OOH TKANSACTIOxVS OF SECTION A. 



both science and metaphysics staii from the same given groundwork of 

 immediate experience, and in the main proceed in opposite directions on their 

 diverse tasks. 



For example, metaphj'sics inquires how our peiceptions of the chair relate us 

 to some ti'ue reality. Science gathers up these perceptions into a determinate 

 class, adds to them ideal perceptions of analogous sort, which under assign- 

 able circumstances would be obtained, and this single concept of that set of 

 perceptions is all that science needs ; unless indeed you prefer that thought find 

 its origin in some legend of those great twin brethren, the Cock and Bull. 



My immediate jsroblem is to inquire into the nature of the texture of science. 

 Science is essentially logical. The nexus between its concepts is a logical 

 nexus, and the grounds for its detailed assertions are logical grounds. King 

 James said, 'No bishops, no king.' With greater confidence we can say, 'No 

 logic, no science.' The reason for the instinctive dislike which most men of 

 science feel towards the recognition of this truth is, I think, the barren faihire 

 of logical theory during the past three or four centuries. We may trace this 

 failure back to the worship of authority which in some respects increased in the 

 learned world at the time of the Renaissance. Mankind then changed its 

 authority, and this fact temporally acted as an emancipation. But the main 

 fact, and we can find complaints ' of it at the very commencement of the 

 modern movement, was the establishment of a reverential attitude towards any 

 statement made by a classical author. Scholars became commentators on truths 

 too fragile to bear translation. A science which hesitates to forget its founders 

 is lost. To this liesitation I ascribe the barrenness of logic. Another reasoH 

 for distrust of logical theory and of mathematics is the belief that deductive 

 reasoning can give you nothing new. Your conclusions are contained in your 

 premises, which by hypothesis are known to you. 



In the first place this last condemnation of logic neglecte the fragmentary, 

 disconnected character of human knowledge. To know one premise on Monday, 

 and another premise on Tuesday, is useless to j'ou on Wednesday. Science is a 

 permanent record of premises, deductions, and conclusions, verified all along 

 the ILne by its correspondence with facts. Secondly, it is untrue that when 

 we know the premises we also know the conclusions. In arithmetic, for 

 example, mankind are not calculating boys. Any theory which prove.s that they 

 are conversant with the consequences of their assumptions must be wrong. We 

 can imagine beings who possess such insight. But we are not such creatures. 

 Both these answers are, I think, true and relevant. But they are not satisfac- 

 tory. They are too much in the nature of bludgeons, too external. We want 

 something more explanatory of the very real difficulty which the question sug- 

 gests. In fact, the true answer is embedded in the discussion of our main 

 problem of the relation of logic to natural science. 



It will be necessary to sketch in broad outline some relevant features of 

 modern logic. In doing so 1 shall try to avoid the profound general discus- 

 sions and the minute technical classifications which occupy the main part of 

 traditional logic. It is characteristic of a science in its earlier stages — and 

 logic has become fossilised in such a stage — to be both ambitiously profound in 

 its aims and trivial in its handling of details. We can discern four depart- 

 ments of logical theory. By an analogy which is not so very remote I will call 

 the.se departments or sections the arithmetic section, the algebraic section, the 

 section of general-function theory, the analytic section. I do not mean that 

 arithmetic arises in the first section, algebra in the second section, and so on; 

 but the names are suggestive of certain qualities of thought in each section 

 which are reminiscent of analogous qualities in arithmetic, in algebra, in the 

 general theory of a mathematical function, and in the analysis of the properties 

 of particular functions. 



The first section — n,\mely, the arithmetic stage — deals with the relations of 

 definite propositions to each other, just as arithmetic deals with definite 

 numbers. Consider any definite proposition; call it ' ^J.' We conceive that there 

 is always anotlicr proposition which is the direct contradictory to ' p' ; call it 

 'not-p.' When we have got two propositions, /j and q, we can form derivative 



' r.f/.. In 1551 by Italian sclioolmcn. 



