The precise value of the service which a correct logical analysis of its procedure might have rendered to Science is perhaps open to dispute, though it must surely be beneficial to operate consciously, and with a full understanding of their nature, the methods which have been hit upon empirically; but even if logicians have commonly been too unfamiliar with the details of scientific problems to offer much practical advice, it would be difficult to overrate the mischiefs which must have resulted from referring scientists to an incorrect analysis of their actual procedures. For the attempt to justify by such a false ideal what they had actually done was bound to divert their attention from the methods that were actually effective and fruitful to others which were impracticable and sterile, to waste energy upon false aims and impossible ideals, and so to hamper scientists fatally in the exercise of their scientific rights and powers.
Hence it is not too much to say that the more deference men of science have paid to Logic, the worse it has been for the scientific value of their reasoning, while the less they have troubled to know about the theory of Science, the better it has been for their practice.
Fortunately for the world, however, the great men of science have usually been kept in salutary ignorance of the logical tradition and left to their own devices, by the accident that the historical organization of academic studies nearly everywhere confined ‘logic’ to the literary curriculum. Nevertheless, the moral of this situation is not that it is right for science to neglect logic and for logic to despise science, but that science should appeal from logic as it is to logic as it ought to be, and should insist on being provided with a reformed logic. For surely if a scientific education is to be more than a narrow and technical specialty, and is to exert a ‘liberalizing’ and broadening effect on the mind, it ought to include a study of scientific method in its generality and a certain understanding of the intellectual instruments by which all others are operated and constructed.
The whole evidence for these contentions it will not, of course, be possible to marshal within the limits of this essay, but the systematic criticism to which the whole traditional logic has been subjected in my Formal Logic[381] may perhaps absolve me from the duty of substantiating them exhaustively. It may suffice to indicate the extent of the scientific grievance against ‘logic’ by drawing up a list of problems in the logic of science which the traditional logic has misconceived, and then to select for fuller treatment a palmary example of the radical discrepancy between the two.
The traditional logic may be convicted of having gravely misrepresented, (1) the value of classification and the formation of classes, scientific processes of which the real logic was only revealed by the Darwinian theory, (2) the function of definition, (3) the importance of analogy, (4) of hypothesis and (5) of fictions, (6) the incomplete dependence of scientific results on the ‘principles’ by which they are (apparently) obtained, (7) the formation of scientific ‘law’ and its relation to its ‘cases’, (8) the nature of causal analysis. Other important features of scientific procedure cannot be said to have been recognized at all, e.g. (9) the problem of determining what is relevant to an inquiry and what practically must be, and safely may be, excluded, (10) the methods and justification of selection, (11) the essentially experimental nature of all thought and consequent inevitableness of risk, (12) the necessity of so conceiving ‘truth’ and ‘error’ that it is possible to discriminate between them, and (13) the need for an inquiry into meaning and into the conditions of its communication.
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§ 2. The most instructive, however, of the discrepancies between ‘logic’ and scientific procedure will appear if we compare the logical notion of proof with the scientific process of discovery, and examine how far it can afford any means of regulating, stimulating, or even apprehending the latter. We shall find that the logical theory of ‘proof’ has no bearing on the scientific process of discovery, is not related to what the sciences call proof, and can only have a paralysing influence on any scientific activities which try to model themselves upon it. On the other hand, the study of the process of discovery will point to an important correction in the notion of logic.
§ 3. The scientific uselessness of the traditional logic should not, however, excite surprise. For what reason was there to expect that the theory of proof should turn out to be adequate, or even relevant, to scientific procedure? It had sprung from a totally different interest, proceeded on different assumptions, and aimed at different ends. It did not spring from interest in the exploration of nature, and did not aim at its prediction and control. Nor did it presuppose an incomplete system of knowledge which it was desired to extend and improve. It originated in a very special context, from the social need of regulating the practice of dialectical debate in the Greek schools, assemblies, and law-courts. It was necessary to draw up rules for determining which side had won, and which of the points that had been scored were good.
These were the aims Greek logic set itself, and successfully achieved. But the impress of this origin remains stamped all over it, and the accounts given of logical proof ever since have retained essential features of Greek dialectics.