In last October’s number of _The Monist_, Professor John Dewey gives a
sketch of what in his view is “the present position of logical theory.”
According to this the basis of the position seems to be that “the only
possible thought is the reflection of the significance of fact,” and
that therefore logic, which is the science of the laws of thought,
rests in reality on an objective basis. He supports Hegel in denying
“the existence of any faculty of thought which is other than the
expression of fact itself.” Now it is doubtless the case that this is
the position at present taken up by a large number of logicians, but as
this position seems to me to be fundamentally erroneous I should like
to put before your readers what I hope will be “the future position of
logical theory.” I have elsewhere worked out in some detail a theory of
reasoning which differs from that commonly accepted chiefly in this,
that it recognises not two, but three kinds of reasoning, which I call
Objective, Subjective, and Symbolic. Reasoning is commonly divided into
two branches, denoted by various pairs of terms, such as Objective and
Subjective, Inductive and Deductive, Empirical and Formal. The lines
of division indicated by these various pairs of terms are not quite
identical; but they none of them indicate what seems to me the most
important distinction of all, namely that between real, and symbolic
argument. There _does_ exist (I will not say a “faculty of thought,” but)
a method of argument which “is other than the expression of fact itself,”
whether of objective or of subjective fact. The term “formal reasoning”
is indeed often used to denote this kind of argument, but this is a bad
name to give it, since it seems to imply, and frequently is held to
imply, that it deals with the _forms_ of objective or subjective facts,
whereas in reality it deals only with symbols, which are arbitrarily
defined, and which do not necessarily correspond to any things whatever,
whether objective or subjective. That this kind of argument not only
exists, but flourishes is evident as soon as it is grasped that pure
mathematics is nothing but a branch of symbolic logic. It may be that
there exists somewhere a fact of which any conceivable mathematical
formula might be regarded as the reflexion, but it must surely be evident
that it was not to the reflexion of such facts that mathematical formulæ
in general owe their existence or validity. It may perhaps be true “that
fact, reality is significant,” and even that thoughts are themselves such
significant realities, but it is the thoughts that are given to us first,
or rather sensations which are the elements of thoughts, and we can only
infer the realities from them, and not _vice versa_.
The essence of my theory of logic may be briefly stated thus. The
meaning of a logical term contains two parts, its denotation and its
connotation. Either of these parts may be laid down arbitrarily as its
_definition_, leaving the other part which I call its _import_ to be
found out by experience. To understand both parts of the meaning of any
term is therefore to possess real knowledge. Pure symbolic reasoning
deals only with the definitions of terms, and is not therefore founded
on real knowledge, nor can it alone ever lead to real knowledge. Thus
if in any proposition the definitions of the terms are deducible from
one another, the proposition may be proved symbolically and is what I
call a truism: it gives no real information. But if the definitions of
the terms are independent of each other, and yet not inconsistent, the
proposition can only be intended to assert the identity of the imports
of the terms; it therefore ascribes import to the terms and gives real
information, whether true or false. If any terms in a symbolic argument
are however known to have real import, it may be ascribed to them in
real propositions, and any conclusions of the argument which contain only
such terms will _ipso facto_ be made to yield real information, which may
be new in the sense that it was not before recognised, though it was of
course implied in the real assertion or assertions which ascribed import
to the terms of the symbolic argument.
It is in this way possible to separate any science into two branches,
one of which consists purely of symbolic argument founded on definitions
alone, while the other may be expressed in a series of propositions,
the definitions of whose terms are independent of each other, and which
ascribe real import (whether objective or subjective) to the terms of the
symbolic science, or some of them.
This is as far as pure logic can go. The question how the truth of any
real propositions comes to be known is not, in my opinion, any part of
logical theory, but belongs to metaphysics. However that is no reason for
not discussing it here, especially as it is the chief question discussed
in Professor Dewey’s paper.
“Truth” means some sort of consistency in a proposition. We may compare
a symbolic argument to a game with counters, the rules of which are laid
down arbitrarily, and to say that a given conclusion of such an argument
is true only means that the game has been “played fair.” But the truth of
a real proposition does not depend on any arbitrary rules. It expresses
a consistency between two real facts, either that two named groups of
things possess certain common attributes, or that certain of the things
possessing named groups of attributes are identical. The essential
element of all real knowledge is then a connecting link between a thing
and an attribute, such as is afforded by a well-understood word.
Now the only “things” which we can apprehend directly are our subjective
sensations and conceptions. We can compare two or more sensations or
conceptions, and recognise in them common attributes. Thus I can say
of my own knowledge that the sensations I denote by “the taste of
sugar” and “the taste of lead acetate” have a common attribute, which
I call “sweetness.” This is a real assertion, for its truth is not
deducible from the definitions of its terms, and yet I know, by direct
apprehension, that it is true. But it is only a subjective truth. The
corresponding objective assertion would be sugar and acetate of lead
both produce, when tasted, the sensation of sweetness. And I have no
direct apprehension of this fact. That the tastes referred to in the
former proposition were produced by objective things denoted by the terms
sugar and acetate of lead, can only be inferred by the process called
induction, which can never lead to a positive or necessary truth.
Thus we may from a pure symbolic science proceed one step further, to a
subjective science, by the aid of direct apprehension, and the results
of such a subjective science may in certain cases attain the position
of absolute, or necessary truths. But on the other hand, all objective
sciences must rest on induction. Now the true nature of induction is,
I am persuaded, commonly misapprehended, because it is not realised
sufficiently clearly that the prime data of induction are not themselves
objective, but subjective facts. An “objective fact” is really only
an hypothesis, postulated to account for certain of our subjective
sensations. The only justification for making such an hypothesis is
that it actually does explain certain sensations, and the measure of
its probability (for we can never assert it as a necessary certainty)
is the number and complexity of the sensations which it accounts for.
The first of all such objective hypotheses is that we have an objective
environment to whose action our sensations, or some of them, are due.
This suggests at once a more general hypothesis, commonly known as the
law of causation, namely that the conditions obtaining in the objective
universe at any one moment are the effective causes of those obtaining
at the next, and so at any subsequent moment. These two hypotheses,
together with certain subsidiary ones, do suffice to account for an
enormous number, if not all, of our sensations, and so we are justified
in entertaining them. But to leave out the notion of _effective_
causation, and to substitute a mere rule of sequence, is to remove the
only justification we have for assuming the hypothesis of causation at
all. It is perhaps conceivable that the hypothesis may be false, that
our sensations are not “caused by” an objective environment but if so
what reason remains for believing in that environment at all? I can never
know anything whatever about an objective universe, unless some of my
sensations about which alone I know anything directly, are caused by
that universe. It is perhaps thinkable that there should be an objective
universe in which events occur which in no sense _cause_ my subjective
sensations, but to which those sensations nevertheless happen to
correspond; but if this is so the sensations afford me no ground whatever
for believing in the occurrence of the events, or the objectivity of the
universe.
Well then, the essence of induction is the assumption of an hypothesis to
account for observed facts—first of all of directly observed sensations,
and then of facts assumed to be objective in virtue of the primary
hypothesis. That this account of induction is the true one is I think
particularly enforced by the consideration of those cases to which at
first sight it does not seem to apply. A common example of induction is
afforded by our belief that the sun will rise to-morrow. That it has
risen every morning for the last four thousand years or more is no reason
whatever for believing that it will rise to-morrow, unless it is held to
point to some explanatory hypothesis. Such an hypothesis has actually
been framed by astronomers, and no one would now pretend to found his
belief in the sun’s rising to-morrow on the mere fact that it has often
risen before, but would go on to explain that it must rise unless the
earth were to stop revolving, etc. If at Monte Carlo the red turned up
ten times running, would that be any reason for expecting it to turn up
again, the eleventh time? No, it would not unless the succession of reds
seemed to point to some explanatory hypothesis, such as a defect in the
roulette. Again, the fact that in the last fifty years the death rate
in London has been about twenty-eight per thousand would be no reason
for believing that it will be about that figure this year except on
the assumption that the constancy of the death rate indicated certain
constant causes, which we have no reason to believe have been altered
this year.
Having once assumed that our environment is objective, and as a corollary
the hypothesis of causation, the whole of physical science follows,
step by step. Subsidiary hypotheses are introduced at each stage and
justified by the way they account for observed results. To show how a
single hypothesis is capable of explaining a large number of observed
results, the full meaning of the hypothesis is elucidated by symbolic
reasoning. By such reasoning it is for example shown that the same
hypothesis, of universal gravitation, is capable of accounting, not only
for the movements of the stars, but for the tides, the flow of rivers,
the falling of unsupported bodies, the rising of balloons, the movements
of the balance in Cavendish’s experiment, and so on. That such wide
extensions of an hypothesis are possible tends greatly to confirm, not
only the hypothesis itself, but the fundamental hypotheses of objectivity
and causation also. But it does not prove either the one or the others.
We cannot know anything about the objective universe with absolute
certainty, but we may reasonably believe a certain hypothesis about it
with any degree of conviction we think suitable; that is we may (and of
course we actually do) act on all occasions _as if_ we knew absolutely
that they were true.
We may then believe, and I for one do believe, not only in the
objectivity of the universe, but that even my own subjective sensations
are mere bye-products of that universe. I _believe_ that objective facts
are, if I may so express it, more real than subjective sensations; that
in fact the objective universe might have existed, and might exist again
without any subjective element in it anywhere. But I cannot _know_
this, it is with me a matter of faith. Thus I cannot agree with Hegel,
that “all possible thought is the reflexion of the significance of
fact” (except perhaps in the sense that thought is the reflexion of the
significance of certain changes in the grey matter of the brain) for
this would seem to imply that stupid or contradictory thoughts reflected
stupid or contradictory significance in certain facts. But I believe that
men of science are gradually evolving a system of thought which will
more and more faithfully reflect the significance of fact, and that thus
science is actually building up truth. But all science must begin with,
and be founded upon, subjective knowledge, and therefore any theory of
positivism contradicts itself for it must be founded on faith. Science
is thus founded on faith, faith in things not directly apprehended, just
as truly as religion is. It is only because we unconsciously acquire
this faith in our infancy, and that it is in most cases amply justified
by subsequent experience, that we do not even recognise the fact that it
is faith, in exactly the same sense that belief in God is. But just as
men have sometimes lost their faith in God, so it may happen to a man to
loose his faith in reality, and logic is quite as incapable of shaking a
man out of the one position as out of the other.
This I take it is the key to the agnosticism of such men of science as
Mr. Huxley. I do not for a moment suppose that Mr. Huxley believes less
than most men; he probably has good grounds for believing a great deal
more. Only he rightly refuses to say that he _knows_ facts of which
he can have had no direct apprehension and which he can only infer
more or less probably, to be true. Hypotheses which as we push our
investigations are shown to be capable of explaining more and more facts,
that is, ultimately, more and more sensations, will in the end come to
be believed in without doubt or hesitation. If a man says he _knows_ the
law of gravitation to be true, he commits a logical blunder; but there
is nothing to prevent a scientific man from believing in any miracle
or prodigy, so long as the account he gives of it does not contradict
itself. Not only may two equally reasonable men form very different
estimates of the probability of the same event, even with the same
evidence before them, but one man may put his faith to a proposition with
admittedly much lower degree of probability than would be required to
convince another. Only, a scientific man will always distinguish between
what he knows and what he believes, and will admit that though he has
made up his mind to act _as if_ he knew to be true the propositions he
only believes to be so, yet another man may reasonably take a different
view of any one of them.