Definitions of number in terms of equivalence

pp. 117-132

in: Edmund Husserl, Philosophy of arithmetic, Berlin, Springer, 2003

Abstract

It is not without reason that we devoted so much attention, in the foregoing chapter, to the elucidation of the misunderstandings that are always linked to the definition of number-equality in terms of reciprocal, one-to-one correlation. Those misunderstandings have in fact entailed unfortunate consequences by leading to a total misconstrual of the concept of number itself. It will perhaps not be inappropriate if at first, without taking into consideration theories that have actually been advanced, we consider the following line of thought, which draws together ideas strewn here and there into the form of a maximally coherent theory.