§ 30. It is clear, then, that the time has come when Science should
break decisively with the logical tradition, and proclaim a logic
of its own which has always been implicit in its procedure. It must
definitely declare that what it needs is not a logic which describes
only the static relations of an unchanging system of knowledge, but
one which is open to perceive motion, and willing to appreciate the
dynamic process of a knowledge that never ceases to grow, and is never
really stereotyped into a system. To show that such a logic is not
inconceivable will be the endeavour of the concluding sections of this
essay.
We have already had occasion to note many of the most important
features of this logic. We have seen that logical, i.e. critical,
reflection upon discovery must start from, and be guided by, the
conception of a scientific _problem_ with which the process of knowing
_experiments_ (§ 21). This problem has, of course, to be attacked
with the existing resources of a science, i.e. with the knowledge it
possesses up to date. These resources form the scientific _capital_
which is necessarily _risked_ in research if it is to yield interest.
It comprises (_a_) approved principles, (_b_) known facts, and (_c_)
established meanings of words. About each of them a little more may
advantageously be said.
(_a_) We have seen (§ 15) that the principles of any science could not
rightly be conceived as inscrutable, ultimate, absolute certainties
of divine descent, and acknowledging no human ancestry. We saw that
they could be understood only as hypotheses which reflection upon a
problem had somehow suggested to an ingenious mind, which had been
provisionally adopted in order to explore and organize a subject of
inquiry, and had finally been verified and confirmed by their success
(§ 15 (_c_), § 24).
The principles thus accepted by a science are often regarded
as descriptive of fact when they are merely methodological and
convenient,[401] but this is a point of secondary importance. And even
the most amply verified principles never quite lose their hypothetical
character. So long as they are used, their meaning, scope, and truth
are not absolutely fixed. They can be extended, restricted, and
modified by the working of the principles.
§ 31. (_b_) It is really obvious to any critical reflection that when
a science appeals to ‘facts’, it is really appealing to the facts _as
known_, or supposed to be known. It cannot from the first presume its
knowledge to be absolute, and, _pace_ some of our ‘neo-realists’,
ignore the question whether the alleged facts are facts at all, and so
pretend to start from ‘the facts as they really are’. Such uncritical
temerity would only conduct to insoluble pseudo-problems like that
with which King Charles plagued the nascent Royal Society, as to _why_
the weight of a bucket full of water was not increased when a fish was
added to it. If, however, it is acknowledged that the ‘facts’ involved
in a scientific inquiry are always relative to a definite state and
date in the history of a science, several important corollaries follow.
(1) Being dependent on the condition of the science, the facts of a
science will not all be ‘facts’. That is, not all that is relevant to
the interest of the science will actually be within its cognizance,
not all that turns out to be fact, and is antedated when it has been
discovered, is as yet recognized as fact. It will be this fact,
moreover, which constitutes the science a field for inquiry and renders
it progressive.
(2) Though the ‘facts’ of the moment fail to include all the facts,
they often manage to include too much. The ‘facts’ are not all fact.
They include unknown, and often large, amounts of prejudice, illusion,
error, superstition, and other remnants of the lurid past and stormy
youth of every science. It is useless to repine at this inevitable
consequence of past history, and childish to try to purge it away
by defining as science only what _ex hypothesi_ is free from such
contaminations. To restrict the logical interest to science _qua_
science, which is by definition infallible, is to forbid any logical
treatment of the sciences we actually possess. But the logician should
surely be encouraged to study the processes by which the sciences
correct their initial errors and consolidate their acquisitions.
(3) It follows on both these grounds that the ‘facts’ of which a
science takes cognizance will be subject to change. As the science
grows, ‘new’ facts will come into it, and old facts will be discarded
as erroneous. In particular, facts which at first were only inferred
on theoretic grounds will be actually observed, even as ‘Neptune’ was
the fruit of a theory about the perturbations of Uranus. Hence the
antithesis of ‘theory’ and ‘fact’ must not be taken as absolute: they
must be expected to play into each other’s hands. It is the business of
theories to forecast ‘facts’, and of facts to form points of departure
for theories, which again, when verified by the new facts to which
they have successfully led, will extend the borders of knowledge.
Incidentally, however, this interaction between fact and theory often
renders it difficult to decide whether a scientific doctrine is better
regarded as a ‘theory’ or as a ‘fact’, and leads to differences of
opinion. But it can hardly be wrong to advise the scientific mind to
practise hospitality towards new facts, while it is no less fitting
to show generosity towards old servants that have done their work and
can now advantageously be retired. It is ungrateful to abuse them as
‘errors’, and to despise them with the lofty contempt of the higher
knowledge to which they have conducted. And in both cases the truly
scientific attitude may be attained if an element of fanaticism is
not imported into the conception of truth by attributing to it an
absoluteness which no human truth in fact possesses.
(4) The same need for tolerance is emphasized by a further corollary of
the conception of fact which has been advocated. It seems at first a
paradox, but on reflection appears to be evident, that the ‘facts’ will
not only _look_ different but may really _be_ different from different
points of view and for different purposes. Once we permit ourselves to
consider this possibility we shall easily perceive that there often
are conflicts between ‘facts’, such that they cannot coexist for an
abstract logic, while, nevertheless, each of the conflicting facts
may be intelligible relatively to its own presuppositions and true
under its own conditions, so that the ‘contradiction’ between them is
generated merely because the logical statement has abstracted from the
special circumstances of the case.
This situation is, of course, recognized very familiarly and
universally in the case of _value-judgements_. We are all willing to
admit that one man’s meat may be another man’s poison, that it is vain
to dispute about tastes, and that the same mode of living does not
suit all constitutions and all circumstances. We recognize, too, that
profound differences of opinion and attitude exist, and always have
existed, among men. The temperamental differences which make e.g. one
man indolent another enterprising, one man daring another prudent, one
a conservative another a radical, one an optimist another a pessimist,
are so deeply rooted in human nature as to be, humanly speaking,
ineradicable. And if so, must it not be conceded that situations
occur which will inevitably, consistently, _and rightly_, be judged
differently by these different persons?
Again, it should be noted that these differences in valuation are not
merely subjective: they spring from objective differences in human
nature, and are as objective as any other facts about it. For example,
that certain persons dislike pork (because they cannot digest it), and
hate cats (because their presence makes them feel ill), rests as much
on a physiological fact of their constitution as that others suffer
from ‘hay fever’. Similarly, it is quite plausible to contend that
‘every little boy and girl that is born alive, is born a little liberal
or a conservative’, and certainly the normal growth of conservatism
as the individual mind ages is proof enough that changes of belief
depend on psychological law, and are correlated with the hardening of
tissue which is a general symptom of senescence. Again, is it possible
to imagine a situation so bad or so good that it cannot be interpreted
either optimistically or pessimistically? In most cases either
interpretation is quite easy, and the choice between them is effected
by sheer temperamental bias. If, then, we succeed in doing what the
natural man will always find difficult, and regard such differences of
opinion in a scientific and non-partisan way, must we not admit that
_both_ the conflicting standpoints are inevitable and justifiable?
Neither can be pronounced wrong in general and _per se_, though in
regard to a particular problem or occasion either may be. Let us
conclude, then, that it may really be a ‘fact’ that the ‘facts’ justify
one interpretation and attitude to one mind and another to another.
This argument is reinforced by the further consideration that even
the most objective statements of fact involve _value-judgements_
in their ultimate analysis. For they express, often explicitly and
always implicitly, the choices and valuations by which a variety of
pretenders to reality have been examined and sifted, and the most
valuable have been declared ‘truly real’. We have seen that in a
scientific inquiry the ‘facts’ must always be taken as _alleged_
facts, discovered up to date; hence a science must always be ready to
defend the ‘facts’ it recognizes, when they are challenged, and to
show wherein they excel conflicting allegations. The accepted ‘facts’
of a science, therefore, are always allegations which are thought to
possess greater _value_ than any known alternative; hence no sharp
or absolute distinction between judgements of fact and judgements of
value can be maintained. It becomes, moreover, quite possible that
incompatible allegations of fact may in the actual state of a science
be so nearly balanced that there is no convincing reason to prefer
one to another, or at any rate none that could prevail against any
ordinary temperamental bias. Consequently, in such cases the bias
will condition the visibility of the ‘fact’; it will be bathed in a
‘subjective’ atmosphere, and the ‘eye of faith’ will be necessary to
perceive it. No doubt such situations are inconvenient, and repellent
to the scientific spirit; but they do not occur only in the misty
regions of religion and philosophy, and scientific alternatives like
‘chance’ or ‘design’, ‘miracle’ or ‘law’, ‘mechanism’ or ‘vitalism’,
determinism or indeterminism are essentially of this order. There is no
reason, therefore, why logic should not recognize them and acknowledge
that the scientific ‘facts’ may be ambiguous, in the sense that further
experience and experiments are needed to determine their character.
As a rule, to judge by the past, further inquiry will resolve the
ambiguity; but it may well be an illusion to assume that it must do so,
and in some of the most important cases the decision will certainly be
long in coming.
Thus the student of animal behaviour will probably long be left with
a choice between minimizing the displays of animal intelligence and
assimilating them to the human, while it will probably always be
possible to put a pessimistic or an optimistic interpretation upon the
facts of life as a whole.
A scientific logic therefore should radically disabuse the mind of
any excessive trust in ‘facts’. It is a superstition that ‘facts’ are
plain, straightforward, and easy to discover; they are often subtle and
recondite and relative to circumstances, changing their aspect to suit
their scientific environment like any chameleon.
§ 32. (_c_) In considering the use of words in research, one cannot
of course overlook the obvious fact that the employment of words is
primarily determined by their established meanings, and that these
greatly limit our freedom to use them as we please. Words naturally
and inevitably suggest their established uses by their mere sounds,
and should always be used with a proper respect for their past history
and present meaning. To be sensitive to this appeal is the mark of
the educated scholar; but it does not require the investigator to
exhaust his energies in vain attempts to stereotype absolutely the
current meanings, and so to deprive words of their essential function.
For their essential function is after all to be instruments for the
conveying of actual meaning, and actual meanings are always more or
less new (cf. § 12). It occurs to a particular person in a particular
situation to express and convey a meaning which has never in its full
concreteness occurred before. If the novelty about this situation is
appreciable and important, it may well be that the old words will
not fully succeed in conveying the new meaning; and yet we shall
always endeavour to use them, and select from the accumulated wealth
of language the words which will suffice for our purpose. For the
alternative is worse; we cannot always be coining new words for every
new meaning we may desire to convey; they would not be understood or
remembered, and even if they were, a science that employed nothing
but technical terms, and was moreover compelled continually to
change them, because it would not use them to convey new meanings,
would speedily degenerate into an abstruse game, and could make no
progress. How impracticable such a policy would be may be gauged
by the grave inconvenience which even now systematists cause by so
frequently changing the scientific names of plants and animals. It is
indispensable, therefore, that words should retain a certain measure
of plasticity, in virtue of which they can be transferred from old
situations to new and be used to convey new meanings. Nor is there
usually any difficulty about thus imposing new duties on the old
terms; under the particular circumstances of the situation even wide
departures from the established meanings may remain intelligible, and
so the progress of science is not impeded.
The traditional logic, however, cannot treat the matter so lightly.
For the plasticity of words may always engender a conflict between
the old meaning and the new, between the scientific use of terms and
the traditional conventions about their use. And this can always
be represented as a defiance of the ‘laws of thought’. For if the
meaning of ‘_A_’ may be altered by the growth of knowledge, it will
no longer be true that everything once called ‘_A_’ is truly _A_,
nor that what was once incompatible with _A_ will continue to be so
for all time. Hence it is no longer necessarily true that ‘_A_ is
_A_’, and that _A_ cannot both be and not be _B_. It may be both in
different senses, and in what sense ‘_A_’ and ‘_B_’ should be taken
may be precisely the point at issue. Thus verbal contradiction ceases
to be a clear proof of error; it may be only a much-needed warning
that our terms have been developing new meanings. Hence, the ‘laws’
of Identity and Contradiction lose their last claims to be regarded
as statements of fact, and have to be conceived as ideal postulates
of just so much stability of meaning as is requisite for effective
understanding.[402] They can be applied to reality only hypothetically,
i.e. experimentally, to discover whether in a given situation the
natural growth in the meaning of the terms may _rightly_ be treated as
irrelevant, and does not vitiate the conclusion which the reasoning
forecasts. Now this problem can never be settled _a priori_ by
reasoning, but only by subsequent experience. Reasoning may forecast a
result which experience fails to confirm; when we discover that comets’
tails are not attracted by the sun but repelled, we do not declare
the facts ‘contradictory’, but modify our notion of ‘gravitation’,
and conceive it as inferior to ‘light pressure’ in its effects upon
particles of a certain minuteness.
It follows that no merely logical scrutiny of the terms of an
argument can ever settle a scientific question. If a ‘contradiction’
is real, it means either a difference of opinion between those
who make the incompatible assertions, or, in the case of a real
‘self-contradiction’, the uttering of ‘nonsense’ and a failure to
propound a meaning at all. But even the most glaring ‘contradictions’
may only be apparent, i.e. verbal: when we inquire into their actual
meaning we may find that they refer to a context in which its terms are
perfectly compatible. Thus the existence of a ‘round square’ may be
predicated of London, and a ‘triangle’s’ angles may equal or may exceed
two right angles, according as it belongs to Euclid’s geometry or to
Riemann’s.
§ 33. The problem of discovery, therefore, is never one of which the
solution can be guaranteed in advance. The resources of a science are
never sufficient to assure us of a prosperous issue of the research,
though, rightly understood, they yield important safeguards. A
recognition of the instrumental value of words as ancillary to meaning,
and of the limitations under which they labour, will guard the inquirer
against the terrible verbalism to which logic has been enslaved. A
critical attitude towards allegations about ‘facts’ will enable him to
minimize the dangers of error, deception, and bigotry. A conception
of ‘principles’ as working hypotheses will discourage a servile and
superstitious reverence for them, and justify the fullest freedom to
experiment with whatever ideas hold out hopes of verification and of
scientific progress. Together these three considerations will pretty
thoroughly emancipate inquiry from the shackles of any mechanical
scheme of ‘proof’. Indeed, proof in the old formal sense will have
become a chimera. It will no longer be possible to cherish the belief
in a self-sufficing, self-satisfied form of absolute proof, of which
the pure logician imagined himself the possessor and retailer.
Scientific proof, on the other hand, will be neither absolute nor
formal. It will not be absolute, because it will always be relative to
the actual condition of a science; it will not be formal, because it
will never be absolute. It will only be the best known interpretation,
and will always imply alternatives, to some of which it may wrongly
have been preferred, while to others it may be destined to succumb
(§§ 26, 27). It will be ‘valid’ so long as it is the strongest; but
to it, as to the priest of Diana Nemorensis, as to Uranus and Cronus,
will come the day when it is invalidated and superseded by a stronger
and better, descended, it may well be, from itself. Scientific proof
then will always be an _evaluation_ of evidence, a making the most of
the available resources of a science, a question of the _comparative
values_ of rival interpretations.
It stands to reason that such an evaluation cannot operate merely
with the criteria of formal logic. Indeed, of the processes known
to the traditional logic, only those which _cannot_ be represented
as ‘formally valid’ will be exemplified in scientific knowing. It
will not be possible to find any genuine cases of absolute certainty
or unconditional proof; but analogies, probabilities, hypotheses,
alternatives, even fallacies and fictions, will abound, and will
somehow have to be discounted. Clearly the evaluation of such things
will be a delicate affair; it cannot be accomplished by reciting
_Barbara Celarent_ and crudely applying a few simple mechanical
formulas. It will demand the energetic co-operation of the whole
intelligence, and indeed of the whole personality, and cannot scorn the
aid of psychological factors. For it is plain that the evaluation of
a complicated scientific situation will require both expert knowledge
of scientific detail and philosophic grasp of general principles
and connexions; it will need also ‘tact’, ‘judgement’, an ‘eye from
experience’, and a host of similar qualities that elude precise verbal
formulation. It will no longer be practicable to flatter mediocrity and
dullness, and to impede discovery, by proclaiming methods that dispense
with imagination, ingenuity, originality, boldness, enterprise, and
vainly endeavour to put genius for discovery on a par with mindless
pedantry in applying stereotyped and sterile rules.
§ 34. But just because a logic that recognizes the actual process of
discovery does not presume to dictate formal methods to the discoverer,
and leaves him a very free hand, it does not relieve him of any of the
responsibility for conducting his researches to a prosperous issue.
As there is no longer any pretence that any logical machinery can be
devised to guarantee success, success and failure become his personal
achievements. If he fails, he can no longer plead that it is not his
fault, seeing that he has kept every letter of the law and broken
no logical rule. This may be precisely _why_ he failed. Perhaps he
should have taken risks. He may have gathered such enormous masses
of fact that he could no longer see through them, nor select the few
that were relevant to his problem. He may have been so sensible of
the need for caution that he dared not speculate or move. He may have
devoted himself to unimportant problems or missed the important sides
of important problems, or have wandered away into barren wastes of
dialectics, or have got bogged in a mire of verbalism, or have pursued
elusive phantoms of unverifiable speculations. For there are clearly
many ways of failing. Only in whatever way he fails, his personal
failure is _pro tanto_ a failure of science to progress. Every science
has somehow to get hold of a clue to guide it through the labyrinth of
fact, and this clue has to lead it right, though it need not ‘follow
necessarily’ from previous knowledge.
Nevertheless, if, and in so far as, a researcher succeeds in making a
discovery, some of his personal credit is reflected upon his methods
_ex-post facto_. Their success does not, of course, establish their
formal ‘validity’; but it stops the mouth of those who argued that what
is ‘invalid’ must be worthless. Methods that succeed must have _value_,
a greater thing than ‘validity’, however far and however boldly they
departed from the canons of formal proof. The success has shown that
_in this case_ the inquirer was right to select the facts he fixed
upon as significant, and to neglect the rest as irrelevant, to connect
them as he did by the ‘laws’ he applied to them, to theorize about
them as he did, to perceive the analogies, to weigh the chances, as he
did, to speculate and to run the risks he did. But only in this case.
In the very next case, which he takes to be ‘essentially the same’ as
the last, and as nearly analogous as is humanly possible, he may find
that the differences (which always exist between cases) are relevant,
and that his methods and assumptions have to be modified to cope with
it successfully. But he should not be discouraged. For the ultimate
ground of the whole cognitive procedure by which we analyse the flow
of events is empirical. It is only an empirical fact that knowledge is
possible, i.e. that the course of events is such that human minds can
analyse it at all, that is, can pick out and construct cases of ‘the
same’, of which the course can be predicted by means of the (verbally)
stable formulas we call ‘the laws of nature’. For logic at any rate
these laws are neither supernatural behests nor metaphysical entities:
they are forms for classifying happenings, in which the blanks have to
be filled in with the variable values of the particular happenings.
What the _right_ values are, and even what is the _right_ formula to
apply, will always depend on the particular case which forms the actual
problem. It is only the empirical fact that the differences between
problems may so often be treated as irrelevant which generates the
illusion that problems may be solved in advance by general formulas: in
reality every problem in its full concreteness is unique, and we are
never absolutely sure that it will submit to the rule we apply to it.
Hence it is solved only when we come to it and find it amenable to our
methods; in principle it eludes logical prediction, because it can be
known as a ‘case’ of the successful ‘law’ only _after_ the experiment
has confirmed the forecast. To the inquirer, therefore, no result can
seem certain until it has occurred; it is only _ex post facto_ that
the logician can describe it as an indubitable case of some law from
which it follows of necessity. But in so doing he has changed it, and
repudiated the duty of describing actual knowing. All he is doing is
to rearrange a piece of knowledge, acquired without his aid by means
he condemns as illicit, in the order he is pleased to call ‘logical’.
This order has a certain aesthetic value, but it is emphatically _not_
the order of discovery, and throws no light on the process of acquiring
knowledge.
§ 35. What function then can be assigned to the logician’s reflection
on the workings of science? In view of his failure to substantiate his
claim to have provided a model for inquiry in his scheme of ‘proof’,
it might seem that he was either useless or pernicious. Useless, if
he merely devotes himself to constructing ‘ideals of proof’ which
he admits to have no relation to the actual problems of science;
pernicious, if he is prompted by these ideals to make demands with
which no science can comply, and to deliver judgements which would
paralyse the science that attempted to carry them into execution.
Fortunately, he cannot enforce them, and the sciences actually go
on their way, ignoring such ‘logic’. The proper inference from his
impotence is that he would do well to take up a position which is more
useful and more influential, if less pretentious.
Let the logician then give up the pretence of dictating to the
sciences and of judging the worth of scientific truth by rigid forms of
absolute proof; let him abandon the vain pursuit of ‘validity’. Nay,
more, let him renounce the claim to determine the scientific value of
an argument by a mere inspection of its logical character. Let him
confess that what alone he can criticize is the incongruities in its
verbal expression, and that its real value lies beyond his ken. If
he will concede all this, his reward will be that he has vindicated
for logic an important right of more real value than the claims he
has abandoned. For he will have obtained the right of summoning the
sciences to state their results in intelligible and consistent terms,
and to confront them with a problem when they do not. Just because he
does not presume to condemn them, and no longer ventures to declare
that incompatible and verbally ‘contradictory’ results are necessarily
wrong and worthless, but only urges that they are not intelligible as
they stand, and need to be reworded or inquired into farther, he gains
the right of _raising problems_, and stimulates the sciences to proceed
to solve them.
It should be noted, moreover, that the problems thus raised are
general, not special, i.e. are properly logical. The problem about
‘contradictory’ results is one about meaning, for contradictory
assertions cancel each other’s (apparent) meaning. This enables
the logician to keep the sciences engaged upon the logical problem
of solving the discrepancies between their results, so long as
the sciences do not form one complete and congruous system, i.e.
indefinitely.
Similarly the denial that truth is absolute is a general truth that
affects all the sciences. It should stimulate them all, for it means
that no statement is so perfect that it cannot be bettered and that no
limits can be set to the progress of science.
Other topics which are ‘logical’, because they concern the general
significance of scientific procedure and not the solution of particular
problems, are the nature and importance of selecting ‘facts’ and
the ‘laws’ they are taken to exemplify, the experimental attitude
and the framing of hypotheses, the evaluation of probabilities and
alternatives, the estimation of relevance and of verifications and of
the amounts of the latter which are requisite and the sorts of it which
are relevant. On all these points logic has hitherto had little or
nothing to say, mainly because they did not lend themselves to formal
treatment. Lastly, there are two extremely important subjects, which
are so vital to the logic of discovery that a brief discussion of them
may fitly conclude this essay. We may call them the problem of Novelty
and the problem of Risk.
§ 36. In Logic we are not concerned with the metaphysics of Novelty,
i.e. with the problem of whether there ever enter the world things
that are really and truly unforeseen and unpredictable, that pop into
it from nowhere, and if so, whether and how we can understand such
things. This problem is deep and difficult, and so, until recently,
philosophers have fought shy of it, and used to settle it off-hand by
a flat denial that such things could be in a ‘rational’ universe. But
now that M. Bergson has given us a radically new metaphysic, and that
we are beginning to perceive that the principles used to dispose of the
matter, viz. causality and the conservation of energy, are essentially
methodological, the question has become an open one.
Logic, however, has no need to probe it; it can treat it more simply.
For its purposes it can, and must, treat novelty as a real logical
fact. It is a psychological fact, and logic must note it, that every
moment of our life has for us a certain flavour of newness; it is
also a fact that every real judgement that is ever made has a certain
relation to novelty.[403] Its maker believes, either that it embodies
a new truth, or that though known to him it is new to his hearers. If
he did not believe this he would have no motive to make it. It would
be stale repetition, devoid of interest or value alike to him and to
others, whom he would merely bore by telling them what they, too, knew
already.
So far, then, the logical nature of novelty seems simple. It gives
rise to problems, however, when we consider the relation of the new
truth to the old. It is clear, in the first place, that the new
truth must affect the old. Even where we are willing to minimize its
novelty, and to call it merely an ‘extension’ of what we already
knew, it must modify it and change its value. For in the light of
the new developments the old truth _means more_: it has relations in
an enlarged field of knowledge. Moreover, the new truth is often not
merely an extension but also a _correction_, and the effect of the
correction may sometimes be revolutionary. It may even seem to upset
the old beliefs altogether, though human ingenuity is far too fertile
in building bridges (often only verbal) from the old to the new to
allow this impression to be permanent. Still in all these cases there
is more or less discrepancy between the new and the old.
The logician, however, should insist that this fact should not be
blinked. He should recognize the discrepancy, and emphasize its
significance, just because for other purposes it is usually convenient
to ignore it. For it is not only the source of real ambiguity in
the facts of science, and of the important differences of opinion
among men and of their obstinate persistence, but the justification
of the policy of open-mindedness and toleration which he regards as
necessary to scientific progress. Inasmuch as of every discrepancy
between the old truth and the new it will be possible to take two
views, and either to cling to the old or to put one’s trust in
the new, there will always be a party of conservation and a party
of innovation, or otherwise a conservative and a liberal bias, in
science as in politics. It is, moreover, futile to discuss, in the
abstract, which of them is right: for it would clearly be fatal to go
all lengths with either. Science could make no progress, either if
every novelty were at once condemned and suppressed because of its
failure to conform with the accepted doctrine, or if everything new
were hailed as true regardless of its concordance with the old truth,
so that the course of science became a series of radical revolutions
that had no consistent direction. In concrete cases of course both
sides are sometimes right, though historically the stronger bias men
have shown has been the conservative. What usually happens is that
the new truth is first denounced as an immoral invention which is
subversive of all intelligible order and cosmic rationality; it is then
quietly assimilated and not infrequently converted in the end into
the strongest support of the beliefs it was alleged to subvert. But
it would be a real gain if logic, by viewing this natural feature of
knowing in its generality, could induce men of science to take it more
calmly. If it were generally recognized that every claim to new truth,
however great the advantages it promises, necessarily entails certain
inconveniences, because the old beliefs and notions have to be modified
and readjusted, and this may involve too great an effort to be worth
while, or an effort too great for certain minds, it would be seen that
there are two sides to every question, and that both may be in a way
legitimate. If, in addition, we recognize that the parties concerned
usually have a bias which may render them dangerously blind to the case
of the other side, and that both should be admonished to discount their
bias duly, we shall have done not a little to secure fair-minded[404]
consideration, reasonable discussion, and intelligent choice between
the alternatives. And all this surely conduces to scientific progress.
It is clear, then, that the problem of relating the new to the old
always exists, and has a vital influence on the fortunes of every
science. But it is not capable of any formal or abstract solution _a
priori_. Which is to be preferred is a matter which must be left to the
expert who is cognizant of the circumstances of the case: logic can
help only by broadening his mind, and putting him on his guard against
his own personal bias, which might otherwise unconsciously determine
his decision.
§ 37. To admit that scientific inquiries concern problems, and that to
every problem (at least) two solutions may be propounded, between which
a choice has to be made, is to admit that knowledge _must take risks_
in order to progress. For there is always the risk of choosing the
wrong solution of a problem, i.e. the one which works _less_ well, just
as there are always risks of choosing a bad problem and of selecting
the wrong facts and the wrong theories to explain them withal.
Nevertheless, we ought not to resent this fact. For the taking of risks
is inevitable: we cannot escape it either by refusing to inquire or by
refusing to decide. For in either case we run the risk of missing a
valuable truth.
It is better, therefore, to recognize that every act of knowing must
involve risks, just as every act of living does; and this for the
simple reason that knowing is an activity comprised in living, and
every judgement is an _act_, which might have been left undone, or
for which another might have been substituted. The readiness of the
new conception of logic to emphasize the existence of risks in all
reasoning, and to sanction the willingness to take them, contrasts
markedly with the vain efforts of the old logic to play for safety, and
to make no move that was not absolutely necessary (cf. § 10). This was
why it postulated absolutely certain premisses, and would contemplate
nothing but ‘valid’ forms of reasoning. In its desire to elevate its
proofs above the perplexities and vicissitudes of mundane problems, the
old logic was expressing and comforting a deep-seated human craving:
for life is so replete with the most hideous risks that it is a natural
instinct to clutch at any promise of security. Hence the passionate and
almost religious reverence with which formal logic has been regarded
for over 2,000 years. Many philosophers still worship the syllogism,
because it seems to them an incomparable exemplar of absolute security
firmly fixed in the sphere of immutable necessity far above the flux
of phenomena, which it illumines with its steady radiance. But to
exalt in this way its ideal of proof, the old logic had to pay a heavy
price. The price was cutting the ideal wholly adrift from the actual,
contemplating exclusively a situation which could never occur in
real life, and leaving all actual inquiry to its devices, unstudied,
uncriticized, and unaided. Thus, the splendid aloofness of the logical
ideal was purchased by a total repudiation of actual science. To
many philosophic minds this price does not seem excessive. The more
useless truth is made to appear, the purer and more admirable it seems
to them. An ideal, they think, should be like Aristotle’s ‘god’; it
should attract, without uplifting, and without running the risk of
contamination by the dirty work of life.
These philosophers have always claimed for their attitude that it is
philosophic _par excellence_. But their claim, besides being based
on a somewhat rare personal idiosyncrasy, is not really sound. It is
neither self-consistent nor a sound policy for life. An ideal which
repudiates the actual, and yet professes somehow to be its exemplar,
is left in the impossible condition of the Platonic ‘Idea’. If it were
as superhuman as it claims to be, no human mind could even speculate
about it. And we have seen (§ 13) that it is not in the end possible
to devise a form of proof which is bomb-proof against the attacks of
experience and superior to verification.
Is it not wiser, then, to admit that life has its claims upon science,
and science upon logic? We simply _must_ have a science that can
handle human life and meet human needs, and does not degenerate into a
game with arbitrary and fantastic rules which depart from the actual
conditions of life in any direction and to any distance unrestrained
imagination carries them; and our logic must deign to study such
a science. If to do so it has to ‘scrap’ its antique ‘ideals’, to
abandon its pose of an inhuman, impassible, infallible aloofness, and
to interest itself in the doubting, questioning, guessing, trying,
risking, blundering, correcting, achieving that make up the sum of
human knowledge, it will receive an ample reward in the gratitude of
man for a logic that has entered his service, and in the salutary
influence which it will exercise upon his actions.
_Conclusions_
(1) We have shown, negatively, that the notion of a form of proof, by
which conclusions can be absolutely demonstrated by dint of pure logic
alone, is a delusion. No such form can be constructed (§§ 13, 15), and
if it could, it could neither find scientific material worthy of it
(§ 28), nor contain the material which is fabricated by the sciences.
(2) We have thereby shown that formal logic cannot represent the
logical nature of discovery or of any of the processes of actual
knowing, and must condemn them all as ‘invalid’ (§§ 18, 20, 26, 28).
(3) We have seen that a logic which attempts to understand actual
knowing cannot prescribe to the sciences how they are to solve their
problems (§ 33).
(4) But it _can_ grasp the general character of scientific procedure,
appreciate its difficulties and dangers, understand the expedients for
meeting them, and trace it to its roots in the constitution of the
human mind and in the needs of life (§ 35).
(5) In virtue of its general grasp of the aim and method of the
sciences a logic of science can at times offer advice to scientists:
it may draw their attention to the general problems which their work
involves, but which are apt to be overlooked by specialists, such as
the claims of consistency and novelty and the regulation of risks
(§ 36). Or, better still, if they will study it themselves, it may
broaden their minds and enable them to handle these general problems
for themselves far more effectively than a pure logician could do it
for them.
(6) By abandoning its pretensions to rigour and conclusiveness logic
does not really lose: it gains immensely by coming into contact with
science and life, and becoming of use in the world.