When Do Some Things Form a Set?

Philosophia Mathematica 23 (3):311-337 (2015)
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Abstract

This paper raises the question under what circumstances a plurality forms a set, parallel to the Special Composition Question for mereology. The range of answers that have been proposed in the literature are surveyed and criticised. I argue that there is good reason to reject both the view that pluralities never form sets and the view that pluralities always form sets. Instead, we need to affirm restricted set formation. Casting doubt on the availability of any informative principle which will settle which pluralities form sets, the paper concludes by affirming a naturalistic approach to the philosophy of set theory.

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Simon Hewitt
University of Leeds

Citations of this work

Critical Plural Logic.Salvatore Florio & Øystein Linnebo - 2020 - Philosophia Mathematica 28 (2):172-203.
Against the iterative conception of set.Edward Ferrier - 2019 - Philosophical Studies 176 (10):2681-2703.
Modal set theory.Christopher Menzel - 2018 - In Otávio Bueno & Scott A. Shalkowski (eds.), The Routledge Handbook of Modality. New York: Routledge.

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References found in this work

Modal Logic as Metaphysics.Timothy Williamson - 2013 - Oxford, England: Oxford University Press.
On what grounds what.Jonathan Schaffer - 2009 - In David Manley, David J. Chalmers & Ryan Wasserman (eds.), Metametaphysics: New Essays on the Foundations of Ontology. Oxford University Press. pp. 347-383.
Material beings.Peter Van Inwagen - 1990 - Ithaca: Cornell University Press.
Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.

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