Chapter VI: Italian Text (8)

But, as we anticipated in § 24 (_s.f._), it is vain to expect to establish any absolute truth by this method. It provides truth with ever-growing probability, but never with absolute certainty. For, however well a theory works, the thought that one may hereafter be found to work better can never logically be excluded. Even if every one alive were perfectly satisfied, and no one could imagine any improvement in an accepted truth--and these conditions are by no means often realized--such psychological considerations would not disprove the logical possibility that the best known was not the best absolutely, and logic would continue to distinguish between a truth that was absolute, and one liable to one billionth chance of error. The latter chance could be disregarded for all practical and scientific purposes, and would not have the slightest psychological effect on the confidence with which the truth was regarded; but logically it would still be there. Science, therefore, has to resign itself to the conclusion that its method cannot conceivably attain to absolute truth, and to make the best of it.

§ 27. Curiously enough this conclusion is fully confirmed by Formal Logic. It prides itself on pointing out that there is a formal fallacy involved in establishing truth by ‘working’. The essence of this method is to argue that if a theory is found to work (after the proper precautions have been taken), it is true. If e.g. the events anticipated by a theory occur, and nothing occurs that could not be anticipated, it grows more and more probable until it convinces every one. But ought it logically to have done this? The logician declares emphatically, it ought not. For the argument suffers from an incurable flaw, which has been recorded as a ‘fallacy’ for over 2,000 years. It is a flagrant ‘affirmation of the consequent’; symbolically, it argues that _if A is, B is, but B is, ∴ A is_. Now this is not ‘cogent’ or ‘valid’. That _A is_ can be proved only from the premiss ‘_only_ if A is, B is’, i.e. if A is the _only_ theory which will account for the observed consequences. But this the fallacious method did not assert, and indeed could not assert. For that the best known is the best absolutely never can be proved (cf. § 26); and even if they happened to be identical, and we had somehow stumbled upon an absolute truth, we should never know that this was so.

§ 28. To the logician this fact only seems to prove the superiority of his conception of ‘proof’. He infers, consistently enough, that no inductive reasoning from ‘facts’, no verification of hypotheses by events, can possibly amount to proof. What he seeks to impress upon his pupils is that _verification is not proof and can never lead to it_.

He considers himself entitled to look down upon science accordingly, its evidence, its methods, and its reasonings, and to contrast them with the absoluteness of his own ideal of demonstration. He upholds its validity in spite of all the failures of the sciences to realize it. As a rule he seems willing to grant that some mathematical proofs amount to logical demonstration;[398] but if pressed he would confess that scientific truth was only probable, whereas certain metaphysical truths, such as the law of contradiction, alone were absolutely certain.

The scientist, of course, is not in a position to deny that the nature of his truth is such as has been stated: but he should not attempt to do so. He should content himself with scientific truth, and contend that at its best it is good enough for any one. And he can carry the war into Africa by a vigorous counter-attack.

(1) He can deny--for the reasons stated in § 13--that the logician’s formal ‘proof’ is as cogent and formally valid as the latter supposes, and show that after a conclusion has been ‘_proved_’ true, it has still to _come true_ before it can be trusted to be ‘true’.

(2) He can point out that there is a serious _lacuna_ in the logician’s plea for his notion of ‘proof’. The logician has assumed that the only alternative to his belief in absolutely certain premisses is complete scepticism, arguing that it must be possible to start from certainty, because otherwise no knowledge would be possible at all. He then urged ‘but there clearly _is_ knowledge--the sciences attest it’, and consistently inferred that absolutely certain premisses must be obtainable. The more or less obvious failure of his attempts to explain their genesis by ‘self-evidence’, ‘intuition’, ‘necessities of thought’, &c. (§ 15), could not deter him from clinging to his belief, because the principles themselves seemed to him to be inevitable and to admit of no alternative.

In fact, however, there _is_ a _via media_ between scepticism and absolutism, and science safely pursues it, though logic has overlooked it. It is _not_ necessary to start with absolutely certain premisses, because it is possible to adopt premisses hypothetically, to take them as true for the argument’s sake and for the purposes of the inquiry, to experiment with them, and to revise them in the light of the results of such experiments. Thus _their_ value may be judged and established, _after_ their adoption, by the experimental results, and they may come to depend logically upon these, and not upon the processes (analogies, suggestions, guesses, fancies, &c.) which led to their adoption. If they show themselves capable of advancing the science and solving its problems, confidence in their ‘truth’ increases progressively, and their initial assumption is justified. They _cease_ to be ‘hypotheses’ and become ‘facts’, and even ‘principles’ beyond dispute. If they fail to ‘work’, they may be discarded in favour of others which are tried in their turn and similarly tested. Hence it is not true that what is uncertain to begin with must always remain so, nor is it hard to understand that hypothesis, willingness to believe, and belief may be the psychological forerunners of logical proof, which, nevertheless, rests not upon them, but upon the solid value of the results subsequently reached by their means. The certainty of scientific premisses then admits of indefinite growth, which at some point or other will overpower even the most obstinately sceptical temper. This point naturally lies at a greater distance from the starting-point for some minds than for others, but when it is reached, and when the last doubts and scruples have been overcome, the triumphant truth will _feel_ absolutely certain, and to all intents and purposes will function as such. But the ‘practical certainty’ thus achieved will still be distinguishable in thought from the absolute certainty which logical theory mistakenly demanded. And logicians, from Plato downwards,[399] will be convicted of having failed to allow for the possibility that the certainty of premisses and principles may be a fruit of continuous experience and experiment, and to perceive that this is the method the sciences have actually employed. In short, necessary (needed) ‘truths’ need _not_ be regarded as ‘_a priori_’, if it is seen how hypotheses are consolidated by experience.

(3) The scientist can deny that the ideal case, contemplated with so much satisfaction by the logician, can ever occur in actual knowing. He can point out that if the logical apparatus of demonstration is to work, it must be supplied with premisses that are absolutely true. But whence is the logician to obtain them? The ‘self-evident’ principles and ‘necessary’ axioms, for which so much has been claimed, have been shown (§ 15) to be highly disputable, and are themselves in need of support and verification. The truths which the sciences supply abundantly are all products of the method to which he takes exception. There are no scientific truths which have not to be, and have not been, verified, and if verification is logically vicious, and cannot amount to proof, they are not absolutely true. But if the premisses of a demonstration are not absolutely true, neither can its conclusion be. What then becomes first of the value, and ultimately of the ‘validity’, of an ideal of proof which can never be exemplified by actual reasoning, and serves only to condemn it?

(4) The ideal of absolute certainty may be repudiated altogether, even as an ideal, for sound scientific reasons. It may be shown that if it were possible it would be scientifically undesirable. For it would mean the creation of absolute bars to scientific progress. If truths existed which were absolutely certain, this would mean that nothing more could be learnt about them, and nothing could be done to strengthen their position. No experience, no inquiry, no experiment, could any longer affect them, and add to or detract from their value. They could not, therefore, form avenues to further knowledge. They would simply be stops which would arrest scientific inquiry. But how could such things form an ideal of scientific knowledge? How could it be in the spirit, and to the interest, of science to recognize them? They would merely be for science brute facts which it was forbidden to investigate. And must not science on principle hold out for the right to inquire into everything, to test every belief, however true it may seem? How, then, can it be the ideal of science to adopt an ideal which would stop inquiry?

Nor will it suffice in reply to point to the fact that the sciences continually assume the truth of the premisses they argue from. For though this is often a convenient assumption for the purpose in hand, it is one thing to assume the truth of premisses for the purposes of an inquiry, and quite another to assume it absolutely. For in the former case our assumption may be, and should be, accompanied by a consciousness that upon another and fitting occasion the premisses now assumed to be true may themselves be inquired into: to regard them, therefore, as absolute is to misinterpret their logical condition.

There are no good reasons, then, why the sciences should surrender to the arbitrary demands of the traditional logic, and sacrifice their practices which have been sanctified by the successes of 2,000 years to theories which sprang from a misunderstanding of scientific procedure, and have since lost all contact with it. The original mistake was pardonable, but it ought not to be regarded as an insult to logic to require it to understand the procedure by which the sciences actually progress.

§ 29. The scientist then should not be terrified by the charge that his ‘truths’ are ‘only probable’. For it is better to be satisfied with probabilities than to demand impossibilities and starve. Moreover, a high degree of probability means ‘practical certainty’, i.e. confidence enough to move to action. Such certainty so convinces and satisfies the mind that it cannot feel more certain about anything; the logical gap between it and absolute certainty is psychologically negligible. We are sacrificing, therefore, nothing but a superstition, nothing that has any value for us, by renouncing the demand for absolute truth and demonstrative ‘proof’, and we gain in return a charter of liberty. For to admit the essential progressiveness of scientific truth and its indefinite capacity for improvement means unlimited freedom to research into truths which are infinitely perfectible, because they are never ‘absolute’. The ideal of the infinite perfectibility of truth, and the infinite progressiveness of science, is more than an adequate substitute for the ‘logical ideal’ which is abandoned. For not only is it an ideal which works, but it really embodies a nobler aspiration than that which represented science as ‘resting’ in absolute perfection on fixed ‘foundations’ of ‘eternal’ truth. The sentiment which inspires this group of metaphors is given away by the word ‘rest’. A science that desires to _rest_ is one that is unwilling to _move_ and unable to _advance_. Fixed ‘foundations’ are needed only for standing firm and standing still, and it turns out that what is strictly meant by ‘eternal’ is not that truths last for ever, but that they are not related to ‘time’ at all, and so have really no application to ‘events’.[400]

On the other hand, a science which sincerely desires to progress needs fixed foundations as little as fixed ideas, and firm ground as little as assurances to ‘rest’ on. It needs only a starting-point, or jumping-off place, whence it can plunge into the unharvested seas of the unknown. Now the essence of a starting-point is to be a place you want to get away from, and its excellence lies in being such as to prompt you to leave it as easily and eagerly as possible. If, therefore, scientific ‘principles’ (ἀρχαί) are really to be starting-points, they need not, and must not, be so comfortable and so deceptively similar to ‘absolute’ truths as to tempt the scientific spirit to repose. They should be tentative assumptions which are gladly abandoned in the hope of reaching something better, stepping-stones to farther and higher things, which are valued for their consequences, and logically dependent on the conclusions to which they formed the premisses. The logic of science, therefore, has no reason to postulate stability or solidity for its initial principles: the most indispensable of them are only principles of method, and even of the tried and tested principles it arrives at the ‘validity’ (= strength) demanded is merely that they should be able to float the accumulated wealth of knowledge down the stream of time.

IV

§ 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).