THE PROBLEM OF INFINITY 157 



an infinite series can " never " be completed by successive 

 synthesis, all that he has even conceivably a right to say 

 is that it cannot be completed in a finite time. Thus what 

 he really proves is, at most, that if the world had no 

 beginning, it must have already existed for an infinite 

 time. This, however, is a very poor conclusion, by no 

 means suitable for his purposes. And with this result 

 we might, if we chose, take leave of the first antinomy. 



It is worth while, however, to consider how Kant came 

 to make such an elementary blunder. What happened 

 in his imagination was obviously something like this : 

 Starting from the present and going backwards in time, 

 we have, if the world had no beginning, an infinite series 

 of events. As we see from the word " synthesis," he 

 imagined a mind trying to grasp these successively, in the 

 reverse order to that in which they had occurred, i.e. going 

 from the present backwards. This series is obviously one 

 which has no end. But the series of events up to the 

 present has an end, since it ends with the present. 

 Owing to the inveterate subjectivism of his mental habits, 

 he failed to notice that he had reversed the sense of the 

 series by substituting backward synthesis for forward 

 happening, and thus he supposed that it was necessary to 

 identify the mental series, which had no end, with the 

 physical series, which had an end but no beginning. It 

 was this mistake, I think, which, operating unconsciously, 

 led him to attribute validity to a singularly flimsy piece of 

 fallacious reasoning. 



The second antinomy illustrates the dependence of the 

 problem of continuity upon that of infinity. The thesis 

 states : " Every complex substance in the world consists 

 of simple parts, and there exists everywhere nothing but 

 the simple or what is composed of it." The antithesis 

 states : " No complex thing in the world consists of 



