ii CONTINUUM NOT DIVISIBLE 237 



to be justifiable, as in the latter case we are concerned 

 not with division but with multiplication or addition, 

 not with a continuum, but with discrete quantities, and 

 it was part of his general theory that the addition of 

 discretes might be carried on ad infinitum ; the inverse 

 process he denied. He thus held opinions directly 

 contrary to those of Aristotle, with whom the mass 

 of the universe was finite, limited by its enclosing 

 sphere, the parts of the universe unlimited. Aristotle had 

 an upper but not a lower limit ; Bruno a lower but not 

 an upper. So time and space, which Aristotle had Time and 

 treated as finite in duration or extent, but as infinitely 3I 

 divisible, like the universe itself, are regarded by Bruno 

 as unlimited in their dimensions, but as consisting of 

 discrete minimal parts. " In every point of duration 

 is beginning without end, and end without beginning" ; 

 it is the centre of two infinities. Therefore the whole 

 of duration is one infinite instant, both beginning and 

 end, as immeasurable space is an infinite minimum or 

 centre. " The beginning and source of all errors, both 

 in physics and in mathematics, is the resolution of the 

 continuous in infinitum. To us it is clear that the 

 resolution both of nature and of true art, which does 

 not advance beyond nature, descends from a finite 

 magnitude and number to the atom, but that there is 

 no limit to the extension of things either in nature or 

 in thought, except in regard to the form of particular 

 species. Everywhere and always we find the minimum, 

 the maximum nowhere and never. The maximum and 

 minimum, however, may in one sense coincide, so that 

 we know the maximum to be everywhere, since from 

 what has been said it is evident that the maxi- 

 mum consists in the minimum and the minimum 

 in the maximum, as in the many is the one, in the 



