PROBLEMS OF TYPE ANALYSIS 151 



added to the type the characters of the species. — To form a parti- 

 cular historical epoch, there was a fixed condition, the main- 

 tenance of the national character, and a changing condition, the 

 new state in which the nation happened to be placed on emerging 

 from the preceding epoch.' ^7 



There are limits, however, to the powers of reason and science. 

 The ultimate parts or elements of real things — for example, in the 

 science of Taine's day, the atoms of matter and cells of living 

 organisms — may never be fully known: 'no one has seen or can 

 see them . . .'.^s Though our knowledge has progressed amazingly 

 in the last century, the fact that the principle of indeterminism 

 has been widely accepted as a working principle in atomic physics 

 has substantiated part of his conclusion, at least: 'Thus, at a 

 certain limit, our explanation is at a standstill, and though, from 

 age to age, we push it further on, it is possible that it may always 

 stop before a certain limit. '^^^ Also, Taine anticipates a develop- 

 ment which reads very much like what the 'quantum' principle in 

 physics may eventually become: 'Perhaps, on the other hand, at a 

 certain point of decomposition, all difference between the com- 

 pound and the factors is at an end, and the properties of the 

 compound are nothing more than the sum of those of its factors, 

 just as the whole weight of a body is nothing more than the sum 

 of the weights of its molecules; in which case the limit would be 

 attained, since, knowing the properties of the compound, we 

 should thereby know the properties of its final elements.' ^^ How- 

 ever, these are very general speculations. 



As a kind of climax to Taine's exposition, we find that his 

 conclusions converge and 'will be led by their convergence, 

 towards a universal law of a higher order, which governs every 

 law'. 51 Here we have a revealing admission: 'At all events, we 

 believe this. We cannot show this reason, but we are persuaded 

 that it exists; we anticipate it by a bold affirmation as to our 

 future discoveries, and even as to discoveries which perhaps we 

 shall never make.'^^ Thus, we assume that a gap in our knowledge 

 or understanding 'never arises from the explanatory reason failing 

 or having failed in things, but always from its failing or having 

 failed in our minds'.^ ^ This universal law involves the statement 

 that 'if we look at the ideal and the real world, we perceive that 

 their structure is similar' ^4. hence our theorems, if true, can be 

 applied everywhere and every when. 



However, Taine is cautious on the issue of absolute determinism: 



