The Individuation of the Natural Numbers

Abstract

It is sometimes suggested that criteria of identity should play acentral role in an account of our most fundamental ways of referringto objects. The view is nicely illustrated by an example due to (Quine,1950). Suppose you are standing at the bank of a river, watchingthe water that floats by. What is required for you to refer to theriver, as opposed to a particular segment of it, or the totalityof its water, or the current temporal part of this water? Accordingto Quine, you must at least implicitly be operating with some criterionof identity that informs you when two sightings of water count assightings of the same referent. For unless you have at least an implicitgrasp of what is required for your intended referent to be identicalwith another object with which you are presented, you have not succeededin singling out a unique object for reference.