284 ROMAN A. KOCOUREK 



the latter point but on the first one I had to say that such 

 motion was " motionless " and that only by using the concept 

 developed by Aristotle could we arrive at the prima via. 

 Furthermore, while admitting that motion as conceived by 

 modern science has a certain validity in the explanations of 

 the mathematical physicist, I said that to attempt to make 

 this the basis of any kind of a complete explanation of the 

 ultimate principles of the universe could lead to a very un- 

 acceptable philosophy. I do not recall whether my mathe- 

 matician friend was convinced or not. In the present paper 

 I would like to elaborate some of these notions. 



Cassirer himself, in his Substance and Function, attempts to 

 make this idea of " motionless motion " the basis of a new 

 explanation which will replace that of Aristotle. In the first 

 chapter he shows how the new developments in logic must 

 necessarily replace the logic of the Philosopher, founded as the 

 latter was an a now out-moded metaphysics. His conception 

 of the Greek synthesis in his analysis of the problem of knowl- 

 edge shows his appreciation of the work of both Plato and 

 Aristotle: 



There is no denying that Plato shaped his conception of knowledge 

 on the pattern of mathematics, and his theory of ideas not only 

 owes separate fundamental insights to mathematics but is deter- 

 mined throughout its whole structure by this science. On the other 

 hand, his theory far transcends whatever Greek mathematics could 

 present in the way of stable results, and Plato seems to have given 

 to the mathematics of his time much more than he took from 

 it. . . . 



What Plato had done for mathematics, Aristotle did for biology. 

 Not only did he conceive of it as a self-contained whole; he was 

 the first to provide a conceptual language for its separate parts. . . ? 



What he has in mind here is shown in the rest of his Intro- 

 duction to this work. He shows how the work of Descartes, 

 Leibniz, and Kant has discovered a new basis for the interpre- 

 tation of Nature. As he says: 



" E. Cassirer, The Problem of Knowledge (New Haven: Yale University Press, 

 1950), p. 12. 



