Abelian mereology

A. J. Cotnoir

DOI: http://dx.doi.org/10.12775/LLP.2015.006


In classical extensional mereology, composition is idempotent: if x is part of y, then the sum of x and y is identical to y. In this paper, I provide a systematic and coherent formal mereology for which idempotence fails. I first discuss a number of purported counterexamples to idempotence that have been put forward in the literature. I then discuss two recent attempts at sketching non-idempotent formal mereology due to Karen Bennett and Kit Fine. I argue that these attempts are incomplete, however, and there are many open issues left unresolved. I then construct a class of models of a non-idempotent mereology using multiset theory, consider their algebraic structure, and show how these models can shed light on the open issues left from the previous approaches.


universalism; extensionality; supplementation; antisymmetry; mereology; parthood; composition

Full Text:



Armstrong, D.M., “In defense of structural universals”, Australasian Journal of Philosophy, 64 (1986): 85–88.

Bennett, K., “Having a part twice over”, Australasian Journal of Philosophy, 91 (2013): 83–103. DOI: 10.1080/00048402.2011.637936

Bigelow, J., and R. Pargetter, “A theory of structural universals”, Australasian Journal of Philosophy, 67 (1989): 1–11. DOI: 10.1080/00048408912343641

Blizard, W., “Multiset theory”, Notre Dame Journal of Formal Logic, 30, 1 (1989): 36–66. DOI: 10.1305/ndjfl/1093634995

Brink, C., “Some background on multisets”, Tech. rep., Australian National University, July 1987. Automated Reasoning Project TR-ARP-2/87.

Cotnoir, A. J., and A. Bacon, “Non-wellfounded mereology”, Review of Symbolic Logic, 5, 2 (2012): 187–204. DOI: 10.1017/S1755020311000293

Singh, D., A.M. Ibrahim, T. Yohanna, and J. N. Singh, “An overview of the applications of multisets”, Novi Sad Journal of Mathematics, 37, 2 (2007): 73–92.

Donnelly, M., “Parthood and multi-location”, pp. 203–243 in D. Zimmerman, (ed.), Oxford Studies in Metaphysics, vol. 5, Oxford University Press, 2010.

Eagle, A., “Location and perdurance”, pp. 53–94 in D. Zimmerman (ed.), Oxford Studies in Metaphysics, vol. 5, Oxford University Press, 2010.

Effingham, N., “Mereological explanation and time travel”, Australasian Journal of Philosophy, 88, 2 (2010): 333–345. DOI: 10.1080/00048400903018972

Effingham, N., and J. Robson, “A mereological challenge to endurantism”, Australasian Journal of Philosophy, 85 (2007): 633–640.

Fine, K., “Towards a theory of part”, Journal of Philosophy, 107, 11 (2010): 559–589.

Fisher, A.R. J., “Bennett on parts twice over”, Philosophia, 41, 3 (2013): 757–761. DOI: 10.1007/s11406-012-9396-z

Forrest, P., “Exemplification and parthood”, Axiomathes, 23 (2013): 323–341. DOI: 10.1007/s10516-013-9215-6

Gilmore, C., “Time travel, coinciding objects, and persistence”, pp. 177–198 in D. Zimmerman (ed.), Oxford Studies in Metaphysics, vol. 3, Oxford University Press, 2007.

Gilmore, C., “Coinciding objects and duration properties: Reply to Eagle”, pp. 95–111 in D. Zimmerman (ed.), Oxford Studies in Metaphysics, vol. 5, Oxford University Press, 2010.

Hawley, K., “Mereology, modality, and magic”, Australasian Journal of Philosophy, 88, 1 (2010): 117–133. DOI: 10.1080/00048400802587341

Kleinschmidt, S., “Multilocation and mereology”, Philosophical Perspectives, 25 (2011): 253–276. DOI: 10.1111/j.1520-8583.2011.00215.x

Lewis, D., “Against structural universals”, Australasian Journal of Philosophy 64, (1986): 25–46. DOI: 10.1080/00048408612342211

Lewis, D., Parts of Classes, Basil Blackwell, Oxford, 1991.

Mormann, T., “Structural universals as structural parts: Towards a general theory of parthood and composition”, Axiomathes, 20 (2010): 229–253.

Smith, D., “Mereology without weak supplementation”, Australasian Journal of Philosophy, 87 (2009): 505–511. DOI: 10.1080/00048400802215703

Varzi, A., “The extensionality of parthood and composition”, The Philosophical Quarterly, 58 (2008): 108–133. DOI: 10.1111/j.1467-9213.2007.542.x

Varzi, A., “Mereology”, in E. N. Zalta (ed.), The Stanford Encyclopedia of Philosophy, 2014. http://plato.stanford.edu/entries/mereology

ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

Partnerzy platformy czasopism