to philosophy without determining the lines of future speculation,
even though to itself they remained obscure. He stumbles upon truths
when he is not looking for them, and the inconsistencies or accidents
of his system are its most valuable part. Thus, in a certain sense,
he may claim the authorship at once of the popular empiricism of
the modern world, and of its refutation. He fixed the prime article
of its creed, that thought has nothing to do with the constitution
of facts, but only with the representation of them by signs and the
rehearsal to itself of what its signs have signified--in brief, that
its function is merely the analytical judgment; yet his admissions
about mathematical knowledge rendered inevitable the Kantian
question, ‘How are synthetic judgments á-priori possible?’--which was
to lead to the recognition of thought as constituting the objective
world, and thus to get rid of the antithesis between thought and
reality. In his separation of the datum of experience from the work
of thought he was merely following the Syllogistic Logic, which
really assigns no work to the thought, whose office it professes to
magnify, but the analysis of given ideas. Taking the work as that
Logic conceived it (and as it must be conceived if the separation is
to be maintained) he showed--conclusively as against Scholasticism--
the ‘trifling’ character of the necessary and universal truths with
which it dealt. Experience, the manifestation of the real, regarded
as a series of events which to us are sensations, can only yield
propositions singular as the events, and having a truth like them
contingent. By consequence, necessity and universality of connection
can only be found in what the mind does for itself, without reference
to reality, when it analyses the complex idea which it retains as
the memorandum of its past single experiences; _i.e._, in a relation
between ideas or propositions of which one explicitly includes the
other. Upon this relation syllogistic reasoning rests, and, except
so far as it may be of use for convicting an opponent (or oneself)
of inconsistency, it has nothing to say against such nominalism
as the above. Hence, with those followers of Locke who have been
most faithful to their master, it has remained the standing rule
to make the generality of a truth consist in its being analytical
of the meaning of a name, and its necessity in its being included
in one previously conceded. Yet if such were the true account of
the generality and necessity of mathematical propositions, their
truth according to Locke’s explicit statement would be ‘verbal and
trifling,’ not, as it is, ‘real and instructive.’
Fatal to the notion that mathematical truths, though general, are got
from experience:
119. The point of this, the most obvious, contradiction inherent
in Locke’s empiricism, is more or less striking according to the
fidelity with which the notion of matter-of-fact, or of the reality
that is not of the mind, proper to that system, is adhered to.
When the popular Logic derived from Locke has so far forgotten
the pit whence it was digged as to hold that propositions of a
certainty at once real and general can be derived from experience,
and to speak without question of ‘general matters-of-fact’ in a
sense which to Locke almost, to Hume altogether, would have been
a contradiction in terms, it naturally finds no disturbance in
regarding mathematical certainty as different not in kind, but only
in degree, from that of any other ‘generalisation from experience.’
Not aware that the distinction of mathematical from empirical
generality is the condition upon which, according to Locke, the
former escapes condemnation as ‘trifling,’ it does not see any need
for distinguishing the sources from which the two are derived, and
hence goes on asserting against imaginary or insignificant opponents
that mathematical truth is derived from ‘experience;’ which, if
‘experience’ be so changed from what Locke understood by it as to
yield general propositions concerning matters-of-fact of other than
analytical purport, no one need care to deny. That it can yield such
propositions is, doubtless, the supposition of the physical sciences;
nor, we must repeat, is it the _correctness_ of this supposition
that is in question, but the validity, upon its admission, of that
antithesis between experience and the work of thought, which is the
‘be-all and end-all’ of the popular Logic.
... and to received views of natural science: but Locke not so clear
about this.
120. Locke, as we have seen, after all the encroachments made
unawares by thought within the limits of that experience which he
opposes to it--or, to put it conversely, after all that he allows
‘nature’ to take without acknowledgment from ‘mind’--is still so far
faithful to the opposition as to ‘suspect a science of nature to be
impossible.’ This suspicion, which is but a hesitating expression
of the doctrine that general propositions concerning substances are
merely verbal, is the exact counterpart of the doctrine pronounced
without hesitation that mathematical truths, being at once real and
general, do not concern nature at all. Real knowledge concerning
nature being given by single impressions of bodies at single times
operating upon us, and by consequence being expressible only in
singular propositions, any reality which general propositions state
must belong merely to the mind, and a mind which can originate a
reality other than nature’s cannot be a passive receptacle of natural
impressions. Locke admits the real generality of mathematical truths,
but does not face its consequences. Hume, seeing the difficulty, will
not admit the real generality. The modern Logic, founded on Locke,
believing in the possibility of propositions at once real and general
concerning nature. does not see the difficulty at all. It reckons
mathematical to be the same in kind with natural knowledge, each
alike being real notwithstanding its generality; not aware that by
so doing, instead of getting rid, as it fancies, of the originative
function of thought in respect of mathematical knowledge, it only
necessitates the supposition of its being originative in respect of
the knowledge of nature as well.
Ambiguity as to real essence causes like ambiguity as to science of
nature. Particular experiment cannot afford general knowledge.
121. It may find some excuse for itself in the hesitation with
which Locke pronounces the impossibility of real generality in
the knowledge of nature--an hesitation which necessarily results
from the ambiguities, already noticed, in his doctrine of real and
nominal essence. So far as the opposition between the nominal and
real essences of substances is maintained in its absoluteness, as
that between every possible collection of ideas on the one side, and
something wholly apart from thought on the other, this impossibility
follows of necessity. But so far as the notion is admitted of
the nominal essence being in some way, however inadequately,
representative of the real, there is an opening, however indefinite,
for general propositions concerning the latter. On the one hand we
have the express statement that ‘universal propositions, of whose
truth and falsehood we can have certain knowledge, concern not
existence’ (Book IV. chap. ix. sec. 1). They are founded only on the
‘relations and habitudes of abstract ideas’ (Book IV. chap xii. sec.
7); and since it is the proper operation of the mind in abstraction
to consider an idea under no other existence but what it has in the
understanding, they represent no knowledge of _real_ existence at all
(Book IV. chap. ix. sec. 1). Here Locke is consistently following
his doctrine that the ‘particularity in time,’ of which abstraction
is made when we consider ideas as in the understanding, is what
specially distinguishes the real; which thus can only be represented
by ‘actually present sensation.’ It properly results from this
doctrine that the proposition representing particular experiment and
observation is only true of real existence so long as the sensation,
in which the experiment consists, continues present. Not only is the
possibility excluded of such experiment yielding a certainty which
shall be general as well as real, but the particular proposition
itself can only be _really_ true so far as the qualities, whose
co-existence it asserts, are present sensations. The former of these
limitations to real truth we find Locke generally recognising, and
consequently suspecting a science of nature to be impossible; but
the latter, which would be fatal to the supposition of there being a
real nature at all, even when he carries furthest the reduction of
reality to present feeling, he virtually ignores. On the other hand,
there keeps appearing the notion that, inasmuch as the combination
of ideas which make up the nominal essence of a substance is taken
from a combination in nature or reality, whenever the connexion
between any of these is necessary, it warrants a proposition
_universally_ true in virtue of the necessary connexion between the
ideas, and _really_ true in virtue of the ideas being taken from
reality. According to this notion, though ‘the certainty of universal
propositions concerning substances is very narrow and scanty,’ it is
yet possible (Book IV. chap. vi. sec. 13). It is not recognised as
involving that contradiction which it must involve if the antithesis
between reality and ideas in the mind is absolutely adhered to. Nay,
inasmuch as certain ideas of primary qualities, _e.g._ those of
solidity and of the receiving or communicating motion upon impulse,
are necessarily connected, it is supposed actually to exist (Book
IV. chap iii. sec. 14). It is only because, as a matter of fact, our
knowledge of the relation between secondary qualities and primary is
so limited that it cannot be carried further. That they are related
as effects and causes, it would seem, we know; and that the ‘causes
work steadily, and effects constantly flow from them,’ we know also;
but ‘their connexions and dependencies are not discoverable in our
ideas’ (Book IV. chap. iii. sec. 29). That, if discoverable in our
ideas, just because there discovered, the connexion would not be a
real co-existence, Locke never expressly says. He does not so clearly
articulate the antithesis between relations of ideas and matters
of fact. If he had done so, he must also have excluded from real
existence those abstract ideas of body which constitute the scanty
knowledge of it that according to him we do possess (Book IV. chap.
iii. sec. 24). He is more disposed to sigh for discoveries that would
make physics capable of the same general certainty as mathematics,
than to purge the former of those mathematical propositions--really
true only because having no reference to reality--which to him formed
the only scientific element in them.
What knowledge it can afford, according to Locke.
122. The ambiguity of his position will become clearer if we resort
to his favourite ‘instances in gold.’ The proposition, ‘all gold is
soluble in aqua regia,’ is certainly true, if such solubility is
included in the complex idea which the word ‘gold’ stands for, and
if such inclusion is all that the proposition purports to state. It
is equally certain and equally trifling with the proposition, ‘a
centaur is four-footed.’ But, in fact, as a proposition concerning
substance, it purports to state more than this, viz. that a ‘body
whose complex idea is made up of yellow, very weighty, ductile,
fusible, and fixed,’ is always soluble in aqua regia. In other words,
it states the invariable co-existence in a body of the complex idea,
‘solubility in aqua regia,’ with the group of ideas indicated by
‘gold.’ Thus understood--as instructive or synthetical--it has not
the certainty which would belong to it if it were ‘trifling,’ or
analytical, ‘since we can never, from the consideration of the ideas
themselves, with certainty affirm’ their co-existence (Book IV. chap.
vi. sec 9). If we see the solution actually going on, or can recall
the sight of it by memory, we can affirm its co-existence with the
ideas in question in that ‘bare instance;’ and thus, on the principle
that ‘whatever ideas have once been united in nature may be so united
again’ (Book IV. chap. iv. sec. 12), infer a capacity of co-existence
between the ideas, but that is all. ‘Constant observation may assist
our judgments in guessing’ an invariable actual co-existence (Book
IV. chap. viii. sec. 9); but beyond guessing we cannot get. If our
instructive proposition concerning co-existence is to be general
it must remain problematical. It is otherwise with mathematical
propositions. ‘If the three angles of a triangle were once equal to
two right angles, it is certain that they always will be so;’ but
only because such a proposition concerns merely ‘the habitudes and
relations of ideas.’ ‘If the perception that the same ideas will
eternally have the same habitudes and relations be not a sufficient
ground of knowledge, there could be no knowledge of general
propositions in mathematics; for no mathematical demonstration
could be other than particular: and when a man had demonstrated any
proposition concerning one triangle and circle, his knowledge would
not reach beyond that particular diagram’ (Book IV. chap. i. sec. 9).
Not the knowledge which is now supposed to be got by induction. Yet
more than Locke was entitled to suppose it could give.
123. To a reader, fresh from our popular treatises on Logic, such
language would probably at first present no difficulty. He would
merely lament that Locke, as a successor of Bacon, was not better
acquainted with the ‘Inductive methods,’ and thus did not understand
how an observation of co-existence in the bare instance, if the
instance be of the right sort, may warrant a universal affirmation.
Or he may take the other side, and regard Locke’s restriction upon
general certainty as conveying, not any doubt as to the validity
of the inference from an observed case to all cases where the
conditions are ascertainably the same, but a true sense of the
difficulty of ascertaining in any other case that the conditions
are the same. On looking closer, however, he will see that, so far
from Locke’s doctrine legitimately allowing of such an adaptation
to the exigencies of science, it is inconsistent with itself in
admitting the reality of most of the conditions in the case supposed
to be observed, and thus in allowing the real truth even of the
singular proposition. This purports to state, according to Locke’s
terminology, that certain ‘ideas’ do now or did once co-exist in a
body. But the ideas, thus stated to co-exist, according to Locke’s
doctrine that real existence is only testified to by actual present
sensation, differ from each other as that which _really_ exists
from that which does not. In the particular experiment of gold
being solved in aqua regia, from the complex idea of solubility an
indefinite deduction would have to be made for qualification by ideas
retained in the understanding before we could reach the present
sensation; and not only so, but the group of ideas indicated by
‘gold,’ to whose co-existence with solubility the experiment is said
to testify, as Locke himself says, form merely a nominal essence,
while the body to which we ascribe this essence is something which we
‘accustom ourselves to suppose,’ not any ‘parcel of matter’ having
a real existence in nature. [1] In asserting the co-existence of
the ideas forming such a nominal essence with the actual sensation
supposed to be given in the experiment, we change the meaning of
‘existence,’ between the beginning and end of the assertion, from
that according to which all ideas exist to that according to which
existence has no ‘connexion with any other of our ideas but those of
ourselves and God,’ but is testified to by present sensation. [2]
This paralogism escapes Locke just as his equivocal use of the term
‘idea’ escapes him. The distinction, fixed in Hume’s terminology as
that between impression and idea, forces itself upon him, as we have
seen, in the Fourth book of the Essay, where the whole doctrine of
real existence turns upon it, but alongside of it survives the notion
that ideas, though ‘in the mind’ and forming a nominal essence, are
yet, if rightly taken from things, ectypes of reality. Thus he does
not see that the co-existence of ideas, to which the particular
experiment, as he describes it, testifies, is nothing else than the
co-existence of an event with a conception--of that which is in a
particular time, and (according to him) only for that reason real,
with that which is not in time at all but is an unreal abstraction
of the mind’s making. [3] The reality given in the actual sensation
cannot, as a matter of fact, be discovered to have a necessary
connexion with the ideas that form the nominal essence, and therefore
cannot be asserted universally to co-exist with them; but with better
faculties, he thinks, the discovery might be made (Book IV. chap.
iii. sec. 16). It does not to him imply such a contradiction as it
must have done if he had steadily kept in view his doctrine that of
particular (_i.e._ real) existence our ‘knowledge’ is not properly
knowledge at all, but simply sensation--such a contradiction as was
to Hume involved in the notion of deducing a matter of fact.
[1] See above, paragraphs 35, 94, &c.
[2] See above, paragraph 30 and the following.
[3] See above, paragraphs 45, 80, 85, 97.
With Locke mathematical truths, though ideal, true also of nature.
124. It results that those followers of Locke, who hold the
distinction between propositions of mathematical certainty and those
concerning real existence to be one rather of degree than of kind,
though they have the express words of their master against them, can
find much in his way of thinking on their side. This, however, does
not mean that he in any case drops the antithesis between matters of
fact and relations of ideas in favour of matters of fact, so as to
admit that mathematical propositions concern matters of fact, but
that he sometimes drops it in favour of relations of ideas, so as
to represent real existence as consisting in such relations. If the
matter of fact, or real existence, is to be found only in the event
constituted or reported by present feeling, such a relation of ideas,
by no manner of means reducible to an event, as the mathematical
proposition states, can have no sort of connection with it. But if
real existence is such that the relations of ideas, called primary
qualities of matter, constitute it, and the qualities included in our
nominal essences are its copies or effects, then, as on the one side
our complex ideas of substances only fail of reality through want of
fulness, or through mistakes in the process by which they are ‘taken
from things,’ so, on the other side, the mental truth of mathematical
propositions need only fail to be real because the ideas, whose
relations they state, are considered in abstraction from conditions
which qualify them in real existence. ‘If it is true of the idea of
a triangle that its three angles equal two right ones, it is true
also of a triangle, wherever it really exists’ (Book IV. chap. iv.
sec. 6). There is, then, no incompatibility between the idea and
real existence. Mathematical ideas might fairly be reckoned, like
those of substances, to be taken from real existence; but though,
like these, inadequate to its complexity, to be saved from the
necessary infirmities which attach to ideas of substances because not
considered as so taken, but merely as in the mind. There is language
about mathematics in Locke that may be interpreted in this direction,
though his most explicit statements are on the other side. It is not
our business to adjust them, but merely to point out the opposite
tendencies between which a clear-sighted operator on the material
given by Locke would find that he had to choose.
Two lines of thought in Locke, between which a follower would have to
choose.
125. On the one hand there is the identification of real existence
with the momentary sensible event. This view, of which the proper
result is the exclusion of predication concerning real existence
altogether, appears in Locke’s restriction of such predication to the
singular proposition, and in his converse assertion that propositions
of mathematical certainty ‘concern not existence’ (Book IV. chap.
iv. sec. 8). The embarrassment resulting from such a doctrine is
that it leads round to the admission of the originativeness of
thought and of the reality of its originations, with the denial of
which it starts. [1] It leads Locke himself along a track, which his
later followers scarcely seem to have noticed, when he treats the
‘never enough to be admired discoveries of Mr. Newton’ as having to
do merely with the relations of ideas in distinction from things,
and looks for a true extension of knowledge--neither in syllogism
which can yield no instructive, nor in experiment which can yield no
general, certainty--but only in a further process of ‘singling out
and laying in order intermediate ideas,’ which are ‘real as well as
nominal essences of their species,’ because they have no reference
to archetypes elsewhere than in the mind (Book IV. chap. vii. sec.
11, and Book IV. chap. xii. sec. 7). On the other hand there is the
notion that ideas, without distinction between ‘actual sensation’
and ‘idea in the mind,’ are taken from permanent things, and are
real if correctly so taken. From this it results that propositions,
universally true as representing a necessary relation between ideas
of primary qualities, are true also of real existence; and that an
extension of such real certainty through the discovery of a necessary
connexion between ideas of primary and those of secondary qualities,
though scarcely to be hoped for, has no inherent impossibility. It
is this notion, again, that unwittingly gives even that limited
significance to the particular experiment which Locke assigns to it,
as indicating a co-existence between ideas present as sensations
and those which can only be regarded as in the mind. Nor is it the
intrinsic import so much as the expression of this notion that is
altered when Locke substitutes an order of nature for substance
as that in which the ideas co-exist. In his Fourth Book he so far
departs from the doctrine implied in his chapters on the reality and
adequacy of ideas and on the names of substances, as to treat the
notion of several single subjects in which ideas co-exist (which he
still holds to be the proper notion of substances), as a fiction
of thought. There are no such single subjects. What we deem so are
really ‘retainers to other parts of nature.’ ‘Their observable
qualities, actions, and powers are owing to something without them;
and there is not so complete and perfect a part that we know of
nature, which does not owe the being it has, and the excellencies
of it, to its neighbours’ (Book IV. chap. vi. sec. 11). As thus
conceived of, the ‘objective order’ which our experience represents
is doubtless other than that collection of fixed separate ‘things,’
implied in the language about substances which Locke found in vogue,
but it remains an objective order still--an order of ‘qualities,
actions, and powers’ which no multitude of sensible events could
constitute, but apart from which no sensible event could have such
significance as to render even a singular proposition of real truth
possible.
[1] See above, paragraph 117, sub. fin.
Transition to doctrine of God and the soul.
126. It remains to inquire how, with Locke, the ideas of self and
God escape subjection to those solvents of reality which, with
more or less of consistency and consciousness, he applied to the
conceptions on which the science of nature rests. Such an enquiry
forms the natural transition to the next stage in the history of his
philosophy. It was Berkeley’s practical interest in these ideas that
held him back from a development of his master’s principles, in which
he would have anticipated Hume, and finally brought him to attach
that other meaning to the ‘new way of ideas’ faintly adumbrated
in the later sections of his ‘Siris,’ which gives to Reason the
functions that Locke had assigned to Sense.
Thinking substance--source of the same ideas as outer substance.