Part 29

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.