On Ellis’ Theory of Quantities

Abstract

A statement of the account of quantities to be discussed and defended in this essay can be found in the second chapter of Brian Ellis’ book Basic Concepts of Measurement (Ellis 1966). I refer to this account as “Ellis’ theory of quantities”, although I should say at the outset that Ellis himself does not fully and unequivocally embrace the account. This has caused some confusion about precisely what his position is with regard to quantities, and has led two of his critics to write “It is not clear in what sense he [Ellis] does allow that quantities exist” (Byerley and Lazara 1972, p. 14)¹. In the second part of this essay — there are three parts in all — I shall state what I believe to be Ellis’ theory and in so doing indicate in what sense he allows that quantities exist. In the third part I shall attempt to defend the theory against five objections, one of which is due to Ellis. It will be necessary to modify the theory in two respects in the light of these objections.

A previous version of this essay was read at the Center for Philosophy of Science. I am grateful for the comments of those who attended, particularly those of Nick Rescher and John Norton. I would like to take this opportunity to thank the Center and its Director for the hospitality I received there in the spring of 1986.