ON THE NOTION OF CAUSE 203 



depends upon ignorance, and is therefore commoner in 

 regard to the future than in regard to the past ; (2) that 

 where a wish concerns the future, it and its reahsation 

 very often form a " practically independent system," 

 i.e. many wishes regarding the future are realised. But 

 there seems no doubt that the main difference in our 

 feelings arises from the accidental fact that the past 

 but not the future can be known by memory. 



Although the sense of " determined " in which the 

 future is determined by the mere fact that it will be what 

 it will be is sufficient (at least so it seems to me) to refute 

 some opponents of determinism, notably M. Bergson and 

 the pragmatists, yet it is not what most people have in 

 mind when they speak of the future as determined. What 

 they have in mind is a formula by means of which the 

 future can be exhibited, and at least theoretically calcu- 

 lated, as a function of the past. But at this point we 

 meet with a great difficulty, which besets what has been 

 said above about deterministic systems, as well as what 

 is said by others. 



If formulae of any degree of complexity, however great, 

 are admitted, it would seem that any system, whose 

 state at a given moment is a function of certain measur- 

 able quantities, must be a deterministic system. Let us 

 consider, in illustration, a single material particle, whose 

 co-ordinates at time t are x^, ^^, z^. Then, however, the 

 particle moves, there must be, theoretically, functions 

 /i f% fzi such that 



It follows that, theoretically, the whole state of the 

 material universe at time t must be capable of being 

 exhibited as a function of t. Hence our universe will be 

 deterministic in the sense defined above. But if this be 



