The individuation of the natural numbers

In Ø. Linnebo O. Bueno (ed.), New Waves in Philosophy of Mathematics. Palgrave-Macmillan (2009)
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Abstract

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

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Øystein Linnebo
University of Oslo

Citations of this work

Abstraction and Four Kinds of Invariance.Roy T. Cook - 2017 - Philosophia Mathematica 25 (1):3–25.
Antireductionism and Ordinals.Beau Madison Mount - 2019 - Philosophia Mathematica 27 (1):105-124.
Cardinals, Ordinals, and the Prospects for a Fregean Foundation.Eric Snyder, Stewart Shapiro & Richard Samuels - 2018 - In Anthony O'Hear (ed.), Metaphysics. Cambridge, United Kingdom: Cambridge University Press.

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