Fundamental Principles of Scientific Inquiry. 389 



to have extremely small prior probabilities, which will render 

 tremendous the amount of verification necessary to give 

 them any weight. This was, for instance, the case with 

 regard to the suggestion that the excess motion of the 

 perihelion of Mercury could be explained if the attraction 

 of the Sim varied inversely as the 2*000000016 power of the 

 distance instead of as the square. The exiguous prior 

 probability of such a law appears to us to make it quite 

 implausible, apart from the empirical results which led 

 to its abandonment. 



Summary. 



It is shown that intensive theories of the structure of 

 Nature which involve the use of infinite classes of entities 

 of: kinds known only by observation are not capable of 

 yielding satisfactory accounts of the method by which 

 we have acquired our knowledge of physics, and that the 

 same applies to the theory of universal consent as a basis 

 of scientific knowledge. The whole of a single persor/s 

 knowledge is based upon a finite number of observations 

 and his individual judgments, and the problem of a theory 

 of scientific knowledge is to show how this can be carried 

 out. 



It is clear that such a theory must depend on the theory 

 of probability, and the question of the probability of physical 

 laws and of inferences based on them is discussed. It is 

 shown that it will never be possible to attach appreciable 

 probability to an inference if it is assumed that all laws of 

 .an infinite class, such as all relations involving only analytic 

 functions, are equally probable a priori. If inference is 

 possible, the admissible laws must not be all equally probable 

 a priori. It is suggested that all admissible law^s can be 

 arranged in a well-ordered sequence, each having a finite 

 prior probability, and such that each is more probable than 

 any that follows it in the sequence. The probabilities of the 

 laws must form a convergent series. On this basis it is 

 shown that with sufficient empirical verification of a law 

 the probability of further inferences from it will approach 

 •certainty. 



There is reason to believe that all admissible laws must 

 form an enumerable aggregate, and this condition, and appa- 

 rently all others which are necessary, are satisfied if we 

 suppose that all laws admissible in physics are expressible 

 as differential equations of finite order and degree, with 



