Part 49

In the first place, it must be made clear that it is not a logical implication of the test that ‘whatever works is true’, and the reasons for disputing this dictum must be set forth. The fact is that we all have a strong psychological tendency to believe in the truth of what is found to work, without much criticism of the sort and extent of the ‘working’. But the logician should carefully investigate the various sorts of working that occur, and take special note of those which either do not themselves lay claim to full truth, or do not (ordinarily) have their claim conceded.

For example, ‘fictions’ are not supposed to be strictly true; but they may ‘work’ and be ‘as good as true’, or ‘pragmatically true’, or ‘sufficiently true for the purpose in hand’. They work, in fact, within limits; but these limits are known, and so they are not confused with full-fledged truths, to the applicability of which there are no known limits.

The case of ‘methodological assumptions’ is more difficult and instructive, and is usually misconceived. In their case the existence of limits to their ‘working’ is either not known or not relevant, because they owe their adoption to their use and convenience in analysing and organizing a subject of inquiry. Thus the principle of Causation, the assumption that every event has a cause which determines it fully, is properly to be regarded as methodological. It declares merely that if we desire to calculate the course of events, it is scientifically convenient to treat events as if they had ‘causes’, from which their occurrence could be predicted, whether or not they have them in fact. This assumption may be purely methodological; it need not, and should not, be turned into a dogmatic, metaphysical denial that there may be indeterminate happenings. There may even be good reasons to suspect their occurrence, and indeterminism may be ultimately true, and yet scientific method may rightly ignore this possibility, because it would render the calculation of events impossible. Even an indeterminist then is fully entitled to reason as if events were determined, and to search for ‘causes’, for the purely methodological reason that this enables him to calculate events, and that after all they may be calculable. So long as they work for scientific purposes it is not, in the case of methodological principles, necessary to raise the question of their metaphysical truth.

The ‘lie’ again is a curious case of ‘working’. A lie, works, as a rule, only so long as it passes for truth, and is believed to have the meaning and value its author claims for it; when it is ‘found out’, it ceases to work. Hence it can both work and fail to work at the same time, according as it is, or is not, known to be a ‘lie’. Clearly nothing can be made of the lie logically, until this double aspect inherent in its nature is recognized; if the logician refuses to distinguish between the persons concerned in its making, acceptance, and rejection, it remains (like ‘error’ to Plato) an insoluble ‘contradiction’. It is, however, a mere prejudice to refuse to make these distinctions.

The ‘working’ of hypotheses is by no means simple and unambiguous. It admits of infinite gradations in amount and kind, and the ‘truth’ which is implicated in ‘working’ is nothing essentially but an index of its logical value, and may vary in quantity between values which cannot be psychologically discriminated from zero and from 100% or 1 (= ‘absolute’ certainty). It is crude, therefore, to confront a scientific hypothesis with the rigid alternative ‘either (absolutely) true, or (utterly) false’; its ‘truth’ really rests on its greater value, as compared with its competitors. Its value, then, is a question of more or less. The more extensively, conveniently, and economically a hypothesis works, the more value has it, i.e. the more likely is it to be called ‘true’, and to be supposed true absolutely: the more continuously and successfully the test of working has been applied to a doctrine, the greater the confidence and affection with which it is regarded, and the greater the presumption that it will continue to approve itself as true.

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; 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, 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’.

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.

§ 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, 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.