classification. The Category Οὐσία was certainly understood by
Aristotle to be a general name for all possible answers to the
question Quid sit? when asked respecting a concrete individual; as
the other Categories are names comprehending all possible answers to
the questions Quantum sit? Quale sit? etc. In Aristotle’s
conception, therefore, the Categories may not have been a
classification of Things; but they were soon converted into one by
his Scholastic followers, who certainly regarded and treated them as
a classification of Things, and carried them out as such, dividing
down the Category Substance as a naturalist might do, into the
different classes of physical or metaphysical objects as
distinguished from attributes, and the other Categories into the
principal varieties of quantity, quality, relation, etc. It is,
therefore, a just subject of complaint against them, that they had
no Category of Feeling. Feeling is assuredly predicable as a summum
genus, of every particular kind of feeling, for instance, as in Mr.
Bain’s example, of Hope: but it can not be brought within any of the
Categories as interpreted either by Aristotle or by his followers.
_ 18 Philosophy of the Inductive Sciences_, vol. i., p. 40.
_ 19 Discussions on Philosophy_, etc. Appendix I., pp. 643, 644.
20 It is to be regretted that Sir William Hamilton, though he often
strenuously insists on this doctrine, and though, in the passage
quoted, he states it with a comprehensiveness and force which leave
nothing to be desired, did not consistently adhere to his own
doctrine, but maintained along with it opinions with which it is
utterly irreconcilable. See the third and other chapters of _An
Examination of Sir William Hamilton’s Philosophy_.
21 “Nous savons qu’il existe quelque chose hors de nous, parceque nous
ne pouvons expliquer nos perceptions sans les rattacher à des causes
distinctes de nous mêmes; nous savons de plus que ces causes, dont
nous ne connaissons pas d’ailleurs l’essence, produisent les effets
les plus variables, les plus divers, et même les plus contraires,
selon qu’elles rencontrent telle nature ou telle disposition du
sujet. Mais savons-nous quelque chose de plus? et même, vu le
caractère indéterminé des causes que nous concevons dans les corps,
y a-t-il quelque chose de plus à savoir? Y a-t-il lieu de nous
enquérir si nous percevons les choses telles qu’elles sont? Non
évidemment.... Je ne dis pas que le problème est insoluble, _je dis
qu’il est absurde et enferme une contradiction_. Nous _ne savons pas
ce que ces causes sont en elles-mêmes_, et la raison nous défend de
chercher à le connaître: mais il est bien évident _à priori_,
qu’_elles ne sont pas en elles-mêmes ce qu’elles sont par rapport à
nous_, puisque la présence du sujet modifie nécessairement leur
action. Supprimez tout sujet sentant, il est certain que ces causes
agiraient encore puisqu’elles continueraient d’exister; mais elles
agiraient autrement; elles seraient encore des qualités et des
propriétés, mais qui ne ressembleraient à rien de ce que nous
connaissons. Le feu ne manifesterait plus aucune des propriétés que
nous lui connaissons: que serait-il? C’est ce que nous ne saurons
jamais. _C’est d’ailleurs peut-être un problème qui ne répugne pas
seulement à la nature de notre esprit, mais à l’essence même des
choses._ Quand même en effet on supprimerait par le pensée tous les
sujets sentants, il faudrait encore admettre que nul corps ne
manifesterait ses propriétés autrement qu’en relation avec un sujet
quelconque, et dans ce cas _ses propriétés ne seraient encore que
relatives_: en sorte qu’il me paraît fort raisonnable d’admettre que
les propriétés déterminées des corps n’existent pas indépendamment
d’un sujet quelconque, et que quand on demande si les propriétés de
la matiere sont telles que nous les percevons, il faudrait voir
auparavant si elles sont en tant que déterminées, et dans quel sens
il est vrai de dire qu’elles sont.”—_Cours d’Histoire de la
Philosophie Morale au 18me siècle_, 8me leçon.
22 An attempt, indeed, has been made by Reid and others, to establish
that although some of the properties we ascribe to objects exist
only in our sensations, others exist in the things themselves, being
such as can not possibly be copies of any impression upon the
senses; and they ask, from what sensations our notions of extension
and figure have been derived? The gauntlet thrown down by Reid was
taken up by Brown, who, applying greater powers of analysis than had
previously been applied to the notions of extension and figure,
pointed out that the sensations from which those notions are
derived, are sensations of touch, combined with sensations of a
class previously too little adverted to by metaphysicians, those
which have their seat in our muscular frame. His analysis, which was
adopted and followed up by James Mill, has been further and greatly
improved upon in Professor Bain’s profound work, _The Senses and the
Intellect_, and in the chapters on “Perception” of a work of eminent
analytic power, Mr. Herbert Spencer’s _Principles of Psychology_.
On this point M. Cousin may again be cited in favor of the better
doctrine. M. Cousin recognizes, in opposition to Reid, the essential
subjectivity of our conceptions of what are called the primary
qualities of matter, as extension, solidity, etc., equally with
those of color, heat, and the remainder of the so-called secondary
qualities.—_Cours_, ut supra, 9me leçon.
23 This doctrine, which is the most complete form of the philosophical
theory known as the Relativity of Human Knowledge, has, since the
recent revival in this country of an active interest in metaphysical
speculation, been the subject of a greatly increased amount of
discussion and controversy; and dissentients have manifested
themselves in considerably greater number than I had any knowledge
of when the passage in the text was written. The doctrine has been
attacked from two sides. Some thinkers, among whom are the late
Professor Ferrier, in his _Institutes of Metaphysic_, and Professor
John Grote, in his _Exploratio Philosophica_, appear to deny
altogether the reality of Noumena, or Things in themselves—of an
unknowable substratum or support for the sensations which we
experience, and which, according to the theory, constitute all our
knowledge of an external world. It seems to me, however, that in
Professor Grote’s case at least, the denial of Noumena is only
apparent, and that he does not essentially differ from the other
class of objectors, including Mr. Bailey in his valuable _Letters on
the Philosophy of the Human Mind_, and (in spite of the striking
passage quoted in the text) also Sir William Hamilton, who contend
for a direct knowledge by the human mind of more than the
sensations—of certain attributes or properties as they exist not in
us, but in the Things themselves.
With the first of these opinions, that which denies Noumena, I have,
as a metaphysician, no quarrel; but, whether it be true or false, it
is irrelevant to Logic. And since all the forms of language are in
contradiction to it, nothing but confusion could result from its
unnecessary introduction into a treatise, every essential doctrine
of which could stand equally well with the opposite and accredited
opinion. The other and rival doctrine, that of a direct perception
or intuitive knowledge of the outward object as it is in itself,
considered as distinct from the sensations we receive from it, is of
far greater practical moment. But even this question, depending on
the nature and laws of Intuitive Knowledge, is not within the
province of Logic. For the grounds of my own opinion concerning it,
I must content myself with referring to a work already mentioned—_An
Examination of Sir William Hamilton’s Philosophy_; several chapters
of which are devoted to a full discussion of the questions and
theories relating to the supposed direct perception of external
objects.
24 Professor Bain (_Logic_, i., 49) defines attributes as “points of
community among classes.” This definition expresses well one point
of view, but is liable to the objection that it applies only to the
attributes of classes; though an object, unique in its kind, may be
said to have attributes. Moreover, the definition is not ultimate,
since the points of community themselves admit of, and require,
further analysis; and Mr. Bain does analyze them into resemblances
in the sensations, or other states of consciousness excited by the
object.
_ 25 Analysis of the Human Mind_, i., 126 et seq.
_ 26 Logic_, i., 85.
27 Instead of Universal and Particular as applied to propositions,
Professor Bain proposes (_Logic_, i., 81) the terms Total and
Partial; reserving the former pair of terms for their inductive
meaning, “the contrast between a general proposition and the
particulars or individuals that we derive it from.” This change in
nomenclature would be attended with the further advantage, that
Singular propositions, which in the Syllogism follow the same rules
as Universal, would be included along with them in the same class,
that of Total predications. It is not the Subject’s denoting many
things or only one, that is of importance in reasoning, it is that
the assertion is made of the whole or a part only of what the
Subject denotes. The words Universal and Particular, however, are so
familiar and so well understood in both the senses mentioned by Mr.
Bain, that the double meaning does not produce any material
inconvenience.
28 It may, however, be considered as equivalent to a universal
proposition with a different predicate, viz.: “All wine is good
_quâ_ wine,” or “is good in respect of the qualities which
constitute it wine.”
_ 29 Logic_, i., 82.
30 Dr. Whewell (_Philosophy of Discovery_, p. 242) questions this
statement, and asks, “Are we to say that a mole can not dig the
ground, except he has an idea of the ground, and of the snout and
paws with which he digs it?” I do not know what passes in a mole’s
mind, nor what amount of mental apprehension may or may not
accompany his instinctive actions. But a human being does not use a
spade by instinct; and he certainly could not use it unless he had
knowledge of a spade, and of the earth which he uses it upon.
31 Professor Bain remarks, in qualification of the statement in the
text (_Logic_, i., 50), that the word Class has two meanings; “the
class definite, and the class indefinite. The class definite is an
enumeration of actual individuals, as the Peers of the Realm, the
oceans of the globe, the known planets.... The class indefinite is
unenumerated. Such classes are stars, planets, gold-bearing rocks,
men, poets, virtuous.... In this last acceptation of the word, class
name and general name are identical. The class name denotes an
indefinite number of individuals, and connotes the points of
community or likeness.”
The theory controverted in the text, tacitly supposes all classes to
be _definite_. I have assumed them to be indefinite; because, for
the purposes of Logic, definite classes, as such, are almost
useless; though often serviceable as means of abridged expression.
(Vide infra, book iii., chap. ii.)
32 “From hence also this may be deduced, that the first truths were
arbitrarily made by those that first of all imposed names upon
things, or received them from the imposition of others. For it is
true (for example) that _man is a living creature_, but it is for
this reason, that it pleased men to impose both these names on the
same thing.”—_Computation or Logic_, chap. iii., sect. 8.
33 “Men are subject to err not only in affirming and denying, but also
in perception, and in silent cogitation.... Tacit errors, or the
errors of sense and cogitation, are made by passing from one
imagination to the imagination of another different thing; or by
feigning that to be past, or future, which never was, nor ever shall
be; as when by seeing the image of the sun in water, we imagine the
sun itself to be there; or by seeing swords, that there has been, or
shall be, fighting, because it used to be so for the most part; or
when from promises we feign the mind of the promiser to be such and
such; or, lastly, when from any sign we vainly imagine something to
be signified which is not. And errors of this sort are common to all
things that have sense.”—_Computation or Logic_, chap. v., sect. 1.
34 Chap. iii., sect 3.
35 To the preceding statement it has been objected, that “we naturally
construe the subject of a proposition in its extension, and the
predicate (which therefore may be an adjective) in its intension
(connotation): and that consequently co-existence of attributes does
not, any more than the opposite theory of equation of groups,
correspond with the living processes of thought and language.” I
acknowledge the distinction here drawn, which, indeed, I had myself
laid down and exemplified a few pages back (p. 77). But though it is
true that we naturally “construe the subject of a proposition in its
extension,” this extension, or in other words, the extent of the
class denoted by the name, is not apprehended or indicated directly.
It is both apprehended and indicated solely through the attributes.
In the “living processes of thought and language” the extension,
though in this case really thought of (which in the case of the
predicate it is not), is thought of only through the medium of what
my acute and courteous critic terms the “intension.”
For further illustrations of this subject, see _Examination of Sir
William Hamilton’s Philosophy_, chap. xxii.
36 Professor Bain, in his _Logic_ (i., 256), excludes Existence from
the list, considering it as a mere name. All propositions, he says,
which predicate mere existence “are more or less abbreviated, or
elliptical: when fully expressed they fall under either co-existence
or succession. When we say there _exists_ a conspiracy for a
particular purpose, we mean that at the present time a body of men
have formed themselves into a society for a particular object; which
is a complex affirmation, resolvable into propositions of
co-existence and succession (as causation). The assertion that the
dodo does not exist, points to the fact that this animal, once known
in a certain place, has disappeared or become extinct; is no longer
associated with the locality: all which may be better stated without
the use of the verb ‘exist.’ There is a debated question—Does an
ether exist? but the concrete form would be this—‘Are heat and light
and other radiant influences propagated by an ethereal medium
diffused in space;’ which is a proposition of causation. In like
manner the question of the Existence of a Deity can not be discussed
in that form. It is properly a question as to the First _Cause_ of
the Universe, and as to the continued exertion of that Cause in
providential superintendence.” (i., 407.)
Mr. Bain thinks it “fictitious and unmeaning language” to carry up
the classification of Nature to one _summum genus_, Being, or that
which Exists; since nothing can be perceived or apprehended but by
way of contrast with something else (of which important truth, under
the name of Law of Relativity, he has been in our time the principal
expounder and champion), and we have no other class to oppose to
Being, or fact to contrast with Existence.
I accept fully Mr. Bain’s Law of Relativity, but I do not understand
by it that to enable us to apprehend or be conscious of any fact, it
is necessary that we should contrast it with some other positive
fact. The antithesis necessary to consciousness need not, I
conceive, be an antithesis between two positives; it may be between
one positive and its negative. Hobbes was undoubtedly right when he
said that a single sensation indefinitely prolonged would cease to
be felt at all; but simple intermission, without other change, would
restore it to consciousness. In order to be conscious of heat, it is
not necessary that we should pass to it from cold; it suffices that
we should pass to it from a state of no sensation, or from a
sensation of some other kind. The relative opposite of Being,
considered as a summum genus, is Nonentity, or Nothing; and we have,
now and then, occasion to consider and discuss things merely in
contrast with Nonentity.
I grant that the _decision_ of questions of Existence usually if not
always depends on a previous question of either Causation or
Co-existence. But Existence is nevertheless a different thing from
Causation or Co-existence, and can be predicated apart from them.
The meaning of the abstract name Existence, and the connotation of
the concrete name Being, consist, like the meaning of all other
names, in sensations or states of consciousness: their peculiarity
is that to exist, is to excite, or be capable of exciting, _any_
sensations or states of consciousness: no matter what, but it is
indispensable that there should be some. It was from overlooking
this that Hegel, finding that Being is an abstraction reached by
thinking away all particular attributes, arrived at the
self-contradictory proposition on which he founded all his
philosophy, that Being is the same as Nothing. It is really the name
of Something, taken in the most comprehensive sense of the word.
37 Book iv., chap. vii.
_ 38 Logic_, i., 103–105.
39 The doctrines which prevented the real meaning of Essences from
being understood, had not assumed so settled a shape in the time of
Aristotle and his immediate followers, as was afterward given to
them by the Realists of the Middle Ages. Aristotle himself (in his
Treatise on the Categories) expressly denies that the δεύτεραι
οὔσιαι, or Substantiæ Secundæ, inhere in a subject. They are only,
he says, predicated of it.
40 The always acute and often profound author of _An Outline of
Sematology_ (Mr. B. H. Smart) justly says, “Locke will be much more
intelligible, if, in the majority of places, we substitute ‘the
knowledge of’ for what he calls ‘the Idea of’” (p. 10). Among the
many criticisms on Locke’s use of the word Idea, this is the one
which, as it appears to me, most nearly hits the mark; and I quote
it for the additional reason that it precisely expresses the point
of difference respecting the import of Propositions, between my view
and what I have spoken of as the Conceptualist view of them. Where a
Conceptualist says that a name or a proposition expresses our Idea
of a thing, I should generally say (instead of our Idea) our
Knowledge, or Belief, concerning the thing itself.
41 This distinction corresponds to that which is drawn by Kant and
other metaphysicians between what they term _analytic_ and
_synthetic_, judgments; the former being those which can be evolved
from the meaning of the terms used.
42 If we allow a differentia to what is not really a species. For the
distinction of Kinds, in the sense explained by us, not being in any
way applicable to attributes, it of course follows that although
attributes may be put into classes, those classes can be admitted to
be genera or species only by courtesy.
43 Professor Bain, in his Logic, takes a peculiar view of Definition.
He holds (i., 71) with the present work, that “the definition in its
full import, is the sum of all the properties connoted by the name;
it exhausts the meaning of a word.” But he regards the meaning of a
general name as including, not indeed all the common properties of
the class named, but all of them that are ultimate properties, not
resolvable into one another. “The enumeration of the attributes of
oxygen, of gold, of man, should be an enumeration of the final (so
far as can be made out), the underivable, powers or functions of
each,” and nothing less than this is a complete Definition (i., 75).
An independent property, not derivable from other properties, even
if previously unknown, yet as soon as discovered becomes, according
to him, part of the meaning of the term, and should be included in
the definition. “When we are told that diamond, which we know to be
a transparent, glittering, hard, and high-priced substance, is
composed of carbon, and is combustible, we must put these additional
properties on the same level as the rest; to us they are henceforth
connoted by the name” (i., 73). Consequently the propositions that
diamond is composed of carbon, and that it is combustible, are
regarded by Mr. Bain as merely verbal propositions. He carries this
doctrine so far as to say that unless mortality can be shown to be a
consequence of the ultimate laws of animal organization, mortality
is connoted by man, and “Man is Mortal” is a merely verbal
proposition. And one of the peculiarities (I think a disadvantageous
peculiarity) of his able and valuable treatise, is the large number
of propositions requiring proof, and learned by experience, which,
in conformity with this doctrine, he considers as not real, but
verbal, propositions.
The objection I have to this language is that it confounds, or at
least confuses, a much more important distinction than that which it
draws. The only reason for dividing Propositions into real and
verbal, is in order to discriminate propositions which convey
information about facts, from those which do not. A proposition
which affirms that an object has a given attribute, while
designating the object by a name which already signifies the
attribute, adds no information to that which was already possessed
by all who understood the name. But when this is said, it is implied
that, by the signification of a name, is meant the signification
attached to it in the common usage of life. I can not think we ought
to say that the meaning of a word includes matters of fact which are
unknown to every person who uses the word unless he has learned them
by special study of a particular department of Nature; or that
because a few persons are aware of these matters of fact, the
affirmation of them is a proposition conveying no information. I
hold that (special scientific connotation apart) a name means, or
connotes, only the properties which it is a mark of in the general
mind; and that in the case of any additional properties, however
uniformly found to accompany these, it remains possible that a thing
which did not possess the properties might still be thought entitled
to the name. Ruminant, according to Mr. Bain’s use of language,
connotes cloven-hoofed, since the two properties are always found
together, and no connection has ever been discovered between them:
but ruminant does not mean cloven-hoofed; and were an animal to be
discovered which chews the cud, but has its feet undivided, I
venture to say that it would still be called ruminant.
44 In the fuller discussion which Archbishop Whately has given to this
subject in his later editions, he almost ceases to regard the
definitions of names and those of things as, in any important sense,
distinct. He seems (9th ed., p. 145) to limit the notion of a Real
Definition to one which “explains any thing _more_ of the nature of
the thing than is implied in the name;” (including under the word
“implied,” not only what the name connotes, but every thing which
can be deduced by reasoning from the attributes connoted). Even
this, as he adds, is usually called not a Definition, but a
Description; and (as it seems to me) rightly so called. A
Description, I conceive, can only be ranked among Definitions, when
taken (as in the case of the zoological definition of man) to
fulfill the true office of a Definition, by declaring the
connotation given to a word in some special use, as a term of
science or art: which special connotation of course would not be
expressed by the proper definition of the word in its ordinary
employment.
Mr. De Morgan, exactly reversing the doctrine of Archbishop Whately,
understands by a Real Definition one which contains _less_ than the
Nominal Definition, provided only that what it contains is
sufficient for distinction. “By _real_ definition I mean such an
explanation of the word, be it the whole of the meaning or only
part, as will be sufficient to separate the things contained under
that word from all others. Thus the following, I believe, is a
complete definition of an elephant: An animal which naturally drinks
by drawing the water into its nose, and then spurting it into its
mouth.”—_Formal Logic_, p. 36. Mr. De Morgan’s general proposition
and his example are at variance; for the peculiar mode of drinking
of the elephant certainly forms no part of the meaning of the word
elephant. It could not be said, because a person happened to be
ignorant of this property, that he did not know what an elephant
means.
45 In the only attempt which, so far as I know, has been made to refute
the preceding argumentation, it is maintained that in the first form
of the syllogism,
A dragon is a thing which breathes flame,
A dragon is a serpent,
Therefore some serpent or serpents breathe flame,
“there is just as much truth in the conclusion as there is in the
premises, or rather, no more in the latter than in the former. If
the general name serpent includes both real and imaginary serpents,
there is no falsity in the conclusion; if not, there is falsity in
the minor premise.”
Let us, then, try to set out the syllogism on the hypothesis that
the name serpent includes imaginary serpents. We shall find that it
is now necessary to alter the predicates; for it can not be asserted
that an imaginary creature breathes flame; in predicating of it such
a fact, we assert by the most positive implication that it is real,
and not imaginary. The conclusion must run thus, “Some serpent or
serpents either do or are _imagined_ to breathe flame.” And to prove
this conclusion by the instance of dragons, the premises must be, A
dragon is _imagined_ as breathing flame. A dragon is a (real or
imaginary) serpent: from which it undoubtedly follows, that there
are serpents which are imagined to breathe flame; but the major
premise is not a definition, nor part of a definition; which is all
that I am concerned to prove.
Let us now examine the other assertion—that if the word serpent
stands for none but real serpents, the minor premise (a dragon is a
serpent) is false. This is exactly what I have myself said of the
premise, considered as a statement of fact: but it is not false as
part of the definition of a dragon; and since the premises, or one
of them, must be false (the conclusion being so), the real premise
can not be the definition, which is true, but the statement of fact,
which is false.
46 “Few people” (I have said in another place) “have reflected how
great a knowledge of Things is required to enable a man to affirm
that any given argument turns wholly upon words. There is, perhaps,
not one of the leading terms of philosophy which is not used in
almost innumerable shades of meaning, to express ideas more or less
widely different from one another. Between two of these ideas a
sagacious and penetrating mind will discern, as it were intuitively,
an unobvious link of connection, upon which, though perhaps unable
to give a logical account of it, he will found a perfectly valid
argument, which his critic, not having so keen an insight into the
Things, will mistake for a fallacy turning on the double meaning of
a term. And the greater the genius of him who thus safely leaps over
the chasm, the greater will probably be the crowing and vainglory of
the mere logician, who, hobbling after him, evinces his own superior
wisdom by pausing on its brink, and giving up as desperate his
proper business of bridging it over.”
47 The different cases of Equipollency, or “Equivalent Propositional
Forms,” are set forth with some fullness in Professor Bain’s
_Logic_. One of the commonest of these changes of expression, that
from affirming a proposition to denying its negative, or _vicè
versa_, Mr. Bain designates, very happily, by the name Obversion.
48 As Sir William Hamilton has pointed out, “Some A is not B” may also
be converted in the following form: “No B is _some_ A.” Some men are
not negroes; therefore, No negroes are _some_ men (_e.g._,
Europeans).
49 Contraries:
All A is B
No A is B
Subtraries:
Some A is B
Some A is not B
Contradictories:
All A is B
Some A is not B
Also contradictories:
No A is B
Some A is B
Respectively subalternate:
All A is B and No A is B
Some A is B and Some A is not B
50 Professor Bain denies the claim of Singular Propositions to be
classed, for the purposes of ratiocination, with Universal; though
they come within the designation which he himself proposes as an
equivalent for Universal, that of Total. He would even, to use his
own expression, banish them entirely from the syllogism. He takes as
an example,
Socrates is wise,
Socrates is poor, therefore
Some poor men are wise,
or more properly (as he observes) “one poor man is wise.” “Now, if
wise, poor, and a man, are attributes belonging to the meaning of
the word Socrates, there is then no march of reasoning at all. We
have given in Socrates, _inter alia_, the facts wise, poor, and a
man, and we merely repeat the concurrence which is selected from the
whole aggregate of properties making up the whole, Socrates. The
case is one under the head ‘Greater and Less Connotation’ in
Equivalent Propositional Forms, or Immediate Inference.
“But the example in this form does not do justice to the syllogism
of singulars. We must suppose both propositions to be real, the
predicates being in no way involved in the subject. Thus
Socrates was the master of Plato,
Socrates fought at Delium,
The master of Plato fought at Delium.
“It may fairly be doubted whether the transitions, in this instance,
are any thing more than equivalent forms. For the proposition
‘Socrates was the master of Plato and fought at Delium,’ compounded
out of the two premises, is obviously nothing more than a
grammatical abbreviation. No one can say that there is here any
change of meaning, or any thing beyond a verbal modification of the
original form. The next step is, ‘The master of Plato fought at
Delium,’ which is the previous statement cut down by the omission of
Socrates. It contents itself with reproducing a part of the meaning,
or saying less than had been previously said. The full equivalent of
the affirmation is, ‘The master of Plato fought at Delium, and the
master of Plato was Socrates:’ the new form omits the last piece of
information, and gives only the first. Now, we never consider that
we have made a real inference, a step in advance, when we repeat
_less_ than we are entitled to say, or drop from a complex statement
some portion not desired at the moment. Such an operation keeps
strictly within the domain of equivalence, or Immediate Inference.
In no way, therefore, can a syllogism with two singular premises be
viewed as a genuine syllogistic or deductive inference.” (_Logic_,
i., 159.)
The first argument, as will have been seen, rests upon the
supposition that the name Socrates has a meaning; that man, wise,
and poor, are parts of this meaning; and that by predicating them of
Socrates we convey no information; a view of the signification of
names which, for reasons already given (Note to § 4 of the chapter
on Definition, _supra_, pp. 110, 111.), I can not admit, and which,
as applied to the class of names which Socrates belongs to, is at
war with Mr. Bain’s own definition of a Proper Name (i., 148), “a
single _meaningless_ mark or designation appropriated to the thing.”
Such names, Mr. Bain proceeded to say, do not necessarily indicate
even human beings: much less then does the name Socrates include the
meaning of wise or poor. Otherwise it would follow that if Socrates
had grown rich, or had lost his mental faculties by illness, he
would no longer have been called Socrates.
The second part of Mr. Bain’s argument, in which he contends that
even when the premises convey real information, the conclusion is
merely the premises with a part left out, is applicable, if at all,
as much to universal propositions as to singular. In every syllogism
the conclusion contains less than is asserted in the two premises
taken together. Suppose the syllogism to be
All bees are intelligent,
All bees are insects, therefore
Some insects are intelligent:
one might use the same liberty taken by Mr. Bain, of joining
together the two premises as if they were one—“All bees are insects
and intelligent”—and might say that in omitting the middle term
_bees_ we make no real inference, but merely reproduce part of what
had been previously said. Mr. Bain’s is really an objection to the
syllogism itself, or at all events to the third figure: it has no
special applicability to singular propositions.
51 His conclusions are, “The first figure is suited to the discovery or
proof of the properties of a thing; the second to the discovery or
proof of the distinctions between things; the third to the discovery
or proof of instances and exceptions; the fourth to the discovery,
or exclusion, of the different species of a genus.” The reference of
syllogisms in the last three figures to the _dictum de omni et
nullo_ is, in Lambert’s opinion, strained and unnatural: to each of
the three belongs, according to him, a separate axiom, co-ordinate
and of equal authority with that _dictum_, and to which he gives the
names of _dictum de diverso_ for the second figure, _dictum de
exemplo_ for the third, and _dictum de reciproco_ for the fourth.
See part i., or _Dianoiologie_, chap, iv., § 229 _et seqq._ Mr.
Bailey (_Theory of Reasoning_, 2d ed., pp. 70–74) takes a similar
view of the subject.
52 Since this chapter was written, two treatises have appeared (or
rather a treatise and a fragment of a treatise), which aim at a
further improvement in the theory of the forms of ratiocination: Mr.
De Morgan’s “Formal Logic; or, the Calculus of Inference, Necessary
and Probable;” and the “New Analytic of Logical Forms,” attached as
an Appendix to Sir William Hamilton’s _Discussions on Philosophy_,
and at greater length, to his posthumous _Lectures on Logic_.
In Mr. De Morgan’s volume—abounding, in its more popular parts, with
valuable observations felicitously expressed—the principal feature
of originality is an attempt to bring within strict technical rules
the cases in which a conclusion can be drawn from premises of a form
usually classed as particular. Mr. De Morgan observes, very justly,
that from the premises most Bs are Cs, most Bs are As, it may be
concluded with certainty that some As are Cs, since two portions of
the class B, each of them comprising more than half, must
necessarily in part consist of the same individuals. Following out
this line of thought, it is equally evident that if we knew exactly
what proportion the “most” in each of the premises bear to the
entire class B, we could increase in a corresponding degree the
definiteness of the conclusion. Thus if 60 per cent. of B are
included in C, and 70 per cent. in A, 30 per cent. at least must be
common to both; in other words, the number of As which are Cs, and
of Cs which are As, must be at least equal to 30 per cent. of the
class B. Proceeding on this conception of “numerically definite
propositions,” and extending it to such forms as these:—“45 Xs (or
more) are each of them one of 70 Ys,” or “45 Xs (or more) are no one
of them to be found among 70 Ys,” and examining what inferences
admit of being drawn from the various combinations which may be made
of premises of this description, Mr. De Morgan establishes universal
formulæ for such inferences; creating for that purpose not only a
new technical language, but a formidable array of symbols analogous
to those of algebra.
Since it is undeniable that inferences, in the cases examined by Mr.
De Morgan, can legitimately be drawn, and that the ordinary theory
takes no account of them, I will not say that it was not worth while
to show in detail how these also could be reduced to formulæ as
rigorous as those of Aristotle. What Mr. De Morgan has done was
worth doing once (perhaps more than once, as a school exercise); but
I question if its results are worth studying and mastering for any
practical purpose. The practical use of technical forms of reasoning
is to bar out fallacies: but the fallacies which require to be
guarded against in ratiocination properly so called, arise from the
incautious use of the common forms of language; and the logician
must track the fallacy into that territory, instead of waiting for
it on a territory of his own. While he remains among propositions
which have acquired the numerical precision of the Calculus of
Probabilities, the enemy is left in possession of the only ground on
which he can be formidable. And since the propositions (short of
universal) on which a thinker has to depend, either for purposes of
speculation or of practice, do not, except in a few peculiar cases,
admit of any numerical precision; common reasoning can not be
translated into Mr. De Morgan’s forms, which therefore can not serve
any purpose as a test of it.
Sir William Hamilton’s theory of the “quantification of the
predicate” may be described as follows:
“Logically” (I quote his words) “we ought to take into account the
quantity, always understood in thought, but usually, for manifest
reasons, elided in its expression, not only of the subject, but also
of the predicate of a judgment.” All A is B, is equivalent to all A
is _some_ B. No A is B, to No A is _any_ B. Some A is B, is
tantamount to some A is _some_ B. Some A is not B, to Some A is _not
any_ B. As in these forms of assertion the predicate is exactly
co-extensive with the subject, they all admit of simple conversion;
and by this we obtain two additional forms—Some B is _all_ A, and No
B is _some_ A. We may also make the assertion All A is all B, which
will be true if the classes A and B are exactly co-extensive. The
last three forms, though conveying real assertions, have no place in
the ordinary classification of Propositions. All propositions, then,
being supposed to be translated into this language, and written each
in that one of the preceding forms which answers to its
signification, there emerges a new set of syllogistic rules,
materially different from the common ones. A general view of the
points of difference may be given in the words of Sir W. Hamilton
(_Discussions_, 2d ed., p. 651):
“The revocation of the two terms of a Proposition to their true
relation; a proposition being always an _equation_ of its subject
and its predicate.
“The consequent reduction of the Conversion of Propositions from
three species to one—that of Simple Conversion.
“The reduction of all the _General Laws_ of Categorical Syllogisms
to a single Canon.
“The evolution from that one canon of all the Species and varieties
of Syllogisms.
“The abrogation of all the _Special Laws_ of Syllogism.
“A demonstration of the exclusive possibility of Three Syllogistic
Figures; and (on new grounds) the scientific and final abolition of
the Fourth.
“A manifestation that Figure is an unessential variation in
syllogistic form; and the consequent absurdity of Reducing the
syllogisms of the other figures to the first.
“An enouncement of _one Organic Principle_ for each Figure.
“A determination of the true number of the Legitimate Moods; with
“Their amplification in number (thirty-six);
“Their numerical equality under all the figures; and
“Their relative equivalence, or virtual identity, throughout every
schematic difference.
“That, in the second and third figures, the extremes holding both
the same relation to the middle term, there is not, as in the first,
an opposition and subordination between a term major and a term
minor, mutually containing and contained, in the counter wholes of
Extension and Comprehension.
“Consequently, in the second and third figures, there is no
determinate major and minor premises, and there are two indifferent
conclusions: whereas in the first the premises are determinate, and
there is a single proximate conclusion.”
This doctrine, like that of Mr. De Morgan previously noticed, is a
real addition to the syllogistic theory; and has moreover this
advantage over Mr. De Morgan’s “numerically definite Syllogism,”
that the forms it supplies are really available as a test of the
correctness of ratiocination; since propositions in the common form
may always have their predicates quantified, and so be made amenable
to Sir W. Hamilton’s rules. Considered, however, as a contribution
to the _Science_ of Logic, that is, to the analysis of the mental
processes concerned in reasoning, the new doctrine appears to me, I
confess, not merely superfluous, but erroneous; since the form in
which it clothes propositions does not, like the ordinary form,
express what is in the mind of the speaker when he enunciates the
proposition. I can not think Sir William Hamilton right in
maintaining that the quantity of the predicate is “always understood
in thought.” It is implied, but is not present to the mind of the
person who asserts the proposition. The quantification of the
predicate, instead of being a means of bringing out more clearly the
meaning of the proposition, actually leads the mind out of the
proposition, into another order of ideas. For when we say, All men
are mortal, we simply mean to affirm the attribute mortality of all
men; without thinking at all of the _class_ mortal in the concrete,
or troubling ourselves about whether it contains any other beings or
not. It is only for some artificial purpose that we ever look at the
proposition in the aspect in which the predicate also is thought of
as a class-name, either including the subject only, or the subject
and something more. (See above, p. 77, 78.)
For a fuller discussion of this subject, see the twenty-second
chapter of a work already referred to, “An Examination of Sir
William Hamilton’s Philosophy.”
53 Mr. Herbert Spencer (_Principles of Psychology_, pp. 125–7), though
his theory of the syllogism coincides with all that is essential of
mine, thinks it a logical fallacy to present the two axioms in the
text, as the regulating principles of syllogism. He charges me with
falling into the error pointed out by Archbishop Whately and myself,
of confounding exact likeness with literal identity; and maintains,
that we ought not to say that Socrates possesses _the same_
attributes which are connoted by the word Man, but only that he
possesses attributes _exactly like_ them: according to which
phraseology, Socrates, and the attribute mortality, are not two
things co-existing with the same thing, as the axiom asserts, but
two things coexisting with two different things.
The question between Mr. Spencer and me is merely one of language;
for neither of us (if I understand Mr. Spencer’s opinions rightly)
believes an attribute to be a real thing, possessed of objective
existence; we believe it to be a particular mode of naming our
sensations, or our expectations of sensation, when looked at in
their relation to an external object which excites them. The
question raised by Mr. Spencer does not, therefore, concern the
properties of any really existing thing, but the comparative
appropriateness, for philosophical purposes, of two different modes
of using a name. Considered in this point of view, the phraseology I
have employed, which is that commonly used by philosophers, seems to
me to be the best. Mr. Spencer is of opinion that because Socrates
and Alcibiades are not the same man, the attribute which constitutes
them men should not be called the same attribute; that because the
humanity of one man and that of another express themselves to our
senses not by the same individual sensations but by sensations
exactly alike, humanity ought to be regarded as a different
attribute in every different man. But on this showing, the humanity
even of any one man should be considered as different attributes now
and half an hour hence; for the sensations by which it will then
manifest itself to my organs will not be a continuation of my
present sensations, but a repetition of them; fresh sensations, not
identical with, but only exactly like the present. If every general
conception, instead of being “the One in the Many,” were considered
to be as many different conceptions as there are things to which it
is applicable, there would be no such thing as general language. A
name would have no general meaning if _man_ connoted one thing when
predicated of John, and another, though closely resembling, thing
when predicated of William. Accordingly a recent pamphlet asserts
the impossibility of general knowledge on this precise ground.
The meaning of any general name is some outward or inward
phenomenon, consisting, in the last resort, of feelings; and these
feelings, if their continuity is for an instant broken, are no
longer the same feelings, in the sense of individual identity. What,
then, is the common something which gives a meaning to the general
name? Mr. Spencer can only say, it is the similarity of the
feelings; and I rejoin, the attribute is precisely that similarity.
The names of attributes are in their ultimate analysis names for the
resemblances of our sensations (or other feelings). Every general
name, whether abstract or concrete, denotes or connotes one or more
of those resemblances. It will not, probably, be denied, that if a
hundred sensations are undistinguishably alike, their resemblance
ought to be spoken of as one resemblance, and not a hundred
resemblances which merely _resemble_ one another. The things
compared are many, but the something common to all of them must be
conceived as one, just as the name is conceived as one, though
corresponding to numerically different sensations of sound each time
it is pronounced. The general term _man_ does not connote the
sensations derived once from one man, which, once gone, can no more
occur again than the same flash of lightning. It connotes the
general type of the sensations derived always from all men, and the
power (always thought of as one) of producing sensations of that
type. And the axiom might be thus worded: Two _types of sensation_
each of which co-exists with a third type, co-exist with another; or
Two _powers_ each of which co-exists with a third power co-exist
with one another.
Mr. Spencer has misunderstood me in another particular. He supposes
that the co-existence spoken of in the axiom, of two things with the
same third thing, means simultaneousness in time. The co-existence
meant is that of being jointly attributes of the same subject. The
attribute of being born without teeth, and the attribute of having
thirty-two teeth in mature age, are in this sense co-existent, both
being attributes of man, though _ex vi termini_ never of the same
man at the same time.
54 Supra, p. 93.
55 Professor Bain (_Logic_, i., 157) considers the axiom (or rather
axioms) here proposed as a substitute for the _dictum de omni_, to
possess certain advantages, but to be “unworkable as a basis of the
syllogism. The fatal defect consists in this, that it is ill-adapted
to bring out the difference between total and partial coincidence of
terms, the observation of which is the essential precaution in
syllogizing correctly. If all the terms were co-extensive, the axiom
would flow on admirably; A carries B, all B and none but B; B
carries C in the same manner; at once A carries C, without
limitation or reserve. But in point of fact, we know that while A
carries B, other things carry B also; whence a process of limitation
is required, in transferring A to C through B. A (in common with
other things) carries B; B (in common with other things) carries C;
whence A (in common with other things) carries C. The axiom provides
no means of making this limitation; if we were to follow A
literally, we should be led to suppose A and C co-extensive: for
such is the only obvious meaning of ‘the attribute A coincides with
the attribute C.’”
It is certainly possible that a careless learner here and there may
suppose that if A carries B, it follows that B carries A. But if any
one is so incautious as to commit this mistake, the very earliest
lesson in the logic of inference, the Conversion of propositions,
will correct it. The first of the two forms in which I have stated
the axiom, is in some degree open to Mr. Bain’s criticism: when B is
said to co-exist with A (it must be by a _lapsus calami_ that Mr.
Bain uses the word _coincide_), it is possible, in the absence of
warning, to suppose the meaning to be that the two things are only
found together. But this misinterpretation is excluded by the other,
or practical, form of the maxim; _Nota notœ est nota rei ipsius._ No
one would be in any danger of inferring that because _a_ is a mark
of _b, b_ can never exist without _a_; that because being in a
confirmed consumption is a mark of being about to die, no one dies
who is not in a consumption; that because being coal is a mark of
having come out of the earth, nothing can come out of the earth
except coal. Ordinary knowledge of English seems a sufficient
protection against these mistakes, since in speaking of a mark of
any thing we are never understood as implying reciprocity.
A more fundamental objection is stated by Mr. Bain in a subsequent
passage (p. 158). “The axiom does not accommodate itself to the type
of Deductive Reasoning as contrasted with Induction—the application
of a general principle to a special case. Any thing that fails to
make prominent this circumstance is not adapted as a foundation for
the syllogism.” But though it may be proper to limit the term
Deduction to the application of a general principle to a special
case, it has never been held that Ratiocination or Syllogism is
subject to the same limitation; and the adoption of it would exclude
a great amount of valid and conclusive syllogistic reasoning.
Moreover, if the _dictum de omni_ makes prominent the fact of the
application of a general principle to a particular case, the axiom I
propose makes prominent the condition which alone makes that
application a real inference.
I conclude, therefore, that both forms have their value, and their
place in Logic. The _dictum de omni_ should be retained as the
fundamental axiom of the logic of mere consistency, often called
Formal Logic; nor have I ever quarreled with the use of it in that
character, nor proposed to banish it from treatises on Formal Logic.
But the other is the proper axiom for the logic of the pursuit of
truth by way of Deduction; and the recognition of it can alone show
how it is possible that deductive reasoning can be a road to truth.
_ 56 Logic_, p. 239 (9th ed.).
57 It is hardly necessary to say, that I am not contending for any such
absurdity as that we _actually_ “ought to have known” and considered
the case of every individual man, past, present, and future, before
affirming that all men are mortal: although this interpretation has
been, strangely enough, put upon the preceding observations. There
is no difference between me and Archbishop Whately, or any other
defender of the syllogism, on the practical part of the matter; I am
only pointing out an inconsistency in the logical theory of it, as
conceived by almost all writers. I do not say that a person who
affirmed, before the Duke of Wellington was born, that all men are
mortal, _knew_ that the Duke of Wellington was mortal; but I do say
that he _asserted_ it; and I ask for an explanation of the apparent
logical fallacy, of adducing in proof of the Duke of Wellington’s
mortality, a general statement which presupposes it. Finding no
sufficient resolution of this difficulty in any of the writers on
Logic, I have attempted to supply one.
58 The language of ratiocination would, I think, be brought into closer
agreement with the real nature of the process, if the general
propositions employed in reasoning, instead of being in the form All
men are mortal, or Every man is mortal, were expressed in the form
Any man is mortal. This mode of expression, exhibiting as the type
of all reasoning from experience “The men A, B, C, etc., are so and
so, therefore _any_ man is so and so,” would much better manifest
the true idea—that inductive reasoning is always, at bottom,
inference from particulars to particulars, and that the whole
function of general propositions in reasoning, is to vouch for the
legitimacy of such inferences.
59 Review of Quetelet on Probabilities, _Essays_, p. 367.
_ 60 Philosophy of Discovery_, p. 289.
_ 61 Theory of Reasoning_, chap. iv., to which I may refer for an able
statement and enforcement of the grounds of the doctrine.
62 On a recent careful reperusal of Berkeley’s whole works, I have been
unable to find this doctrine in them. Sir John Herschel probably
meant that it is implied in Berkeley’s argument against abstract
ideas. But I can not find that Berkeley saw the implication, or had
ever asked himself what bearing his argument had on the theory of
the syllogism. Still less can I admit that the doctrine is (as has
been affirmed by one of my ablest and most candid critics) “among
the standing marks of what is called the empirical philosophy.”
_ 63 Logic_, book iv., chap. i., sect. 1.
64 See the important chapter on Belief, in Professor Bain’s great
treatise, _The Emotions and the Will_, pp. 581–4.
65 A writer in the “British Quarterly Review” (August, 1846), in a
review of this treatise, endeavors to show that there is no _petitio
principii_ in the syllogism, by denying that the proposition, All
men are mortal, asserts or assumes that Socrates is mortal. In
support of this denial, he argues that we may, and in fact do, admit
the general proposition that all men are mortal, without having
particularly examined the case of Socrates, and even without knowing
whether the individual so named is a man or something else. But this
of course was never denied. That we can and do draw conclusions
concerning cases specifically unknown to us, is the datum from which
all who discuss this subject must set out. The question is, in what
terms the evidence, or ground, on which we draw these conclusions,
may best be designated—whether it is most correct to say, that the
unknown case is proved by known cases, or that it is proved by a
general proposition including both sets of cases, the unknown and
the known? I contend for the former mode of expression. I hold it an
abuse of language to say, that the proof that Socrates is mortal, is
that all men are mortal. Turn it in what way we will, this seems to
me to be asserting that a thing is the proof of itself. Whoever
pronounces the words, All men are mortal, has affirmed that Socrates
is mortal, though he may never have heard of Socrates; for since
Socrates, whether known to be so or not, really is a man, he is
included in the words, All men, and in every assertion of which they
are the subject. If the reviewer does not see that there is a
difficulty here, I can only advise him to reconsider the subject
until he does: after which he will be a better judge of the success
or failure of an attempt to remove the difficulty. That he had
reflected very little on the point when he wrote his remarks, is
shown by his oversight respecting the _dictum de omni et nullo_. He
acknowledges that this maxim as commonly expressed—“Whatever is true
of a class, is true of every thing included in the class,” is a mere
identical proposition, since the class _is_ nothing but the things
included in it. But he thinks this defect would be cured by wording
the maxim thus—“Whatever is true of a class, is true of every thing
which _can be shown_ to be a member of the class:” as if a thing
could “be shown” to be a member of the class without being one. If a
class means the sum of all the things included in the class, the
things which can “be shown” to be included in it are part of the
sum, and the _dictum_ is as much an identical proposition with
respect to them as to the rest. One would almost imagine that, in
the reviewer’s opinion, things are not members of a class until they
are called up publicly to take their place in it—that so long, in
fact, as Socrates is not known to be a man, he _is not_ a man, and
any assertion which can be made concerning men does not at all
regard him, nor is affected as to its truth or falsity by any thing
in which he is concerned.
The difference between the reviewer’s theory and mine may be thus
stated. Both admit that when we say, All men are mortal, we make an
assertion reaching beyond the sphere of our knowledge of individual
cases; and that when a new individual, Socrates, is brought within
the field of our knowledge by means of the minor premise, we learn
that we have already made an assertion respecting Socrates without
knowing it: our own general formula being, to that extent, for the
first time _interpreted_ to us. But according to the reviewer’s
theory, the smaller assertion is proved by the larger: while I
contend, that both assertions are proved together, by the same
evidence, namely, the grounds of experience on which the general
assertion was made, and by which it must be justified.
The reviewer says, that if the major premise included the
conclusion, “we should be able to affirm the conclusion without the
intervention of the minor premise; but every one sees that that is
impossible.” A similar argument is urged by Mr. De Morgan (_Formal
Logic_, p. 259): “The whole objection tacitly assumes the
superfluity of the minor; that is, tacitly assumes we know Socrates
(Mr. De Morgan says ‘Plato,’ but to prevent confusion I have kept to
my own _exemplum_.) to be a man as soon as we know him to be
Socrates.” The objection would be well grounded if the assertion
that the major premise includes the conclusion, meant that it
individually specifies all it includes. As, however, the only
indication it gives is a description by marks, we have still to
compare any new individual with the marks; and to show that this
comparison has been made, is the office of the minor. But since, by
supposition, the new individual has the marks, whether we have
ascertained him to have them or not; if we have affirmed the major
premise, we have asserted him to be mortal. Now my position is that
this assertion can not be a necessary part of the argument. It can
not be a necessary condition of reasoning that we should begin by
making an assertion, which is afterward to be employed in proving a
part of itself. I can conceive only one way out of this difficulty,
viz., that what really forms the proof is _the other_ part of the
assertion: the portion of it, the truth of which has been
ascertained previously: and that the unproved part is bound up in
one formula with the proved part in mere anticipation, and as a
memorandum of the nature of the conclusions which we are prepared to
prove.
With respect to the minor premise in its formal shape, the minor as
it stands in the syllogism, predicating of Socrates a definite class
name, I readily admit that it is no more a necessary part of
reasoning than the major. When there is a major, doing its work by
means of a class name, minors are needed to interpret it: but
reasoning can be carried on without either the one or the other.
They are not the conditions of reasoning, but a precaution against
erroneous reasoning. The only minor premise necessary to reasoning
in the example under consideration, is, Socrates is _like_ A, B, C,
and the other individuals who are known to have died. And this is
the only universal type of that step in the reasoning process which
is represented by the minor. Experience, however, of the uncertainty
of this loose mode of inference, teaches the expediency of
determining beforehand what _kind_ of likeness to the cases
observed, is necessary to bring an unobserved case within the same
predicate; and the answer to this question is the major. The minor
then identifies the precise kind of likeness possessed by Socrates,
as being the kind required by the formula. Thus the syllogistic
major and the syllogistic minor start into existence together, and
are called forth by the same exigency. When we conclude from
personal experience without referring to any record—to any general
theorems, either written, or traditional, or mentally registered by
ourselves as conclusions of our own drawing—we do not use, in our
thoughts, either a major or a minor, such as the syllogism puts into
words. When, however, we revise this rough inference from
particulars to particulars, and substitute a careful one, the
revision consists in selecting two syllogistic premises. But this
neither alters nor adds to the evidence we had before; it only puts
us in a better position for judging whether our inference from
particulars to particulars is well grounded.
66 Infra, book iii., chap. ii.
67 Infra, book iii., ch. iv., § 3, and elsewhere.
68 It is justly remarked by Professor Bain (_Logic_, ii., 134) that the
word Hypothesis is here used in a somewhat peculiar sense. An
hypothesis, in science, usually means a supposition not proved to be
true, but surmised to be so, because if true it would account for
certain known facts; and the final result of the speculation may be
to prove its truth. The hypotheses spoken of in the text are of a
different character; they are known not to be literally true, while
as much of them as is true is not hypothetical, but certain. The two
cases, however, resemble in the circumstance that in both we reason,
not from a truth, but from an assumption, and the truth therefore of
the conclusions is conditional, not categorical. This suffices to
justify, in point of logical propriety, Stewart’s use of the term.
It is of course needful to bear in mind that the hypothetical
element in the definitions of geometry is the assumption that what
is very nearly true is exactly so. This unreal exactitude might be
called a fiction, as properly as an hypothesis; but that
appellation, still more than the other, would fail to point out the
close relation which exists between the fictitious point or line and
the points and lines of which we have experience.
_ 69 Mechanical Euclid_, pp. 149 _et seqq._
70 We might, it is true, insert this property into the definition of
parallel lines, framing the definition so as to require, both that
when produced indefinitely they shall never meet, and also that any
straight line which intersects one of them shall, if prolonged, meet
the other. But by doing this we by no means get rid of the
assumption; we are still obliged to take for granted the geometrical
truth, that all straight lines in the same plane, which have the
former of these properties, have also the latter. For if it were
possible that they should not, that is, if any straight lines in the
same plane, other than those which are parallel according to the
definition, had the property of never meeting although indefinitely
produced, the demonstrations of the subsequent portions of the
theory of parallels could not be maintained.
71 Some persons find themselves prevented from believing that the
axiom, Two straight lines can not inclose a space, could ever become
known to us through experience, by a difficulty which may be stated
as follows: If the straight lines spoken of are those contemplated
in the definition—lines absolutely without breadth and absolutely
straight—that such are incapable of inclosing a space is not proved
by experience, for lines such as these do not present themselves in
our experience. If, on the other hand, the lines meant are such
straight lines as we do meet with in experience, lines straight
enough for practical purposes, but in reality slightly zigzag, and
with some, however trifling, breadth; as applied to these lines the
axiom is not true, for two of them may, and sometimes do, inclose a
small portion of space. In neither case, therefore, does experience
prove the axiom.
Those who employ this argument to show that geometrical axioms can
not be proved by induction, show themselves unfamiliar with a common
and perfectly valid mode of inductive proof; proof by approximation.
Though experience furnishes us with no lines so unimpeachably
straight that two of them are incapable of inclosing the smallest
space, it presents us with gradations of lines possessing less and
less either of breadth or of flexure, of which series the straight
line of the definition is the ideal limit. And observation shows
that just as much, and as nearly, as the straight lines of
experience approximate to having no breadth or flexure, so much and
so nearly does the space-inclosing power of any two of them approach
to zero. The inference that if they had no breadth or flexure at
all, they would inclose no space at all, is a correct inductive
inference from these facts, conformable to one of the four Inductive
Methods hereinafter characterized, the Method of Concomitant
Variations; of which the mathematical Doctrine of Limits presents
the extreme case.
72 Whewell’s _History of Scientific Ideas_, i., 140.
73 Dr. Whewell (_Philosophy of Discovery_, p. 289) thinks it
unreasonable to contend that we know by experience, that our idea of
a line exactly resembles a real line. “It does not appear,” he says,
“how we can compare our ideas with the realities, since we know the
realities only by our ideas.” We know the realities by our
sensations. Dr. Whewell surely does not hold the “doctrine of
perception by means of ideas,” which Reid gave himself so much
trouble to refute. If Dr. Whewell doubts whether we compare our
ideas with the corresponding sensations, and assume that they
resemble, let me ask on what evidence do we judge that a portrait of
a person not present is like the original. Surely because it is like
our idea, or mental image of the person, and because our idea is
like the man himself.
Dr. Whewell also says, that it does not appear why this resemblance
of ideas to the sensations of which they are copies, should be
spoken of as if it were a peculiarity of one class of ideas, those
of space. My reply is, that I do not so speak of it. The peculiarity
I contend for is only one of degree. All our ideas of sensation of
course resemble the corresponding sensations, but they do so with
very different degrees of exactness and of reliability. No one, I
presume, can recall in imagination a color or an odor with the same
distinctness and accuracy with which almost every one can mentally
reproduce an image of a straight line or a triangle. To the extent,
however, of their capabilities of accuracy, our recollections of
colors or of odors may serve as subjects of experimentation, as well
as those of lines and spaces, and may yield conclusions which will
be true of their external prototypes. A person in whom, either from
natural gift or from cultivation, the impressions of color were
peculiarly vivid and distinct, if asked which of two blue flowers
was of the darkest tinge, though he might never have compared the
two, or even looked at them together, might be able to give a
confident answer on the faith of his distinct recollection of the
colors; that is, he might examine his mental pictures, and find
there a property of the outward objects. But in hardly any case
except that of simple geometrical forms, could this be done by
mankind generally, with a degree of assurance equal to that which is
given by a contemplation of the objects themselves. Persons differ
most widely in the precision of their recollection, even of forms:
one person, when he has looked any one in the face for half a
minute, can draw an accurate likeness of him from memory; another
may have seen him every day for six months, and hardly know whether
his nose is long or short. But every body has a perfectly distinct
mental image of a straight line, a circle, or a rectangle. And every
one concludes confidently from these mental images to the
corresponding outward things. The truth is, that we may, and
continually do, study nature in our recollections, when the objects
themselves are absent; and in the case of geometrical forms we can
perfectly, but in most other cases only imperfectly, trust our
recollections.
_ 74 Logic_, i., 222.
75 Ibid., 226.
_ 76 History of Scientific Ideas_, i., 65–67.
77 Ibid., i., 60.
78 Ibid., 58, 59.
79 “If all mankind had spoken one language, we can not doubt that there
would have been a powerful, perhaps a universal, school of
philosophers, who would have believed in the inherent connection
between names and things, who would have taken the sound _man_ to be
the mode of agitating the air which is essentially communicative of
the ideas of reason, cookery, bipedality, etc.”—De Morgan, _Formal
Logic_, p. 246.
80 It would be difficult to name a man more remarkable at once for the
greatness and the wide range of his mental accomplishments, than
Leibnitz. Yet this eminent man gave as a reason for rejecting
Newton’s scheme of the solar system, that God _could not_ make a
body revolve round a distant centre, unless either by some impelling
mechanism, or by miracle: “Tout ce qui n’est pas explicable,” says
he in a letter to the Abbé Conti, “par la nature des créatures, est
miraculeux. Il ne suffit pas de dire: Dieu a fait une telle loi de
nature; donc la chose est naturelle. Il faut que la loi soit
exécutable par les natures des créatures. Si Dien donnait cette loi,
par exemple, à un corps libre, de tourner à l’entour d’un certain
centre, _il faudrait ou qu’il y joignît d’autres corps qui par leur
impulsion l’obligeassent de rester toujours dans son orbite
circulaire, ou qu’il mît un ange à ses trousses, ou enfin il
faudrait qu’il y concourût extraordinairement_; car naturellement il
s’écartera par la tangente.”—_Works of Leibnitz_, ed. Dutens, iii.,
446.
_ 81 Novum Organum Renovatum_, pp. 32, 33.
_ 82 History of Scientific Ideas_, i., 264.
83 Ibid., i., 263.
84 Ibid., 240.
_ 85 Hist. Scientific Ideas_, ii., 25, 26.
_ 86 Phil. of Disc._, p. 339.
_ 87 Phil. of Disc._, p. 338.
88 Ibid., p. 463.
_ 89 Phil. of Disc._, pp. 472, 473.
90 The _Quarterly Review_ for June, 1841, contained an article of great
ability on Dr. Whewell’s two great works (since acknowledged and
reprinted in Sir John Herschel’s Essays) which maintains, on the
subject of axioms, the doctrine advanced in the text, that they are
generalizations from experience, and supports that opinion by a line
of argument strikingly coinciding with mine. When I state that the
whole of the present chapter (except the last four pages, added in
the fifth edition) was written before I had seen the article (the
greater part, indeed, before it was published), it is not my object
to occupy the reader’s attention with a matter so unimportant as the
degree of originality which may or may not belong to any portion of
my own speculations, but to obtain for an opinion which is opposed
to reigning doctrines, the recommendation derived from a striking
concurrence of sentiment between two inquirers entirely independent
of one another. I embrace the opportunity of citing from a writer of
the extensive acquirements in physical and metaphysical knowledge
and the capacity of systematic thought which the article evinces,
passages so remarkably in unison with my own views as the following:
“The truths of geometry are summed up and embodied in its
definitions and axioms.... Let us turn to the axioms, and what do we
find? A string of propositions concerning magnitude in the abstract,
which are equally true of space, time, force, number, and every
other magnitude susceptible of aggregation and subdivision. Such
propositions, where they are not mere definitions, as some of them
are, carry their inductive origin on the face of their
enunciation.... Those which declare that two straight lines can not
inclose a space, and that two straight lines which cut one another
can not both be parallel to a third, are in reality the only ones
which express characteristic properties of space, and these it will
be worth while to consider more nearly. Now the only clear notion we
can form of straightness is uniformity of direction, for space in
its ultimate analysis is nothing but an assemblage of distances and
directions. And (not to dwell on the notion of continued
contemplation, _i.e._, mental experience, as included in the very
idea of uniformity; nor on that of transfer of the contemplating
being from point to point, and of experience, during such transfer,
of the homogeneity of the interval passed over) we can not even
propose the proposition in an intelligible form to any one whose
experience ever since he was born has not assured him of the fact.
The unity of direction, or that we can not march from a given point
by more than one path direct to the same object, is matter of
practical experience long before it can by possibility become matter
of abstract thought. _We can not attempt mentally to exemplify the
conditions of the assertion in an imaginary case opposed to it,
without violating our habitual recollection of this experience, and
defacing our mental picture of space as grounded on it._ What but
experience, we may ask, can possibly assure us of the homogeneity of
the parts of distance, time, force, and measurable aggregates in
general, on which the truth of the other axioms depends? As regards
the latter axiom, after what has been said it must be clear that the
very same course of remarks equally applies to its case, and that
its truth is quite as much forced on the mind as that of the former
by daily and hourly experience, ... _including always, be it
observed, in our notion of experience, that which is gained by
contemplation of the inward picture which the mind forms to itself
in any proposed case, or which it arbitrarily selects as an
example—such picture, in virtue of the extreme simplicity of these
primary relations, being called up by the imagination with as much
vividness and clearness as could be done by any external impression,
which is the only meaning we can attach to the word intuition, as
applied to such relations_.”
And again, of the axioms of mechanics: “As we admit no such
propositions, other than as truths inductively collected from
observation, even in geometry itself, it can hardly be expected
that, in a science of obviously contingent relations, we should
acquiesce in a contrary view. Let us take one of these axioms and
examine its evidence: for instance, that equal forces
perpendicularly applied at the opposite ends of equal arms of a
straight lever will balance each other. What but experience, we may
ask, in the first place, can possibly inform us that a force so
applied will have any tendency to turn the lever on its centre at
all? or that force can be so transmitted along a rigid line
perpendicular to its direction, as to act elsewhere in space than
along its own line of action? Surely this is so far from being
self-evident that it has even a paradoxical appearance, which is
only to be removed by giving our lever thickness, material
composition, and molecular powers. Again, we conclude, that the two
forces, being equal and applied under precisely similar
circumstances, must, if they exert any effort at all to turn the
lever, exert equal and opposite efforts: but what _a priori_
reasoning can possibly assure us that they _do_ act under precisely
similar circumstances? that points which differ in place _are_
similarly circumstanced as regards the exertion of force? that
universal space may not have relations to universal force—or, at all
events, that the organization of the material universe may not be
such as to place that portion of space occupied by it in such
relations to the forces exerted in it, as may invalidate the
absolute similarity of circumstances assumed? Or we may argue, what
have we to do with the notion of angular movement in the lever at
all? The case is one of rest, and of quiescent destruction of force
by force. Now how is this destruction effected? Assuredly by the
counter-pressure which supports the fulcrum. But would not this
destruction equally arise, and by the same amount of counteracting
force, if each force simply pressed its own half of the lever
against the fulcrum? And what can assure us that it is not so,
except removal of one or other force, and consequent tilting of the
lever? The other fundamental axiom of statics, that the pressure on
the point of support is the sum of the weights ... is merely a
scientific transformation and more refined mode of stating a coarse
and obvious result of universal experience, viz., that the weight of
a rigid body is the same, handle it or suspend it in what position
or by what point we will, and that whatever sustains it sustains its
total weight. Assuredly, as Mr. Whewell justly remarks, ‘No one
probably ever made a trial for the purpose of showing that the
pressure on the support is equal to the sum of the weights.’ ... But
it is precisely because in every action of his life from earliest
infancy he has been continually making the trial, and seeing it made
by every other living being about him, that he never dreams of
staking its result on one additional attempt made with scientific
accuracy. This would be as if a man should resolve to decide by
experiment whether his eyes were useful for the purpose of seeing,
by hermetically sealing himself up for half an hour in a metal
case.”
On the “paradox of universal propositions obtained by experience,”
the same writer says: “If there be necessary and universal truths
expressible in propositions of axiomatic simplicity and obviousness,
and having for their subject-matter the elements of all our
experience and all our knowledge, surely these are the truths which,
if experience suggest to us any truths at all, it ought to suggest
most readily, clearly, and unceasingly. If it were a truth,
universal and necessary, that a net is spread over the whole surface
of every planetary globe, we should not travel far on our own
without getting entangled in its meshes, and making the necessity of
some means of extrication an axiom of locomotion.... There is,
therefore, nothing paradoxical, but the reverse, in our being led by
observation to a recognition of such truths, as _general_
propositions, co-extensive at least with all human experience. That
they pervade all the objects of experience, must insure their
continual suggestion _by_ experience; that they are true, must
insure that consistency of suggestion, that iteration of
uncontradicted assertion, which commands implicit assent, and
removes all occasion of exception; that they are simple, and admit
of no misunderstanding, must secure their admission by every mind.”
“A truth, necessary and universal, relative to any object of our
knowledge, must verify itself in every instance where that object is
before our contemplation, and if at the same time it be simple and
intelligible, its verification must be obvious. _The sentiment of
such a truth can not, therefore, but be present to our minds
whenever that object is contemplated, and must therefore make a part
of the mental picture or idea of that object which we may on any
occasion summon before our imagination.... All propositions,
therefore, become not only untrue but inconceivable_, if ... axioms
be violated in their enunciation.”
Another eminent mathematician had previously sanctioned by his
authority the doctrine of the origin of geometrical axioms in
experience. “Geometry is thus founded likewise on observation; but
of a kind so familiar and obvious, that the primary notions which it
furnishes might seem intuitive.”—_Sir John Leslie_, quoted by Sir
William Hamilton, _Discourses_, etc., p. 272.
91 Principles of Psychology.
92 Mr. Spencer is mistaken in supposing me to claim any peculiar
“necessity” for this axiom as compared with others. I have corrected
the expressions which led him into that misapprehension of my
meaning.
93 Mr. Spencer, in recently returning to the subject (Principles of
Psychology, new edition, chap. xii.: “The Test of Relative
Validity”), makes two answers to the preceding remarks. One is:
“Were an argument formed by repeating the same proposition over and
over again, it would be true that any intrinsic fallibility of the
postulate would not make the conclusion more untrustworthy than the
first step. But an argument consists of unlike propositions. Now,
since Mr. Mill’s criticism on the Universal Postulate is that in
some cases, which he names, it has proved to be an untrustworthy
test; it follows that in any argument consisting of heterogeneous
propositions, there is a risk, increasing as the number of
propositions increases, that some one of them belongs to this class
of cases, and is wrongly accepted because of the inconceivableness
of its negation.”
No doubt: but this supposes new _premises_ to be taken in. The point
we are discussing is the fallibility not of the premises, but of the
reasoning, as distinguished from the premises. Now the validity of
the reasoning depends always upon the same axiom, repeated (in
thought) “over and over again,” viz., that whatever has a mark, has
what it is a mark of. Even, therefore, on the assumption that this
axiom rests ultimately on the Universal Postulate, and that, the
Postulate not being wholly trustworthy, the axiom may be one of the
cases of its failure; all the risk there is of this is incurred at
the very first step of the reasoning, and is not added to, however
long may be the series of subsequent steps.
I am here arguing, of course, from Mr. Spencer’s point of view. From
my own the case is still clearer; for, in my view, the truth that
whatever has a mark has what it is a mark of, is wholly trustworthy,
and derives none of its evidence from so very untrustworthy a test
as the inconceivability of the negative.
Mr. Spencer’s second answer is valid up to a certain point; it is,
that every prolongation of the process involves additional chances
of casual error, from carelessness in the reasoning operation. This
is an important consideration in the private speculations of an
individual reasoner; and even with respect to mankind at large, it
must be admitted that, though mere oversights in the syllogistic
process, like errors of addition in an account, are special to the
individual, and seldom escape detection, confusion of thought
produced (for example) by ambiguous terms has led whole nations or
ages to accept fallacious reasoning as valid. But this very fact
points to causes of error so much more dangerous than the mere
length of the process, as quite to vitiate the doctrine that the
“test of the relative validities of conflicting conclusions” is the
number of times the fundamental postulate is involved. On the
contrary, the subjects on which the trains of reasoning are longest,
and the assumption, therefore, oftenest repeated, are in general
those which are best fortified against the really formidable causes
of fallacy; as in the example already given of mathematics.
94 Mr. Spencer makes a distinction between conceiving myself looking
into darkness, and conceiving _that I am_ then and there looking
into darkness. To me it seems that this change of the expression to
the form _I am_, just marks the transition from conception to
belief, and that the phrase “to conceive that _I am_,” or “that any
thing _is_,” is not consistent with using the word conceive in its
rigorous sense.
95 I have myself accepted the contest, and fought it out on this
battle-ground, in the eleventh chapter of _An Examination of Sir
William Hamilton’s Philosophy._
96 Chap. xi.
97 In one of the three cases, Mr. Spencer, to my no small surprise,
thinks that the belief of mankind “can not be rightly said to have
undergone” the change I allege. Mr. Spencer himself still thinks we
are unable to conceive gravitation acting through empty space. “If
an astronomer avowed that he could conceive gravitative force as
exercised through space absolutely void, my private opinion would be
that he mistook the nature of conception. Conception implies
representation. Here the elements of the representation are the two
bodies and an agency by which either affects the other. To conceive
this agency is to represent it in some terms derived from our
experiences—that is, from our sensations. As this agency gives us no
sensations, we are obliged (if we try to conceive it) to use symbols
idealized from our sensations—imponderable units forming a medium.”
If Mr. Spencer means that the action of gravitation gives us no
sensations, the assertion is one than which I have not seen, in the
writings of philosophers, many more startling. What other sensation
do we need than the sensation of one body moving toward another?
“The elements of the representation” are not two bodies and an
“agency,” but two bodies and an effect; viz., the fact of their
approaching one another. If we are able to conceive a vacuum, is
there any difficulty in conceiving a body falling to the earth
through it?
_ 98 Discussions_, etc., 2d ed., p. 624.
99 Professor Bain (_Logic_, i., 16) identifies the Principle of
Contradiction with his Law of Relativity, viz., that “every thing
that can be thought of, every affirmation that can be made, has an
opposite or counter notion or affirmation;” a proposition which is
one of the general results of the whole body of human experience.
For further considerations respecting the axioms of Contradiction
and Excluded Middle, see the twenty-first chapter of _An Examination
of Sir William Hamilton’s Philosophy_.
100 Dr. Whewell thinks it improper to apply the term Induction to any
operation not terminating in the establishment of a general truth.
Induction, he says (_Philosophy of Discovery_, p. 245), “is not the
same thing as experience and observation. Induction is experience or
observation _consciously_ looked at in a _general_ form. This
consciousness and generality are necessary parts of that knowledge
which is science.” And he objects (p. 241) to the mode in which the
word Induction is employed in this work, as an undue extension of
that term “not only to the cases in which the general induction is
consciously applied to a particular instance, but to the cases in
which the particular instance is dealt with by means of experience
in that rude sense in which experience can be asserted of brutes,
and in which of course we can in no way imagine that the law is
possessed or understood as a general proposition.” This use of the
term he deems a “confusion of knowledge with practical tendencies.”
I disclaim, as strongly as Dr. Whewell can do, the application of
such terms as induction, inference, or reasoning, to operations
performed by mere instinct, that is, from an animal impulse, without
the exertion of any intelligence. But I perceive no ground for
confining the use of those terms to cases in which the inference is
drawn in the forms and with the precautions required by scientific
propriety. To the idea of Science, an express recognition and
distinct apprehension of general laws as such, is essential: but
nine-tenths of the conclusions drawn from experience in the course
of practical life, are drawn without any such recognition: they are
direct inferences from known cases, to a case supposed to be
similar. I have endeavored to show that this is not only as
legitimate an operation, but substantially the same operation, as
that of ascending from known cases to a general proposition; except
that the latter process has one great security for correctness which
the former does not possess. In science, the inference must
necessarily pass through the intermediate stage of a general
proposition, because Science wants its conclusions for record, and
not for instantaneous use. But the inferences drawn for the guidance
of practical affairs, by persons who would often be quite incapable
of expressing in unexceptionable terms the corresponding
generalizations, may and frequently do exhibit intellectual powers
quite equal to any which have ever been displayed in science; and if
these inferences are not inductive, what are they? The limitation
imposed on the term by Dr. Whewell seems perfectly arbitrary;
neither justified by any fundamental distinction between what he
includes and what he desires to exclude, nor sanctioned by usage, at
least from the time of Reid and Stewart, the principal legislators
(as far as the English language is concerned) of modern metaphysical
terminology.
101 Supra, p. 145.
_ 102 Novum Organum Renovatum_, pp. 72, 73.
_ 103 Novum Organum Renovatum_, p. 32.
_ 104 Cours de Philosophie Positive_, vol. ii., p. 202.
105 Dr. Whewell, in his reply, contests the distinction here drawn, and
maintains, that not only different descriptions, but different
explanations of a phenomenon, may all be true. Of the three theories
respecting the motions of the heavenly bodies, he says (_Philosophy
of Discovery_, p. 231): “Undoubtedly all these explanations may be
true and consistent with each other, and would be so if each had
been followed out so as to show in what manner it could be made
consistent with the facts. And this was, in reality, in a great
measure done. The doctrine that the heavenly bodies were moved by
vortices was successfully modified, so that it came to coincide in
its results with the doctrine of an inverse-quadratic centripetal
force.... When this point was reached, the vortex was merely a
machinery, well or ill devised, for producing such a centripetal
force, and therefore did not contradict the doctrine of a
centripetal force. Newton himself does not appear to have been
averse to explaining gravity by impulse. So little is it true that
if one theory be true the other must be false. The attempt to
explain gravity by the impulse of streams of particles flowing
through the universe in all directions, which I have mentioned in
the _Philosophy_, is so far from being inconsistent with the
Newtonian theory, that it is founded entirely upon it. And even with
regard to the doctrine, that the heavenly bodies move by an inherent
virtue; if this doctrine had been maintained in any such way that it
was brought to agree with the facts, the inherent virtue must have
had its laws determined; and then it would have been found that the
virtue had a reference to the central body; and so, the ‘inherent
virtue’ must have coincided in its effect with the Newtonian force;
and then, the two explanations would agree, except so far as the
word ‘inherent’ was concerned. And if such a part of an earlier
theory as this word _inherent_ indicates, is found to be untenable,
it is of course rejected in the transition to later and more exact
theories, in Inductions of this kind, as well as in what Mr. Mill
calls Descriptions. There is, therefore, still no validity
discoverable in the distinction which Mr. Mill attempts to draw
between descriptions like Kepler’s law of elliptical orbits, and
other examples of induction.”
If the doctrine of vortices had meant, not that vortices existed,
but only that the planets moved _in the same manner_ as if they had
been whirled by vortices; if the hypothesis had been merely a mode
of representing the facts, not an attempt to account for them; if,
in short, it had been only a Description; it would, no doubt, have
been reconcilable with the Newtonian theory. The vortices, however,
were not a mere aid to conceiving the motions of the planets, but a
supposed physical agent, actively impelling them; a material fact,
which might be true or not true, but could not be both true and not
true. According to Descartes’s theory it was true, according to
Newton’s it was not true. Dr. Whewell probably means that since the
phrases, centripetal and projectile force, do not declare the nature
but only the direction of the forces, the Newtonian theory does not
absolutely contradict any hypothesis which may be framed respecting
the mode of their production. The Newtonian theory, regarded as a
mere _description_ of the planetary motions, does not; but the
Newtonian theory as an _explanation_ of them does. For in what does
the explanation consist? In ascribing those motions to a general law
which obtains between all particles of matter, and in identifying
this with the law by which bodies fall to the ground. If the planets
are kept in their orbits by a force which draws the particles
composing them toward every other particle of matter in the solar
system, they are not kept in those orbits by the impulsive force of
certain streams of matter which whirl them round. The one
explanation absolutely excludes the other. Either the planets are
not moved by vortices, or they do not move by a law common to all
matter. It is impossible that both opinions can be true. As well
might it be said that there is no contradiction between the
assertions, that a man died because somebody killed him, and that he
died a natural death.
So, again, the theory that the planets move by a virtue inherent in
their celestial nature, is incompatible with either of the two
others: either that of their being moved by vortices, or that which
regards them as moving by a property which they have in common with
the earth and all terrestrial bodies. Dr. Whewell says that the
theory of an inherent virtue agrees with Newton’s when the word
inherent is left out, which of course it would be (he says) if
“found to be untenable.” But leave that out, and where is the
theory? The word inherent _is_ the theory. When that is omitted,
there remains nothing except that the heavenly bodies move “by a
virtue,” _i.e._, by a power of some sort; or by virtue of their
celestial nature, which directly contradicts the doctrine that
terrestrial bodies fall by the same law.
If Dr. Whewell is not yet satisfied, any other subject will serve
equally well to test his doctrine. He will hardly say that there is
no contradiction between the emission theory and the undulatory
theory of light; or that there can be both one and two
electricities; or that the hypothesis of the production of the
higher organic forms by development from the lower, and the
supposition of separate and successive acts of creation, are quite
reconcilable; or that the theory that volcanoes are fed from a
central fire, and the doctrines which ascribe them to chemical
action at a comparatively small depth below the earth’s surface, are
consistent with one another, and all true as far as they go.
If different explanations of the same fact can not both be true,
still less, surely, can different predictions. Dr. Whewell quarrels
(on what ground it is not necessary here to consider) with the
example I had chosen on this point, and thinks an objection to an
illustration a sufficient answer to a theory. Examples not liable to
his objection are easily found, if the proposition that conflicting
predictions can not both be true, can be made clearer by many
examples. Suppose the phenomenon to be a newly-discovered comet, and
that one astronomer predicts its return once in every 300
years—another once in every 400: can they both be right? When
Columbus predicted that by sailing constantly westward he should in
time return to the point from which he set out, while others
asserted that he could never do so except by turning back, were both
he and his opponents true prophets? Were the predictions which
foretold the wonders of railways and steamships, and those which
averred that the Atlantic could never be crossed by steam
navigation, nor a railway train propelled ten miles an hour, both
(in Dr. Whewell’s words) “true, and consistent with one another?”
Dr. Whewell sees no distinction between holding contradictory
opinions on a question of fact, and merely employing different
analogies to facilitate the conception of the same fact. The case of
different Inductions belongs to the former class, that of different
Descriptions to the latter.
_ 106 Phil. of Discov._, p. 256.
_ 107 Essays on the Pursuit of Truth._
108 In the first edition a note was appended at this place, containing
some criticism on Archbishop Whately’s mode of conceiving the
relation between Syllogism and Induction. In a subsequent issue of
his _Logic_, the Archbishop made a reply to the criticism, which
induced me to cancel part of the note, incorporating the remainder
in the text. In a still later edition, the Archbishop observes in a
tone of something like disapprobation, that the objections,
“doubtless from their being fully answered and found untenable, were
silently suppressed,” and that hence he might appear to some of his
readers to be combating a shadow. On this latter point, the
Archbishop need give himself no uneasiness. His readers, I make bold
to say, will fully credit his mere affirmation that the objections
have actually been made.
But as he seems to think that what he terms the suppression of the
objections ought not to have been made “silently,” I now break that
silence, and state exactly what it is that I suppressed, and why. I
suppressed that alone which might be regarded as personal criticism
on the Archbishop. I had imputed to him the having omitted to ask
himself a particular question. I found that he had asked himself the
question, and could give it an answer consistent with his own
theory. I had also, within the compass of a parenthesis, hazarded
some remarks on certain general characteristics of Archbishop
Whately as a philosopher. These remarks, though their tone, I hope,
was neither disrespectful nor arrogant, I felt, on reconsideration,
that I was hardly entitled to make; least of all, when the instance
which I had regarded as an illustration of them, failed, as I now
saw, to bear them out. The real matter at the bottom of the whole
dispute, the different view we take of the function of the major
premise, remains exactly where it was; and so far was I from
thinking that my opinion had been fully “answered” and was
“untenable,” that in the same edition in which I canceled the note,
I not only enforced the opinion by further arguments, but answered
(though without naming him) those of the Archbishop.
For not having made this statement before, I do not think it needful
to apologize. It would be attaching very great importance to one’s
smallest sayings, to think a formal retractation requisite every
time that one falls into an error. Nor is Archbishop Whately’s
well-earned fame of so tender a quality as to require that in
withdrawing a slight criticism on him I should have been bound to
offer a public _amende_ for having made it.
109 But though it is a condition of the validity of every induction that
there be uniformity in the course of nature, it is not a necessary
condition that the uniformity should pervade all nature. It is
enough that it pervades the particular class of phenomena to which
the induction relates. An induction concerning the motions of the
planets, or the properties of the magnet, would not be vitiated
though we were to suppose that wind and weather are the sport of
chance, provided it be assumed that astronomical and magnetic
phenomena are under the dominion of general laws. Otherwise the
early experience of mankind would have rested on a very weak
foundation; for in the infancy of science it could not be known that
_all_ phenomena are regular in their course.
Neither would it be correct to say that every induction by which we
infer any truth, implies the general fact of uniformity _as
foreknown_, even in reference to the kind of phenomena concerned. It
implies, _either_ that this general fact is already known, _or_ that
we may now know it: as the conclusion, the Duke of Wellington is
mortal, drawn from the instances A, B, and C, implies either that we
have already concluded all men to be mortal, or that we are now
entitled to do so from the same evidence. A vast amount of confusion
and paralogism respecting the grounds of Induction would be
dispelled by keeping in view these simple considerations.
110 Infra, chap. xxi.
111 Infra, chap. xxi., xxii.
112 In strictness, wherever the present constitution of space exists;
which we have ample reason to believe that it does in the region of
the fixed stars.