158 SCIENTIFIC METHOD IN PHILOSOPHY 



simple parts, and everywhere in it there exists nothing 

 simple." Here, as before, the proofs of both thesis and 

 antithesis are open to criticism, but for the purpose of 

 vindicating physics and the world of sense it is enough 

 to find a fallacy in one of the proofs. We will choose for 

 this purpose the proof of the antithesis, which begins as 

 follows : 



"Assume that a complex thing (as substance) consists 

 of simple parts. Since all external relation, and therefore 

 all composition out of substances, is only possible in 

 space, the space occupied by a complex thing must 

 consist of as many parts as the thing consists of. Now 

 space does not consist of simple parts, but of spaces/' 



The rest of his argument need not concern us, for the 

 nerve of the proof lies in the one statement : " Space 

 does not consist of simple parts, but of spaces." This 

 is like Bergson's objection to " the absurd proposition 

 that motion is made up of immobilities." Kant does 

 not tell us why he holds that a space must consist of 

 spaces rather than of simple parts. Geometry regards 

 space as made up of points, which are simple ; and 

 although, as we have seen, this view is not scientifically 

 or logically necessary \ it remains prima facie possible, and 

 its mere possibility is enough to vitiate Kant's argu- 

 ment. For, if his proof of the thesis of the antinomy 

 were valid, and if the antithesis could only be avoided 

 by assuming points, then the antinomy itself would 

 afford a conclusive reason in favour of points. Why, 

 then, did Kant think it impossible that space should 

 be composed of points ? 



I think two considerations probably influenced him. 

 In the first place, the essential thing about space is spatial 

 order, and mere points, by themselves, will not account 

 for spatial order. It is obvious that his argument 



