§ 1. Among the obstacles to scientific progress a high place must
certainly be assigned to the analysis of scientific procedure which
Logic has provided. This analysis has not only been inadequate in
itself, but has set itself a mistaken aim. It has not tried to describe
the methods by which the sciences have actually advanced, and to
extract from their experience the logical rules which might be used to
regulate scientific progress, but has treated scientific discoveries
almost entirely as illustrations of a preconceived ideal of proof,
and so has freely rearranged the actual procedure in accordance with
its prejudices. For the order of discovery there has been substituted
an order of ‘proof’, and this substitution has been justified by the
assumption that if discovery had taken the ideally best course, it
would have coincided with the process of proof. It followed, of course,
that the same logic would do for both, and that this logic was already
in existence.
The damage thus inflicted upon Science was twofold. Not only were the
logicians given a plausible excuse for persisting in their profound
misapprehension of scientific inquiry and rendered incapable of giving
any help or guidance in the solution of actual problems, but, what was
much worse, the scientists themselves were misled about the nature of
their operations.
The precise value of the service which a correct logical analysis
of its procedure might have rendered to Science is perhaps open to
dispute, though it must surely be beneficial to operate consciously,
and with a full understanding of their nature, the methods which have
been hit upon empirically; but even if logicians have commonly been
too unfamiliar with the details of scientific problems to offer much
practical advice, it would be difficult to overrate the mischiefs which
must have resulted from referring scientists to an incorrect analysis
of their actual procedures. For the attempt to justify by such a false
ideal what they had actually done was bound to divert their attention
from the methods that were actually effective and fruitful to others
which were impracticable and sterile, to waste energy upon false aims
and impossible ideals, and so to hamper scientists fatally in the
exercise of their scientific rights and powers.
Hence it is not too much to say that the more deference men of science
have paid to Logic, the worse it has been for the scientific value of
their reasoning, while the less they have troubled to know about the
theory of Science, the better it has been for their practice.
Fortunately for the world, however, the great men of science have
usually been kept in salutary ignorance of the logical tradition
and left to their own devices, by the accident that the historical
organization of academic studies nearly everywhere confined ‘logic’
to the literary curriculum. Nevertheless, the moral of this situation
is not that it is right for science to neglect logic and for logic to
despise science, but that science should appeal from logic as it is to
logic as it ought to be, and should insist on being provided with a
_reformed_ logic. For surely if a scientific education is to be more
than a narrow and technical specialty, and is to exert a ‘liberalizing’
and broadening effect on the mind, it _ought_ to include a study of
scientific method in its generality and a certain understanding of
the intellectual instruments by which all others are operated and
constructed.
The whole evidence for these contentions it will not, of course, be
possible to marshal within the limits of this essay, but the systematic
criticism to which the whole traditional logic has been subjected
in my _Formal Logic_[381] may perhaps absolve me from the duty of
substantiating them exhaustively. It may suffice to indicate the extent
of the scientific grievance against ‘logic’ by drawing up a list of
problems in the logic of science which the traditional logic has
misconceived, and then to select for fuller treatment a palmary example
of the radical discrepancy between the two.
The traditional logic may be convicted of having gravely
misrepresented, (1) the value of classification and the formation
of classes, scientific processes of which the real logic was only
revealed by the Darwinian theory, (2) the function of definition, (3)
the importance of analogy, (4) of hypothesis and (5) of fictions, (6)
the incomplete dependence of scientific results on the ‘principles’ by
which they are (apparently) obtained, (7) the formation of scientific
‘law’ and its relation to its ‘cases’, (8) the nature of causal
analysis. Other important features of scientific procedure cannot
be said to have been recognized at all, e.g. (9) the problem of
determining what is _relevant_ to an inquiry and what practically must
be, and safely may be, excluded, (10) the methods and justification of
_selection_, (11) the essentially _experimental_ nature of all thought
and consequent inevitableness of _risk_, (12) the necessity of so
conceiving ‘truth’ and ‘error’ that it is possible to _discriminate_
between them, and (13) the need for an inquiry into _meaning_ and into
the conditions of its communication.
I
§ 2. The most instructive, however, of the discrepancies between
‘logic’ and scientific procedure will appear if we compare the logical
notion of _proof_ with the scientific process of _discovery_, and
examine how far it can afford any means of regulating, stimulating, or
even apprehending the latter. We shall find that the logical theory of
‘proof’ has no bearing on the scientific process of discovery, is not
related to what the sciences call proof, and can only have a paralysing
influence on any scientific activities which try to model themselves
upon it. On the other hand, the study of the process of discovery will
point to an important correction in the notion of logic.
§ 3. The scientific uselessness of the traditional logic should not,
however, excite surprise. For what reason was there to expect that
the theory of proof should turn out to be adequate, or even relevant,
to scientific procedure? It had sprung from a totally different
interest, proceeded on different assumptions, and aimed at different
ends. It did not spring from interest in the exploration of nature,
and did not aim at its prediction and control. Nor did it presuppose
an incomplete system of knowledge which it was desired to extend and
improve. It originated in a very special context, from the social need
of regulating the practice of dialectical debate in the Greek schools,
assemblies, and law-courts. It was necessary to draw up rules for
determining which side had won, and which of the points that had been
scored were good.
These were the aims Greek logic set itself, and successfully achieved.
But the impress of this origin remains stamped all over it, and the
accounts given of logical proof ever since have retained essential
features of Greek dialectics.
Thus it was assumed that science could start from principles, as
indisputable as are the current meanings of words in a dialectical
debate, and the end of the whole theory of proof was always conceived
as being to secure the conviction (ἔλεγχος) of one party to a dispute,
who was to be definitely crushed by the triumphant cogency of a
syllogistic demonstration, while the more real and fruitful analogy
between scientific inquiry and debate, viz. that _there is always
another side_, to which also it is well to listen, was unfortunately
obscured by Aristotle’s discovery of the syllogistic form and its show
of conclusiveness. But for the purpose of apprehending scientific
procedure the syllogism is a snare: by putting scientific reasoning
into syllogisms, the difference between the true and the false
views is made to appear qualitative and absolute, instead of being
a quantitative question of more or less of scientific value. Thus
dogmatism is fostered at the expense of progressiveness, and the
mistake is committed of approaching the discovery of truth in a party
spirit. Hence its dialectical origin has become _fons et origo malorum_
for logic.
§ 4. It is true that this mistake is very old, and has grown deeply
into the fabric of logic. For Aristotle had no sooner worked out the
classic formulation of the rules of dialectical proof than he proceeded
to extend their scope by applying them to the theory of science, in
the _Posterior Analytics_. His instinct in so doing was sound enough;
for there is no better verification of a theory than its capacity to
bear extension to analogous cases. And of course if this extension had
been successful, it would have supported the belief that the theory of
discovery could profitably be amalgamated with that of proof.
Unfortunately, however, the verification only seemed to be successful.
Aristotle chose to exemplify his theory of scientific proof from the
mathematical sciences. His choice was natural enough, because they
were the only sciences which had reached any considerable development
in his day, and they had, moreover, an apparent necessity and
universality and a fascinating appearance of exactness. But he had
unwittingly chosen the most difficult and deceptive exemplification
of scientific procedure. Because the mathematical sciences were in a
relatively advanced condition they seemed to lend themselves to his
design. He could there find terms whose meaning, and principles whose
truth, was no longer in dispute. They could in consequence be argued
from with as much assurance as debaters could assume the recognized
meanings of words. And the fact that results seemed to follow from
mathematical definitions and premisses which were not merely verbal,
shed a delusive glory on the forms of dialectical proof by which they
had been reached. Hence it easily escaped notice that the logical
superiority of mathematics was an achievement, not a datum. Just
because the mathematical sciences were very ancient, their origins had
been forgotten, and with them the tentative gropings which had first
selected, and subsequently confirmed, their principles. They had become
immediately certain and ‘self-evident’, and no one was disposed to
dispute them. On this psychological fact the whole theory of logical
proof was erected.
Again, it was natural to suppose that the true nature of scientific
knowing must be revealed in its most perfect specimens: no one stopped
to reflect that even so the real difficulties of making a science are
more keenly felt and more easily seen in the nascent stage than in one
which has victoriously overcome them, and has rewritten its history in
the assurance of its prosperous issue.
Lastly, the subtle ambiguity which pervades all mathematical reasoning,
according as its terms are taken as _pure_ or as applied, was
overlooked entirely--with the disastrous result that the universality,
certainty, and exactness pertaining (hypothetically) to the ideal
creations of ‘pure’ mathematics were erroneously transferred to their
‘applied’ counterparts. To this day logicians are found to argue
that real space is homogeneous because it is convenient in Euclidean
geometry to abstract from the multitudinous deformations to which
bodies moving through it are subjected, and to leave them to be treated
by physics;[382] nor are they aware of any lack of ‘exactness’ and
discrimination when they identify the ideal triangle with the figures
they draw on the blackboard.
§ 5. After its apparent success in analysing mathematical procedure
there was no more disputing the supremacy of the theory of ‘proof’.
The facts that its field of application was soon found to be much
narrower than that of science, and that it failed egregiously to apply
to the procedures of the (openly) empirical sciences, and _a fortiori_
could not justify them, if they were noticed at all, were held merely
to show that these sciences stood on a low level of thought, which
from the loftier standpoint of logic could be contemplated only with
contempt; if they required help and got none, so much the worse for
them. Accordingly the whole theory of science was so interpreted,
and the whole of logic was so constructed, as to lead up to the
ideal of demonstrative science, which in its turn rested on a false
analogy which assimilated it to the dialectics of ‘proof’. Does not
this mistake go far to account for the neglect of experience and the
unprogressiveness of science for nearly 2,000 years after Aristotle?
§ 6. Yet the deplorable consequences of this error should not render us
unjust. The influence of Aristotelian logic on the theory of science
was natural, and in a sense deserved. For Aristotelian logic is perhaps
the mightiest discovery any man has achieved single-handed. Its
might is sufficiently attested by the length of its reign. Euclidean
geometry alone is comparable with it, and Euclid owed far more to his
predecessors than Aristotle. Moreover, the Aristotelian logic may be
said to have achieved its purpose. It was able to regulate dialectical
discussion. The syllogism did determine whether a disputant had proved
his case, and for any one who had accepted its assumptions its decision
was final, while even its severest critics had to admit that it was an
indisputable fact, the interpretation of which was a real problem.
Unfortunately, there is not yet any agreement among logicians about
the solution of this problem. Aristotle’s own analysis did not go back
far enough: he stopped short at the _Dictum de Omni_ and the reduction
of syllogisms in the second and third figures to the first. He did
not penetrate to the ultimate assumptions which were implied in the
dialectical purpose and social function of the syllogism. But the truth
is that syllogistic reasoning presupposes quite a number of conventions
which Aristotle did not state, and which can hardly be said to have
been adequately recognized since.
§ 7. (1) The first of these may be called the _Fixity of Terms_.
Syllogistic reasoning manifestly depends on the assumption that the
terms occurring in it have meanings sufficiently stable to stand
transplantation from one context to another; for only so can they
establish connexions between one context and another. Thus a syllogism
in _Barbara_ argues that because _all M is P_ and _all S is M, all S
must be P_. But it can do this ‘validly’ only if _M_, its middle term,
remains immutably itself, and is the same in both premisses. Doubt,
dispute, or confute this assumption, and the cogency of the syllogism
as a form of ‘proof’ is overthrown at once. If the sense in which _M is
P_ is not the same as that in which _S is M_, the syllogism breaks in
two, and its conclusion becomes precarious. Raise the question of how
far reality conforms to this assumption, and you get at once a subtle
problem of the applicability of the syllogistic form to the case in
hand, which is precisely analogous to the question whether a theorem
of pure mathematics is applicable to the behaviour of a real thing. In
either case the cogency of the ‘proof’ which establishes the conclusion
is impaired and ceases to be unconditional. The conclusion of a ‘valid’
syllogism will only follow _if_ the middle term can be known to be
unambiguous, and if the objects designated by the terms do not change
rapidly enough to defeat the inference. And that this is the case can
usually be ascertained only by actual experience. The conclusion,
therefore, cannot be simply deduced; it has actually to _come true_,
before we can be sure that the reasoning _was_ sound. Absolutely _a
priori_ proof thus becomes impossible, if the assumption of the fixity
of terms is contested: all proof becomes, in a sense, empirical.
Nevertheless, experience shows that the fixity of terms, though not a
‘fact’, is _a valid ‘fiction’_: in ordinary discussion the terms may
usually be taken as fixed enough to render valid syllogisms common. An
ordinary debate proceeds upon the assumption that the meaning of the
terms involved is fixed, and cannot be varied arbitrarily. To science,
however, this assumption does not apply without restriction. In a
progressive science the meaning of terms often develops so rapidly that
such verbal reasoning does _not_ suffice. Hence the mere occurrence of
verbal contradictions in a scientific reasoning is no proof that the
argument is unsound. It may show merely that its terms are _growing_.
It should be observed further that this same assumption is implied in
the fundamental ‘laws of thought’ on which the traditional logic rests.
Indeed, the notorious ‘Law of Identity’ seems to be merely another
statement of it. It is usually formulated as ‘_A is A_’, but in its
actual logical use it is really the assumption that ‘everything _is_
what it is called’. It is, of course, anything but self-evident that
‘_A_’ _is A_, but _unless_ the _S_, _M_, and _P_ of the syllogism are
_rightly_ so called, the syllogism will not hold. Similarly, the Law
of Contradiction collapses at once if the terms to which it is applied
are allowed to change. The inability of ‘_A_’ both to be _B_ and not to
be _B_ vanishes if ‘_A_’ is not fixed and may change its habits. And of
course the real things known to science all change, and are fixed only
by a fiction. Hence every application of the logical convention to real
things may be challenged: it involves a fiction and takes a risk, and
both of these may be bad. But the traditional logic ignores both the
risk and the fiction and the lack of cogency in its attitude.
§ 8. (2) It is a further presupposition of the syllogism that the
meaning of its terms is _known_. When a discussion is begun the
parties to it are supposed to understand each other, and not to have
first to find out and form the meaning of the terms they use. This
assumption also is roughly true in ordinary debate, and its convenience
is manifest. If things are rightly named, and if this feat has been
accomplished once for all--presumably by Adam and Eve before they were
turned out of Paradise for trying to know too much--we shall escape
many of the most trying difficulties of scientific inquiry. We need
no longer trouble whether the best names have been given, and whether
a name good for one purpose is equally good for another, nor need
we inquire whether our names may not unite what is alien on account
of a superficial likeness, or separate what is akin on account of a
superficial difference.
In science, on the other hand, the assumption that we know what
meanings our terms can convey is not made as a matter of course. We may
begin with roughly labelling objects of interest, and then inquiries
may be conducted into, e.g., ‘electricity’, ‘elements’, ‘life’,
‘species’, &c., in the hope of settling what these terms _shall_ mean,
and of finding out _more_ about their meaning, and without making the
assumption that whatever new facts are discovered about them must
conform to our preconceptions and confirm our nomenclature. Thus
to a man of science it will not be cogent to argue that because an
‘element’ is (by definition) an ultimate form of matter which cannot
be broken up, and ‘radium’ breaks up, ‘radium’ is not an ‘element’,
or that because ‘species’ are eternal forms, and the Darwinian theory
claims that they are not immutable, it can be dismissed as involving
the ‘contradiction’ that a ‘species’ is not a species. Thus the best
syllogisms lose their cogency so soon as a question is raised whether
the verbal identity of their terms is an adequate guarantee of the
real identity of the things they are applied to.
§ 9. (3) It is a further presupposition of the logician’s conception of
‘proof’ that absolute truths exist, and that in the ideal demonstration
they form the premisses from which the conclusion follows. This
presupposition is not stated, and is not implied in the form of the
syllogism. For a syllogism is no less ‘valid’ if its premisses are
true only hypothetically, and not absolutely. Indeed, it is not
thought to impair the ‘validity’ of a syllogism that its premisses
should be utterly false. At any rate we can _reason_ quite as well
with hypotheses and probabilities as with absolute truths, and this
is in fact what we usually do, whether or not we are aware that our
premisses are conditional and hypothetical. This ordinary practice,
however, is resented by the traditional logic. For if our premisses are
only hypothetically true, how can they lead to conclusions which can
be declared absolutely true? And if our conclusions are not absolutely
true, how can they be certain? Are they not bound to remain infected
with the doubts which beset their premisses?[383] As we value the
certainty of our conclusions, therefore, absolutely true and certain
premisses must be procured. If they cannot be procured, even the best
formal proofs will remain hypothetical, and all truth will become
dependent on experience. For if nothing is true absolutely, and every
truth has originated humbly in a guess that has grown into a successful
hypothesis, it can always be suggested that after all it may benefit by
a little more verification. It may be true enough psychologically and
for practical purposes, but it does not realize the ideal of ‘logical
certainty’.
§ 10. This ideal Logic has formulated from the first. Aristotle
already was not content with merely analysing the form of reasoning;
he aspired to formulate the norm of scientific demonstration. The
‘demonstrative syllogism’, which he held to be the form of truly
scientific reasoning, differs from the formal syllogism in two
essential respects. Its premisses are absolutely true, and its middle
term states the real ‘cause’, which connects its terms and is not
merely a _ratio cognoscendi_. The reasoning proceeds, therefore, from
premisses which are unambiguous, true, and certain, i.e. _necessarily_
true and _absolutely_ certain. Nor does the conclusion lose any of this
excellence. Logic puts on a fine air of modesty, and merely claims
that the syllogistic form is a guarantee that no truth can be _lost_
on the way from the premisses to the conclusion in a ‘valid’ argument.
If, therefore, our thought is properly arranged, our conclusion will be
as true and certain as were its premisses, and no man will be able to
gainsay it. It is the great beauty and merit of the syllogistic form
that it is an arrangement which gives us this guarantee.
It was natural, therefore, that throughout the history of logic
enormous importance should be attached to the acquisition of
unquestionable starting-points. For the possession of ‘valid forms’ was
not enough. It only insured against loss of truth, it did not provide
for its acquisition. It seemed, however, to imply that truth could only
be generated out of truth, and handed down from the premisses to the
conclusion. Hence the insistent demand for assured starting-points,
self-evident ‘principles’, which the infallible method of syllogistic
deduction might conduct to equally certain conclusions.
In reality, however, this demand for certainty was extra-logical: it
is not required for the purpose of analysing reasoning. For it is
just as easy to reason from doubtful and probable premisses as from
certainties, nor need the doubt in the reasoner’s mind affect the
form of the reasoning. If, however, there is an imperative desire for
certainty, it must be somehow gratified by logic. And there seemed to
be no way of doing so except by ascribing absolute truth and certainty
to the initial principles of science.
Of course it was covertly assumed that certainty could only be reached
by _starting_ from certainty, and that no possibility of a growth of
assurance in the progress of the reasoning could be entertained. In a
sense this assumption was correct (cf. §§ 27, 28), because it is true
that the gradual verification of scientific truths does not render them
absolute; but it led to neglect of all methods which appeared to start
with premisses initially doubtful and hardening into certainties by
gradual confirmation. No doubt it was not strictly impossible to reason
from premisses not known to be true, but such reasoning was despised
as ‘dialectical’, and no inquiry was made into the frequency of its
occurrence in actual science. Why, then, waste time upon so unworthy
a procedure, instead of fixing one’s whole attention upon the truly
logical ideal, the absolute proof of absolute truth? Let us maintain,
rather, the old Aristotelian[384] conviction that the truly scientific
syllogism proceeds from premisses that are true and underivative
(because ‘self-evident’) and inerrant, and demonstrates its conclusion
with ineluctable necessity! Thus the attainment of _absolute truth_
was unobtrusively smuggled in as the aim of reasoning, and became an
integral feature of the ideal of ‘demonstration’.
§ 11. From the standpoint of the scientific inquirer, however, this
whole theory of proof is open to the gravest objections. He finds
first that it is impracticable, being composed throughout of counsels
of perfection with which he cannot comply, and then that, even if he
could, they would be perfectly useless, and destructive of his aims.
(1) It strikes him at once that the Fixity of Terms is an obvious
_fiction_. He will of course be aware, from his scientific experience,
that fictions have their uses and are often indispensable; but he will
know also that not all fictions are useful, and that the adoption of a
fiction has in each case to be justified by its usefulness. Moreover,
it is not so much its immediate and prospective use which justifies it,
though this yields the usual motive for its adoption, as the ulterior
uses ascertained _ex post facto_ by experience.
He will ask, therefore, for evidence that an _absolute_ fixity of terms
is the vital necessity for logic it is declared to be. He will admit,
of course, the familiar arguments for a certain _stability_ of meanings
which have come down from the days of Plato, but he will suggest that
a _relative_ fixity of terms is quite sufficient to content them. He
will point out that in a progressive science any absolute fixity in its
terms is precluded by the very progress of the science. For the terms
in use must somehow manage to convey the _growing_ knowledge they are
employed to ‘fix’. The term ‘gas’, for example, must not be tied down
to the meaning Van Helmont desired to convey when he invented it; it
must incorporate all that physics has discovered about ‘gases’ ever
since. Similarly, when Darwinism transforms the notion of ‘species’,
and the discovery of radio-activity that of ‘atom’, these developments
of meaning must be recognized as perfectly proper. To object to
these conceptions as modern science uses them, on the ground that,
because to Plato and Aristotle species were eternal and immutable,
a ‘species’ that changes cannot be truly a species, or that because
an ‘atom’ is etymologically ‘indivisible’, it becomes an impossible
self-contradiction when it is made up out of ‘electrons’, will seem to
him to reveal only the fatuous pedantry of an utterly unscientific mind.
§ 12. (2) If he is acquainted with psychology, he will perceive also
that the fiction of the fixity of terms is subject to a further
restriction. It is not only in science as such--for all sciences
must be conceived as progressive--that the fixity of terms cannot
be made absolute: a real fixity is strictly inconceivable for and
in every human mind. For every term that is actually used to convey
a meaning must be held to form part of a _new_ truth,[385] i.e.
of a truth that was not previously in being. It is not a question
of principle whether the truth is supposed to be new only to the
person to whom it is addressed, or claims to be new to all, i.e. to
science. For no judgement would be made unless it had something new
to say.[386] Hence _every real judgement_, as opposed to the verbal
formulas which are called judgements in the logic-books, _more or
less modifies the meaning of its terms_. If it succeeds in being a
real judgement and a new truth, it establishes a new and previously
unknown relation between its subject and its predicate. ‘_S_’ is
henceforth an _S_-which-can-have-_P_-predicated-of-it, and ‘_P_’
a _P_-which-can-be-predicated-of-_S_. Thus both the psychological
associations and the logical associates of _S_ and _P_ are changed.
That logicians should not have noticed so obvious a fact can be
attributed only to their inveterate habit of not using in their
illustrations real judgements intended to cope with actual problems,
but operating with their verbal skeletons, which are not being used by
any one to convey his meaning, and so do not have any _actual_ meaning.
Clearly, then, no science can interpret the fixity of terms quite
literally. Or rather, it can only interpret it literally--as a matter
of the literal integrity of the _words_ that _may_ convey a meaning.
But in a scientific inquiry the convention of formal logic must be
reversed; the fixity of terms must be _understood_ not to be absolute,
but to be merely _ad hoc_ and sufficient to convey a definite meaning,
which it is desired to develop. Accordingly it must always be assumed
that the results of an inquiry are to modify its terms, and that it is
permissible, and indeed inevitable, to develop their meaning, so long
as they remain capable of expressing and conveying the new truth. We
must come to every inquiry with a willingness to learn and to expand
our terms. The Fixity of Terms, as it is tacitly presupposed in the
traditional logic, is a scientific blunder of the gravest kind.
§ 13. (3) To renounce it, however, entails further consequences. It
appears to undermine the whole notion of _formal validity_. For if we
admit in principle that the meaning of terms depends vitally on that
of the judgement in which they occur, how can we continue to rely
absolutely on the mere verbal identity of its terms to hold together a
syllogism? In any syllogism the middle term, _M_, may have one shade of
meaning in relation to _P_, another in relation to _S_. It may be quite
right to call _M_ _P_ in one connexion, and to call _S_ _M_ in another;
and yet, when the two assertions are put together, they may lead to
a conclusion which is an error or an absurdity. The man who (in his
laboratory) would rightly declare that ‘all salt is soluble in water’
and (at his dinner table) as properly hold that ‘all Cerebos is salt’,
could not combine these assertions to draw the conclusion that ‘all
Cerebos is soluble in water’, without finding that the facts confuted
his anticipation.
No doubt, when this had happened, he might explain it, _ex post facto_
(if he knew logic), by alleging a hidden ‘ambiguity of the middle
term’. We need not here discuss whether it is fair to treat as an
inherent ambiguity what is really a juxtaposition of shades of meaning
which were relative to different purposes and right in their original
contexts, thus manufacturing a fallacy by selecting the premisses: the
important thing is that the logician should be driven to admit that
_any_ middle term may become ambiguous in this way when a syllogism is
constructed, and that this completely stultifies his assumption that
the _verbal_ identity of the middle guarantees the _real_ identity of
the objects to which it refers.[387] If we call two things, which are
and must be different if they are to be two, both ‘_M_’, we necessarily
take the risk that the differences are irrelevant for the purpose
of our argument. We may legitimately assume this, but if we do, our
hypothesis has to be confirmed in fact; it is naïve to think that the
verbal identity of the terms is quite enough. If, then, actual identity
cannot be absolutely guaranteed, if there is _always_ a possibility
that the same term when put into a syllogism and used in reasoning may
develop an ambiguity and become effectively two, it is evident that no
amount of formal validity will safeguard the truth of a conclusion,
even when the premisses are in themselves severally true. The
syllogistic form is convicted of _losing_ truth which it started from,
and this is the very thing it boasted it could never do. Moreover,
its coercive ‘cogency’ is exploded: whoever wishes to deny a ‘valid’
conclusion after admitting its premisses, has merely to suggest that by
putting the premisses together a fatal ambiguity has been generated in
the middle term.
§ 14. (4) The assumption that everything has been named rightly, and
is what it is called, will scarcely commend itself to the scientific
researcher. He will know from much painful experience that language
only embodies the knowledge which has been acquired up to date, and too
often is only a compendium of popular errors. Hence in any research
which really breaks new ground the existing terminology will always
prove inadequate, and new technical terms have usually to be devised
in order to embody the new knowledge. The reason is obvious. _Ex
hypothesi_ we are inquiring _farther_ into the subject, because our
knowledge is felt to be insufficient. Accordingly the probable defects
of the terminology we are initially forced to use must be borne in
mind: we may expect it to omit what is unknown, to misdescribe and
to classify wrongly what is partially known, putting together what
does not belong together and separating what does, emphasizing the
unimportant and slurring over the important, and generally failing to
provide the mind with words that give it a real apprehension of the
objects under inquiry. Hence the tacit assumption of Aristotelian logic
that the terms reasoned with are fully known, that adequate notions are
already extant, that truth has merely to be _disentangled_ by a verbal
criticism of existing opinions, and has not to be discovered outright,
is false; nor can any argument from a verbal identity be taken as final.
§ 15. (5) But of all the assumptions lurking in the theory of proof,
the belief that reasoning can and should start from certainty will
seem the falsest and most pernicious to the man of science. For it
means that we are committed to a search for absolutely certain
premisses as a preliminary to every inquiry, and proscribes consciously
hypothetical, i.e. truly experimental, reasoning altogether, or at
least condemns it as incapable of leading to certainty. This search,
however, will either be perfunctory and uncritical, if it accepts false
claims to certainty; or else vain, if it is conscientious. For every
attempt to prove a conclusion absolutely demands _two_ absolutely true
premisses; hence the more we try to prove, the more we have to prove,
and our search grows the more endless and futile, the longer it is
continued. An immutable basis of absolutely certain truths, therefore,
for reasoning to start from, is nowhere to be found. In no science
is it possible to _start_ with truths that are absolutely certain.
In every science the initial ‘facts’ are doubtful; they are alleged,
but not yet approved. They embody only unsystematic observation
and prescientific experience of the subject, and so are probably
the products of inaccurate observation, bad interpretation, false
preconceptions, and popular superstitions. To acquire any considerable
scientific value, such material has to be thoroughly revised and
refined.
The validity of methods and the certainty of ‘principles’ are no more
assured than the ‘facts’, initially. Every science has to work out its
own appropriate methods experimentally; even if it borrows methods
from another, it has to find out how and how far they apply to a new
subject. Neither does a science acquire its principles by divine
revelation; even if they fell from heaven ready-made, it would insist
on testing the authenticity of the revelation. But philosophers have
been extremely reluctant to admit that the certainty of principles is
a gradual growth: for over 2,000 years they have been endeavouring to
discover some way of securing an infallibility to principles which
would render them independent of the working of the sciences which use
them. But if their labours have proved anything, it is that no such way
can be found.
(_a_) They have recognized many principles as ‘_self-evident_’, and
equipped the mind with a variety of ‘faculties’, expressly invented to
enable it to apprehend the ‘self-evident’ inerrantly. But they have not
been able to agree upon a list of self-evident principles,[388] nor
even to find any truth whose claims to self-evidence have not been
denied by competent critics. Nor have they been able to define their
notion of ‘self-evidence’ itself; they cannot discriminate between
the sound ‘logical’ self-evidence, which they conceived to guarantee
truth, and its merely ‘psychological’ ‘mimic’, which is certainly much
commoner, and becomes more intense and extensive the more unsound is
the mind that ‘apprehends’ it.[389] Hence an unprejudiced observer has
no reason to put the ‘intuitions’ of philosophers and the ‘faculties’
which apprehend them on a higher cognitive level than those of women
or even lunatics. They all impose themselves psychologically; but this
proves nothing as to their logical value, and science has to test them
just the same.
(_b_) The principles which are said to be _necessary_ or _logical_
‘_presuppositions_’ all turn out to be hypothetical when they are
examined. They are needed, no doubt, to solve the problem in hand, _if_
the particular way it is formulated is taken for granted. But if either
the order or the formulation of problems is altered, they cease to be
either ‘necessary’ or ‘presuppositions’. For example, the ‘axiom of
parallels’, _alias_ ‘Euclid’s postulate’, is a necessary presupposition
of geometry, if the existence of parallels is assumed. But if we
prefer it, we can just as well (with Aristotle) make it our axiomatic
‘presupposition’ that the interior angles of a triangle are equal to
two right angles, and can then deduce the existence of parallels. I.e.
Euclid might have deduced what he assumed, and assumed what he deduced.
If, moreover, we do not desire to construct a Euclidean geometry at
all, we can deny _both_ presuppositions, and proceed from _alternative_
postulates, which lead to the various metageometries. The only things,
in short, which all scientific principles presuppose are the desire to
construct a science, and the desire to construct it in a particular
way, which is simplest, or easiest, or most systematic, or most in
accordance with the reigning prejudices. But these desires are the
very things which the logician’s account of principles always omits to
mention.
Again, the whole of Kant’s scheme of _a priori_ presuppositions in
the theory of knowledge rests upon an arbitrary assumption, viz.
that mental data are to be conceived as originally discrete and
are therefore in need of ‘synthesis’. But it is just as possible
to conceive an analysis of knowledge which starts from the
‘presupposition’ of a continuum or flux, and proceeds to trace out the
principles by means of which this continuum is broken up into a world
of apparently distinct things and processes. Nor is it possible to say
in advance of experience which of such ‘presuppositions’ is going to be
more convenient and more conducive to scientific progress.
(_c_) It demands a high and rare degree of philosophic insight to
perceive that very many principles are neither certain, necessary,
nor probable, but simply _methodological_. Whether we think them true
or not, we adopt them because of their eminent convenience. If they
turn out to be false, candour compels us to call them _methodological
fictions_; but they continue in use. Our belief in the trustworthiness
of memory is a good example. For though we often find that our memory
has played us tricks, we continue to accept as true what we ‘distinctly
remember’. If no limitations to the truth-claim of such assumptions
are discovered, enthusiasts will probably insist on promoting them to
the rank of indisputable ‘axioms’, and hail them as absolute truths.
But their scientific value is not thereby enhanced, and the cautious
will eschew such exaggerations. For there is no real reason why the
scientific rank of principles should not rest openly and entirely on
their actual services, and why a ‘methodological assumption’ should
not rank higher than a ‘self-evident truth’. For the latter is at most
a fact of our mental organization which nothing has so far turned up
in nature to set at naught, and as such a fact it is itself a thing to
marvel at rather than an explanation of other things. The scientific
spirit will always hesitate to acquiesce in the limits which are set
to inquiry by sheer brute facts, and if the absolute truth of certain
principles were merely an ultimate fact which could neither be impugned
nor explained, this would go far to make these principles appear
unintelligible and would be a constant challenge to dispense with them,
or somehow to evade them. A principle, then, should always be prepared
to state the reasons a science had for adopting it: only the reasons
will appear from the actual working of the science. They will involve
a reference _forward_ to the facts it copes with, not _back_ to higher
principles or to any claim that proves itself by its self-assertion.
(_d_) Indisputable principles, then, are not consonant with the
spirit of inquiry: it will gladly let them go, if it can attain truth
and advance knowledge in other ways. It will not shrink even from
repudiating the ideal of absolutely true and demonstrated truth, if it
can be realized only by sacrificing the progressiveness of science; nor
will it be dismayed to find that this ideal is unrealizable. For when
the inquirer reflects upon his own procedure, he finds that it points
to a radically different ideal, and that the existence of absolute
truths would only be a hindrance and a restriction upon his endeavour
(cf. § 28 (4)).