, 
a mental diagram) from the beginning, when the 
premisses are translated into signs, till the end, when 
the conclusion is translated back into things. But, 
though this is so, yet in every step of the calculation, 
there is a real inference of facts from facts : but it 
is disguised by the comprehensive nature of the 
induction, and the consequent generality of the 
language. For numbers, though they must be 
numbers of something, may be numbers of any- 
thing; and therefore, as we need not, when using 
an algebraical symbol (which represents all numbers 
without distiliction), or an arithmetical number, 
picture to ourselves all that it stands for, we may 
picture to ourselves (and this not as a sign of things, 
but as being itself a thing) the number or symbol 
itself as conveniently as any other single thing. 
That we are conscious of the numbers or symbols, 
in their character of things, and not of mere signs, 
is shown by the fact that our whole process of 
reasoning is carried on by predicating of them the 
properties of things. 

Another reason why the propositions in arithmetic 
and algebra have been thought merely verbal, is 
that they seem to be identical propositions. But in 
*Two pebbles and one pebble are equal to three 
pebbles,' equality but not identity is affirmed ; the 
subject and predicate, though names of the same 


objects, being names of them in different states^ that 
is^ as producing different impressions on the senses. 
It is on such inductive truths, resting on the evidence 
of sense, that the Science of Number is based ; and 
it is, therefore, like the other deductive sciences, an 
inductive science. It is also, like them, hypotheticaL 
Ite inductions are the definitions (which, as in geo- 
metry, assert a fact as well as explain a name) of the 
numbers, and two axioms, viz. The sums of equals are 
equal; the differences of equals are equaL These 
axioms, and so-called definitions are themselves ex- 
actly, and not merely hypothetically, true. Yet the 
conclusions are true only on theassumption that, 1 = 1, 
Le. that all the numbers are nimibers of the same or 
equal units. Otherwise, the certainty in arithmetical 
processes, as in those of geometry or mechanics, is 
not Tnathematical, i.e. unconditional certainty, but 
only certainty of inference. It is the enquiry (which 
can be gone through once for all) into the inferences 
which can be drawn from assumptions, which pro- 
perly constitutes all demonstrative science. 

New conclusions may be got as well from fictitious 
as from real inductions ; and this is even consciously 
done, viz. in the reductio ad ahaurdum, in order to 
show the falsity of an assumption. It has even been 
argued that all ratiocination rests, in the last resort, 
on this process. But as this is itself syllogistic, it is 
useless, as a proof of a syllogism, against a man who 
denies the validity of this kind of reasoning process 
itself. Such a man cannot in fact be forced to a 
contradiction in terms, but only to a contradiction, 
or rather an infringement, of the fundamental maxim 

of ratiocination, viz. ' Whatever has a mark, has 


52 BEAfiONINa. 

what it is a mark of; ' and^ since it is only by ad- 
mitting premisses, and yet rejecting a conclusion 
from them, that this asiom is infringed, consequently 
nothing is neceaaa/ry except the connection between 
a conclusion and premissea. 

BOOK m. 




As all knowledge not intuitive comes exclusively 
from inductions, induction is the main topic of Logic ; 
and yet neither have metaphysicians analysed this 
operation with a view to practice, nor, on the other 
hand, have discoverers in physics cared to generalise 
the methods they employed. 

Inferences are equally inductive^ whether, as in 
science, which needs its conclusions for record, not for 
instant use, they pass through the intermediate stage 
of a general proposition (to which class Dr. Whewell, 
without sanction from facts, or from the usage of Seid 
and Stewart, the founders of modem English meta- 
physical terminology, limits the term induction), or 
are drawn direct from particulars to a supposed 
parallel case. Neither does it make any difference 
in the character of the induction, whether the process 
be experiment or ratiocination, and whether the 
object be to infer a general proposition or an indi- 
vidual fact. That, in the latter case, the difficulty of 
the practical enquiries, e.g. of a judge or an advocate, 
lies chiefly in selecting from among all approved 
general propositions those inductions which suit bis 


case (just as, even in deductive sciences, the ascer- 
taining of the inductions is easy, their combination 
to solve a problem hard) is not to the point: the 
legitimacy of the inductions so selected must at all 
events be tried by the same test as a new general 
truth in science. Induction, lihen, may be treated 
here as though it were the operation of discovering 
and proving general propositions ; but this is so only 
because the evidence which justifies an inference 
respecting one unknown case, would justify a like 
inference about a whole class, and is really only 
another fonn of the same process : because, in shorty 
the logic of science is the universal logic applicable 
to all human enquiries. 



Induction is the process by which what is true at 
certain times, or of certain individuals, is inferred to 
be true in like circumstances at all times, or of a 
whole class. There must be an inference from the 
known to the unknown, and not merely from a less 
to a more general expression. Consequently, there is 
no valid induction, 1, in those cases laid down in the 
common works on Logic as the only perfect instances 
of induction, viz. where what we affirm of the class 
has already been ascertained to be true of each indi- 
vidual in it, and in which the seemingly general 
proposition in the conclusion is simply a number of 
singular propositions written in an abridged form ; 


or, 2, when^ as often in mathematics, the conclusion, 
though really general, is a mere summing up of the 
different propositions from which it is dra^n (whether 
actually ascertained, or, as in the case of the uncalcu- 
lated terms of an arithmetical series, when once its law 
is known, readily to be understood) ; or, 3, when the 
several parts of a complex phenomenon, which are 
only capable of being observed separately, have been 
pieced together by one conception, and made, as it 
were, one fact represented in a single proposition. 

Dr. Whewell sets out this last operation, which he 
terms the colligation of facts, as induction, and even 
as the type of induction generally. But, though 
induction is always colligation, or (as we may, with 
equal accuracy, characterise such a general expression 
obtained by abstraction simply connecting observed 
facts by means of common characters) description, 
colligation, or description, as such, though a necessary 
preparation for induction, is not induction. Induc- 
tion explains and predicts (and, as an incident of these 
powers, describes). Different explanations collected 
by real induction from supposed parallel cases (e.g. 
the Newtonian and the Impact doctrines as to the 
motions of the heavenly bodies), or different predic- 
tions, i.e. different determinations of the conditions 
imder which similar facts may be expected again to 
occur (e.g. the stating that the position of one planet 
or satellite so as to overshadow another, and, on the 
other hand, that the impending over mankind of some 
great calamity, is the condition of an eclipse), cannot 
be true together. But, for a colligation to be correct, 
it is enough that it enables the mind to represent to 
itself as a whole all the separate facts ascertained at 


a given time, so that successive tentative descriptions 
of a phenomenon, got by guessing till a guess is found 
which tallies with the facts, may, though conflicting 
(e.g. the theories respecting the motions of the 
heavenly bodies), be all correct so far as they go. 
Induction is proof, the inferring something unob- 
served from something observed ; and to provide a 
proper test of proof is the special purpose of inductive 
logic. But colligation simply sums up the fects 
observed, as seen under a new point of view. Dr. 
Whewell contends that, besides the sum of the facts, 
colligation introduces, as a principle of con^ection, a 
•conception of the mind not existing in the facts. But, 
in fact, it is only because this conception is a copy of 
something in the facts, although our senses are too 
weak to recognise it directly, that the facts are rightly 
classed under the conception. The conception is 
often even got by abstraction from the facts which it 
<;olligates ; but also when it is a hypothesis, borrowed 
from strange phenomena, it still is accepted as true 
only because found actually, and as a fact, whatever 
the origin of the knowledge of the fact, to fit and to 
describe as a whole the separate observations. Thus, 
though Kepler's consequent inference that, because 
the orbit of a planet is an ellipse, the planet would 
continue to revolve in that same ellipse, was an in- 
duction, his previous application of the conception of 
an ellipse, abstracted from other phenomena, to sum 
. up his direct observations of the successive positions 
occupied by the different planets, and thus to describe 
their orbits, was no induction. It altered only the 
'predicate^ changing — The successive places of, e.g. 
Mars, are A, B, C, and so forth, into — The succes- 


give places of, e.g. Mars^ are points in an ellipse : 
whereas induction always widens the subject* 



Induction is generalisation from experience. It as- 
sumes, that whatever is true in any one case, is true 
in all cases of a certain description, whether past, 
present, or future (and not merely in future cases, as 
is wrongly implied in the statement by Eeid's and 
Stewart's school, that the principle of induction is 
* our intuitive conviction that the future will resemble 
the past '). It assumes, in short, that the course of 
nature is uniform, that is, that all things take place 
according to general laws. But this general axiom 
of induction, though by it were discovered the obscure 
laws of nature, is no explanation of the inductive 
process, but is itself an induction (not, as some think, 
an intuitive principle which experience verifies only), 
and is arrived at after many separate phenomena 
have been first observed to take place according lo 
general laws. It does not, then, prove all other in- 
ductions. But it is a condition of their proof. For 
any induction can be turned into a syllogism by sup- 
plying a major premiss, viz. What is true of this, 
that, &c. is true of the whole class ; and the process 
by which we arrive at this immediate major may be 
itself represented by another syllogism or train of 
syllogisms, the major of the ultimate syllogism, and 
which therefore is the warrant for the immediate 



major, being this axiom, viz. that there is unifonnitj, 
at all events, in the class of phenomena to which the 
induction relates, and a uniformity which, if not 
foreknown, may now be known. 

But though the course of nature is uniform, it is 
al^o infinitely various. Hence there is no certainty 
in the induction in use with the ancients, and all 
non -scientific men, and which Bacon attacked, viz. 
*Inductio per enumerationem simplicem, ubi noh 
reperitur instantia contradictoria' — unleaa^ as in a few 
cases, we must have known of the contradictory in- 
stances if existing. The scientific theory of induction 
alone can show why a general law of nature may 
sometimes, as when the chemist first discovers the ex- 
istence and properties of a before unknown substance, 
be inferred from a single instance, and sometimes 
(e.g. the blackness of all crows) not from a million. 



The uniformity of the course of nature is a complex 
fact made up of all the separate uniformities in re- 
spect to single phenomena. Each of these separate 
uniformities, if it be not a mere case of and result 
from others, is a law of nature ; for, though law is 
used for any general proposition expressing a uni- 
formity, law of nature is restricted to cases where it 
has been thought that a separate act of creative will 
is necessary to account for the uniformity. Laws of 
nature, in the aggregate, are the fewest general 


propositions from which all the uniformities in the 
universe might be deducted. Science is ever tending 
to resolve one law into a higher. Thus, Kepler's three 
propositions, since having been resolved by Newton 
into, and shown to be cases of the three laws of motion, 
may be indeed called laws, but not laws of nature. 

Since every correct inductive generalisation is 
either a law of nature, or a result from one, the pro- 
blem of inductive logic is to unravel the web of nature, 
tracing each thread separately, with the view, 1, of 
ascertaining what are the severallsiws of nature, and, 
2, of following them into their results. But it is im- 
possible to frame a scientific method of induction, or 
test of inductions, unless, unlike Descartes, we start 
with the hypothesis that some trustworthy inductions 
have been already ascertained by man's involuntary 
observation. These spontaneous generalisations must 
be revised ; and the same principle which common 
sense has employed to revise them, correcting the 
narrower by the wider (for, in the end, experience 
must be its own test), serves also, only made more pre- 
cise, as the real type of scientific induction. As preli- 
minary to the employment of this test, nature must be 
surveyed, that we may discover which are respectively 
the invariable and the variable inductions at which 
man has already arrived unscientifically. Then, by 
connecting these diflferent ascertained inductions with 
one another through ratiocination, they become mutu- 
when bound up with the weaker, and the weakest at 
least as strong as the weakest of those from which 
they are deduced (as in the case of the Torricellian 
experiment) while those leading deductively to 


incompatible consequences become each other's test, 
showing that one must be given up (e.g. the old 
farmers' bad induction that seed never throve if not 
sown di^ring the increase of the moon). It is be- 
cause a survey of the uniformities ascertained to 
exist in nature makes it clear that there are certain 
and universal uniformities serving as premisses whence 
crowds of lower inductions may be deduced, and so 
be raised to the same degree of certainty, that a logic 
of induction is possible. 



Phenomena in nature stand to each other in two re- 
lations, that of simultaneity, and that of succession. 
On a knowledge of the truths respecting the succes- 
sion of facts depends our power of predicting and 
influencing the future. The object, therefore, must 
be to find some law of succession not liable to be 
defeated or suspended by any change of circum- 
stances, by being tested by, and deduced from which 
law, all other uniformities of succession may be raised 
to equal certainty. Such a law is not to be found in 
the class of laws of number or of space ; for though 
these are certain and universal, no laws except those 
of space and number can be deduced from them by 
themselves (however important elements they maybe 
in the ascertainment of uniformities of succession). 
But causation is such a law; and of this, moreover,^ 
all cases of succession whatever are examples. 


This Law of Causation implies no particular 
theory as to the ultimate production of eflfects by 
efficient causes, but simply implies the existence of 
an invariable order of succession (on our assurance 
of which the validity of the canons of inductive logic 
depends) foimd by observation, or, when not yet ob- 
served, believed, to obtain between an invariably 
antecedent, i.e. the physical cause, and an invariable 
consequent, the effect. This sequence is generally 
between a consequent and the sum of several ante- 
cedents. The cause is really the sum total of the 
conditions, positive and negative ; the negative being 
stated as one condition, the same always, viz. the 
absence of counteracting causes (since one cause 
generally counteracts another by the same law where- 
by it produces its own effects, and, therefore, the 
particular mode in which it counteracts another may 
be classed under the positive causes). But it is 
usual, even with men of science, to reserve the name 
cause for an antecedent ev&rd which completes the 
assemblage of conditions, and begins to exist im- 
mediately before the effect (e.g. in the case of death 
from a fall, the slipping of the foot, and not the 
weight of the body), and to style the permanent facts 
or states^ which, though existing immediately before, 
have also existed long previously, the conditions. 
But indeed, popularly, any condition which the 
hearer is least likely to be aware of, or which needs 
to be dwelt upon with reference to the particular 
occasion, will be selected as the cause, even a 
negative condition (e.g. the sentinel's absence from 
his post, as the cause of a surprise), though from a 
mere negation no consequence can really proceed. 

62 iHnucTioN. 

On the other hand, the object which ia popularly 
regarded aa standing in the relation of patient, and 
as being the mere theatre of the effect, is never 
atyled cause, being included in the phrase deHcribing 
the effect, viz. as the object, of which the effect is a 
state. But really these so-called patients are them- 
selves agents, and their properties are positive con- 
ditions of the effect. Thus, the death of a man who 
has taken prussic acid is as directly the effect of the 
oiganic properties of the man, i.e. the patient^ as of 
the poison, i.e. the agent. 

To be a cause, it is not enough that the sequence 
has been invariable. Otherwise, night might be 
called the cause of day; whereas it ia not even a 
condition of it. Such relations of succession or co- 
existence, as the succession of day and night (which 
Dr. Whewell contrasts as laws of pliemnnena with 
causes, though, indeed, the latter also are laws of 
phenomena, only more imiveraal ones), result from 
the coexistence of real causes. The causes them- 
selves are followed by their effects, not only invari- 
ably, but also necessarily, i.e. unconditionally, or 
subject to none but negative conditions. This is 
material to the notion of a cause. But another ques- 
tioE is not material, viz. whether causes must pre- 
cede, or may, at times, be simultaneous with (they 
certainly are never preceded by) their effects. In 
some, though not in all cases, the causes do invariably 
continue together with their effects, in accordance 
with the schools' dognla, Cessante causa, ceseat et 
effectUiB ; and the hypotheaiB that, in such cases, the 
effects are produced afresh at each instant by their 
cause, is only a verbal explanation. But the question 



does not affect the theory of causation, which remains 
intact, even if (in order to take in cases of eimul- 
taoeity of cause and effect) we have to define a cause, 
as the asaemblage of phenomena, which occurring, 
aome other phenomeaou invariably and uncondition- 
ally commences, or has its origin. 

There exist certain original natural agents, called 
permanent causes (some being objects, e.g. the earth, 
air, and sun ; others, cycles of events, e.g. the rota- 
tiou of the earth), which together make up nature. 
All other phenomena are immediate or remote effects 
of these causes. Consequently, as the state of the 
universe at one instant is the consequence of its state 
at the previous instant, a person (but only if of more 
than human powers of calculation, and subject also 
to the possibility of the order being changed by a 
new volition of a supreme power) might predict the 
whole future order of the universe, if he knew the 
original distribution of all the permanent causes, 
with the laws of the succession between each of them 
and its different mutually independent effects. But, 
in feet, the distribution of these permanent causes, 
with the reason for the proportions in which they 
coexist, has not been reduced to a law; and this is 
why the sequences or coexistences among the effects 
of several of them together cannot rank as laws of 
nature, though they are invariable while the causes 
coexist. For this same reason (since the proximate 
causes are traceable ultimately to permanent causes) 
there are no original and independent uniformities 
of coexistence between effects of different (proximate) 
causes, though there may be such between different 
effects of the same cause. 



Some, and particularly Reid, have regarded man's 
voluntary agency as the true type of causation and 
the exclusive source of the idea. The facts of in- 
animate nature, they argue, exhibit only antecedence 
and sequence, while in volition (and this would dis- 
tinguish it from physical causes) we are conscious, 
prior to experience, of power to produce efiPects: 
volition, therefore, whether of men or of God, must 
be, they contend, an efficient cause, and the only^ 
one, of all phenomena. But, in fact, they bring no 
positive evidence to show that we could have known^ 
apart from experience, that the efifect, e.g. the motion 
of the limbs, would follow from the volition, or that 
a volition is more than a physical cause. In lieu of 
positive evidence, they appeal to the supposed con- 
ceivableness of the direct action of will on matter, 
and inconceivableness of the direct action of matter 
on matter. But there is no inherent law, to this 
effect, of the conceptive faculty : it is only because 
our voluntary acts are, from the first, the most direct 
and familiar to us of all cases of causation, that men, 
as is seen from the structure of languages (e.g. their 
active and passive voices, and impersonations of 
inanimate objects), get the habit of borrowing them 
to explain other phenomena by a sort of original 
Fetichism. Even Eeid allows that there is a tendency 
to assume volition where it does not exist, and that 
the belief in it has its sphere gradually limited, in 
proportion as fixed laws of succession among external 
objects are discovered. 

This proneness to require the appearance of some 
necessary and natural connection between the cause 
and its effect, i.e. some reason per ae why the one 


should produce the other, has infected most theories 
of causation. But the selection of the particular 
agency which is to make the connection between the 
physical antecedent and its consequent seem con- 
cdvablcy has perpetually varied, since it depends on 
a person's special habits of thought. Thus, the 
Greeks, Thales, Anaximenes,and Pythagoras, thought 
respectively that water, air, or number is such an 
agency explaining the production of physical effects. 
Slany moderns, again, have been unable to conceive 
the production of effects by volition itseli^ without 
some intervening agency to connect it with them. 
This medium, Leibnitz thought, was some per se effi- 
cient physical antecedent ; while the Cartesians ima- 
gined for the purpose the theory of Occasional Causes, 
that is, supposed that God, not qud mind, or qua 
volition, but qu& omnipotent, intervenes to connect 
the volition and the motion : so far is the mind from 
being forced to think the action of mind on matter 
more natural than that of matter on matter. Those 
who believe volition to be an efficient cause are 
guilty of exactly the same error as the Greeks, or 
Leibnitz or Descartes ; that is, of requiring an ex- 
planation of physical sequences by something avsv 
oh TO alrLov ov/e av iror^ sttf aXriov. But they are 
guilty of another error also, in inferring that volition, 
even if it is an efficient cause of so peculiar a pheno- 
menon as nervous action, must therefore be the 
efficient cause of all other phenomena, though having 
scarcely a single circumstance in common with 




An effect is almost always the result of the con- 
currence of several causes. When all have their full 
effect, precisely as if they had operated anecesswely, 
the joint effect (and it is not inconsistent to give the 
name of joint effect even to the mutual obliteration 
of the separate ones) may be ded/aced from the laws 
which govern the causes when acting separately. 
Sciences in which^ as in mechanics, this principle, 
viz. the com/position of causes, prevails, are deduc- 
tive and demonstrative. Phenomena, in effect, do 
generally follow this principle. But in some classes, 
e.g. chemical, vital, and mental phenomena, the laws 
of the elements when called on to work together, 
cease and give place to others, so that the joint 
effect is not the sum of the separate effects. Yet 
even here the more general principle is exemplified. 
For the new heteropathic laws, besides that they 
never supersede oM the old laws (thus. The weight of a 
chemical compound is equal to the sum of the weight 
of the elements), have been often found, especially 
in the case of vital and mental phenomena, to enter 
unaltered into composition with one another, so that 
complex facts may thus be dedudble &om compara- 
tively simple laws. It is even possible that, as has 
been already partly effected by Dalton's law of 
definite proportions, and the law of isomorphism, 
chemistry itself, which is now the least deductive of 
sciences, may be made deductive, through the laws 
of the combinations being ascertained to be, though 


not compounded of the laws of the separate agencies, 
yet derived from them according to a fixed prin- 

The proposition, that effects are proportional to 
their causes, is sometimes laid down as an independent 
axiom of causation : it is really only a particular case 
of the composition of causes ; and it fails at the same 
point as the latter principle, viz. when an addition does 
not become compounded with the original cause, but 
the two together generate a new phenomenon. 



Since the whole of the present facts are the infallible 
result of the whole of the past, so that if the prior 
state of the entire imiverse could recur it would be 
followed by the present, the process of ascertaining 
the relations of cause and effect is an analysis or 
resolution of this complex uniformity into the simpler 
uniformities which make it up. We must first men- 
tally analyse the facts, not making this analysis 
zninuter than is needed for our object at the time, 
but at the same time not regarding (as did the 
Greeks their verbal classifications) a mental decom- 
position of facts as ultimate. When we have thus 
succeeded in looking at any two successive chaotic 
masses (for such nature keeps at each instant pre- 
senting to us) as so many distinct antecedents and 
consequents, we must analyse the facts themselves, 
fmd try, by varying the circumstances, to discover 


which of the antecedents and consequents (for many 
are always present together) are related to each 

Experiment and observation are the two instru- 
ments for thus varying the circumstances* When 
the enquiry is, What are the effects of a given cause ? 
experiment is hx the superior, since it enables us not 
merely to produce many more and more opportune 
variations than nature, which is not arranged on the 
plan of facilitating our studies, offers spontaneously, 
but, what is a greater advantage, though one less 
attended to, also to insulate the phenomenon by 
placing it among known circumstances, which can be 
then infinitely varied by introducing a succession of 
well-defined new ones. 

Observation cannot ascertain the effects of a given 
cause, because it cannot, except in the simplest cases, 
discover what are the concomitant circumstances; 
and therefore sciences in which experiment can- 
not be used, either at all, as in astronomy, or 
commonly, as in mental and social science, must 
be mainly deductive, not inductive. When, how- 
ever, the object is to discover causes by means of their 
effects, observation alone is primarily available, since 
new effects could be artificially produced only through 
their causes, and these are, in the supposed case, 
unknown. But even then observation by itself cannot 
directly discover causes, as appears from the case of 
zoology, which yet contains many recognised uniform- 
ities. We have, indeed, ascertained a real uniformity 
when we observe some one antecedent to be invariably 
found along with the effects presented by nature. 
But it is only by reversing the process, and experi- 


mentally producing the effects by means of that 
antecedent, that we can prove it to be imconditional^ 
i.e. the cause. 



Five canons may be laid down as the principles 
of experimental enquiry. The first is that of the 
Method of Agreement, viz. : If two or more instances 
of the phenomenon under investigation have only 
one circumstance in common, the cvrcumstan.ce in 
which alone all the drcumsta/nces agree is the ca/ase 
or the effect of the gvven phenomenon. The second 
canon is that of the Method of Difference, viz. : Ifa/n 
instance m which the phenomenon occurs and an 
instance in which it does not occur have every 
ci/rcumstan/ie in common, save one, and that one 
occurs only m the former, that one ci/rcumsta/nce is 
the effect, or the cause, or a n^ecessary part of the 
cause, of the phenomenon. 

These two are the simplest modes of singling out 
from the facts which precede or follow a phenomenon, 
those with which it is connected by an invariable 
law. Both are methods of elimination, their basis 
being, for the method of agreement, that whatever 
can be eliminated is not, and for that of difference, 
that whatever cannot be eliminated is connected with 
the given phenomenon by a law. It is only, however, 

* Chap. IX. consists of ^Hiscellaneous Examples of the Four 
Methods,' which cannot be well represented in an abridged form. 


by the method of diCFerence, which is a method of 
artificial experiment (and by experiment we can in- 
troduce into the pre-existing facts a change perfectly 
definite), that we can, at least by direct experience, 
arrive with certainty at causes^ The method of 
agreement is chiefly useful as preliminary to and 
suggestive of applications of the method of diflference, 
or as an inferior resource in its stead, when, as in 
the case of many spontaneous operations of nature, 
we have no power of producing the phenomenon. 

"When we have power to produce the phenomenon, 
but only by the agency, not of a single antecedent^ 
but of a combination, the method of agreement can 
be improved (though it is even then inferior to the 
direct method of diflference) by a double process 
being used, each proof being independent and cor- 
roborative of the other. This may be called the 
Indirect Method of Diflference, or the Joint Method 
of Agreement and Diflference, and its canon will be : 
If two or Tnore instances in which the pheTUxmemm 
occurs have only one circumstance in common, 
while two or more vnstances in which it does not 
occur have nothvag in common save the ahscTice of 
that d/rcumstancey the circumstance in which alone 
the two sets of instances differ y is the effect^ or the 
cause, or a necessary part of the cause, of the ph^ 

The fourth canon is that of the Method of Besidues, 
viz. : Subduct from any phenomenmi such part as 
is known by previous inductions to be the effect of 
certain antecedents, and the residue of the pheno^ 
m£non is the effect of the remaining antecedents. 
This method is a modification of the method of 


diflFerence, from which it diflFers in obtaining, of the 
two required instances, only the positive instance, by 
observation or experiment, but the negative, by 
deduction. Its certainty, therefore, in any given 
case, is conditional on the previous inductions having 
been obtained by the method of diflFerence, and on 
there being in reality no remaining antecedents 
besides those given as such. 

The fifth canon is that of the Method of Concomi- 
tant Variations, viz. : Whatever pheTiomenon va/ries 
m any ma/nner whenever another phenomenon 
varies in some particular manner, is either a cause 
or an effect of that phenomenon, or (since they may 
be effects of a common cause) is connected with it 
through some fact of causation. Through this 
method alone can we find the laws of the permanent 
causes. For, though those of the permanent causes 
whose influence is local may be escaped from by 
changing the scene of the observation or experiment, 
many can neither be excluded nor even kept isolated 
from each other ; and, therefore, in such cases, the 
method of difference, which requires a negative in- 
stance, and that of agreement, which requires the 
different instances to agree only in one circum- 
stance, in order to prove causation, are (together with 
the methods which are merely forms of these) equally 
inapplicable. But, though many permanent antece- 
dents insist on being always present, and never 
present alone, yet we have the resource of making 
or finding instances in which (the accompanying 
antecedents remaining unchanged) their influence is 
va/ried and modified. This method can be used 
most effectually when the variations of the cause are 


variations of quantity; and th.en, if we know the 
absolute quantities of the cause and the effect^ we 
may affirm generally that, at least within otir limits 
of observation, the variations of the cause will be 
attended by similar variations of the effect; it being 
a corollary from the principle of the composition of 
causes, that more of the cause is followed by more of 
the effect This method is employed usually when 
the method of difference is impossible; but it is 
also of use to determine according to what law the 
quantity or different relations of an effect ascertained 
by the method of difference follow those of the 

These four methods are the only possible modes 
of experimental enquiry. Dr. Whewell attacks them, 
first, on the ground (and the canon of ratiocination 
was attacked on the same) that they assume the 
reduction of an argument to formulae, which (with 
the procuring the evidence) is itself the chief diffi- 
culty. And this is in truth the case : but, to reduce 
an argument to a particular form, we must first know 
what the form is ; and in showing us this. Inductive 
Logic does a service the value of which is tested 
by the number of faulty inductions in vogue. Dr.. 
Whewell next implies a complaint that no discoveries 
have ever been made by these four methods. But, 
as the analogous argument against the syllogism was 
invalidated by applying equally as against all reason*- 
ing, which must be reducible to syllogism, so this 
also falls by its own generality, since, if true against 
these methods, it must be true against all observation 
and experiment, since these must ever proceed by 
one of tlie four. And, moreover, even if the four 


methods were not methods of discovery, as they are, 
they would yet be subjects for logic, as being, at all 
events, the sole methods of Proof, which (unless Dr. 
Whewell be correct in his view that inductions are 
simply conceptions consistent with the facts they 
colligate) is the principal topic of logic. 




The difficulty in tracing the laws of nature arises 
chiefly from the Intermixture of Effects, and from 
the Plurality of Causes. The possibility of the latter 
in any given case — that is, the possibility that the 
same effect may have been produced by different causes 
— makes the Method of Agreement (when applied to 
positive instances) inconclusive, if the instances are 
few ; for that Method involves a tacit supposition, that 
the same effect in different instances, which have one 
common antecedent, must follow in all from the same 
cause, viz. from their common antecedent. When 
the instances are varied and very many (how many, 
it is for the Theory of Probability to consider), the 
supposition, that the presence in all of the common 
antecedent may be simply a coincidence, is rebutted ; 
and this is the sole reason why mere number of 
instances, differing only in immaterial points, is of 
any value. As applied, indeed, to negative instances, 
Le. to those resembling each other in the absence of 
a certain circumstance, the Method of Agreement 



is not vitiated by Plurality of Causes. But the 
negative premiss cannot generally be worked unless 
an affirmative be joined with it: and then the 
Method is the Joint Method of Agreement and 
Difference. Thus, to find the cause of Transparency, 
we do not enquire in what circumstance the num- 
berless non-transparent objects agree; but we en- 
quire, first, in what the few transparent ones agree ; 
and then, whether all the opaque do not agree in 
the absence of this circumstance. 

Not only may there be Plurality of Causes, the 
whole of the effect being produced now by one, now 
by another antecedent; but there may also be Inter- 
mixture of Effects, through the interference of dif- 
ferent causes with each other, so that part of the 
total effect is due to one, and part to another cause. 
This latter contingency, which, more than all else, 
complicates the study of nature, does not affect the 
enquiry into those (the exceptional) cases, where, as 
in chemistry, the total effect is something quite dif- 
ferent to the separate effects, and governed by different ! 
laws. There the great problem is to discover, not 
the properties, but the cause of the new phenomenon, 
i.e. the particular coDJunction of agents whence it 
results ; which could indeed never be ascertained by 
specific enquiry, were it not for the peculiarity, not of 
all these cases (e.g. not of mental phenomena), but of 
many, viz. that the heterogeneous effects of combined 
causes often reproduce, Le. are transformed into their 
causes (as, e.g. water into its components, hydrogen 
and oxygen). The great difficulty is not there to 
discover the properties of the new phenomenon itseli^ 
for these can be found by experiment like the evm/pU 


effects of any other cause ; since, in this class of cases 
the effects of the separate causes give place to a new 
effect, and thereby cease to need consideration as 
separate effects. But in the far larger class of cases, 
viz. when the total effect is the exact sum of the 
separate effects of all the causes (the case of the 
Composition of Causes), at no point may it be over- 
looked that the effect is not simple but complex, the 
result of various separate causes, all of which are 
always tending to produce the whole of their several 
natural effects ; having, it may be, their effects modi- 
fied, disturbed, or even prevented by each other, but 
always preserving their action^ since laws of causation 
cannot have exceptions. 

These complex effects must be investigated by de- 
ducing the law- of the effect from the laws of the 
separate causes on the combination of which it de- 
pends. No inductive method is conclusive in such 
cases (e.g. in physiology, or a fortiori^ in politics and 
history), whether it be the method of simple obser- 
vation, which compares instances, whether positive 
or negative, to see if they agree in the presence or 
the absence of one common antecedent, or the em- 
pirical method, which proceeds by directly trying 
different combinations (either made or found) of 
causes, and watching what is the effect. Both are 
inconclusive ; the former, because an effect may be 
due to the concurrence of many causes, and the latter, 
because we can rarely know what all the coexisting 
causes are ; and still more rarely whether a certain 
portion (if not all) of the total effect is not due to 
these other causes, and not to the combination of 
causes which we are observing. 

E s 

76 iNDUCnoii 



The deductive method is the main source of our 
knowledge of complex phenomena^ and the sole source 
of all the theories through which vast and complicated 
facts have been embraced under a few simple laws. 
It consists of processes of Induction, Ratiocination, 
and Verification. First, by one of the four inductive 
methods, the simple laws (whence may be decbiced 
the complex) of each separate cause which shares in 
producing the effect, must be first ascertained. This 
is difficult, when the causes or rather tendencies cannot 
be observed singly. Such is the case in physiology, 
since the different agencies which make up an orga- 
nized body cannot be separated without destroying 
the phenomenon; consequently there our sole re- 
source is to produce experimentally, or find (as in the 
case of diseases), pathological instances in which only 
one organ at a time is afifected. Secondly, when the 
laws of the causes have been found, we calculate the 
effect of any given combination of them by ratio- 
cination, which may have (though not necessarily) 
among its premisses the theorems of the sciences of 
number and geometry. Lastly, as it might happen 
that some of the many concurring agencies have been 
unknown or overlooked, the conclusions of ratiocina- 
tion must be verified ; that is, it must be explained 
why they do not, or shown that they do, accord with 
observed cases of at least equal complexity, and (which 
is the most effectual test) that the empirical laws and 
uniformities, if any, arrived at by direct observation. 


can be deduced from and so accounted for by them, 
as, e.g, Kepler's laws of the celestial motions bj 
Newton's theory. 




The aim, in the deductive method, is either to dis- 
cover the law of the effect, or to account for it by 
explaining it, that is, by pointing out some more 
general phenomenon (though often less familiar to 
us) of which this is a case and a partial exemplifi- 
cation, or some laws of causation which produce it 
by their joint or successive action. This explanation 
may be made, either — 1. By resolving the laws of the 
complex effect into its elements, which consist as well 
of the separate laws of the causes which share in pro- 
ducing it, as also of their collocation, i.e. the fact that 
these separate laws have been so combined; or — 2. By 
resolving the law which connects two links, not proxi- 
mate, in a chain of causation, into the laws which 
connect each link with the intermediate links ; or — 3, 
By the subsumption or gathering up of several laws 
under one which amounts to the sum of them all, and 
which is the recognition of the same sequence in dif- 
ferent sets of instances. In the first two of the pro- 
cesses, laws are resolved into others, which both extend 
to more cases, i.e. are more general^ and also, as being 
laws of nature, of which the complex laws are but 
results, are more certain^ i.e. more unconditional 


and more universally true. In the third process, 
laws are resolved into others which are indeed more 
general^ but not more certain^ since they are in fact 
thq same laws, and therefore, subject to the same 

Liebig's researches, e.g. into the Contagious In- 
fluence of Chemical Action, and his Theory of Eespi- 
ration, are among the finest examples, since Newton's 
exposition of the law of gravitation, of the use of the 
deductive method for explanation.* But the method 
is as available for explaining mental as physical facts. 
It is destined to predominate in philosophy. Before 
Bacon's time deductions were accepted as sufficient, 
when neither had the premisses been established by 
proper canons of experimental enquiry, nor the results 
tested by verification by specific experience. He 
therefore changed the method of the sciences from 
deductive to experimental. But, now that the prin- 
ciples of deduction are better understood, it is rapidly 
reverting from experimental to deductive. Only it 
must not be supposed that the inductive part of the 
process is yet complete. Probably, few of the great 
generalisations fitted to be the premisses for future 
deductions will be found among truths now knowih 
Some, doubtless, are yet unthought of; others known 
only as laws of some limited class of facts, as elec- 
tricity once was. They will probably appear first in 
the shape of hypotheses, needing to be tested by 
canons of legitimate induction. 

*' These, and other illustratioiis in chap. ziiL, cannot be useful^ 
represented in an abridged form. 





The constant, tendency of science, operating by the 
Deductive Method, is to resolve all laws, even those 
which once seemed ultimata and not derivative, into 
others still more general. But no process of resolving 
will ever reduce the nimiber of ultimate laws below 
the number of those varieties of our feelings which 
are distinguishable in quality, and not merely in 
quantity or degree. The ideal limit of the explana- 
tion of natural phenomena is to show that each of 
these ultimate facts has (since the differences in the 
different cases of it affect our sensations as differences 
in degree only, and not in quality) only one sort of 
cause or mode of production; and that all the 
seemingly different modes of production or causes of 
it are resolvable into one. But practically this limit 
is never attained. Thus, though various laws of 
Causes of Motion have been resolved into others (e.g. 
the fall of bodies to the earth, and the motions of the 
planets, into the one law of mutual attraction), many 
causes of it remain still unresolved and distinct. 

Hypotheses are made for the sake of this resolving 
and explaining of laws. When we do not know of 
any more general laws into which to resolve an unifor- 
mity, we then (either on no or on insuflScient evidence) 
suppose some, imagining either causes (as, e.g. Des- 
cartes did the Vortices), or the laws of their operation 
(as did Newton respecting the planetary central force ) ; 
but we never feign both cause and law. The use of 


a hypothesis is to enable iis to apply the Deductive 
Method before the laws of the causes have been ascer- 
tained by Induction. In, those cases where a false 
law could not have led to a true result (as was the 
case with Newton's hypothesis as to the law of the 
Attractive force) the third part of the process in the 
Deductive Method, viz. Verification, which shows 
that the results deduced are true, amounts to a com- 
plete induction, and one conforming to the canon of 
the Method of Difiference. But this is the case only 
when either the cause is known to be one given agent 
(and only its law is unknown), or to be one of several 
given agents. 

An assumed cause, on the other hand, cannot be 
accepted as true simply because it explains the phe- 
nomena (since two conflicting hypotheses often do this 
even originally, or, as Dr. Whewell himself allows, 
may at any rate by modifications be made to do it) ; 
nor because it moreover leads to the prediction of 
other results which turn out true (since this shows 
only what was indeed apparent already from its agree- 
ment with the old facts, viz. that the phenomena 
are governed by laws partially identical with the laws 
of other causes) ; nor because we cannot imagine any 
other hypothesis which will account for the facts 
(since there may be causes unknown to our present 
experience which will equaUy account for them). The 
utility of such assumptions of causes depends on their 
being, in their own nature, capable (as Descartes' 
Vortices were not, though possibly the Luminiferous 
Ether may be) of being, at some time or other, 
proved directly by independent evidence to be the 
causes. And this was, perhaps, all that Newton meant 


by his vercB causce, which alone, he said, may he 
assigned as causes of phenomena. Assumptions of 
causes, which fulfil this condition, are, in science, 
even indispensable, with a view both to experimental 
inqui^, and still more to the application of the De- 
ductive Method. They may be accepted, not indeed, 
as Dr. Whewell thinks they may be, as proof, but as 
suggesting a line of experiment and observation which 
may result in proof. And this is actually the method 
used by practical men for eliciting the truth from 
involved statements. They first extemporise, from a 
few of the particulars, a rude theory of the mode in 
which the event happened ; and then keep altering 
it to square with the rest of the facts, which they 
review one by one. 

The attempting, as in Geology, to conjecture, in 
conformity with known laws, in what former colloca- 
tions of known agents (though not known to have 
been formerly present) individual existing facts may 
have originated, is not Hypothesis but Induction; 
for then we do not suppose causes, but legitimately 
infer from known effects to unknown causes. Of 
this nature was Laplace's theory, whether weak or 
not, as to the origin of the earth and planets. 




Sometimes a complex effect results, not (as has been 
supposed in the last four chapters) from several, but 
from one law. The following is the way. 

Some effects are instantaneous (e.g. some sensa- 

E 3 


tions), and are prolonged only by the prolongation of 
the causes ; others are in their own nature permanent. 
In some cases of the latter class^ the original is also 
the proximate cause (e.g. Exposure to moist air is 
both the original and the proximate cause of iron 
rust). But in others of the same class, the perma- 
nency of the eflfect is only the permanency of a 
series of changes. Thus, e.g. in cases of Motion, the 
original force is only the remote cause of any link 
(after the very first) in the. series; and the motion 
immediately preceding it, being itself a compound 
of the original force and any retarding agent, is its 
'proximate cause. When the original cause is perma- 
nent as well as the effect (e.g. Suppose a continuance 
of the iron's exposure to moist air), we get a pro- 
gressive series of effects arising from the cause's 
accumulating influence ; and the sum of these effects 
amounts exactly to what a number of successively 
introduced similar causes would have produced. 
Such cases fall under the head of Composition of 
Causes, with this peculiarity, that, as the causes (to 
regard them as plural) do not come into play all at 
once, the effect at each instant is the sum of the 
effects only of the then acting causes, and the result 
will appear as an ascending series. Each addition 
in such case takes place according to a fixed law 
(equal quantities in equal times) ; and therefore it can 
be computed deductively. Even when, as is some- 
times the case, a cause is at once permanent and 
progressive (as, e.g. the sun, by its position becoming 
more vertical, increases the heat in summer) so that 
the quantities added are unequal, the effect is still 
progressive, resulting from its cause's continuance 
and progressiveness combined. 


In all cases whatever of progressive effects, the 
succession not merely between the cause and the 
effect, but also between the first and latter stages of 
the effect, is uniform. Hence, from the invariable 
sequence of two terms (e.g. Spring and Summer) in 
a series going through any continued and uniform 
process of variation, we do not presume that one is 
the cause and the others the effect, but rather that 
the whole series is an effect. 



Empirical laws are derivative laws, of which the 
derivation is not known. They are observed unifor- 
mities, which we compare with the result of any de- 
duction to verify it ; but of which the why^ and also 
the limits, are unrevealed, through their being, though 
resolvable, not yet resolved into the simpler laws. 
They depend usually, not solely on the ultimate laws 
into which they are resolvable ; but on those, together 
with an ultimate fact, viz. the mode of coexistence of 
some of the component elements of the universe. 
Hence their untrustworthiness for scientific purposes ; 
for, till they have been resolved (and then a derivative 
law ceases to be empirical), we cannot know whether 
they result from the different effects of one cause, or 
from effects of different causes ; that is, whether they 
depend on laws, or on laws and a collocation. And 
if they thus depend on a collocation, they can be re- 
ceived as true only within the limits of time and 


space, and also circumstance, in which they have been 
observed, since the mode of the collocation of the 
permanent causes is not reducible to a law, there being 
no principle known to us as governing the distribu- 
tion and relative proportions of the primaeval natural 

Uniformities cannot be proved by the Method of 
Agreement alone to be laws of causation ; they must 
be tested by the Method of Difference, or explained 
deductively. But laws of causation themselves are 
either ultimate or derivative. Signs, previous to 
actual proof by resolution of them, of their being 
derivative, are, either that we can sui^Tnise the ex- 
istence of a link between the known antecedent and 
the consequent, as e.g. in the laws of chemical action ; 
or, that the antecedent is some very complex fact, 
the effects of which are probably (since most complex 
cases fall under the Composition of Causes) com- 
pounded of the effects of its different elements. But 
the laws which, though laws of causation, are thus 
presumably derivative laws only, need, equally with 
the uniformities which are not known to be laws of 
causation at all, to be explained by deduction (which 
they then in turn verify), and are less certain than 
when they have been resolved into the ultimate laws. 
Consequently they come under the definition of Em- 
pirical Laws, equally with uniformities not known to 
be laws of causation. However, the latter are far 
more uncertain \ for as, till they are resolved, we 
cannot tell on how many collocations, as well as laws, 
they may not depend, we must not rely on them be- 
yond the exact limits in which the observations were 
made. Therefore, the name Empirical Laws will 
generally be confined here to these. 




Empirical Laws are certain only in those limits 
within which they have been observed to be true. 
But, even within those limits, the connection of two 
phenomena may, as the same effect may be produced 
by several different causes, be due to Chance ; that 
is, it may, though being, as all facts must be, the 
result of some law, be a coincidence whence, simply 
because we do not know all the circumstances, we 
have no ground to infer an uniformity. When nei- 
ther Deduction, nor the Method of Difference, can 
be applied, the only way of inferring that coinci- 
dences are not casual, is by observing the frequency 
of their occurrence, not their absolute frequency, but 
whether they occur more often than chance would 
(that is, more often than the positive frequency of 
the phenomena would) account for.- If, in such 
cases, we could ascend to the causes of the two phe- 
nomena, we should find at some stage some cause or 
causes common to both. Till we can do this, the 
fact of the connection between them is only an em- 
pirical law ; but still it is a law. 

Sometimes an effect is the result partly of chance, 
and partly of law : viz. when the total effect is the 
result partly of the effects of casual conjunctions of 
causes, and partly of the effects of some constant 
cause which they blend with and modify. This is a 
case of Composition of Causes. The object being to 
find how much of the result is attributable to a given 


constant cause, the only resource, when the variable 
causes cannot be wholly excluded from the experi- 
ment, is to ascertain what is the efifect of all of th&m 
taken together, and then to eliminate this, which is 
the casual part of the effect, in reckoning up the re- 
sults. If the results of frequent experiments, in 
which the constant cause is kept invariable, oscillate 
round one point, that average or middle point is due 
to the constant cause, and the variable remainder to 
chance ; that is, to causes the coexistence of which 
with the constant cause was merely casual. The test 
of the sufficiency of such an induction is, whether or 
not an increase in the number of experiments ma- 
terially alters the average. 

We can thus discover not merely how much of the 
effect, but even whether any part of it whatever is 
due to a constant cause, when this latter is so unin- 
fluential as otherwise to escape, notice (e.g. the load- 
ing of dice). This case of the Elimination of Chance 
is called The discovery of a residual phenomenon 
by elvminating the effects of chance. 

The mathematical doctrine of chances, or Theory 
of Probabilities, considers what deviation from the 
average chance by itself can possibly occasion in some 
number of instances smaller than is required for a 
fair average. 




In order to calculate chances, we must know that of 
seTeral events one, and no more, must happen, and 
also not know, or have any reason to suspect, which 
of them that one will be. Thus, with the simple 
knowledge that the issue must be one of a certain 
number of possibilities, we raay conclude that one 
supposition is most probable to us. For this purpose 
it is not necessay^y that specific experience or reason 
should have also proved the occurrence of each of the 
several events to be, as a fact, equally frequent. For, 
the probability of an event is not a quality of the 
event (since every event is in itself certain), but is 
merely a name for the degree of ground we have, 
with our present evidence, for expecting it. Thus, if 
we know that a box contains red, white, and black 
balls, though we do not know in what proportions 
they are mingled, we have numerically appreciable 
grounds for considering the probability to be two to 
one against any one colour. Our judgment may 
indeed be said in this case to rest on the experience 
we have of the laws governing the frequency of occur- 
rence of the different cases ; but such experience is 
universal and axiomatic, and not specific experience 
about a particular event. Except, however, in games 
of chance, the purpose of which requires ignorance, 
such specific experience can generally be, and should 
be gained. And a slight improvement in the data 
profitfl more than the most elaborate application of 
the calculus of probabilities to the bare original data, 


e.g. to such data, when we are calculating the credi- 
bility of a witness, as the proportion, even if it could 
be verified, between the number of true and of 
erroneous statements a man, qua man, may be sup- 
posed to make during his life. Before applying the 
Doctrine of Chance, therefore, we should lay a foun- 
dation for an evaluation of the chances by gaining 
positive knowledge of the facts. Hence, though not 
a necessary, yet a most usual condition for calculating 
the probability of a fact is, that we should possess a 
specific knowledge of the proportion which the cases 
in which facts of the particular sort occur bear to the 
cases in which they do not occur. 

Inferences drawn correctly according to the Doc- 
trine of Chances depend ultimately on causation. 
This is clearest, when, as sometimes, the probability 
of an event is deduced from the frequency of the 
occurrence of the causes. When its probability is 
calculated by merely counting and comparing the 
number of cases in which it has occurred with those 
in which it has not, the law, being arrived at by the 
Method of Agreement, is only empirical. But even 
when, as indeed generally, the numerical data are 
obtained in the latter way (since usually we can 
judge of the frequency of the causes only through 
the medium of the empirical law, which is based on 
the frequency of the effects), still then, too, the in- 
ference really depends on causation alone. Thus, an 
actuary infers from his tables that, of any hundred 
living persons under Uke conditions, five will reach 
a given age, not simply because that proportion have 
reached it in times past, but because that fact shows 
the existence there of a particular proportion between 


the causes which shorten and the causes which pro- 
long life to the given extent. 




Debivative Laws are inferior to ultimate laws, both 
in the extent of the propositions, and in their degree 
of certainty within that extent. In particular, the 
uniformities of coexistence and sequence which obtain 
between effects depending on different primaeval 
causes, vary along with any variation in the colloca- 
tion of these causes. Even when the derivative uni- 
formity is between different effects of the same cause, 
it cannot be trusted to, since one or more of the 
effects may be producible by another cause also. 
The effects, even, of derivative laws of causation 
(resulting, i.e. the laws, from the combination of 
several causes) are not independent of collocations ; 
for, though laws of causation, whether ultimate or 
derivative, are themselves universal, being fulfilled 
even when counteracted, the peculiar probability of 
the latter kind of laws of causation being counter- 
acted (as compared with ultimate laws, which are 
liable to frustration only from one set of coimteract- 
ing causes) is fatal to the universality of the derivative 
imiformities made up of the sequences or coexist- 
ences of their effects ; and, therefore, such derivative 
uniformities as the latter are to be relied on only 
when the collocations are known not to have changed. 


Derivative laws, not causative, may certainly be 
extended beyond the limits of observation, but only 
to cases adjacent in time. Thus, we may not predict 
that the sun will rise this day 20,000 years, but we 
can predict that it will rise to-morrow, on the ground 
that it has risen every day for the last 5,000 years. 
The latter prediction is lawful, because^ while we 
know the causes on which its rising depends, we 
know, also, that there has existed hitheltto no percep- 
tible cause to coimteract them ; and that it is opposed 
to experience that a cause imperceptible for so long 
should start into immensity in a day. If the uni- 
formity is empirical only, that is, if we do not know 
the causes, and if we infer that they remain imcounter- 
acted from their efifects alone, we still can extend the 
law to adjacent cases, but only to cases still more 
closely adjacent in time ; since we can know neither 
whether changes in these unknown causes may not 
have occurred, nor whether there may not exist now 
an adverse cause capable after a time of counteracting 

An empirical law cannot generally be extended, 
in reference to Place, even to adjacent cases (since 
there is no uniformity in the collocations of primaeval 
causes). Such an extension is lawful only if the 
new cases are presumably within the influence of 
the same individual causes, even though unknown. 
When, however, the causes are known, and the con- 
junction of the effects is deducible from laws of the 
causes, the derivative uniformity may be extended 
over a wider space, and with less abatement for the 
chance of coimteracting causes. 




One of the many meanings of Anahgy is, Sesem* 
blance of Relations, The value of an analogical 
argument in this sense depends on the showing that, 
on the common circumstance which is the funda- 
TTientum relationis^ the rest of the circumstances 
of the case depend. But, generally, to argue from 
analogy signifies to infer from resemblance in some 
points (not necessarily in relations) resemblance in 
others. Induction does the same : but analogy dififers 
from induction in not requiring the previous proof, 
by comparison of instances, of the invariable con- 
junction between the known and the unknown pro- 
perties; though it requires that the latter should 
not have been ascertained to be unconnected with 
the common properties. 

If a fair proportion of the properties of the two 
cases are known, every resemblance affords groimd 
for expecting an indefinite number of other resem- 
blances, among which the property in question may 
perhaps be found. On the other hand, every dis- 
similarity will lead us to expect that the two cases 
differ in an indefinite number of properties, including, 
perhaps, the one in question. These dissimilarities 
may even be such as would, in regard to one of the 
two cases, imply the absence of that property ; and 
then every resemblance, as showing that the two 
cases have a similar nature, is even a reason for 
presuming against the presence of that property. 
Hence, the value of an analogical argument depends 


on the extent of ascertained resemblance as compared^ 
first, with the amount of ascertained difference, and 
next, with the extent of the unexplored region of 
unascertained properties. 

The conclusions of analogy are not of direct use, 
unless when the case to, which we reason is a case 
adjacent, not, as before, in time or place, but in 
drcumatances. Even then a complete induction 
should be sought after. But the great value of 
analogy, even when faint, in science, is that it may 
suggest observations and experiments, with a view 
to establishing positive scientific truths, for which, 
however, the hypotheses based on analogies must 
never be mistaken. 



The validity of all the four inductive methods de- 
pends on our assuming that there is a cause for every 
event. The belief in this, i.e. in the law of universal 
causation, some affirm, is an instinct which needs no 
warrant other than all men's disposition to believe 
it ; and they argue that to demand evidence of it is 
to appeal to the intellect from the intellect. But, 
though there is no appeal from the faculties all 
together, there may be from one to another : and, as 
belief is not proof (for it may be generated by 
association of ideas as well as by evidence), a case of 
belief does require to be proved by an appeal to 
something else, viz. to the faculties of sense and 


The law of universal causation is, in fact, a 
generalisation from many partial uniformities of 
sequence. Consequently, like these, which cannot 
have been arrived at by any strict inductive method 
(for all such methods presuppose the law of causation 
itself), it must itself be based on inductions per 
amiplicemenumeratiimemj that 18 J generalisations of 
observed facts, from the mere absence of any known 
instances to the contrary. This unscientific process 
is, it is true, usually delusive; but only because, 
and in proportion as, the subject-matter of the ob- 
servation is limited in extent. Its results, whenever 
the number of coincidences is too large for chance 
to explain, are empirical laws. These are ordinarily 
true only within certain limits of time, place, and 
circumstance, since, beyond these, there may be 
different collocations or counteracting agencies. But 
the subject-matter of the law of universal causation 
is so diffused that there is no time, place, or set of 
circumstances, at least within the portion of the uni- 
verse within our observation, and adjacent cases, but 
must prove the law to be either true or false. It 
has, in fact, never been found to be false, but in ever 
increasing multitudes of cases to be true ; and phe- 
nomena, even when, from their rarity or inaccessi- 
bility, or the number of modifying causes, they are 
not reducible universally to any law, yet in some 
instances do conform to this. Thus, it may be re- 
garded as coextensive with all human experience, at 
which point the distinction between empirical laws and 
laws of nature vanishes. Formerly, indeed, it was 
only a very high probability ; but, with our modem 
experience, it is, practically, absolutely certain, and 


it confirms the particular laws of causation^ whence 
itself was drawn, when there seem to be exceptions 
to them. All narrower inductions got by simple 
enumeration are unsafe, till, by the application to 
them of the four methods, the supposition of their 
falsity is shown to contradict this law, though it was 
itself arrived at by simple enumeration. 




Besides uniformities of succession, which always de- 
pend on causation, there are imiformities of coexist- 
ence. These also, whenever the coexisting phenomena 
are efifects of causes, whether of one common cause 
or of several different causes, depend on the laws of 
their cause or causes ; and, till resolved into these 
laws, are mere empirical laws. But there are some 
uniformities of coexistence, viz. those between the 
ultimate properties of kinds, which do not depend 
on causation, and therefore seem entitled to be classed 
as a peculiar sort of laws of nature. As, however, 
the presumption always is (except in the case of those 
kinds which are called simple substances or ele- 
mentary natural agents), that a thing's properties 
really depend on causes though not traced, and we 
never can be certain that they do not ; we cannot 
safely claim (though it may be an ultimate truth) 
higher certainty than that of an empirical law for 
any generalisation about coexistence, that is to say 


(since kiTids are known to us only by their properties, 
and, consequently, all assertions about them are 
assertions about the coexistence of something with 
those properties), about the properties of kinds. 

Besides, no rigorous inductive system can be ap- 
plied to the imiformities of coexistence, since there 
is no general axiom related to them, as is the law of 
causation to those of succession, to serve as a basis 
for such a system. Thus, Bacon's practical appli- 
cations of his method failed, from his supposing 
that we can have previous certainty that a property 
must have an invariable coexistent (as it must have 
an invariable antecedent), which he called its form- 
He ought to have seen that his great logical instru- 
ment, elimination, is inapplicable to coexistences, 
since things which agree in having certain ap- 
parently ultimate properties, often agree in nothing 
else; even the properties which (e.g. Hotness) are 
effects of causes, generally being not connected with 
the ultimate resemblances or diversities in the ob- 
jects, but depending on some outward circumstance. 

Our only substitute for an universal law of co- 
existence is the ancients' induction per enumerO' 
tionem simplicem ubi non reperitur instantia 
contradictoria^ that is, the improbability that an 
exception, if any existed, could have hitherto re- 
mained unobserved. But the certainty thus arrived 
at can be only that of an empirical law, true within 
the limits of the observations. For the coexistent 
property must be either a property of the Mnd^ or 
an accident, that is, something due to an extrinsic 
cause, and not to the hind (whose own indigenous 
properties are always the same). And the ancients' 


class of induction can only prove that withi/ti given 
limitSj either (in the latter case) one common, though 
unknown, cause has always been operating, or (in 
the former case) that no new Jmid of the object has 
as yet or by us been discoverecL 

The evidence is, of course (with respect both to 
the derivative and the ultimate uniformities of co- 
existence), stronger in proportion as the law is more 
general; for the gi-eater the amount of experience 
from which it is derived, the more probable is it 
that counteracting causes, or that exceptions, if any, 
would have presented themselves. Consequently, it 
needs more evidence to establish an exception to a 
very general, than to a special, empirical law. And 
common usage agrees with this principle. Still, 
even the greater generalisations, when not based on 
connection by causation, are delusive, unless grounded 
on a separate examination of each of the included 
infimce species, though certainly there is a probability 
(no more) that a sort of parallelism will be found in 
the properties of different kinds; and that their 
degree of unlikeness in one respect bears some pro- 
portion to their unlikeuess in others. 




The infdrences called 'probable rest on approximate 
generalisations. Such generalisations, besides the 


inferior assurance with which they can be applied to 
individual cases, are generally almost useless as pre- 
misses in a deduction ; and therefore in Science they 
are valuable chiefly as steps towards universal truths, 
the discovery of which is its proper end. But in 
prcLctice^e are forced to use them — 1, when we have 
no others, in consequence of not knowing what general 
property distinguishes the portion of the class which 
have the attribute predicated, from the portion which 
have it not (though it is true that we can, in such a 
case, usually obtain a collection of exactly true pro- 
positions by subdividing the class into smaller classes) ; 
and, 2, when we do know this, but cannot examine 
whether that general property is present or not in 
the individual case; that is, when (as usually m 
moral inquiries) we could get universal majors, but 
not minors to correspond to them. In any case an 
approximate generalisation can never be more than 
an empirical law. Its authority, however, is less 
when it composes the whole of our knowledge of the 
subject, than when it is merely the most available 
form of our knowledge for practical guidance, and 
the causes, or some certain mark of the attribute 
predicated, being known to us as well as the effects, 
the proposition can be tested by our trying to deduce 
it from the causes or mark. Thus, our belief that 
most Scotchmen can read, rests on our knowledge, 
not merely that most Scotchmen that we have known 
about could read, but also that most have been at 
efl&cient schools. 

Either a single approximate generalisation may 
be applied to an individual instance, or several to 
the same instance. In the former case, the proposi- 



tion, as stating a general average, must be applied 
only to average cases ; it is, therefore, generally use- 
less for guidance in afifairs which do not concern 
large numbers, and simply supplies, as it were, the 
first term in a series of approximations. In the 
latter case, when two or more approximations (not 
connected with each other) are separately applicable 
to the instance, it is said that two (or more) probor- 
bilities are jomed by addition^ or, that there is a 
self-corroborative chain of evidence. Its type is: 
Most A. are B ; most C are B ; this is both an A and 
a C; therefore it is probably a B. On the other 
hand, when the subsequent approximation or approxi- 
mations is or are applicable only by virtue of the 
application of the first, this is joining two (or more) 
probabilities, by way of Deduction, which produces 
a adf-infirrriative chain ; and the type is : Most A 
are B; most C are A; this is a C; therefore it is 
probably an A ; therefore it is probably a B. As, in 
the former case, the probability increases at each 
step, so, in the latter, it progressively dwindles. It 
is measured by the probability arising from the first 
of the propositions, abated in the ratio of that arising 
from the subsequent ; and the error of the conclusion 
amounts to the aggregate of the errors of all the 

In two classes of cases (exceptions which prove the 
rule) approximate can be employed in deduction as 
usefully as complete generalisations. Thus, first, we 
stop at them sometimes, from the inconvenience, not 
the impossibility, of going further ; and, by adding 
provisos, we might change the approximate into an 
imi versa! proposition; the sum of the provisos being 


then the sum of the errors liable to affect the con- 
clusion. Secondly, they are used in Social Science 
with reference to masses with absolute certainty, 
even without the addition of such provisos. Although 
the premisses in the Moral and Social Sciences are 
only probable, these sciences differ from the exact 
only in that we cannot decipher so many of the laws, 
and not in the conclusions that we do arrive at being 
less scientific or trustworthy. 



There are, we have seen, five facts, one of which every 
proposition must assert, viz. Existence, Order in 
Place, Order in Time, Causation, and Resemblance. 
Causation is not fundamentally difi^erent from Coex- 
istence and Sequence, which are the two modes of 
Order in Time. They have been already discussed. 
Of the rest. Existence, if of things in themselves, is 
a topic for Metaphysics, Logic regarding the exist- 
ence oi 'phenomena only ; and as this, when it is not 
perceived directly, is proved by proving that the im- 
known phenomenon is connected by succession or 
coexistence with some known phenomenon, the fact 
of Existence is not amenable to any peculiar induc- 
tive principles. There remain Resemblance and 
Order in Place. 

As for Resemblance, Locke indeed, and, in a more 
unqualified way, his school, asserted that all reason- 
ing is simply a comparison of two ideas by means of a 

F 2 


third, and that knowledge is only the perception of the 
agreement or disagreement, that is, the resemblance 
or dissimilarity, of two ideas : they did not perceive, 
besides erring in supposing ideas, and not the phe- 
nomena themselves, to be the subjects of reasoning, 
that it is only sometimes (as, particularly, in the 
sciences of Quantity and Extension) that the agree- 
ment or disagreement of two things is the one thing 
to be established. Eeasonings, however, about jRe- 
eemblances, whenever the two things cannot be 
directly compared by the virtually simultaneous 
application of our faculties to each, do agree with 
Locke's account of reasoning ; being, in fact, simply 
such a comparison of two things through the medium 
of a third. There are laws or formulaB for guiding 
the comparison; but the only ones which do not 
come under the principles of Induction already dis- 
cussed, are the mathematical axioms of Equality, 
Inequality, and Proportionality, and the theorems 
based on them. For these, which are true of all 
phenomena, or, at least, without distinction of origin, 
have no connection with laws of Causation, whereas 
all other theorems asserting resemblance have, being 
true only of special phenomena originating in a 
certain way, and the resemblances between which 
phenomena must be derived from, or be identical 
with, the laws of their causes. 

In respect to Order in Place, as well as in respect 
to Kesemblance, some mathematical truths are the 
only general propositions which, as being independent 
of Causation, require separate consideration. Such 
are certain geometrical laws, through which, from the 
position of certain points, lines, or spaces, we infer 


the position of others, without any reference to their 
physical causes, or to their* special nature, except as 
regards position or magnitude. There is no other 
peculiarity as respects Order in Place. For, the 
Order in Place of efifects is of course a mere conse- 
quence of the laws of their causes; and, as for 
primaeval causes, in their Order in Place, called 
their coUocation^ no imiformities are traceable. 

Hence, only the methods of Mathematics remain 
to be investigated ; and they are partly discussed in 
the Second Book. The directly inductive truths of 
Mathematics are few: being, first, certain proposi- 
tions about existence, tacitly involved in the so- 
called definitions ; and secondly, the axioms, to which 
latter, though resting only on induction, per svm- 
plicem enuToerationemy there could never have been 
even any apparent exceptions. Thus, every arith- 
metical calculation rests (and this is what makes 
Arithmetic the type of a deductive science) on the 
evidence of the axiom : The sums of equals are equals 
(which is coextensive with nature itself) — combined 
with the definitions of the numbers, which are seve- 
rally made up of the explanation of the name, 
which connotes the way in which the particular 
agglomeration is composed, and of the assertion of a 
fact, viz. the physical property so connoted. 

The propositions of Arithmetic affirm the modes 
of formation of given numbers, and are true of all 
things under the condition of being divided in a 
particular way. Algebraical propositions, on the other 
hand, affirm the equivalence of different modes of 
formation of numbers generally, and are true of all 
things under condition of being divided in any way* 


Though the laws of Extension are not, like those 
of Number, remote from visual and tactual imagina- 
tion, Geometry has not commonly been recognised 
as a strictly physical science. The reason is, first, 
the possibility of collecting its facts as effectually 
from the ideas as from the objects; and secondly, 
the illusion that its ideal data are not mere hypo- 
theses, like those in now deductive physical sciences, 
but a peculiar class of realities, and that therefore 
its conclusions are eoaceptionally demonstrative. 
Eeally, all geometrical theorems are laws of external 
nature. They might have been got by generalising 
from actual comparison and measurement; only, 
that it was found practicable to deduce them from a 
few obviously true general laws, viz. The sums of 
equals are equals ; things equal to the same thing 
are equal to one another (which two belong to the 
Science of Number also) ; and, thirdly (what is no 
merely verbal definition, though it has been so called) : 
Lines, surfaces, solid spaces, which can be so applied 
to one another as to coincide, are equal. The rest 
of the premisses of Geometry consist of the so-called 
definitions, which assert, together with one or more 
properties, the real existence of objects corresponding 
to the names to be defined. The reason why the 
premisses are so few, and why Geometry is thus 
almost entirely deductive, is, that all questions of 
position and figure, that is, of quality, may be re- 
solved into questions of quantity or magnitude, and 
so Geometry may be reduced to the one problem of 
the measurement of magnitudes; that is, to the 
finding the equalities between them. 

Mathematical principles can be applied to other 


sdences. All causes operate according to mathema- 
tical laws; an effect being ever dependent on the 
quantity or a function of the agent, and generally on 
its position too. Mathematical principles cannot, 
indeed, as M. Comte has well explained, be usefully 
applied to physical questions, whenever the causes are 
either too inaccessible for their numerical laws to 
be ascertained, or are too complex for vs to compute 
the effect, or are ever fluctuating. And, in propor- 
tion as physical questions cease to be abstract and 
hypothetical, mathematical solutions of them become 
imperfect. But the great value of mathematical 
training is, that we learn to use its method (which is 
the most perfect type of the Deductive Method), that 
is, we learn to employ the laws of simpler phenomena 
to explain and predict those of the more complex. 



The result of examining evidence is not always belief, 
or even suspension of judgment, but is sometimes 
positive disbelief. This can ensue only when the 
affirmative evidence does not amount to full proof, 
but is based on some approximate generalisation. In 
such cases, if the negative evidence consist of a 
stronger, though still only an approximate, generalisa- 
tion, we think the fact improbable, and disbelieve it 
provisionally; but if of a complete generalisation based 
on a rigorous induction, it is disbelieved by us totally, 
and thought impossible. Hence, Hume declared 
miracles incredible, as being, he considered, contrary 


to a complete induction. Now, it is true that in the 
absence of any adequate counteracting cause, sl fact 
contrary to a complete induction is incredible, what- 
ever evidence it may be grounded on ; unless, indeed, 
the evidence go to prove the supposed law inconsistent 
with some better established one. But when a mi- 
racle is asserted, the presence of an adequate count- 
eracting cause is asserted, viz. a direct interposition 
of an act of the will of a Being having power over 
nature. Therefore, all that Hume proved is, that we 
cannot believe in a miracle unless we believe in the 
power, and the will, of the Deity to interfere with exist- 
ing causes by introducing new ones ; and that, in de- 
fault of such belief, not the most satisfactory evidence 
of our senses or of testimony can hinder us from hold- 
ing a seeming miracle to be merely the result of 
some unknown natural cause. The argument of Dr. 
Campbell and others against Hume, however, is im- 
tenable, viz. that, as we do not disbelieve an alleged 
^act (which may be something conforming to the 
uniform course of experience) merely because the 
chances are against it, therefore we need never dis- 
believe any fact supported by credible testimony 
(even if contrary to the uniform course of experience). 
But this is to confoimd improbability before the fact, 
which is not always a ground for disbelief, with im- 
probability after the fact, which always is. 

Facts which conflict with special laws of causation 
are only improbable before the fact ; that is, our dis- 
belief depends on the improbability that there could 
have been present, without our knowledge, at the 
time and place of the event, an adequate counter- 
acting cause. So, too, with facts which conflict with 


the properties of kinds (which, are uniformities of 
mere coexistence not proved to be dependent on cau- 
sation), that is, facts which assert the existence of a 
new kind ; such facts we disbelieve only if, the genera- 
lisation being sufficiently comprehensive, some pro- 
perties are said to have been found in the supposed 
new kind disjoined from others which always have 
been known to accompany them. When the asser- 
tion would amount, if admitted, only to the existence 
of an unknown cause or an anomalous kmd, uncon- 
formahlCy but, as Hume puts it, Tvot contrary to ex- 
perience, in circumstances so little explored, that it 
is credible hitherto unknown things may there be 
found, and when prejudice cannot have tempted to the 
assertion, one ought neither to admit nor to reject 
the testimony, but to suspend judgment till it be 
confirmed or disproved from other sources. Only 
facts, then, which are contradictory to the laws of 
Number, Extension, and Universal Causation (since 
these know no counteraction or anomaly), or to laws 
nearly as general, are improbable after, as well as 
before the fact, and only these we should term a6so- 
lutely impossible^ calling other facts improbable 
only, or, at most, impossible in the circumstances of 
the case. 

Between these two species of improbabilities lie 
coincidences ; that is, combinations of chances pre- 
senting some unexpected regularity assimilating 
them in so far to the results of law. It was thought 
by d'Alembert that, though regular combinations 
are as probable as others according to the mathe- 
matical theory, some physical law prevents them 
from occurring so often. Now, stronger testimony 



may indeed be needed to support the assertion of such 
a combination as, e.g. ten successive throws of sixes 
at dice, because such a regular series is more likely 
than an irregular series to be the result of design ; 
and because even the desire to excite wonder is likely 
to tempt men to assert the occurrence falsely, though 
this probability must be estimated afresh in every 
instance. But though such a series aeefma peculiarly 
improbable, it is only because the comparison is 
tacitly made, not between it and any one particular 
previously fixed series of throws, but between all 
regular and all irregular successions taken together. 
The fact is not in itself more improbable ; and no 
stronger evidence is needed to give it credibility, 
apart from the reasons above mentioned, than in the 
case of ordinary events. 





The mental process which Logic deals with, viz. the 
investigation of truth by means of evidence, is always 
a process of Induction. Since Induction is simply 
the extension to a class of something observed to be 
true of certain members of it. Observation is the first 
preliminary to it. It is, therefore, right to consider, 
not indeed how or what to observe (for this belongs 
to the art of Education), but under what conditions 
observation is to be relied on. The sole condition 
is, that the supposed observation should really be an 
observation, and not an inference, whereas it is usually 
a compound of both, there being, in our propositions, 
besides observation which relates only to the sensa- 
tions, an inference from the sensations to the objects 
themselves. Thus so-called errors of sense are only 
erroneous inferences from sense. The sensations 
themselves must be genuine ; but, as they generally 
arise on a certain arrangement of outward objects 
being present to the organs, we, as though by instinct, 
infer this arrangement even when not existing. The 
sole object, then, of the logic of observation, is to 
separate the inferences from observation from the 


observations themselves, the only thing really 
observed by the mind (to waive the metaphysical 
problem as to the perception of objects) being its 
own feelings or states of consciousness, outward, viz. 
Sensations, and inward, viz. Thoughts, Emotions, and 

As in the simplest observation much is inference, 
so, in describing an observed fact, we not merely 
describe the fact, but are always forced to class it, 
affirming the resemblance, in regard of whatever is 
the ground of the name being given, between it 
and all other things denoted by the name. The 
resemblance is sometimes perceived by direct com- 
parison of the objects together; sometimes (as, e.g. 
in the description of the earth's figure as globular 
and so forth) it is inferred through intermediate 
marks, i.e. deductively. When a hypothesis is made 
(e.g. by Kepler, as to the figure of the earth's orbit), 
and then verified by comparison with actual obser- 
vations. Dr. Whewell calls the process Colligation of 
Facts by appropriate Conceptions, and affirms it to 
be the whole of Induction. But this also is only de- 
scription, being really the ordinary process of ascer- 
taining resemblance by a comparison of phenomena ; 
and, though subsidiary to Induction, it is not itself 
Induction at all. 



TTiis Chapter is a digression. 

Abstract Ideas, that is, General Conceptions, cer- 
tainly do exist;, however Metaphysics may decide as 


to their composition. They represent in our minds 
the whole classes of things called by the general 
names ; and, being implied in the mental operation 
whereby classes are formed, viz. in the comparison 
of phenomena, to ascertain in what they agree, cannot 
be dispensed with in induction, since such a com- 
parison is a necessary preliminary to an induction, 
and more than two objects cannot well be compared 
without a type, in which capacity conceptions 

But, though implied in the comparison, it does not 
follow that, as Dr. Whewell supposes, they must have 
existed in the mind prior to comparison. Some- 
times, but only sometimes, they are pre-existent to 
the comparison of the particular facts in question, 
being, as was Kepler's hypothesis of an ellipse, familiar 
conceptions borrowed from different facts, and super- 
induced, to use Dr. Whewell's expression, on the facts 
in question. But even such conceptions are the re- 
sults of former comparisons of individual facts. And 
much more commonly (and these are the more diffi- 
cult cases in science) conceptions are not pre-existent 
even in this sense ; but they have to be got (e.g. the 
Idea of Polarity) by abstraction, that is, by compari- 
son, from among the very phenomena which they 
afterwards serve to arrange, or, as Dr. WheweU says, 
to connect They seem to be pre-existent ; but this 
is only because the mind keeps ever forming concep- 
tions from the facts, which at the time are before it, 
and then tentatively applies these conceptions (which 
it is always remodelling, dropping some which are 
found not to suit after-found facts, and generalising 
others by a further effort of abstraction) as types of 


comparison for phenomena subsequently presented 
to it; so that, being found in these later stages of 
the comparison already in the mind, they appear in 
the character simply of types, and not as being also 
themselves results of comparison. Really they are 
always both ; and the term comparison expresses as 
well their origin as (and this far more exactly than 
to connect or to superindiLce) their function. 

Dr. Whewell says that conceptions must be appro- 
priate and clea/r. They must, indeed, be appropriate 
relatively to the purpose in view (for appropriateness 
is only relative) ; but they cannot avoid being appro- 
priate (though one may be more so than another) if 
our comparison of the objects has led to a conception 
corresponding to any real agreement in the facts : the 
ancients' and schoolmen's conceptions were often 
absolutely inappropriate, because grounded on only 
apparent agreement. So, again, they must be clear 
in the following sense; that is to say, a sufficient 
number of facts must have been carefully observed^ 
and accurately remembered. It is also a condition 
(and one implied in the latter qualities) of clearness, 
that the conception should be determinate^ that is, 
that we should know precisely what agreements we 
include in it, and never vary the connotation except 

Activity, carefulness, and accuracy in the observing 
and comparing faculties are therefore needed; the 
first quality to produce appropriateness, and the latter 
two, clearness. Moreover, scientific vmagination, 
i.e. the faculty of mentally arranging known elements 
into new combinations, is necessary for forming true 
conceptions; and the mind should be stored with 


previously acquired conceptions, kindred to the sub- 
ject of inquiry, since a comparison of the facts them- 
selves often fails to suggest the principle of their 
agreement ; just as, in seeking for anything lost, we 
often have to ask ourselves in what places it may be 
hid, that we may search for it ther§. 



As reaaoning is from particulars to particulars, and 
consists simply in recognising one fact as a mark of 
another, or a mark of a mark of another, the only 
necessary conditions of the exertion of the reasoning 
power are senses, to perceive that two facts are con- 
joined ; and association, as the law by which one of 
the two facts raises up the idea of the other. The 
existence of artificial signs is not a third necessary 
condition. It is only, however, the rudest inductions 
(and of such even brutes are capable) that can be 
made without language or other artificial signs. 
Without such we could avail ourselves but little of 
the experience of others ; and (except in cases involv- 
ing our intenser sensations or emotions) of none of 
our own long past experience. It is only through 
the medium of such permanent signs that we can 
register uniformities ; and the existence of uniformi- 
ties is necessary to justify an inference, even in a 
single case, and they can be ascertained once for all. 
General names are not, as some have argued, a 
mere contrivance to economise words. For, if there 


yreie a name for every individual object, but no gene- 
ral names, we could not record one uniformity, or 
the result of a single comparison. To eflfect this, all 
indeed, that are indispensable, are the abstract names 
of attributes ; but, in fact, men have always given 
general names to objects also. 



Concrete general names (and the meaning of ab' 
stract names depends on the concrete) should have a 
fixed and knowable connotation. This is easy enough 
when, as in the case of new technical names, we 
choose the connotation for ourselves ; but it is hard 
when, as generally happens with names in common 
use, the same name has been appUed to diflferent 
objects, from only a vague feeling of resemblance. 
For, then, after » a time, general propositions are 
made, in which predicates are applied to those names; 
and these propositions make up a loose connotation 
for the class name, which, and the abstract at about 
this same period formed from it, are consequently 
never understood by two people, or by the same person 
at different times, in the same way. The logician has 
to fix this fluctuating connotation, but so that the 
name may, if possible, still denote the things of which 
it is currently affirmed. To effect this double object 
(which is called, though improperly, defining not 
the name but the thing\ he must select from the 


attributes in which the denoted objects agree, choos- 
ing, as the common properties are always many, and, 
in a hirid, innumerable, those which are familiarly 
predicated of the class, and out of them, if possible, 
or otherwise, even in preference to them, the ones 
on which depend, or which are the best marks of, 
those thus familiarly predicated. To do this suc- 
cessfully, presumes a knowledge of all the common 
properties of the class, and the relations between 
them of causation and dependence. Hence the dis- 
cussion of non-verbal definitions (which Dr. WheweU 
calls the Explication of Conceptions) is part of the 
business of discovery. Hence, too, disputes in 
science have often assumed the form of a battle of 
definitions ; such definitions being not arbitrary, but 
made with a view to some tacitly assumed principle 
needing expression. 

We ought, if possiijle, to define in consonance' 
with the denotation. But sometimes this is im- 
possible, through the name having accumulated 
transitive applications, in its gradual extension from 
one object, in relation to which it connotes one 
property, to another which resembles the former, but 
in quite a different attribute. These transitive ap- 
plications, even when found to correspond in different 
languages, may have arisen, not from any common 
quality in the objects, but from some association of 
ideas founded on the common nature and condition 
of mankind. When the association is so natural and 
habitual as to become virtually indissoluble, the 
transitive meanings are apt to coalesce in one com- 
plex conception ; and every new transition becomes 
a more comprehensive generalisation of the term in 


question. In such cases the ancients and schoolmen 
did not suspect, what otherwise they carefully watched 
for, viz. ambiguities: not Plato, though his Com- 
parisons and Abstractions preparatory to Induction 
are perfect ; not even Bacon, in his speculations on 
Heat. Hence have sprung the various vain attempts 
to trace a common idea in all the uses of a word, 
such as Cause (Efficient, Material, Formal, and Final 
Cau8e\ the Ooody the Fit 

When a term is applied to many diflFerent objects 
agreeing all only in one quality (e.g. things beauti- 
fuly in Ojgreeahleneaa), though moat agree in some- 
thing besides, it is better to exclude part of the 
denotation than of the connotation, however indis- 
tinct : else language ceases to keep alive old experi- 
ence, alien perhaps to present tendencies. In any case, 
words are always in danger of losing part of their 
connotation. For, just one or two out of a complex 
cluster of ideas, and sometimes merely the look or 
sound of the word itself, is often all that is absolutely 
necessary for the suggesting another set of ideas to 
continue the process of thought ; and consequently, 
some metaphysicians have even fancied that all 
reasoning is but the mechanical use of terms accord- 
ing to a certain form. If persons be not of active 
imaginations, the only antidote against the propensity 
to let slip the connotation of names, is the habit of 
predicating of them the properties connoted ; though 
even the propositions themselves, as may be seen from 
the way in which maxims of Eeligion, Ethics, and 
Politics are used, are often repeated merely mechani- 
cally, not being questioned, but also not being felt, 
^luch of our knowledge recorded in words is ever 


oscillating between its tendency, in consequence of 
diflferent generations attending exclusively to different 
properties in names, to become partially dormant, 
and the counter-efforts of individuals, at times, to 
revive it by tracing the forgotten properties histori- 
cally in the almost mechanically repeated formulas of 
propositions ; and, when they have been there redis- 
covered, promulgating them, not as discoveries, but 
with authority as what men still profess to believe. 
The danger is, lest the formula itself be dismissed 
by clear-headed narrow-minded logicians, and the 
connotation fixed by them (in order that the denota- 
tion may be extended) in accordance with the present 
use of the term. Then, if the truths be at any time 
rediscovered, the prejudice is against them as novel- 
ties. The selfish theory of xnorals partly feU because 
the inconsistency of received formulas with it 
prompted a reconsideration of its basis. What would 
have been the result if the formulas attaching odium 
to selfishness, praise to self-sacrifice, had been dis- 
missed, if this indeed had been possible I Language^ 
in short, is the depositary of all experience, which, 
being the inheritance of posterity, we have a right to 
vary, but none to curtail. We may improve the con- 
clusions of our ancestors ; we should not let drop any 
of their premisses ; we may alter a word's connotation ; 
but we must not destroy part of it. 




The connotation of names shifts not only by reason of 
gradual inattention to some of the common properties. 


which, if language were ruled by convention alone, 
would be in their entirety both the perpetual and 
the sole constituents of the connotation; but also 
from the incorporation in the connotation, in addition 
to these, and often, finally, to the exclusion of them 
altogether, of other circumstances at first only casually 
associated with it. These collateral associations are 
the cause why there are so few exact synonymes; 
and why the dictionary meaning, or Definition, is 
so bad a guide to its uses, as compared with its 
history, since the latter explains the law of the sue- 

successive uses. 

Two counter-movements are always going on in 
language. One is generalisation, by which words are 
ever losing part of their connotation, and becoming 
more general. This arises, partly from men, such 
as historians and travellers, using words, especially 
those expressing complicated mental and social facts 
strange to them, in a loose sense, in ignorance of the 
true connotation ; partly, from known things multi- 
plying faster than names for them ; partly, also, from 
the wish to give people some notion of a new object 
by reference to a known thing resembling it however 
slightly. The other movement is specialisation ; and 
by it words (even the same words which, as, e.g. 
pagan and villain, later get generalised in a new 
direction) are ever taking a fresh connotation, 
through their denotation being diminished. Spe- 
cialisations often occur even in scientific nomen- 
clature, a word which expressed general characters 
becoming confined to a specific substance in which 
these characters are predominant. So it is when any 


set of persons has to think of one species oftener 
than of any other contained in* the genus : e.g. some 
sportsmen mean partridges hy the term bi/rds. But, 
as ideas of our pleasures and pains and their supposed 
causes, cling, most of all, by association to what they 
have been once connected with, the great source of 
specialisation is the addition of the ideas of agreeable- 
ness or painfulness, and approbation or censure, to 
the connotation. And hence arises the fallacy of 
qv£8tion-begging names referred to later on. 

It is the business of logicians not to ignore, for 
they cannot prevent, transformations of terms in 
common use, but to trace and embody them, and 
men's half unconscious reasons for them, in distinct 



Not only must words have a fixed and knowable 
meaning ; but also, no important meaning should be 
without its word : that is, there should be a name 
for everything which we have often to make asser- 
tions about. There should be, therefore, first, names 
suited to describe all the individual facts ; secondly, 
a name for every important common property de- 
tected by comparing those facts; and, thirdly, a 
name for every kind. 

First, it conduces to brevity and clearness to have 
separate names for the oft-recurring combinations of 
feelings ; but, as these can be defined without refer- 
ence back to the feelings themselves, it is enough 


for a descriptive terminology, if there be a name for 
every variety of elementary feeling, since none of 
these can be defined, or indicated to a person, except 
either by his having the sensation itself, or being 
referred through a known mark to his remembrance 
of it. The meaning of the name when given to a 
feeling is fixed, in the first instance, by convention, 
and must be associated immediately , not through 
the usage of ordinary language, with the feeling, so 
that it may at once recall the latter. But even 
among the elementary feelings, those purely mental, 
and also sensations, such as those from disease, the 
identity of which in different persons cannot be de- 
termined, cannot be exactly desmhed. It is only 
the impressions on the outward senses, or those in- 
ward feelings connected uniformly with outward ob- 
jects (and, consequently, sciences, such as botany, 
conversant with outward objects), which are sus- 
ceptible of an exact descriptive language. 

Secondly, there must also be a separate name 
for every important common property recognised 
through that comparison of observed instances which 
is preparatory to induction (including names for the 
classes which we artificially construct in virtue of 
those properties). For, although a definition would 
often convey the meaning, both time and space are 
saved, perspicuity promoted, and the attention excited 
and concentrated, by giving a brief and compact 
name to each of the new general conceptions^ as 
Dr. Whewell calls them, that is, the new results of 
abstraction. Thenceforward the name nails down 
and clenches the \mfamiliar combination of ideas, 
and suggests ite own definition. 


Thirdly, as, besides the artificial classes which are 
marked out from neighbouring classes by definite 
properties to be arrived at by abstraction, there are 
classes, viz. hmdsy distinguished severally by an 
unknown multitude of independent properties (and 
about which classes therefore many assertions will be 
made), there must be a name for every kind. That 
is, besides a terminology, there must be a nomen- 
clature, i.e. a collection of the names of all the 
lowest kmds, or injimce spedea. The Linnsean 
arrangements of plants and animals, and the French 
of chemistry, are nomenclatures. The peculiarity of 
a name which belongs to a nomenclature is, not that 
its meaning resides in its denotation instead of its 
connotation (for it resides in its connotation, like 
that of other concrete general names); but that, 
besides connoting certain attributes which its defi- 
nition explains, it also connotes that these attributes 
are distinctive of a kind ; and this fact its definition 
cannot explain. 

A philosophical language, then, must possess, first, 
precision, and next (the subject of the present 
chapter), completeness. Some have argued that, in 
addition, names are fitted for the purposes of thought 
in proportion as they approximate to mere symbols 
in compactness, through meaninglessness, and capa- 
bility of use as counters without reference to the 
various objects which, though utterly diflferent, they 
may thus at diflferent times equally well represent. 
Such are, indeed, the qualities enabling us to employ 
the figures of arithmetic and the symbols of algebra 
perfectly mechanically according to general technical 
rules. But, in the first place, in our direct inductions. 

120 OPERATIONS subsidiahy to induction. 

at all events, depending as they do on our perception 
of the particulars of the agreement' and difference of 
the phenomena, we could never dispense with a 
distinct mental image of the latter. Further, even 
in deduction, though a syllogism is conclusive from 
its mere form, if the terms are unambiguous, yet the 
practical validity of the reasoning depends on the 
hypothesis that no counteracting cause has interfered 
with the truth of the premisses. We can assure 
ourselves of this only by studying the phenomena at 
every step. For it is only in geometry and algebra 
that there is no danger from the Composition of 
Causes, or the superseding of one set of laws by 
another; and that, therefore, the propositions are 
categorically true. In sciences in general, then, the 
object should be, so far from keeping individualising 
peculiarities out of «ight, to contrive the greatest 
possible obstacles to a merely mechanical use of 
language : we should carefully keep alive a conscious- 
ness of its meaning, by referring, by aid of derivation 
and the analogies between the ideas of the roots and 
the derivatives, to the origin of words ; and as words, 
however philosophically constructed, are always 
tending, like coins, to have their inscription worn 
off, we should 'be ever stamping them afresh. This 
we shall effect, if we contemplate habitually, not the 
formulas which record the laws of the phenomena 
(for, if so, the formulas will themselves progressively 
lose their meaning), but the phenomena whence the 
laws were collected; and we must conceive these 
phenomena in the concrete, and clothe them in cir- 




Eyert name which connotes an attribute thereby 
divides, but only incidentally, all things, known and 
unknown, real and imagined, into two classes, viz, 
those which have, and those which have not the attri- 
bute. But sometimes the naming itself is but the 
secondary and subsidiary, and the classification, the 
primary object. The general problem of such classi- 
fication is, to provide that things shall be thought of 
in such groups, and the groups in such an order, as 
will best promote the remembrance and ascertainment 
of their laws. Its subjects are real things ex- 
clusively, but all real things, since, to place one 
object in a group, we ought to know the divisions of 
nature at large. 

Any property may be the basis for a classification , 
but those best suited are properties which are causes, 
or, next, as the cause of a class's chief peculiarities 
seldom serves as its diagnostic, any effect which is a 
sure mark both of the cause and of the other effects. 
Only a classification so grounded is scientific ; the 
same also is not technical or artificial, but natural, 
and emphatically natural (as compared with classi- 
fications in an inferior degree also na^uraZ, which are 
based on properties important with reference to the 
reasoner's special practical objects), when the classi- 
fication is based on those properties which would 
most impress one who knew all the properties, but 
was not interested particularly in any one. Further, 
it is a great recommendation of a classification, that 




it groups together things of like general aspect ; but 
this is not a sine qua non : a group may be natural 
even if based on very unobvious properties, provided 
these are marks of many other properties, though 
certainly then there should be also some more obvious 
property to act as a mark of the unobvious ones 
which form the real basis. 

As the first principle of natural classification is 
that the classes must be so formed that the objects 
composing each may have as many properties in 
common as possible to serve as predicates, all kinds 
should have places among the natural groups, since 
the common properties of hindsy and, therefore, the 
general assertions that can be made about them, are 
innumerable. But kinds are too few to make up 
the whole of a classificJsftion : other classes also may 
be eminently natural^ though marked out from each 
other only by a definite number of properties. Of 
neither sort of natural groups is Dr. Whewell's 
theory strictly true, viz. that every natural group is 
not determined by definition, that is, by definite 
characters which can be expressed in words, but is 
fixed by Type. He explains that a type is an ex- 
ample of any class, for instance, a species of a genus, 
which possesses all the characters and properties of 
the genus in a marked way ; that round this type- 
species are grouped all the other species, which, 
though deviating from it in various directions and 
degrees, yet are of closer affinity to it than to the 
centre of any other group; and that this is the 
reason why propositions about natural groups so 
often state matters as being true not in all cases, but 
only in most. Now, there is a truth, but only a 


partial truth, in this doctrine. It is this : in forming 
natural groups, species which want certaiji of the 
class-characters, some one, and others another, are 
classed with those (the majority) that have them all, 
because they are more like (that is, in fact, have 
more of the common characters of) that particular 
group than of any other. On account of the feeling 
of vagueness hence engendered, we certainly, in de- 
ciding if an object belong to the group, do generally 
(and must, when the classification is made expressly 
with a view to a special inductive enquiry) refer 
mentally, not as a substitute for, but in illustration 
of the definition of the group, to some standard 
specimen which has all the characters well developed. 
But not the less, therefore, are all natural^ equally 
with all artificial, groups framed with distinct refer- 
ence to certain definite characters. In the case of 
hinds, a few characters are chosen as marks of the 
rest. In the case of other natural groups, the for- 
mation of the larger groups, into which we collect 
the infimce spedes^ is suggested indeed by resemb- 
lance to types (since we form each such larger group 
roimd a selected kind which serves as its exemplar) ; 
but the group itself, when formed, is determined by 
definite characters. 

Class names should by the mode of their construc- 
tion help those who have learnt about the thing, to 
remen^ber it, and those who have not learnt, now to 
leam, by being merely told the name. This is best 
eficcted, in the case of kinds, when the word indicates 
by its very formation the properties it connotes. But 
this is seldom possible. For, though a Hnd-name 

connotes not all the fciricZ-properties, but some only 

o 2 


which serve as sure marks of the rest, even these 
have been found too many to be included conveni- 
ently in a name (except in Elementary Chemistry, 
where every compound substance has one distinctive 
index-property, viz. the chemical composition). A 
subsidiary resource is to point out the kincFs nearest 
natural aflSnities. For instance, in the binary No- 
menclature of Botany and of Zoology, the name of 
every species consists of the name of the naturcd 
group next above, with a word added expressive of 
some quality in the nature or mode of discovery, or 
what not, of the particular species itself. By this 
device (obtaining at present only in Botany and 
Zoology), as well is the expression, in the name, of 
many of the kincPa characters secured, as the use of 
names economised, and the memory relieved. Except 
for some such plan, what hope of naming the 60,000 
known species of Plants ? 



The object of Classification generally is to bring our 
ideas of objects into the order best fitted for prose- 
cuting inductive enquiries into the laws of the phe- 
nomena generally. But a Classification which aims 
at facilitating an inductive enquiry into the laws of 
some special phenomenon, must be based on that 
phenomenon itself. The requisites of such a classi- 
fication are, first, the bringing into one class all 
kinds of things which exhibit the phenomenon ; next, 


the arranging them in a series^ according to the 
degrees in which they exhibit it. Such a classifica- 
tion has been largely applied in Comparative Anatomy 
and Physiology (and these alone), since there has 
been found a recognisable difference in the degree in 
which animals possess one main phenomenon, viz. 
Animal Life. 

This arrangement of the instances, whence the law 
is to be collected, in a series, is that which is always 
implied in and is a condition of any application of 
the method, viz. that of Concomitant Variations, 
which must be used when conjoined circumstances 
cannot easily be separated by experiment. But some- 
times (and it is so in Zoology) the law of the subject 
of the special encjuiry (e.g. Animal Life) has such 
influence over the general character of the objects, 
that all other differences among them seem mere 
modifications of it; and then the classification re- 
quired for the special purpose becomes the deter- 
mining principle of the classification of the same 
objects for general purposes. 

To recognise the identity of phenomena which thus 
differ only in degree, we must assume a type-species. 
This will be that kind which has the class-properties 
in their greatest intensity (and, therefore, most easily 
studied with all their effects); and we must conceive 
the other varieties as instances of degeneracy from 
that type. 

The divisions of the series must be determined by 
the principles of natural grouping in general (that 
is, in effect, by natural affinity); in subordination, 
however, to the principle of a natural series ; that 
is, in the same group must not be placed things 


which ought to occupy diflferent points of the general 

Zoology affords the only complete example of the 
true principles of rational classification, whether as 
to the formation of groups or of series. Yet the 
same principles are applicable to all cases (to art and 
business as well as science) where the various parts 
of a wide subject have to be brought into mental 





The habit of reasoning well is the only complete 
safeguard against reasoning ill, that is, against draw- 
ing conclusions with insufficient evidence, a practice 
which the various contradictory opinions, particularly 
about the phenomena relating to Man, show to be 
even now common, and that too among the most 
enlightened. But, to be able to explain an error is 
a necessary condition of seeing the truth ; for, * Con- 
trariorum eadem est Scientia.' Consequently, a work 
on Logic must classify Fallacies, that is, the varieties 
of Apparent Evidence; for they can be classified, 
though not in respect of their negative quality of 
being either not evidence at all, or inconclusive, yet 
in respect of the positive property they have of apr 
pearing to be evidence. 

As Logic has been here treated as embracing the 
whole reasoning process, so it must notice the falla- 
cies incident to any part of it (not to Eatiocination 
merely), whether arising from faulty Induction, or 
from faulty Ratiocination, or from dispensing wholly 
with either or both of them. It does not treat of 
errors from negligence, or from inexpertness in using 


right methods, nor does it treat of errors from moral 
causes, viz. Indiflference to truth, or Bias by our wishes 
or our fears; for the moral causes are but the remote 
ajid predisposinffy not the exciting causes of opinions ; 
and therefore inferences from them, since they must 
always involve the intellectual operation of admitting 
insufficient evidence as sufficient, really come under 
a classification of the things which wrongly appear 
evidence to the understanding. 

Fallacies may be arranged, with reference either 
to the cause which makes them (erroneously) appear 
evidence, or to the particular kind of evidence they 
simulate. The following classification is grounded 
on both these considerations jointly. 



The business of Logic is, not to enumerate false 
opinions, but to enquire what property in the facts 
led to them, that is, what peculiarity of relation 
between two facts made us suppose them habitually 
conjoined or disjoined, and thus regard the presence 
or absence of the one as evidence of that of the other. 
For every such property in the facts, or our mode of 
considering them, there is a corresponding class of 

As the supposed habitual connexion or repugiiance 
of two facts may be admitted, either as a self-evident 
and axiomatic truth, or as itself an inference, the 
first great division is into Fallacies of Simple In- 


spection or a priori Fallacies, and Fallacies of Infer- 
ence. But there is also an intermediate class. For, 
sometimes an inference is erroneous through our not 
conceiving what our premisses precisely are, and 
from our therefore substituting new premisses for 
the old, or a new conclusion for the one we under- 
took to prove; and this is called the Fallacy of 
Confusion. Under this head, indeed, of Fallacies 
of Confusion, might strictly be brought almost any 
fallacy, though falling also under some other head : 
for, some of the links in an argument, especially if 
sophistical, are sure to be suppressed ; and, it being 
left doubtful which is the proposition to be supplied, 
we can seldom tell with certainty under which class 
the fallacy absolutely comes. It is, however, con- 
venient to reserve the. name Fallacy of Confusion for 
cases where Confusion is the sole cause of the error. 
Cases, then, where there is more or less ground for 
the error in the nature of the apparent evidence it- 
self, the evidence being assumed to be of a certain 
sort, and a false conclusion being drawn from it, may 
be classed as Fallacies of Inference. According as 
the apparent evidence consists of particular facts, or 
of foregone generalisations, we call the errors Falla- 
cies of Induction or of Deduction. Each of these 
classes, again, may be subdivided into two species, 
according as the apparent evidence is either false, or, 
though true, inconclusive. Such subdivisions of the 
Fallacy of Induction are respectively called, in the 
former' case. Fallacies of Observation (including cases 
where the fjEicts are not directly observed, but in- 
ferred), and, in the latter. Fallacies of Generalisation, 

Among Fallacies of Deduction, those which proceed 

o 3 


on false premisses have no specific name, for they 
must fall under one of the other heads of Fallacies ; 
but those, the premisses of which, though true, do 
not support the conclusion, compose a subdivision, 
which may be specified as Fallacies of Eatiocination. 




There must be some a priori knowledge, some pro- 
positions to be received withoitt proof; for there 
cannot be a chain suspended from nothing. What 
these are is disputed, one school recognising as ulti- 
mate premisses only the facts of our subjective con- 
sciousness, e.g. Sensations, while Ontologists hold 
that the mind intuitively, and not through experi- 
ence, recognises as realities other existences, e.g. 
Substances, which are suggested by, though not in- 
ferrible from, those facts of consciousness. But, as 
both schools, in fact, allow that the mind infers the 
reality from the idea of a thing, and that it may do 
this unduly, there results a class of Fallacies resting 
on the tacit assumption that the objects in nature 
have the same order as our ideas of them. Hence 
not only arose the vulgar belief that facts which 
make us think of an event are omens foreboding (e.g. 
lucky or unlucky names), or even causing its occur- 
rence ; but even men of science both did and do fall 
into this Fallacy. The following dogmas express 
the diflferent forms of this error : — 


1. a. Things which we cannot help thinking of 
together must coexist ; thus Descartes held that, be- 
cause existence is involved (though really only by 
the thinker himself) in the idea of a geometrical 
figure, a thing like the idea must exist. /3. Whatever 
is inconceivable is false. The latter proposition has 
been defended by drawing a distinction between the 
principle, and its possibly wrong application to facts, 
e.g. to Antipodes ; but how can we ever know that it 
has been rightly applied ? Coleridge, again, has dis- 
tinguished between the unimaginable, which he thinks 
may possibly be true, and the inconceivable, which 
he thinks cannot be ; but Antipodes were imagin- 
able at the same period when they were inconceivable 
In fact, as even to Newton it seemed inconceivable, 
that a thing should act where it is not (e.g. that the 
sun should act upon the earth without the medium 
of an ether), simply because his mind was not familiar 
with the idea, so it may be with our incapability (if 
not, indeed, resulting merely from our limited facul- 
ties) of conceiving, e.g. that matter cannot think; 
that space is infinite ; that ex nihilo nihil At Leib- 
nitz's tenet that ull natural phenomena must be ex- 
plicable a priori, aod the further assumption by 
some that Nature always acts by the simplest, i.e. by 
the most easily conceivable means (and that, there- 
fore, e.g. the heavenly bodies have a circular jnove- 
ment), exhibit vividly this Fallacy of Simple In- 

2. Whatever can be thought of apart, or has a 
separate name, exists apart as a separate entity, e.g. 
Nature, Time, qualities, as e.g. Whiteness, and, worst 
of all, the SubstantisB Secundae. Mysticism is this 


habit of ascribing objective existence to the subjective 
creations of the mind, and reasoning from them to 
the things themselves. 

3. A fact must follow a certain law, because we 
see no reason for its deviating from it in one way 
rather than in another. This, which is the same as 
the Principle of the SufiScient Reason, has been used 
to prove the Law of Inertia (the very point to be 
proved, viz. that only external force can be a suflScient 
reason for motion in a particular directioUy being 
assumed), and also the First Law of Motion, the argu- 
ment being, in the latter case, that a moving body, if 
it do 710^ continue of itself to move uniformly in a 
straight line, must deviate right or left, and that there 
is no reason for its going one way more than the 
other : to which the answer is, that, apart from expe- 
rience, we could not know whether or not there were 
a reason. Geometers often fall into this Fallacy. 

4. The differences in nature must correspond to 
our received distinctions (in names and classifica- 
tions). Thus, the Greeks thought that, by deter- 
mining the meanings of words, they ascertained facts. 
Aristotle usually starts with ' We say thus or thus.' 
So, with the Doctrine of Contrarieties^ in which the 
Pythagoreans and others assimied that oppositions in 
language imply similar ones in nature. Hence, too, 
the ancient belief in the essential difference between 
the laws of things terrestrial and things celestial, and 
in man's incapability of imitating nature's works. 
Bacon's terror (which vitiates his inductive system) 
was analogous, in looking (either through his eager- 
ness for practical results, or a lingering belief that 
causes were the sole object of philosophy) for the cause 


of given effects rather than the eflfects of a given 
cause. Hence sprang his tacit assumption (and that 
in enquiries into the causes of a thing's sensible 
qualities, where it was especially fatal), that in all 
cases, e.g. of heat or cold, the f(yrma^ or set of con- 
ditions, is one thing. A similar notion, viz. that each 
property of gold, as of other things, has its one 
formay produced the belief in Alchemy. 

5. The conditions of a phenomenon often do re- 
semble the phenomenon itself, e.g. in cases of Motion, 
Contagion, Feelings ; hut it is a Fallacy to suppose 
that they must or probably will. By this fancied 
law men guided their conjectures. Thus, the Doctrine 
of Signatures was, that substances showed their 
uses as medicines by external resemblance, either 
to their supposed effect, or to the disease. So, the 
Cartesians, and even Leibnitz, argued, that nothing 
physical but previous motion could account for mo- 
tion, explaining the human body's voluntary motions 
by Nervous Vibrations or by Animal Spirits. Hence, 
too, the inference that there is a correspondence 
between the physical qualities of the cause, and like 
or like-named ones, either of the phenomenon (e.g. 
between sharp particles and a sharp taste), or of its 
effects (e.g. between the redness of Mars, and fire 
and slaughter as results of that planet's influence). In 
metaphysics, the Epicureans' doctrine of species sensi- 
biles, and the modems' o{ perception through ideas, 
arose from this fallacy (combined with another, viz. 
that a thing cannot act where it is not). Again, the 
conditions of a thing are sometimes spoken of even 
as though they were the thing itself. Thus, in the 
Novum Organon, heat (i.e. really the conditions of the 


feeling of it) is called a kind of motion ; and Darwin^ 
in his Zoonomia, after describing idea ^s s. kind of 
notion of external things^ defines it as a motion of 
the fibres. Cousin says : * Tout ce qui est vrai de 
I'eflfet est vrai de la cause,' though the reverse might 
be true ; and Coleridge aflSrms, as an evident truth, 
that mind and matter, as having no common pro- 
perty, cannot act on each other. The same fallacy 
led Leibnitz to his pre established harmony y and 
Malebranche to his occasional causes. So, Cicero 
argues that mental pleasures, if arising from the 
bodily, could not, as they do, exceed their cause ; and 
Descartes, that the Efiicient Cause must have all the 
perfections of the effect. Conversely Descartes, too, 
and persons who assail, e.g. the Principle of Popu- 
lation by reference to Divine benevolence (thus im- 
plying that, because Grod is perfect, therefore what 
they think perfection must obtain in nature), assume 
that effects must resemble their causes. 



A FALLACY of Observation (the first of the three fal- 
lacies of Proof) may be either negative or positive. 

1. The former, which is called Non-observation, is a 
case, not of a positive mis-estimate of evidence, or of 
the proper faculties (whether the senses or reason) 
not having been employed, but simply of the non- 
employment of any of the faculties. It arises (a) 
from neglect of instances. Sometimes tliis is 


when there is a stronger motive to remember the 
instances on the one side, and the observers have 
neglected the principle of the Elimination of Chance. 
Hence (the mind, as Bacon says, being more moved 
by affirmative than by negative instances) the belief 
in predictions, e.g. about the weather, because they oc- 
casionally turn out correct ; and the credit of the pro- 
verb, that ' Fortune favours fools,' since the cases of a 
wise man's success through luck are forgotten in his 
more nimierous successes through genius. But a pre- 
conceived opinion is the chief cause why opposing 
instances are overlooked. Hence originate the errors 
about physical facts (e.g. of Copemicus's foes, and 
friends, too, about the falling stone), and a fortiori, 
on moral, social, and religious subjects, where yet 
stronger feelings are involved. 

The fallacy of Non-observation may occur (^) from 
neglect, not of the material instances wholly, but of 
some material facts in them, e.g. in cases of cures by 
quack remedies (such as Kenelm Digby's ' sympathetic 
powder'), of some attendant fact (as exclusion of 
air from a wound, rest, regimen, and the like) which 
really worked the cure. Sometimes the neglected 
fact is one ascertainable, not by the senses, but by 
reasoning, which has been overlooked. Thus, Cousin's 
argument that, if the sole end of punishment were to 
prevent crime by intimidating intending criminals, 
the punishment of the innocent, indiscriminately with 
the guilty, would have the same effect, ignores the 
fact that the innocent would then be equally intimi- 
dated, and so the punishment would be of no use as 
an example to criminals. So, in Political Economy, 
where the effects of a cause often consist of two sets 


of phenomena, the one obvious, the other deeper 
under the surface, and exactly contrary, the latter is 
often neglected. This was why the rapidly spent 
capital of the prodigal was supposed formerly to em- 
ploy more labour than the invested savings of the 
parsimonious, and the .purchase of native goods to 
encourage native industry more than the purchase of 

2. The error in Mal-observation, which is the 
positive kind of Mis-observation, is not the overlook- 
ing facts, but the seeing them wrong. It arises from 
mistaking what is in fact inference (as much must be, 
whenever we try to observe or to describe) for per- 
ception, which is infallible evidence of what is really 
perceived. The Anti-Copemicans, when they ap- 
pealed to common sense, made this mistake. So 
do untrained persons generally in describing facts, 
especially natural phenomena (e.g. apothecaries and 
nurses in stating symptoms), and that, too, in pro- 
portion to their ignorance. We might expe,ct this, 
since usually the actual perceptions of the senses (e.g. 
th# colour and extension) are not of interest, except 
as marks whence to draw inferences about something 
else (e.g. about the body, to which these qualities 
belong). Painters, therefore, to know what the sen- 
sation actually was, have to go through a special 
training. But this confusion of inference with per- 
ception is still more likely in highly abstract subjects ; 
and, consequently, in these, mere, and often false in- 
ferences, have continually been regarded as intuitive 



This class includes whatever errors of generalisation 
are not mere blunders, but arise from some wrong 
general conception of the inductive process. Only a 
few kinds can be noted. 1. Under this Fallacy come 
generalisations which cannot be established by ex- 
perience, e.g. inferences from the order in the Solar 
System to other and unknown parts of the universe ; 
and also, except when a particular effect would^contra- 
dict either the laws of number and extension, or the 
universal law of causality, all inferences from the fact 
that we have never known of a particular effect to its 
impossibility. 2. Those generalisations also are fal- 
lacious which resolve, either, as in early Greece, all 
things into one element, or, as often in modem times, 
impressions on the senses, differing in quality, and 
not merely in degree, into the same ; e.g. heat, light, 
and (through vibrations) sensation, into motion; 
mental, into nervous states; and vital phenomena* 
into mechanical or chemical processes. In these 
theories, one fact has its laws applied to another. It 
may possibly be a condition of that other ; but even 
then the mode in which the new fact is actually pro- 
duced would have to be explained by its own law, and 
not by that of the condition. 3. Again, generalisa- 
tions got by Simple Eniuneration, fall under this 
Fallacy. That sort of Induction * precario concludit,' 
says Bacon, * et periculo exponitur ab instantia con- 
tradietoria, • • • • ex his tantummod6 qu^ prsesto 
sunt pronuncians.' The ancients used it; and in 


vahie, and its value on its scarcity). Such, also, were 
the Pythagorean inferences that there is a music of 
the spheres, because the intervals between the planets 
have the same proportion as the divisions of the 
monochord ; and, again, that the movements of the 
stars as being divine must be regular, because so are 
those even of orderly men. So, Aristotle and other 
ancients supposed perfection to obtain in all natural 
facts, because it appeared to exist in some ; and so, 
the Stoics tried to prove the equality of all crimes by 
reference to various similes and metaphors (as, that 
the man held half an inch below the surface will be 
drowned as certainly as the man at the bottom of the 
sea ; and that want of skill is shown as much in steer- 
ing a straw-laden boat as a treasure galleon on to the 
rocks). But, in fact, the connection by causation be- 
tween the known and the inferred resemblance, which 
is assumed by these metaphors, is the very thing 
which they are brought to prove. The real use of such 
cases of analogy as metaphors is that they serve, not 
as an argument, but as an assertion that one exists. 
Though they cannot prove, they sometimes suggest the 
proof, and point to a case in which the same grounds 
for a conclusion have been found adequate. Such are 
d'Alembert's classification of successful politicians as 
either eagles or serpents ; and the statement, as an 
argument for education, that, in waste land weeds 
will spring up; and such is not Bacon's inference 
from the levity of floating straw to the worthlessness 
of the extant scientific works of the ancients. 

The great source of fallacious generalisation is 
bad classification, by which things with no, or no 
important, common properties, are grouped together. 


Worst is it, when a word which commonly signifies 
some definite fact is applied to other facts only slightly 
similar. Bacon (who has himself thus erred in his 
enquiries into heat) specifies, as examples of this, 
the various applications (got, by unscientific abstrac- 
tion, from the original sense) of the word * wet,' to 
flame, air, dust, and glass, as well as to water. The 
application by Plato, Aristotle, and other ancients, 
of the terms Generation, Corruption, and xlmjais to 
many heterogeneous phenomena, with a mixture of 
the ideas belonging to them severally, caused many 
perplexities, which may be noticed under Fallacies 
of Confusion. 



These fallacies (to which the name Fallacy is com- 
monly applied exclusively) would generally be de- 
tected if the arguments were set out formally; and 
the value of the syllogistic rules is, that they force 
the reasoner to be aware what it is that he is really 
asserting. The frequent errors in processes such as 
Conversion and Opjlosition, which are in appearance, 
though not in reality, inferences from premisses, may 
fgr convenience be here referred to. Such are the 
simple conversion of an universal affirmative; the 
corresponding error in a hypothetical proposition of 
inferring the truth of the antecedent from that of 
the consequent ; and the confusing of a contrary with 
a contradictory, which amounts, in practice, to mis- 
taking the reverse of wrong for right. But fallacies 
of Katiocination properly lie in syllogisms. They 


commonly resolve themselves, when in a single 
syllogism, into the having more than three terms, 
whether covertly, as through an undistributed middle, 
or an illicit process, or avowedly. But the most 
dangerous and the commonest of these fallacies arise 
in a chain of argument from changing the premisses* 
One of the obscurer forms of this is the fallacy 
a dicto secundum quid (i.e. with a qualification, 
or condition, expressed, or, more usually, under- 
stood) ad dictum simplidter. Thus, the Mercantile 
Theory was in favour of prohibiting all trade which 
tends to carry out more money than it brings in, on 
the ground that money is riches, though it is so only 
if the money can be freely spent. Such, too, was 
the argument (used to support the doctrine that 
tithes fall on the landlord) that, because now the 
rent of tithe-free land exceeds that of tithed land, 
the rent from the latter would be increased by the 
abolition of all tithes. There was a similar fallacy 
in the use of the maxim, that individuals are the 
best judges of their pecuniary interests, against 
Mr. Wakefield's scheme for concentrating settlers. 
Cases in which the condition of time is dropped, fall 
under this same particular fallacy, as, when the maxim 
that prices always find their level, is construed as 
meaning that they are always at their level. It is 
the same with the reasoning (especially in political 
and social subjects), upon principles, which are true 
in the absence of all modifying causes, as though no 
such causes could exist. Other analogous fallacies 
are those a dicto simplidter ad dictum secundum 
quid (the converse of the preceding), and a dicto 
secundum quid ad dictum secundum alterv/m, quid. 




Under this head come all fallacies which arise, not 
so much from a false estimate of the probative force 
of known evidence, as frbm an indistinct conception 
what the evidence is. 

1. Thus, where there is an ambiguous middle, or a 
term used in different senses in the premisses and in 
the conclusion, the argument proceeds as though 
there were evidence to the point, when, in fact, there 
is none. This error does not occur much in direct 
inductions, since the things themselves are there 
present to the senses or memory; but chiefly, in 
Ratiocination, where we are deciphering our own or 
others' notes. The ambiguity arises very often from 
assuming that a word corresponds precisely in mean- 
ing with the root itself (e.g. representative)^ or with 
cognate words from the same root, cdlledparonymous 
words (as, artfuly with art). Other examples of 
ambiguities are : ' Money,' which, meaning both the 
currency and also capital seeking investment, is often 
thought to be scarce in the former sense, because 
scarce in the latter ; * Influence of Property,' which, 
signifying equally the influence of respect for the 
power for good, and of fear of the power for evil, 
which is possessed by the rich, is represented as being 
assailed under its former form when attacked really 
only under the latter; 'Theory,' which, because 
applied popularly to the accounting for an effect apart 
from facts, is ridiculed, even when expressing, as it 
properly does, the result of philosophical induction 


from experience ; * The Church,' which refers (as in 
the question of the inviolability of Church property) 
sometimes to the clergy alone, sometimes to all its 
members ; * Good,' in the Stoic argument that virtue, 
as alone good (in the Stoic sense), must therefore 
include freedom and beauty, because these are good 
(in the popular sense). So, the meaning of 'I' 
shifts from the laws of my nature to my luUl, in 
Descartes' a priori argument for the being of a God, 
viz. that there must be an external archetype whence 
I got the conception, for if I (i.e. the laws of my 
nature) made it, / (i.e. my wilt, and not, as it 
should consistently be, the laws of ray nature) could 
unmake it ; but / (i.e. my will) cannot. In the Free- 
Will controversy, * I ' is used ambiguously for voli- 
tions, actions, and mental dispositions, and ' Necessity' 
both for Certainty and for Compulsion. From the 
application of ^ same,' ' one,' * identical,' which pri- 
marily refer to a single object, to several objects 
because similar^ grew up (for the purpose of account- 
ing for the supposed oneness in things said to have 
the same nature or qualities) both the Platonic IdeaSy 
and also the Substantial Forms and Second Sub* 
stances of the Aristotelians, even though the latter did 
see the distinction between things differing both specie 
and numerOy and those differing numero only. And 
thence, too, sprang Berkeley's proof of the existence 
of a Universal Mind from the supposed need of such 
a Being to harbour, in the interval, the idea, which, 
one and the same (really, only two similar ideas), 
a man's mind has entertained at two distinct times. 
The difficulty in Achilles and the Tortoise arises 
from the use of infinity ^ or, for ever, in the premisses. 


to signify a finite time which is infinitely divisible, 
and, in tlie conclusion, to signify an infinite time. 
Thus, again, * right ' is used to express, both what 
others have no right to stop a man from doing, and 
also what it is not against his own duty to do ; both 
what people are entitled to expect from, and also 
what they may enforce from others. The Fallacy of 
Composition and Division, i.e. the use of the same 
term in a syllogism, at one time in a collective, at 
another in a distributive sense, is one of the Fallacies 
of Ambiguous Terms. Examples of it are the argu- 
ments, that great Tnen (collectively) could be dis- 
pensed with, because the place of any particular 
great man might have been supplied (i.e., in fact, by 
some other great man); and, that a high prize in 
a lottery may be reasonably expected (by a certain 
individual, viz. oneself), because a high prize is 
commonly gained {by some one or other). 

2. In Petitio Principii, the premisses are not even 
verbally suiB&cient for the conclusion, since one pre- 
miss is either clearly the same as the conclusion, or 
actually proved from it, or not susceptible of any 
other proof. Men commonly fall into it, through 
believing that the premiss was verified, though they 
have forgotten how. But the variety, termed Kea- 
soning in a Circle, implies a conscious attempt to 
prove two' propositions reciprocally from each other. 
This formal proof is not often attempted, except 
under the pressure of controversy; but, from mis- 
taking mutual coherency for truth, propositions, 
which cannot be proved except from each other, are 
often admitted, when expressed in different language, 
without other proof. Frequently a proposition ia 


presented in abstract terms as a proof of the same in 
concrete, as, in Moli^re's parody, * L'opium endormit 
parcequ'il a ime vertu soporifique.' So, some qualities 
of a thing selected arbitrarily are termed its nature 
or essence, and then reasoned from as though not 
able to be counteracted by any of the rest. ' Ques- 
tion-begging appellatives,' particularly, are cases of 
Petitio Principii, e.g. the styling any reform an mno- 
vatiorVj which it really is, only that innovation con- 
veys, besides its dictionary meaning, a covert sense of 
something extreme. Thus, in Cicero's De Finibus, 
' Cupiditas,' which usually implies vice, is used to 
express certain desires the moral character of which 
is the point in question. Again, the infinite divisi- 
bility of matter was assumed by the argument which 
was used to prove it, viz. that the least portion of 
matter must have both an upper and an imder sur- 
face (which, as every other Fallacy of Confusion, 
when cleared up, appears as a fallacy of a dilBFerent 
sort, under shelter of which, as indeed in ratioci- 
native fallacies generally, the mere verbal juggle at 
first escapes detection). Such, again, was Euler's 
argument, that rainua multiplied by mim^ gives 
plusy because it could not give the same as minus 
multiplied by plus, which gives Trdnus. So,- some 
ethical writers begin by assuming, that certain gene- 
ral sentiments are the natural sentiments of mankind, 
and thence argue that any which differ are morbid 
and unnatural. Thus, lastly, Hobbes and Rousseau 
rested the existence of government and law on a 
supposed social compact, and not on men's percep- 
tion of the interests of society, which, however, could 
be the only ground for their abiding by such com- 
pact if a fact. 


3. In Ignoratio Elenchi, or, the Fallacy of Irre- 
levant Conclusion, the error lies not either in mis- 
taking the import of the premisses, or in forgetting 
what they are, but in piistaking what ig the con^Jj^sion 
to be proved. Sometimes, a particular is substituted 
for the universal as the proposition needing proof, 
and sometimes, a proposition with different terms. 
Under this fallacy come the cases, not only of proving 
what was not denied, but of disproving what was not 
asserted; e.g. the argument used against Malthus 
(whose own position was, that population increases 
only in so far as not kept down by prudence, or by 
poverty and disease), that, at times, population has 
been nearly stationary ; or again, that, in some coun- 
try or other, population and comfort are increasing 
together, Malthus himself having asserted that this 
might be so, if capital has increased. Similarly, 
even Reid, Stewart, and Brown (not merely Dr. 
Johnson) urged that Berkeley ought, if consistent, to 
have run his head against a post, as though the non- 
recognition of an occult cause of sensations implies 
disbelief in any fioced order among them. 






Many complex problems have been resolved through 
the use of the Scientific Methods, and thus only. 
The most complex of all problems are the problems 
relating to Man himself; and of them those con- 
cerned with the Mind and Society have never been 
scientifically resolved. They can be rescued from 
empiricism, if at all, only by being submitted to some 
of the methods already characterised as applicable to 
science in general. Which of these methods must 
be selected, and why ; what are the causes of previous 
failures ; and what degree of success now is possible 
or probable, will be considered in this book, when 
a preliminary objection (based on the theory of free 
%vill\ that men's actions are not, like other natural 
events, subject to invariable laws, has been first 



The theory of free wUlj viz. that the will is deter- 
mined by itself, and not by antecedents, was invented 


as being more in accordance with the dignity of 
human nature and our consciousness of freedom, than 
philosophical necessity. The latter doctrine, in 
laying down simply that our volitions and actions 
are invariable consequents of our antecedent states 
of mind, and that, given our motives, character, and 
disposition, other men could predict our conduct as 
certainly as any physical event, states indeed nothing 
which is in itself either contradicted by our conscious- 
ness, or degrading ; yet the doctrine of causation, as 
applied to volition, is supposed, from the natural 
tendency of the mind to imagine falsely that a mys- 
terious constraint is exercised by any antecedent over 
the consequent, to imply some state of dependence 
which our consciousness does contradict. Moreover, 
the erroneous notion that something more than imi- 
formity of order and capability of being predicted is 
meant, has been favoured by the use of the ambiguous 
term necessity (which, it is true, commonly implies 
irresistibleness), to signify simply that the given cause 
will be followed by the effect subject to all possi- 
bilities of counteraction by other causes. Most neces- 
sarians have been themselves deceived by the expres- 
sion : they are apt to be partially fatalists as to their 
own actions, with a weaker spirit of self-culture than 
the believers in free-will, and to fail to see that the 
fact of their character being formed for them, that 
is, by their circumstances, including their own organi- 
sation, is consistent with its being formed by them- 
selves, as intermediate agents, moulding it in any 
particular way which they may wish. The belief 
that the wishing is excited by external causes, e.g. 
by education, casual aspirations, and experience of 


ills resulting from our previous character, can be of 
no practical harm, and does not conflict with our 
feeling of moral freedom, that is, of power, if we 
wiahy to modify or conquer our own character. 

The ambiguity of the word motive has also caused 
confusion. A motive, when used to signify that 
which determines the will, means not always or only 
the anticipation of a pleasure or a pain, but often the 
desire of the action itself. The action having finally 
become by association in itself desirable, we may get 
the habit of willing it (that is, get a purpose) without 
reference to its being pleasurable. We are then said 
to have a confirmed character. 



Ant facts may be a subject of science, if they follow 
one another according to constant laws ; and this, 
whether, although the ultimate laws are known, yet, 
of the derivative laws on which a phenomenon directly 
depends, either none, sua in Meteorology, or, as in 
Tidology, only the laws of the greater causes on 
which the chief part of a phenomenon directly de- 
pends, have been ascertained, and not those of all the 
minor modifying causes ; or, as in Astronomy (which 
is therefore called an exact science), both the ulti- 
mate laws are known, and also the derivative laws as 
well of the greater as of all the minor causes. The 
science of Human Nature cannot be exact, the causes 
of human conduct being only approximately known. 
Hence it is impossible to predict with scientific 


dccuracy any one man's acts, resulting as they do 
partly from his circumstances, which, in the future, 
cannot be precisely foreseen, and, partly, from his 
character, which can never be exactly calculated, be- 
cause the causes which have determined it are sure, 
in the aggregate, not to be entirely like those which 
have determined any other man's. But approximate 
generalisations, though only probably true as to the 
acts and characters of individuals, will be certainly 
true as to those of masses, whose conduct is deter- 
mined by general causes chiefly ; and they are there- 
fore sufficient for political and social science. They 
must, however, be connected deductively with the 
universal laws of human nature on which they rest, 
or they will be only low empirical laws. This is the 
text of the next two chapters. 



By the laws of mind (i.e. as considered in this treatise, 
the laws of mental phenomena) are meant the laws 
according to which one state of mind is produced by 
another. If M. Comte and others be right in sajring 
that, in Uke manner with the mental phenomena 
called sensations, all the other states of mind have 
for their proximate causes nervous states, there would 
be no original laws of mind, and Psychology would 
be a mere branch of Physiology. But at present, 
this tenet is not proved, however highly probable ; 
and, at all events, the characteristics of those nervous 


states are quite imknown ; consequently the unifor- 
mities of .succession among the mental phenomena, 
which undoubtedly do exist, and which are not proved 
to result from more general' laws, must be considered 
as the subject of a distinct science called Psychology. 
We can ascertain only by experiment the simple laws 
of Mind, such as — 1. That a state of consciousness 
can be reproduced in the absence of the cause which 
first excited it (i.e. that every mental impression has 
its idea), and — 2. That these secondary mental states 
themselves are produced according to the three laws 
of ideas. But the complex laws are got from these 
simple laws, according either to the Composition of 
Causes, when the complex idea is said to consist of 
the Simple Ideas, or to chemical combination, when 
it is said to be generated by> them. Hartley and 
Mr. James Mill indeed hold all the mental phenomena 
to be generated by chemical combination from simple 
ideas of sensation^ however unlike to the alleged 
results; but even though they had proved their 
theory, employing the Method of Difference, and not 
only the Method of Agreement (which latter itself 
they have used only partially), we should still have 
to study the complex ideas themselves inductively, 
before we could ascertain their sequences. 

The analytical enquiry (neglected alike by the 
German metaphysical school, and by M. Comte) into 
the general laws of mind, will show that the mental 
differences of individuals are not ultimate facts, but 
may be referred generally to their particular mental 
history, their education and circumstances, but some- 
times also to organic differences influencing the 
mental phenomena, not directly, but through the 


medium of the psychological causes of the latter. 
Men's animal instincts, however, are probably, 
equally with the mere sensations, connected directly 
with physical conditions of the brain and nerves. 
Whether or not there be any direct relation between 
organic causes and any other mental phenomena, 
Physiology is likely in time to show ; but at least 
Phrenology does not embody the principles of the 




Till the Empirical laws of Mind, i.e. the truths of 
common experience, are explained by being resolved 
into the causal laws (the subject of the last chapter), 
they are mere approximate generalisations which 
cannot be safely applied beyond the limits in which 
they were collected by observation. But this does 
not prove aught against the universality and sim- 
plicity of the ultimate mental laws ; for the same is 
the case with the empirical laws even in astronomy, 
where each effect results from but few causes; a 
fortiori, therefore, will it be so in regard to man's 
character, which is influenced by each of his circum- 
stances, which differ in the case of each nation, gene- 
ration, and individual. But though mankind have 
not one universal character, yet there exist universal 
laws of the formation of character. These tmiversal 
laws cannot be discovered experimentally, i.e. either 
by artificial experiment, since we can seldom vary the 

H 3 


experiment sufficiently, and exclude all but known 
circumstances, or by observation, since, even in the 
most favourable instances for the latter, viz. National 
acts, only the Method of Agreement can be applied. 
Observation has its uses in relation to this subject ; 
but only as verification of the results arrived at by 
the Deductive Method. The Deductive Method must 
be employed to obtain the laws of the formation of 
character. They are got by supposing any given 
circumstances, and then considering how these wiU, 
according to the general laws of mind, influence the 
formation of character. So, contrary to Bacon's rule, 
laid down wrongly as universal, for the discovery of 
principles, the highest generalisations must be first 
ascertained by the experimental science of Psycho- 
logy ; and then will come what is in fact a system of 
corollaries from the latter science, viz. Ethology, i.e. 
(as dealing only with tendencies) the eocact science of 
human character, or of education both national and 
individual, and which has for its principles the middle 
principles {aodomata media) of mental science. It 
does not yet, but it will soon, exist as a science. Its 
object must be to determine, from the general laws 
of mind, combined with man's generalposition in the 
universe, what circumstances will aid or check the 
growth of good or bad qualities, so that the Art of 
Education will be merely the transformation of these 
middle principles into precepts and their adaptation 
to the special cases. But at every step these middle 
principles, got by deduction, must be verified a 'pos- 
teriori by empirical laws, and by specific experience 
respecting the assumed circumstances. 




Political and social phenomena have been thought 
too complex for scientifio treatment. Practitioners 
hitherto have been the only students ; and so, as in 
medicine, before the rise of Physiology and Natural 
History, eocpervmenta fructifera^ and not ludfera, 
have been sought. The scheme of such a science has 
even been thought quackery, through the vain at- 
tempts of some theorists to frame universal precepts, 
as though their failure (arising from the variety of 
human circumstances) proved that the phenomena do 
not conform to universal laws. Social phenomena, 
however, being phenomena of human nature in 
masses, must, as human natiure is itself subject to 
fixed laws, obey fixed laws resulting from the fixed 
laws of human nature. The number and change- 
fulness of the data (unlike those of Astronomy) will 
prevent our ever predicting the far future of society. 
But, when general laws have been ascertained, an 
application of them to the individual circumstances 
of a given age and country will show us the causes 
and tendencies of, and the means of modifying, its 
actual condition. A consideration of two methods, 
erroneously used for this science, viz. the Experi- 
mental or Chemical, and the Abstract or Greometrical, 
will introduce us to the true one. 





The followers of this method do not recognise the 
laws of social phenomena as merely a composition of 
the laws of individual human nature. They demand 
specific experience in all cases ; and they attempt to 
make effects, which depend on the greatest possible 
complication of causes, the subject of induction by 
observation and experiment. The attempt must fail ; 
for, we can neither get by experiment appropriate 
artificial instances, nor, by observation, spontaneous 
instances (from history), with the circumstances 
enough varied for a true induction. Neither the 
direct nor the indirect Method of Difference can be 
applied, for we cannot find either two single instances 
differing in nothing but the presence or absence of a 
given circumstance (the direct^ or two classes re- 
spectively agreeing in nothing but the presence of a 
circumstance on one side and its absence on the 
other (the indirect). Then, again, the Method of 
Agreement is of small value, because social pheno- 
mena admit the widest plurality of causes ; and so 
also is that of Concomitant Variations, on account of 
the mutual action of the coexisting elements of 
society being such that what affects one affects all. 
The Method of Kesidues is better suited to social 
enquiries than the other three. But it is not a method 
of pure observation and experiment. It presupposes 
that we know, by previous deduction from principles 
of human nature, the causes of part of the effect. 


But if thus part of the truths axe, why may not 
all be, ascertained by Deduction, and the experi- 
mental argument be confined to the verifying of the 
deductions ? 



The Methods of Elementary Chemistry are applied 
to social phenomena from carelessness as to, or 
ignorance of, any of the higher physical sciences : the 
Geometrical Method, from the belief that Geometry, 
that is, a science of coexistent, not successive facts, 
where there are no conflicting forces, is, and that the 
now deductive physical sciences of Causation, where 
there are conflicting forces, are not, the type of 
deductive science. Thus, it seems to have been 
supposed by many philosophers, that each social 
phenomenon results from only one force, one single 
property of human nature. For instance, Hobbes 
assumed (eking out his assumption by the fiction of 
an original contract), that government is foimded on 
fear. Even the scientific Bentham School based a 
general theory on one premiss, viz. that men's actions 
are always determined by their interests, meaning 
probably thereby, that the bulk of the conduct of any 
succession, or of the majority of any body of men, is 
determined by their private or worldly interests. 
They inferred thence, that those rulers alone will 
govern according to the interest of the governed, 
whose selfish interests are identified with it (for- 
getting that, apart from the philanthropy and sense 


of duty of many, the conduct of all rulers must be 
influenced by the habits of mind, both of the whole 
community, and also of their own class in it, and by 
the maxims of their predecessors). Lastly, they laid 
down that this sense of identity of interest with the 
governed is producible only by responsibility (whereas 
the personal interest of rulers often prompts them 
to acts, e.g. for the suppression of anarchy, which 
are also for the interest of the governed). In fact, 
this school was pleading for parliamentary reform, 
and saw truly, that it is against the selfish interests 
of rulers that constitutional checks are needed, and 
that, in modern Europe, a feeling in the governors 
of identity of interest, when not active enough, can 
be roused only by responsibility to the governed. 
Their mistake was, that they based on just these few 
premisses a general theory of government, in forget- 
fulness that such should proceed by deduction from 
the whole of the laws of human nature, since each 
effect is an aggregate result of many causes operat- 
ing now through the same ones, now through different 
ones, of these laws. 



The complexity in social effects arises from the 
number, not of the laws, but of the data. Therefore, 
Sociology, ie. Social Science, must use the Concrete 
Deductive Method, compounding with one another 
the Jaws of all the causes on which any one effect 
depends,/and inferring its law from them all. As in 


the easiest case to which the Method of Deduc- 
tion applies, so in this, the most difficult, the conclu- 
sions of ratiocination must be verified by collation 
with the concrete phenomena, or, if possible, witli 
their empirical laws ; and then the only effect of an 
increase in the complication of the subject will be a 
tendency to a disturbance, and sometimes even to an 
inversion (which, indeed, M. Comte thinks insepar- 
able from all Sociological enquiries) in the order of 
the two processes, obliging us, first, to conjecture the 
conclusions by specific experience, and Ihen verify 
them by a priori reasonings showing their connec- 
tion with the principles of human nature. 

Sociology is a system not of positive predictions, 
but of tendencies. Of tendencies themselves, not 
many can be laid down as true of all societies alike. 
Even in the case of any single feature of society, the 
consenaua which exists in the body politic, as in the 
body natural, makes it uncertain whether a cause 
with a special tendency in one age or country will 
have quite the same in another. General proposi- 
tions, therefore, in this deductive science, as, to be 
true, they must be hypothetical, and state the opera- 
tion of a given cause in given circumstances, so, to 
be of any utility, should be limited to those classes 
of facts, which, though influenced by all sociological 
agents, are yet influenced immediately by a few only, 
certain fixed combinations of which are likely to re- 
cur often. Thus, Political Economy, taking the one 
psychological law that men prefer a greater gain to 
a smaller, and ignoring every other motive, except 
what are perpetually adverse principles to this, vi^s. 
men's aversion to labour and desire of prese^^t costiy 


pleasures, assumes, in enquiring what acts this desire 
of gain will produce, that, within the department' 
of human affairs, where it is actually the main end, it 
is the sole end. Yet its general propositions are of 
great practical use, even though it thus provisionally 
overlooks as well miscellaneous concurrent causes 
(with some exceptions, as e.g. the principle of popu- 
lation), as also the fact of the non-existence elsewhere 
of the conditions of any one particular country (e.g. the 
peculiarly British mode of distribution of the produce 
of industry among three classes). Another hypo- 
thetical or abstract science, which can be carved out 
of Sociology, is the as yet unexplored Political Etho- 
logy, i.e. the theory of the causes which determine 
a people's, or age's, type of character, which col- 
lective character, besides being the most interesting 
phenomenon in the particular state of society, is the 
main cause of the social state which follows, and 
moulds entirely customs and laws. The neglect of 
national diversities sometimes (as e.g. the assumption 
by our political economists, that in commercial popu- 
lations everywhere, equally as in Grreat Britain and 
America, all motives yield to the desire of gain) 
vitiates only the practical application of a proposition; 
but when the national character is mixed up at every 
step with the phenomena (as is the case in questions 
respecting the tendencies of forms of government), 
the phenomena cannot properly be insulated in a 
separate branch of Sociology. 

As in Ethology and other deductive sciences, so 
in Statistics and History there are empirical laws. 
The immediate causes of social facts are often not 
open to direct observation ; and the deductive science 


can determine only what causes produce a given 
effect, and not the frequency and quantities of them ; 
in such cases, the empirical law of the causes (which, 
however, can be applied to new cases only if we know 
that the remoter causes, on which these latter causes 
depend, remain unchanged) must be found through 
that of the effects, the Deductive Science relying 
then for its data on indirect observation. But, in 
the separate branches of Sociology, we cannot obtain 
empirical laws by specific experience. It is so par- 
ticularly (on accoimt both of the number of the 
causes^ and also the fewness of the instances to be 
compared with the one in point) when the effect of 
any one (e.g. Com Laws) of many simultaneous 
social causes has to be determined. We can, how- 
ever, in such cases, verify indirectly a theory as to 
the influence of a particular cause in given circum- 
stances, by seeing if the same theory accounts for 
the eodsting state of actual social facts which that 
cause has a tendency to influence. 



The general Science of Society, as contrasted with 
the branches, shows, not what effect will follow from 
a given cause under given circumstances, but what 
are the causes and characteristic phenomena of States 
of Society generally. A State of Society is the 
simultaneous state of all the chief social facts (e.g. 
employments, beliefs, laws). It is a condition of the 


whole organism; and, when analysed, it exhibits 
uniformities of coexistence between its different ele- 
ments. But, as this correlation between the pheno- 
mena is itself a law resulting from the laws which 
regulate the succession between one state of society 
and another, the fundamental problem of Social 
Science is to find these latter laws. The form of 
this succession, by which (on account of the excep- 
tionally constant reaction, in social facts, of the 
effects, i.e. human character, on their causes, i.e. 
human circumstances) one social state is ever in 
process of changing into a different one, is now 
allowed to be, not, as in the solar system, a cycle, 
but a progress (by which is not here necessarily 
meant iw/provem&rit^ whatever the fact may be). 
In France it has been thought, that a law of pro- 
gress, to be found by an analysis of the course of 
history, woidd enable us to predict the whole future. 
But such a law would be empirical, and not true 
beyond its own facts ; for the succession of mental 
and social states cannot have an independent law. 
Empirical laws must indeed be found ; or a general 
Science of Society would be impossible: for, the 
character of any one generation is so much the result 
of the characters of all prior ones, that men could 
not compute so long a series from the elementary laws 
producing it. But the empirical laws, when found 
(as they can be, since the series of the effects as a 
whole is ever growing in uniformity), must be shown 
by deductions to be, if not the only possible, or even 
the most probable, at least possible, consequences of 
the laws of human nature. 
The empirical laws of society are uniformities, 


either of coexistence, or of succession. The former 
are ascertained and verified by Social Statics (which 
is the theory of the conaensuSy i.e. the mutual 
actions and reactions, of contemporaneous social ele- 
ments) ; the latter, by Social Dynamics (the theory 
of Society considered as in a state of progress). As 
to Social Statics — there is, M. Comte thinks, a per- 
petual reciprocity of influence between all aspects 
of the same organism, and to such an extent, that 
the condition of any one which we cannot directly 
observe can be estimated by that of another which 
we can. There is, he considers, such an interdepend^ 
ence, not only between the different sciences and 
arts among themselves, but between the sciences in 
general and the arts in general, even between the 
condition of different nations of the same age, and 
between a form of government and the civilisation 
of the period. Social Statics will ascertain for us 
the requisites of stable political union : it will en- 
quire what special circumstances have always attended 
on such union, increasing and decreasing in propor- 
tion to its completeness ; and will then verify these 
facts as requisites by deducing them from general 
laws of human nature. Thus, history indicates as 
such requisites and conditions of free political union : 
1. A system of educational discipline checking man's 
tendency to anarchy; 2. Loyalty, i.e. a feeling of 
there being something, whether persons, institutions, 
or individual freedom and political and social equality, 
which is not to be, at least in practice, called in ques- 
tion; 3. That which the Koman Empire, notwith- 
standing all its tyranny, established, viz. a strong sense 
of common interest among fellow-citizens (a very 


different feeling, by the bye, to mere antipathy to 

Social Dynamics regards sequences. But the con- 
sensus in social facts prevents our tracing the leading 
facts in one generation to separate causes in a prior 
one. Therefore, we must find the law of the corre- 
spondence not only between the simultaneous states, 
but between the simultaneous changes of the ele- 
ments of society. To find this law, which, when duly 
verified, will be the scientific derivative law of the 
development of humanity, we must combine the 
statical view of the phenomena with the dynamical. 
Fortunately, the state of mankind's speculative 
faculties and beliefs, being the prime agent of the 
social movement, famishes a clue in the maze of 
social elements, since the order of human progression 
in all respects will mainly depend on the order of 
progression of this prime agent. That the other 
dispositions which aid in social progress (e.g. the 
desire for increased material comfort) owe their means 
of working to this (however relatively weak a 
propensity it may be) is a conclusion from the laws 
of human nature ; and this conclusion is in accord- 
ance also with the course of history, in which internal 
social changes have ever been preceded by propor- 
tionate intellectual changes. To determine the law 
of the successive transformations of opinions all past 
time must be searched, since such changes appear, 
definitely only at i(png intervals. M. Comte alone 
has followed out this conception of the Historical 
Method; and his generalisation, to the effect that 
speculation has, on all subjects, three successive 
stages, has high scientific value. 


The Historical Method will trace the derivative 
laws of social order and progress. It will enable us 
both to predict the future, and (thus founding the 
noblest part of the Political Art) partly to shape it. 
At present, both the Science and the Art are in the 
rudiments ; but they are progressing. 




Practical Ethics, i.e. Morality, is an art ; and there- 
fore its Method must be that of Art in general. 
Now, Art from the major premiss, supplied by itself, 
viz. that the end is desirable, and from the theorem, 
lent by Science, of the combinations of circum- 
stances by which the end can be reached, concludes 
that to secure this combination of circumstances is 
desirable ; if it also appear practicable, it turns the 
theorem into a rule.. Unless Science's report as to 
the circumstances is a full one, the rule may fail ; and 
as, in any case, rules of conduct cannot comprise 
more than the ordinary conditions of the eflPect (or 
they would be too cumbrous for use), they must, at 
least in moral subjects, be consid^d, till confronted 
with the theorems, which are the reasons of them, 
provisional only. Practical maxims, therefore, till so 
confronted, are not universally true even for a given 
end, much less for conduct generally, and must not 


be used, as they are by the gecmietrical school, as 
ultimate premisses. 

Any particular art consists of its rules, together 
with the theorems on which they depend ; and Art 
in general consists of the truths of Science; only 
these must be arranged in the order most convenient, 
not, as in Science (which is an enquiry into the 
course of nature), for thought, but for practice. In- 
termediate scientific truths must be framed to serve 
as first principles of the various arts : and through 
them the end or purpose of an art will be connected 
with the means for realising the conditions of its 
attainment. The end itself, however, is defined by 
the art, not by the science. Each art has one first 
principle or major premiss which does not, as the 
propositions of Science, assert that a thing is or will 
be^ but recommends it as what ought to be, A scien- 
tific theory, however complete, of the history and 
tendencies of society does not show us (without Teleo- 
logy, i.e. the Doctrine of Ends) what are the preferable 
ends. Art itself has its PMlosophia Prima, for ascer- 
taining the standard of ends. There can be but one 
such standard or general principle to which all rules of 
practice should conform ; for, if there were several, 
a higher yet would be needed, as umpire when they 
disagreed. In Morality the felt need of a standard 
has been sometimes supplied by the hypothesis of in- 
tuitive moral principles : but a standard would still 
be wanted for the ..other two branches of the Art of 
Life, viz. Prudence or Policy, and Taste ; and their 
standard when found would serve for Morality as 
well. The true standard, or general principle, is, the 
promotion of Hie happiness of all sentient beings^ 


This is not the sole end ; for instance, ideal noble- 
ness of will or conduct should be pursued in prefer- 
ence to the specific pursuit of happiness; but all 
ends whatsoever must be justified and should be 
controlled by it. 

Lomtoir : PBiiriBD bt 



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