A.— MATHEMATICAL AND PHYSICAL SCIENCES 25 



the point of my mentioning it is that I found I did not care much whether 

 it was right or wrong, because the quantum theory must be right anyhow. 

 The cumulative weight is so overwhelming that it is not conceivable 

 that anyone could upset it in a single column oi Nature. A little doctoring 

 of the axioms would certainly put the matter right again, and hardly anyone 

 would be any the better. We have then to believe that axioms are not 

 important things, but that it is the whole body of accumulated doctrine 

 that matters. 



Take it from a different angle. The ' logic ' school of thought has in 

 its repertory the idea of a ' crucial experiment,' that is the single experi- 

 ment which gives the answer yes or no to a whole theory. I suppose the 

 most striking crucial experiment ever done was the Michelson-Morley 

 experiment on aether drift, which was made the basis of the whole 

 gigantic theory of relativity. Michelson and Morley showed that to the 

 order of the square of the earth's velocity there was no aether drift, 

 and they showed it to the limits of the precision of their apparatus. For 

 some twenty years the theory of relativity grew enormously, based on this 

 one experiment, and then it was felt that it would be proper for some 

 one else to repeat the work, and Dr. Dayton Miller undertook the 

 task. We cannot see any reason to think that his work should be inferior 

 to Michelson's, as he had at his disposal not only all the experience of 

 Michelson's work, but also the very great technical improvements of the 

 intervening period, but in fact he failed to verify the exact vanishing of 

 the aether drift. What happened } Nobody doubted relativity. There 

 must therefore be some unknown source of error which had upset Miller's 

 work. But as Miller was improving on Michelson, this contains the 

 implication that Michelson's work must have had two unknown sources 

 of error which happened to cancel one another. What has become of 

 the crucial experiment ? We do not believe in relativity because of the 

 Michelson-Morley experiment ; it is one, and an important one, of a 

 number of cumulative pieces of evidence which all fit together, and it 

 is this cumulation and not any one of its pieces that makes us believe in 

 relativity. 



From examples like these we conclude that an axiomatic basis, of the 

 kind demanded for the operations of formal logic, is too narrow for the 

 understanding of the physical world. Something wider is needed. 

 Now for more than a century there has been growing up the recognition 

 that probability plays a part in much reasoning, and that there must 

 exist a wider system of logic which has probability as one of its features. 

 Attempts have been made, and are still being made, to bring probability 

 back into the narrow fold of the old logic. It appears to me that these 

 attempts are hopeless, but before approaching the question directly I 

 want to develop an analogy which seems to me important. Like every- 

 one else I feel the compelling power of the old logic, and I cannot feel 

 how when we try to go beyond it we can get the same compulsive force. 

 But on the other hand I know of a case where our thoughts are driven 

 in one direction by a force which seems to have the same psychological 

 compulsion as does formal logic, and yet where the result is undoubtedly 

 wrong. 



To anyone who has thought at all seriously about the world, or at any 



