ON THE NOTION OF CAUSE 195 



is not in any sameness of causes and effects that the con- 

 stancy of scientific law consists, but in sameness of 

 relations. And even " sameness of relations " is too 

 simple a phrase ; " sameness of differential equations " 

 is the only correct phrase. It is impossible to state this 

 accurately in non-mathematical language ; the nearest 

 approach would be as follows : *' There is a constant 

 relation between the state of the universe at any instant 

 and the rate of change in the rate at which any part of 

 the universe is changing at that instant, and this relation 

 is many-one, i.e. such that the rate of change in the 

 rate of change is determinate when the state of the 

 universe is given." If the " law of causality " is to be 

 something actually discoverable in the practice of science, 

 the above proposition has a better right to the name 

 than any " law of causality " to be found in the books of 

 philosophers. 



L In regard to the above principle, several observations 

 must be made 



(i) No one can pretend that the above principle is a 

 priori or self-evident or a " necessity of thought." Nor 

 is it, in any sense, a premiss of science : it is an empirical 

 generalisation from a number of laws which are them- 

 selves empirical generalisations. ^ 



(2) The law makes no difference between past and 

 future : the future " determines " the past in exactly 

 the same sense in which the past " determines " the future. 

 The word " determine," here, has a purely logical signifi- 

 cance : a certain number of variables " determine " 

 another variable if that other variable is a function of 

 them. 



(3) The law will not be empirically verifiable unless 

 the course of events within some sufficiently small volume 



