Composition and Relative Counting

Dialectica 71 (4):489-529 (2017)
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Abstract

According to the so-called strong variant of Composition as Identity (CAI), the Principle of Indiscernibility of Identicals can be extended to composition, by resorting to broadly Fregean relativizations of cardinality ascriptions. In this paper we analyze various ways in which this relativization could be achieved. According to one broad variety of relativization, cardinality ascriptions are about objects, while concepts occupy an additional argument place. It should be possible to paraphrase the cardinality ascriptions in plural logic and, as a consequence, relative counting requires the relativization either of quantifiers, or of identity, or of the is one of relation. However, some of these relativizations do not deliver the expected results, and others rely on problematic assumptions. In another broad variety of relativization, cardinality ascriptions are about concepts or sets. The most promising development of this approach is prima facie connected with a violation of the so-called Coreferentiality Constraint, according to which an identity statement is true only if its terms have the same referent. Moreover - even provided that the problem with coreferentiality can be fixed - the resulting analysis of cardinality ascriptions meets several difficulties.

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Author Profiles

Giorgio Lando
Università degli Studi dell'Aquila
Massimiliano Carrara
University of Padua

Citations of this work

Ordinary objects.Daniel Z. Korman - 2011 - Stanford Encyclopedia of Philosophy.
Failure of Boredom: The Pendulum of Composition as Identity.Claudio Calosi - 2018 - American Philosophical Quarterly 55 (3):281-292.
How to identify wholes with their parts.Jonathan D. Payton - 2019 - Synthese 198 (Suppl 18):4571-4593.
Counting, measuring, and the fractional cardinalities puzzle.Eric Snyder - 2020 - Linguistics and Philosophy 44 (3):513-550.

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References found in this work

On the Plurality of Worlds.David Lewis - 1986 - Revue Philosophique de la France Et de l'Etranger 178 (3):388-390.
Objects: Nothing Out of the Ordinary.Daniel Z. Korman - 2015 - New York, NY: Oxford University Press UK. Edited by Dana Zemack.
On the Plurality of Worlds.William G. Lycan - 1988 - Journal of Philosophy 85 (1):42-47.

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