Part 48

Yet his condition will not contravene Aristotle’s dictum that all inquiry and research proceed from knowledge previously acquired. In a sense he will still start from what he knows, or thinks he knows. For it is psychologically impossible to do anything else. The knowledge he believes himself to have cannot but affect all his ideas, and he cannot get away from it. His boldest speculations, his most hazardous hypotheses, will have some relation, however subtle and recondite, to the knowledge at his disposal. It will influence all his thoughts and guide his guesses. As he cannot divest himself of his knowledge and the ideas it has rendered familiar to him, he has to accept its limitations. His only problem is to use it as effectively as possible.

But it is clear that he cannot regard his knowledge with the same sort and amount of confidence as the believer in demonstrative proof. He must conceive himself as an explorer, and his attitude must be tentative throughout. Knowing that his premisses are questionable and only doubtfully true, he will recognize that his inferences are only probable, and stand in need of confirmation. As a rule he can, no doubt, find accepted truths to argue from; but these being relative to the existing state of knowledge are known to be subject to correction. Even where he has started with premisses of the most superior kind, which are generally deemed absolutely self-evident and certain in themselves, he will still be conscious of a doubt whether they will prove to be the right premisses for his purpose. If they are not, their truth is irrelevant and will lead him astray. In no case, therefore, can he escape the responsibility of choosing the right ones from his limited stock of known truths and familiar ideas, as he contemplates the infinite expanse of possible discovery. In whatever direction he moves, the unknown lies before him; he may come upon surprises or be stopped by unsuspected obstacles. In short, there is nothing of the irresistible about his progress; it has not the faintest resemblance to the majestic march from inevitable premisses to a predestined conclusion which so fascinates us in the theory of proof.

§ 21. But, it may be said, all this is not enough. The differences in the attitudes assumed by the reasoner in discovery and in proof may be only psychological. They do not prove any real logical difference between them; the logician’s account may still be what the discoverer would acknowledge to have been his best course, if he could have seen it. It has, therefore, to be shown that the differences in question arise out of, and develop into, differences which are indisputably logical.

Thus, the ignorance which the inquirer feels is doubtless a psychological fact, but the lack of knowledge which engenders it is surely a logical fact of some importance. In general, the feelings of doubt, expectancy, and perplexity which beset the mind of the inquirer, and contrast so distinctly with the feelings of confidence, knowledge, certainty, and necessity which accompany a ‘proof’, originate in a logical fact. Every inquiry starts from a problem, of which the solution is not yet known. An inquiry is, as the name implies, a question, put, not to nature at large and at random, but to some part of it, which is taken to be relevant and to contain a possible answer to the inquirer’s question. Now this dependence of inquiry upon problems springs no doubt from the psychological fact that until there is something put before it the mind cannot get to work upon it; but it is surely a fact of the utmost logical significance, and it is astounding that the logical tradition should have slurred it over so completely.

Especially as in the very beginnings of logic some of the Greeks distinctly caught a glimpse of it. For, having started their reflection upon reasoning from a desire to regulate debate and to argue a case at law, they naturally noticed that there are two sides (at least) to every question. Accordingly, Protagoras appears to have taught systematically that there were always two reasonings (λόγοι) to be considered, Socrates, treated scientific inquiry as an extension of the art of cross-examination, and Plato conceived the search for ideal truth as a ‘dialectical’ process, as a sort of dialogue of the soul with itself. Now this whole doctrine is equally good as logic and as psychology. It is profoundly true of the inquirer’s mind; he must be keenly alive, not only to the evidence for, but also to that against his working theory. But it is also true of the logical nature of inquiry that it is a process of determining which of the alleged ‘facts’ and of the theories to interpret them are real and true. Inquiry logically ‘presupposes’ a conflict between the data, and a dispute about them.

Unfortunately, however, the conception of scientific research as an inquiry lapses from the logical consciousness in consequence of Aristotle’s work. His discovery of the forms and formulas of demonstration overshadowed it, and restored the reign of dogma which is so congenial to the authorities everywhere. The true conception of inquiry does not revive again until our days, when Mr. Alfred Sidgwick and Professor John Dewey have endeavoured, not with the success they deserved, to reopen the eyes of logicians to the facts of the scientific situation.

§ 22. To conceive an inquiry as a question then is, we see, implicitly to conceive it as having a plurality of answers, all of which have to be examined. All these answers are initially hypotheses, and a choice has to be made between them. This renders the recognition of alternatives a paramount necessity for a logic of discovery, which can no longer dismiss them with a jejune chapter on ‘disjunctive propositions’. Their existence is no longer to be treated as an annoying complication which delays the progress of science, but must be taken to inhere in the logical nature of problems, and to be essential to their proper elucidation.

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.