Functions and Categories and Universals

Abstract

I have now considered the ontological correlates of all the various parts of the function ‘fx’ except the functor f. This appears to me to be the most interesting of the symbols used in expressing the function. It is easy enough to see that the ‘x’ in ‘fx’ intends an object of some sort and serves as a proper name. When we replace ‘f’ by constant expressions we are at the heart of the problem as to the nature of what it intends. If ‘f’ is also treated as a symbol to be replaced by proper names, the proper name which ‘f’ intends is of a different nature from that which ‘x’ intends because whatever can replace ‘x’ cannot replace ‘f’ in so far as it remains the sort of name that can replace ‘x.’ This could be taken to signify that those events whose names can be used to replace ‘x’ are of a different nature than those whose names can be used to replace ‘f.’