ABSTRACT
There is no logical necessity for any of the intuitive assumptions outlined in the previous paragraph. In the end it is the first of these assumptions, that the series of numbers is infinite, which is the most questionable. True, this proposition may be inherent in the logical definition of cardinal numbers, but then what is the necessity for allowing such numbers any logical priority? Are they an essential part of every numerical culture, and even if they are, must every such culture include the logical conclusions of western philosophy?1 It may be that modern Japan, as much as the western world, takes for granted that numbers are in some way made for arithmetic, but in Japan, in particular, there are any number of number systems which are so illsuited for arithmetic that no attempt is made to subject them to arithmetical operations. Once a number system does not have to satisfy
this requirement, there is no longer any need for a place-value system, or a single numerical base. This presents the problem of conceiving of numbers in a form deprived of attributes which are, intuitively at least, implicit in their most common form of representation.2 This is, of course, the series 1, 2, 3,….
