Part 27

Logic, therefore, should regard it as its duty to inquire (1) how the inquirer is furnished with an adequate supply of theories for analysing and testing the apparent facts of his subject, (2) what methods are used to sift hypotheses and to select the more valuable, and (3) if it can, to add some hints as to how theories and methods _ought_ to be handled.

(1) To the first question there is no exhaustive answer. No logic can guarantee that _all_ the possible theories which concern the facts under inquiry will be available. They may not yet have occurred to any human mind, and may never do so. This alone ought to be considered a fatal objection to all methods which presuppose exhaustiveness, and are pressed by the logician upon the man of science. It ought to dispose of methods which demand that _all_ the facts should be assembled before theorizing is begun, or that _all_ the alternatives should be stated and the true one extracted by the successive elimination of the false ones, or that define a ‘cause’ as reciprocating with its ‘effect’, and assume that the true cause has been discovered when no other has been thought of, or that if a theory works we may take it that it alone will do so and is (absolutely) true. All these notions demand an impossible exhaustion of the alternatives, and try to convert a (psychological) failure to think of any more into a logical proof that there are no more. And they all regard the plurality of alternatives as a hindrance to be got rid of, and not as a safeguard and a help to proper inquiry.

Hence the real difficulty was not perceived, viz. that there is no formal guarantee that the supply of hypotheses for use upon the facts in any inquiry will be adequate. It may well be that for lack of a good working theory to go upon, all the theorizing on a subject proves vain and sterile. In the beginnings of all the sciences this sort of condition always exists and often lasts for centuries, and it is a main reason why some sciences make little progress even now.

Nevertheless, the difficulty is not in practice as fatal as it looks on paper. It is probable that the inquirer will in fact usually have a supply of alternatives to start from. For (_a_) he will naturally select a subject in which there are disputed points. And (_b_), what is even more important, human minds are naturally various: they put, therefore, different interpretations on the same facts and value them differently. Some are attracted by novelty, others by orthodoxy; some incline to one type of theory and method of inquiry, others to another. Hence in any inquiry upon which a number of minds are actively engaged, there will always be differences of opinion, and these will be most marked in the rapidly growing regions of every progressive science, which, like the growing cells in the trunk of a tree, are always on the outskirts. There will always be a conservative and a liberal party, even in science, and the clash between their views will always provide alternative solutions of problems, the comparative merits of which the inquirer can examine. But the sciences owe their progress largely to the man who raises new questions, and should provide for him in their organization.

§ 23. It should be noted further that if this feature in discovery were properly recognized and emphasized, it would have important educational and ethical effects. At present the study of logic can hardly be said to liberalize and broaden the mind or to improve the temper. So long as its chief interest is in a theory of absolute proof and complete certainty, it will tend to breed pedants and bigots. The effect would be very different if an adequate logic of discovery had imbued the mind with an ever-present thought that every subject may and must be considered from several points of view, and that an inquirer should beware of letting his predilections and preconceptions blind him to possible alternatives. The logical attitude of inquiry, when fully understood, demands a tolerant and open mind, and excludes the narrow-mindedness and dogmatism which the theory of proof has fostered by its pretence of showing that there was but one truth and one inevitable way of reaching it. Moreover, the necessity of continually choosing between a number of alternatives should cultivate a judicial temper, conducing to fair-mindedness and consideration towards the views of others. For a mind which is in the habit of choosing between alternatives must be impressed by the facts that there is something to be said for the views it does not accept, that the view accepted is often not so very much superior to those rejected, and that new facts and new knowledge may always revive views which were supposed to be defunct.

Of course our natural dogmatism will take alarm at the flabby toleration of ideas which this attitude seems to imply. It will be objected that no one who can see the good and truth in beliefs he does not accept, can really be strenuous in upholding those he does. The full answer to this bigots’ argument can only be appreciated when the attitude of progressive science is fully understood (cf. § 33), but in general it may be pointed out that a power of first weighing alternatives, choosing the best and acting upon it strenuously, is precisely what life demands of us at every step. It should not, therefore, be impossible to compass it in science.

§ 24. (2) To the second question of § 22, viz. what are the methods used by the inquirer in sifting the alternative hypotheses in the field, and picking out the most valuable, the answer is comparatively easy. It is substantially the answer given by the pragmatist analysis of knowledge. That theory is preferred, and tends to be accepted as true, which for the time being _works_ best. The formula looks simple, but needs more thinking out than its critics usually bestow upon it.

(_a_) It implies, of course, that _all_ the alternatives (before the mind) ‘work’ more or less. They must be (or appear) scientifically plausible, and proffer a more or less satisfactory explanation of some or all of the admitted ‘facts’. This is why agencies like the Devil, who could once be extensively alleged to explain anything unusual, have dropped out of the purview of science.

(_b_) ‘Working’ must be conceived somewhat widely. Its _primary_ appeal is to the accepted principles and recognized interests of the science; practically to ‘work’ means to conduce to the development of the science on the recognized lines, and the proper judges of what ‘working’ counts are the experts who cultivate each science.

(_c_) But there will often be complications due to certain disputable workings, of which the relevance is not yet established, and about these there will legitimately be differences of opinion. These should not be suppressed, but candidly argued out.

(_d_) Moreover, every _new_ departure will be _pro tanto_ disputable, because it will conflict more or less with the vested interests of the established doctrines. One great factor in the ‘working’ of a new truth is the extent to which it upsets, or is thought to upset, the old, and demands a reconstruction of beliefs, a correction of authorities, a revision of text-books, a renewal of plant, &c. Hence what works best in the abstract may not do so under the actual conditions. It may ‘pay’ a professor better to be ‘orthodox’ than to be an innovator, and he is usually quite alive to this, though it does not render him a good investment scientifically for the institution that appoints him. If then we looked at this side of the matter alone, the verdict would always go against the novelty. For very few new truths are fortunate enough to find the field free and unoccupied. Usually they have to spring up in a soil densely overgrown with a rank growth of prejudices, dogmas, and superstitions, to which the world is accustomed and even devoted. So they have to fight for an opening in which they can take root and grow up.

(_e_) The ‘working’, however, need not amount to a claim to represent ‘the’ truth. A discoverer may know that by reason of his deliberate use of fictions, his results have forfeited their claims to be strictly true; yet they may ‘work’ better than anything else in sight. The typical example here is, of course, mathematics. When physical objects are treated mathematically, they are identified by a fiction with the objects of pure mathematics, and it is only on this assumption that their behaviour can be calculated. They are, of course, vastly _more_ than mathematical objects, but their surplus meaning becomes irrelevant wherever objects admit of mathematical treatment. And apart from the restriction of the claim to truth necessitated by the use of fictions, it should, of course, be recognized also that there are sound logical reasons for denying that truths which rest on their ‘workings’ can ever be ‘absolute’ (§ 26 _s.f._). Their truth is pragmatic, and is _optimi iuris_ only if pragmatism establishes that no other and no better truth exists.

(_f_) More specifically a very important form of working is the prediction of events. Knowledge of the future is an almost universal object of human desire, which men have sought to compass by fair means and foul, and the calculation of the future is the avowed aim of many scientific inquiries. Hence there is nothing more potent to dispose the mind to accept a theory than the success of the predictions it has led to. Yet here again this form of ‘working’ differs generically from ‘proof’. It is clear that prediction is not strictly proof. For predictions may be made with considerable accuracy by the aid of hypotheses which turn out to be false or impossible. Thus eclipses and other celestial events were predicted for centuries by means of the Ptolemaic astronomy, and they cannot be predicted even now with absolute accuracy. Indeed, physically speaking, absolute accuracy is unthinkable. No instrument and no organ of observation can be conceived to measure to more than a finite degree of accuracy, and the _best value_ for any physical ‘fact’ will always be the mean of a number of good observations after all the accessible sources of error have been allowed for.

At no point, then, does the test of ‘working’ conduct to the notion that absolute truth is discoverable. But the right inference may be, not that the test is worthless, but that absolute truth is a chimera.

§ 25. (3) It cannot then be seriously disputed either that alternative hypotheses are always (more or less consciously) present to the mind of the inquirer, or that the working of a theory is in fact used, in all the sciences, to test its claim to be true. But does it follow that logic should bow to scientific fact and recognize these practices? Should it set itself to devise a _technique_ for regulating the formation of hypotheses and the establishment of their truth by their working? It is here that the traditional logic demurs, and disputes begin. Nevertheless, strong reasons may be advanced for answering both questions in the affirmative.

(_a_) An abundance of hypotheses is a guarantee of great logical value that all the important facts will be properly observed. For it is evident that every theory will produce a certain _bias_ in the observer. It will direct his attention upon those facts and those features which are _relevant_ to his theory, and, more particularly, which _support_ it. This is usually an advantage, because it helps him to select what is relevant to his inquiry from the chaos of events; but it will _pari passu_ blind him to whatever does not seem to be related to, and to fit into, his theory. He will, therefore, fail to observe and to appreciate what will seem to him to have little or no scientific interest. And in so thinking he may be quite wrong.

The old theory of ‘induction,’ thought to get over this difficulty by saying, ‘Well, of course, _all_ the facts must be observed’. It did not observe the fact that in practice this is impossible, and is never done. Nothing is observed but what the knowledge and preconceptions of the time make visible to the scientific eye. Of what is visible at any time only a small part seems worthy of the scientific microscope. Complete observation, therefore, of literally all the facts is scientifically impracticable.

As a logical ideal also this notion of all-inclusiveness is absurd. If no inquiry could ever begin until _all_ the facts had been assembled, how could anything be discovered until omniscience had been achieved, i.e. when there was nothing left to discover? For how are we to know that our assembly of ‘facts’ really is complete? And if literally all the facts have to be used as data in any inquiry, shall we not speedily find that every fact ramifies into infinity, and drags in the totality of reality, and a knowledge of all things present, past, and future? This ‘logical ideal’, therefore, renders inquiry impossible.

In point of fact the data of any inquiry are always a _selection_. They are such of the recognized facts as are thought to be _relevant_, i.e. to be truly ‘facts’ for the purpose in hand. But being a selection they involve us in the risk that we may have selected wrongly, and omitted what is important while admitting what is not. _From this risk there is no escape._ For we cannot effect a compromise by including merely so much of the facts as we can lay hold of. Not only does this yield no guarantee that everything that is needed has been included, but it may be a positive hindrance to try to include too much. For if our data grow into an unwieldy mass, they will not seem susceptible of any order or principle, and even the most penetrating inquirer will lose his way.

It is better, therefore, to give up altogether the idea of securing formal validity by postulating an all-inclusive exhaustiveness. The obvious alternative is to operate simultaneously with a plurality of theories, each of which means a certain ordering of the ‘facts’ relatively to what seems a relevant and promising point of view. Each will involve a selection and induce a bias; but with any luck they will neutralize each other’s bias, and so will increase the probability that no really relevant fact has escaped notice. This will not satisfy the logical ‘ideal’, but in practice it means a good deal, and is enough for scientific progress. Of course it must be understood that the hypotheses employed are in a general way relevant to the problems and the condition of the sciences, and not random guesses. This proviso will cut down their exuberance even more than the limitations of the human imagination, which seems to be psychologically incapable of really departing very far from the suggestions of experience.

§ 26. When logic has recognized the use and value of ‘working’ as the test of truth, it must, however, make it clear to itself and to others both what precisely this test is, and what it can, and cannot, accomplish.

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.[397] 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;[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.