Is it not wiser, then, to admit that life has its claims upon science, and science upon logic? We simply _must_ have a science that can handle human life and meet human needs, and does not degenerate into a game with arbitrary and fantastic rules which depart from the actual conditions of life in any direction and to any distance unrestrained imagination carries them; and our logic must deign to study such a science. If to do so it has to ‘scrap’ its antique ‘ideals’, to abandon its pose of an inhuman, impassible, infallible aloofness, and to interest itself in the doubting, questioning, guessing, trying, risking, blundering, correcting, achieving that make up the sum of human knowledge, it will receive an ample reward in the gratitude of man for a logic that has entered his service, and in the salutary influence which it will exercise upon his actions. _Conclusions_ (1) We have shown, negatively, that the notion of a form of proof, by which conclusions can be absolutely demonstrated by dint of pure logic alone, is a delusion. No such form can be constructed (§§ 13, 15), and if it could, it could neither find scientific material worthy of it (§ 28), nor contain the material which is fabricated by the sciences. (2) We have thereby shown that formal logic cannot represent the logical nature of discovery or of any of the processes of actual knowing, and must condemn them all as ‘invalid’ (§§ 18, 20, 26, 28). (3) We have seen that a logic which attempts to understand actual knowing cannot prescribe to the sciences how they are to solve their problems (§ 33). (4) But it _can_ grasp the general character of scientific procedure, appreciate its difficulties and dangers, understand the expedients for meeting them, and trace it to its roots in the constitution of the human mind and in the needs of life (§ 35). (5) In virtue of its general grasp of the aim and method of the sciences a logic of science can at times offer advice to scientists: it may draw their attention to the general problems which their work involves, but which are apt to be overlooked by specialists, such as the claims of consistency and novelty and the regulation of risks (§ 36). Or, better still, if they will study it themselves, it may broaden their minds and enable them to handle these general problems for themselves far more effectively than a pure logician could do it for them. (6) By abandoning its pretensions to rigour and conclusiveness logic does not really lose: it gains immensely by coming into contact with science and life, and becoming of use in the world. INDEX Abano: _see_ Peter of Abano. Abercrombie, John, _Inquiries concerning the Intellectual Powers_, 249 _n._ Abi ‘Uṣaibia, Ibn, 227 and _n._ 4, 228 _n._ 5, 229. Abu’l Faraj Gregory, cited, 228 _n._ 3. Achillini, Alessandro, 95, 98, 105; _Annotationes anatomiae_, 95 _n._ 4.