Cut the Pie Any Way You Like? Cotnoir on General Identity
Hawley (Katherine)
Source: St. Andrews' Website; forthcoming in Oxford Studies in Metaphysics, Vol. 8, edited by Karen Bennett and Dean Zimmerman
Paper - Abstract

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Author’s Introduction

  1. Aaron Cotnoir does all sorts of interesting things in his contribution to this volume1. He makes a helpful distinction between syntactic and semantic objections to the thesis that composition is identity, and outlines some empirical points relevant to the syntactic issue. But the centrepiece is his development of a formal framework for addressing the semantic objections.
  2. Cotnoir articulates a general notion of ‘identity’ which can hold one-one, one-many, or many-many (where the identical manys don’t have to be equinumerous). The necessary and sufficient condition in each case for general identity is that the same portion of reality appear on each side of the identity sign; it doesn’t matter whether that single portion of reality is counted in different ways on each side, perhaps as a copse on one side and several trees on the other, or as three string quartets on one side and two ice-hockey teams on the other. Any such attempt to generalise identity must show how the more general relation is still an identity relation, and in particular how it conforms to Leibniz’s Law that identicals must be indiscernible. So Cotnoir offers us two alternative ways of preserving Leibniz’s Law, either by introducing an index, or by using subvaluational techniques
  3. There is a lot to like and a lot to think about here. If Cotnoir’s generalisation of both identity and Leibniz’s Law succeeds, this may have consequences for other philosophical puzzles which turn on worries about discernibility. Perhaps we now have space for a novel account of the relationship between (e.g.) the statue2 and the lump of clay, at least where these permanently coincide. They are surely the same portion of reality in the relevant sense, albeit ‘counted as’ a statue3 and ‘counted as’ a lump, respectively, and so perhaps they are generally identical despite their apparent differences. And might we now have a new solution to the problem of temporary intrinsics4? The unripe green banana and the ripe yellow banana are the same portion of reality (counted at different times?) so they may be generally identical without being identical in the narrowest one-one way.
  4. Now, these and other applications require a distinction amongst one-one identities which Cotnoir does not make in this paper: that is, a distinction between those one-one identities which are governed by Leibniz’s Law in the strictest sense (‘numerical identities’, in Cotnoir’s terms), and those which are governed by Leibniz’s Law only in its indexed or subvaluational version. Moreover, considering such extensions of Cotnoir’s framework forces us to think harder about what it is for some objects to be the same portion of reality as each other: perhaps the unripe banana is the same portion of reality as the later ripe banana, but can we say the same of objects (like living organisms) which undergo very significant turnover of material parts even while continuing to exist?
  5. In this brief note I will focus on the notion of ‘same portion of reality’: what metaphysical assumptions must we accept if we are to acknowledge Cotnoir’s general identity as a genuine identity relation? We need to understand the metaphysics behind the semantics so that we can judge the significance of the claim that composition is general identity; moreover we need to understand the metaphysics so that we can understand how, and whether, Cotnoir’s framework can extend to address other philosophical problems.

  1. Introduction
  2. Why Antipodean Counterparts are not even Slightly Identical
  3. Portions of Reality Distinguished From Objects?
  4. Portions of Reality are Objects


See Link.

In-Page Footnotes

Footnote 1: See "Cotnoir (Aaron J.) - Composition as General Identity".

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  1. Blue: Text by me; © Theo Todman, 2018
  2. Mauve: Text by correspondent(s) or other author(s); © the author(s)

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