LAW, CAUSE 377 



chanics. Until a few years ago the laws descriptive of the 

 movements of particles acted upon by forces were presumed 

 to be the most perfect illustrations of purely deterministic 

 systems. Though the systems were known to be ideal, since 

 particles are portions of matter without extension, never- 

 theless the presumption was that any actual system could 

 be made to approximate as closely as one wished to such 

 ideal systems by progressive refinement. The law descriptive 

 of behavior in such a system took the form of a functional 

 relation between one variable representing the state of a 

 system (its position and velocity) at one time and another 

 representing its state at an earlier or later time. This law 

 was presumed to be universal. It was, of course, nomically 

 necessary in the sense that it was deducible from the basic 

 postulates of mechanics and therefore could not possibly 

 be violated. But it was also empirically verified in all cases in 

 which a high degree of refinement could be introduced. It was 

 therefore presumed to represent a basic structure of nature. 

 Hence nature was supposed to be a deterministic system, at 

 least so far as its mechanical features were concerned. 



The generalized mechanical view of nature which arose 

 out of this conception has been accurately formulated by 

 Laplace. "We ought then to regard the present state of the 

 universe as the effect of its anterior state and as the cause 

 of the one which is to follow. Given for one instant an intel- 

 ligence which could comprehend all the forces by which 

 nature is animated, and the respective situation of the 

 beings who compose it — an intelligence sufficiently vast to 

 submit these data to analysis — it would embrace in the 

 same formula the movements of the greatest bodies of the 

 universe and those of the lightest atom; for it, nothing would 

 be uncertain and the future, as the past, would be present 

 to its eyes. The human mind offers, in the perfection which 

 it has been able to give to astronomy, a feeble idea of this 

 intelligence. Its discoveries in mechanics and geometry, 

 added to that of universal gravity, have enabled it to com- 

 prehend in the same analytical expressions the past and 



