A.— MATHEMATICAL AND PHYSICAL SCIENCES 23 



would have been possible for me to choose a narrower subject, but I 

 could not feel that this would have possessed the general interest that 

 such an occasion demands, and so with some trepidation I am venturing 

 on an even wider theme and am going to touch on the philosophy of our 

 subject. This is a dangerous thing to do for one who has never made 

 more than the most superficial study of pure philosophy, but still I do 

 not apologise for it, because it appears to me that recent scientific history 

 has revealed a deep schism between the professional philosophers and 

 the scientists, and this schism is worthy of examination. 



General philosophy claims to be the critical subject which lays down 

 for all of us what we may be allowed to think, and yet it has played no 

 part whatever in the great revolutions of human thought of the present 

 century — those connected with relativity and the quantum theory. It 

 might have been expected that the scientists would have been constantly 

 consulting the philosophers as to the legitirnacy of their various specula- 

 tions, but nothing of the kind has happened. Since no one can dispense 

 with some sort of metaphysic, each scientist has made one for himself, 

 and no doubt they contain many crudities, but it would seem that a deep 

 interest in metaphysic is a disadvantage rather than an advantage to the 

 physicist — at least I have the impression that those of my friends who 

 are most inclined to speculate on the ultimate things appear to be the ones 

 whose scientific work is most hampered by doing so. Now I propose 

 to risk a similar indiscretion. I want to embody in it the practical 

 philosophy of a physicist, and I do not mean it as an attack on the pure 

 philosophers, who are very reasonable people, only chargeable with the 

 minor offence of not having made me want to read their books 1 



I had better begin by stating shortly the ideas I intend to discuss. 

 There is a notable contrast between the way we think about things and 

 the way we think we ought to think about them. We have set up as an 

 ideal form of reasoning the formal logic which has held the field since 

 the days of Aristotle. We rarely conform to this ideal, but instead we 

 usually make use of arguments having no accurate axiomatic basis, 

 which compel belief because of some large accumulation of favourable 

 evidence. I intend to develop the idea that the old logic was devised 

 for a world that was thought to have hard outlines, and that, now that 

 the new mechanics has shown that the outlines are not hard, the method 

 of reasoning must be changed. The key to the modification has already 

 long been in our hands in the principle of probability, but whereas in 

 the past constant attempts were made to fit this into the old system, 

 the new mechanics suggests the possibility of a different synthesis. 

 Though I hope this subject will be found interesting in itself, I would 

 not have ventured to bring it forward if 1 had not also a very practical 

 purpose in doing so, and that is to urge that our mathematical education 

 both at school and university has been gravely deficient in that it has 

 put all the emphasis on matters susceptible of rigorous proof, while it 

 has very completely neglected the equally important subjects of statistics 

 and probability. I shall enter into these matters at the end of my 

 address. 



I have said that there is a contrast between the way we all think about 

 things and the way we think we ought to think about them. This is 



