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. I § 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.