ii MATHEMATICAL ATOMISM 245 



way, therefore, was that which he followed. Hence the 

 curious attempt to remodel mathematical theory on the 

 basis of the atom, which we have described above, and 

 the reduction of mathematical certainty to an illusion of 

 sense. Figure is to be found only in the combinations 

 of atoms ; and owing to the spherical form of the atom, 

 the infinite number of them existing in any body which 

 is presented to sense, and the space which lies between 

 their surfaces, mathematical equality and exactness are 

 impossible. Neither straight line, therefore, nor perfect 

 circle are to be found in reality. Mathematics, which 

 should be based upon, or which presupposes, continuity, 

 is confounded with physics, which presupposes the 

 analysis of body into discrete, impenetrable atoms. 

 Physical atomism finds its justification in the experienced 

 fact of resistance, which is the primary quality of body 

 as perceived by our senses. In mathematical space, on 

 the other hand, we abstract from all qualities except 

 that of dimension only. Resistance would be in- 

 explicable were it possible to proceed ad infinitum in 

 dividing matter ; it implies an ultimate irreducible and 

 indestructible unit, whether we regard this unit as a 

 centre of force or as an inert substance merely. 



The same influence of Aristotelian thought led 

 Bruno to posit a subtle matter, the Ether, as filling up 

 the interstices between the atoms. Space and body 

 having been identified, it was seen that a vacuum was 

 inconsistent with the nature of things. The Aristotelian 

 -plenum was reintroduced in this form, that there might 

 be some reality where the discrete atoms were not. The 

 bolder step of asserting the fact, and indeed, the neces- 

 sity of a vacuum as a presupposition of knowledge of the 

 material world, was not taken until there appeared the 

 work of Gassendi, by whom the final blow was given to 



