Abstract
Both extended simples and unextended complexes have been extensively discussed and widely used in metaphysics and philosophy of physics. However, the characterizations of such notions are not entirely satisfactory inasmuch as they rely on a mereological notion of extension that is too simplistic. According to such a mereological notion, being extended boils down to having a mereologically complex exact location. In this paper, I make a detailed plea to supplement this notion of extension with a different one that is phrased in terms of measure theory. This proposal has significant philosophical payoffs. I provide new characterizations of both extended simples and unextended complexes, that help re-evaluating the question of whether such entities are metaphysically possible. Finally, I advance several suggestions as to how different notions of extension relate, first, to one another and, second, to mereological structure.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Code Availability
There is no code.
References
Abbott, S. (2015). Understanding analysis. New York: Springer.
Arntzenius, F. (2008). Gunk, topology and measure. In D. Zimmerman (Ed.) Oxford studies in metaphysics (vol. 4, pp. 225–247). Oxford University Press.
Arntzenius, F., & Dorr, C. (2012). Calculus as geometry. In F. Arntzenius (Ed.) Space, time and stuff (pp. 172–225). Oxford: Oxford University Press.
Baker, D. (2016). Does string theory posit extended simples? Philosopher’s Imprint, 16(18), 1–15.
Balashov, Y. (1999). Zero-value physical quantities. Synthese, 119(3), 253–286.
Baron, S. (2021). Parts of spacetime. American Philosophical Quarterly, 58(4), 387–398.
Baron, S., & LeBihan, B. (Forthcoming). Quantum gravity and mereology: not so simple. Philosophical Quarterly at https://academic.oup.com/pq/advance-article/doi/10.1093/pq/pqab016/6208240?login=true. Accessed 18 July 2021.
Braddon-Mitchell, D., & Miller, K. (2006). The physics of extended simples. Analysis, 66(3), 222–226.
Calosi, C. (2021). Is Parthood Identity? Synthese 198:4503–4517.
Calosi, C., & Costa, D. (2022). The multi-location trilemma. Erkenntnis, 87, 1063–1079.
Casati, R., & Varzi, A. (1999). Parts and places. Cambridge: MIT Press.
Cotnoir, A., & Varzi, A. (2021). Mereology. Oxford: Oxford University Press.
Eagle, A. (2010). Perdurance and location. In D. W. Zimmerman (Ed.) Oxford studies in metaphysics, (Vol. 5 pp. 53–94). Oxford: Oxford University Press.
Eagle, A. (2019). Weak location. Dialectica, 73(1–2), 149–181.
Field, H. (1980). Science without numbers. Princeton: Princeton University Press.
Giberman, D. (2012). Against zero-dimensional material objects (and other bare particulars). Philosophical Studies, 160, 305–321.
Gilmore, C. (2006). Where in the relativistic world are we? Philosophical Perspectives, Metaphysics, 20, 199–236.
Gilmore, C. (2008). Persistence and location in relativistic spacetimes. Philosophy Compass, 3(6), 1224–1254.
Gilmore, C. (2018). Location and mereology. Stanford Encyclopedia of Philosophy. At: http://plato.stanford.edu/entries/location-mereology/. Accessed 18 July 2021.
Goodsell, Z., Duncan, M., & Miller, K. (Forthcoming). What is an extended simple region. Philosophy and Phenomenological Research. https://doi.org/10.1111/phpr.12623.
Grünbaum, A. (1967). Modern science and zeno’s paradoxes. Middletown: Connecticut Wesleyan University Press.
Gruszczynski, R., & Pietruszczak, A. (2009). Space, points and mereology. On foundations of point-free Euclidean geometry. Logic and Logical Philosophy, 18, 145–188.
Hudson, H. (2002). The liberal view of receptacles. Australasian Journal of Philosophy, 80(4), 432–439.
Hudson, H. (2005). The metaphysics of hyperspace. Oxford: Oxford University Press.
Hughes, R. (1992). The structure and the interpretation of quantum mechanics. Cambridge: Harvard University Press.
Kleinschmidt, S. (2016). Placement permissivism and the logic of location. Journal of Philosophy, 113(3), 117–136.
Lando, T., & Scott, D. (2019). A calculus of regions respecting both measure and topology. Journal of Philosophical Logic. https://doi.org/10.1007/s10992-018-9496-8.
Leonard, M. (2016). What is mereological harmony? Synthese, 193, 1949–1965.
Limpan, M. (2021). Defense of disjointism. Inquiry. At: https://www.tandfonline.com/doi/full/10.1080/0020174X.2021.2006773. Accessed 24 February 2022.
Markosian, M. (1998). Simples. Australasian Journal of Philosophy, 76(2), 213–228.
Markosian, N. (2014). A spatial approach to mereology. In S. Kleinshmidt (Ed.) Mereology and location (pp. 69–90). Oxford: Oxford University Press.
McDaniel, K. (2007a). Extended simple. Philosophical Studies, 133, 131–141.
McDaniel, K. (2007b). Brutal simples. Oxford Studies in Metaphysics, 3, 233–265.
McDaniel, K. (2014). Parthood is identity. In S. Kleinshmidt (Ed.) Mereology and location (pp. 13–32). Oxford: Oxford University Press.
Meyer, U. (Forthcoming). The Banach-Tarsky Paradox.
Parsons, J. (2007). Theories of location. Oxford Studies in Metaphysics, 3, 201–232.
Pashby, T. (2016). How do things persist? Location relations in physics and the metaphysics of persistence. Dialectica, 70(3), 269–309.
Payton, J. (Forthcoming). Mereological destruction and relativized parthood: a reply to Costa and Calosi. Erkenntnis. At https://doi.org/10.1007/s10670-021-00423-8.
Pickup, M. (2016). Unextended complexes. Thought, 5, 257–264.
Rettler, B. (2019). Mereological nihilism and puzzles about material objects. Pacific Philosophical Quarterly, 99, 842–68.
Saucedo, R (2011). Parthood and location. Oxford Studies in Metaphysics, 6, 223–284.
Scala, M. (2002). Homogeneous simples. Philosophy and Phenomenological Research, 64(2), 393–397.
Sider, T. (2007). Parthood. The Philosophical Review, 116, 51–91.
Simons, P. (2004). Extended simples. A third way between atoms and gunk. The Monist, 83, 371–384.
Simons, P. (2014). Where it’s at: modes of occupation and kinds of occupant. In S. Kleinschmidt (Ed.) Mereology and location (pp. 59–68). Oxford: Oxford University Press.
Tao, T. (2011). An introduction to measure theory. Providence: American Mathematical Society.
Tognazzini, N. (2006). Simples and the possibility of discrete space. Australasian Journal of Philosophy, 84, 117–128.
Uzquiano, G. (2011). Mereological harmony. Oxford Studies in Metaphysics, 6, 199–224.
Varzi, A. (2007). Spatial reasoning and ontology: parts, Wholes and Location. In M. Aiello, I. Pratt-Hartmann, & J. Van Bentham (Eds.) Handbook of spatial logic (pp. 945–1038). Berlin: Springer.
Wald, R. (1984). General relativity. Chicago: Chicago University Press.
Wasserman, R. (2002). The standard objection to the standard account. Philosophical Studies, 111(3), 197–216.
Acknowledgments
I would like to thank two anonymous referees for this journal for their insightful suggestions which improved the paper greatly. For discussions on previous drafts of the paper I would like to thank Fabrice Correia, Alessandro Giordani, Gonzalo Rodriguez-Pereyra, and Achille Varzi. This work has been funded by the Swiss National Science Foundation, (SNF), project number PCEFP1_181088.
Funding
Open access funding provided by University of Geneva. Swiss National Science Foundation, (SNF), project number PCEFP1_181088.
Author information
Authors and Affiliations
Contributions
I am the sole author of the manuscript.
Corresponding author
Ethics declarations
Competing Interests
I have no competing interests.
Additional information
Availability of Data and Material
There is no data material.
Ethical Approval
N/A
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Calosi, C. Extended Simples, Unextended Complexes. J Philos Logic 52, 643–668 (2023). https://doi.org/10.1007/s10992-022-09683-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10992-022-09683-3