§ 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.