MEASUREMENTS 217 



degree of probability. Any near approach to mathematical 

 certainty is not to be hoped for. 



It may be objected that in statistics, at any rate, we 

 find a safe basis for prophecy ; we may be confident that 

 the same numbers of crimes, of births, deaths, and marriages 

 which have been ascertained for past years will be repeated 

 with substantial accuracy in the near future. The mere 

 statement of the claim carries with it the answer. The 

 predictions are never exact, nor do they apply to distant 

 ages. Moreover, they have a further limitation. They 

 are applicable to large aggregate numbers only ; for smaller 

 numbers, and, still more clearly, for individuals, they are 

 of no value whatever. 



It may be thought superfluous to spend so much pains 

 in insisting on distinctions which are so obvious and so in 

 contestable. The frequency with which they are overlooked 

 is a sufficient excuse. The most influential of English 

 thinkers in the nineteenth century regards it as a popular 

 error to hold that speculations on society and govern 

 ment, as resting on merely probable evidence, must be 

 inferior in certainty and scientific accuracy to the con 

 clusions of what are called the exact sciences, and less to 

 be relied on in practice. x A still greater thinker assures 

 us that if, as some believe, this world consists of a finite 

 number of atoms moving in obedience to the laws of 

 mechanics, it is certain that a finite intellect might reach 

 a height whence it could grasp all that must happen at 

 any specified moment, and predict it with mathematical 

 accuracy. It could, moreover, construct a body that 

 would repeat the actions of a man. And the realization 

 of this aim in some remote future still remains the favourite 

 dream of natural philosophers. We are tempted to trans 

 pose the terms in a sentence of Bacon s, and exclaim : * Quan 

 tum agmen idolorum philosophiae immisit humanarum 

 actionum ad similitudinem naturalium operationum re- 

 ductio ! 2 The confident belief in a future when the 



1 J. S. MiU, Logic. 



a De augmentis, I. v. cap. iv. 



