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Logic and Logical Philosophy

Composition as identity and plural Cantor's theorem
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  3. Vol. 25 No. 3 (2016): September /
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Composition as identity and plural Cantor's theorem

Authors

  • Einar Duenger Bohn University of Agder

DOI:

https://doi.org/10.12775/LLP.2016.009

Keywords

composition as identity, Cantor’s theorem, mereology, modal realism, necessitism

Abstract

In this paper, I argue that the thesis of Composition as Identity blocks the plural version of Cantor’s Theorem, and that this in turn has implications for our use of Cantor’s theorem in metaphysics. As an example, I show how this result blocks a recent argument by Hawthorne and Uzquiano, and might be turned around to become an abductive argument for Composition as Identity

References

Baxter, D., and A. Cotnoir (eds.), 2014, Composition as Identity, Oxford University Press. DOI: 10.1093/acprof:oso/9780199669615.001.0001

Bohn, E.D., 2014, “Unrestricted composition as identity”, pages 143–165 in [Baxter and Cotnoir, 2014]. DOI: 10.1093/acprof:oso/9780199669615.003.0008

Bohn, E.D., 2011, “Commentary on Parts of Classes”, Humana.Mente, 19: 151–158.

Bohn, E.D., 2009, “Composition as identity”, PhD dissertation, UMass Amherst.

Bricker, P., forthcoming, “Composition as a kind of identity”, Inquiry.

Cameron, R., 2012, “Composition as identity doesn’t settle the special composition question”, Philosophy and Phenomenological Research, LXXXIV, 3: 531–554.

Cotnoir, A., 2013, “Composition as Generalized Identity”, pages 294–322 in Oxford Studies in Metaphysics, Vol. 8, K. Bennett and D.W. Zimmerman (eds.), Oxford University Press. DOI: 10.1093/acprof:oso/9780199682904.003.0007

Florio, S., 2014, “Untyped pluralism”, Mind, 123, 490: 317–337. DOI: 10.1093/mind/fzu069

Frege, G., 1884, The Foundations of Arithmetic, as translated by J.L.Austin, Blackwell, 1980.

Geach, P., 1967, “Identity”, Review of Metaphysics, 21, 3: 3–12.

Hawley, K., 2013, “Cut the pie anyway you like? Cotnoir on General Identity”, pages 294–322 in Oxford Studies in Metaphysics, Vol. 8, K. Bennett and D.W. Zimmerman (eds.), Oxford University Press. DOI: 10.1093/acprof:oso/9780199682904.003.0008

Hawthorne, J., and G. Uzquiano, 2011, “How many angels can dance on the point of a needle? Transcendental theology meets modal metaphysics”, Mind, 120, 477: 53–81. DOI: 10.1093/mind/fzr004

Hovda, P., 2014, “Logical considerations on composition as identity”, pages 192–221 in [Baxter and Cotnoir, 2014]. DOI: 10.1093/acprof:oso/9780199669615.003.0010

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Merricks, T., 2003, Objects and Persons, Oxford University Press. DOI: 10.1093/0199245363.001.0001

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Oliver, A., and T. Smiley, 2013, Plural Logic, Oxford University Press. DOI: 10.1093/acprof:oso/9780199570423.001.0001

Rosen, G., 1995, “Armstrong on classes as states of affairs”, Australasian Journal of Philosophy, 73, 4: 613–625. DOI: 10.1080/00048409512346971

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Sider, T., 2007, “Parthood”, Philosophical Review, 116: 51–91. DOI: 10.1215/00318108-2006-022

Sider, T., 2014, “Consequences of collapse”, pages 211–221 in [Baxter and Cotnoir, 2014]. DOI: 10.1093/acprof:oso/9780199669615.003.0011

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Yi, Byeong-Uk, 2006, “The logic and meaning of plurals. Part II”, Journal of Philosophical Logic, 35, 3: 239–288. DOI: 10.1007/s10992-005-9015-6

Logic and Logical Philosophy

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Published

2016-05-19

How to Cite

1.
BOHN, Einar Duenger. Composition as identity and plural Cantor’s theorem. Logic and Logical Philosophy. Online. 19 May 2016. Vol. 25, no. 3, pp. 411-428. [Accessed 18 May 2025]. DOI 10.12775/LLP.2016.009.
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