Skip to main content



This paper is a systematic exploration of non-wellfounded mereology. Motivations and applications suggested in the literature are considered. Some are exotic like Borges’ Aleph, and the trinity; other examples are less so, like time traveling bricks, and even Geach’s Tibbles the Cat. The authors point out that the transitivity of non-wellfounded parthood is inconsistent with extensionality. A non-wellfounded mereology is developed with careful consideration paid to rival notions of supplementation and fusion. Two equivalent axiomatizations are given, and are compared to classical mereology. We provide a class of models with respect to which the non-wellfounded mereology is sound and complete.

Corresponding author
Hide All
Abelard P. (2006). Theologica christiana. In Bosley R. N., and Tweedale M. M., editors. Basic Issues in Medieval Philosophy, Chapter V.3. Ontario, CA: Broadview Press, pp. 296303.
Barwise J., & Etchemendy J. (1987). The Liar. Oxford: Oxford University Press.
Casati R., & Varzi A. C. (1999). Parts and Places: The Structures of Spatial Representation. Cambridge, MA: MIT Press.
Cotnoir A. J. (2010). Anti-symmetry and non-extensional mereology. The Philosophical Quarterly, 60(239), 396405.
Eagle A. (2010). Location and perdurance. Oxford Studies in Metaphysics, 5, 5394.
Effingham N. (2010). Mereological explanation and time travel. Australasian Journal of Philosophy, 88, 333345.
Effingham N., & Robson J. (2007). A mereological challenge to endurantism. Australasian Journal of Philosophy, 85, 633640.
Forrest P. (2002). Non-classical mereology and its application to sets. Notre Dame Journal of Formal Logic, 43, 7994.
Geach P. T. (1962). Reference and Generality. Ithaca, NY: Cornell University Press.
Gilmore C. (2007). Time travel, coinciding objects, and persistence. Oxford Studies in Metaphysics, 3, 177198.
Gilmore C. (2010). Coinciding objects and duration properties: Reply to Eagle. Oxford Studies in Metaphysics, 5, 95111.
Hawthorne J. (2006). Three dimensionalism. Metaphysical Essays, 85111.
Hovda P. (2009). What is classical mereology? Journal of Philosophical Logic, 38(1), 5582.
Kearns S. (2011). Can a thing be part of itself? American Philosophical Quarterly, 48(1).
Lewis D. (1991). Parts of Classes. Oxford, UK: Basil Blackwell.
Link G. (1983). The logical analysis of plural and mass terms: A lattice-theoretical approach. In Bäuerle R., et al. ., editors. Meaning, Use, and Interpretation of Language. Berlin: de Gruyter, pp. 303323.
Mascaró J., editor. (1965). Upanishads. London: Penguin.
Niebergall K. (2009). On 2nd order variants of calculi of individuals. Theoria, 24, 169202.
Noonan H. (2009). Identity. In Zalta E. N., editor. The Stanford Encyclopedia of Philosophy. Winter 2009 edition.
Quine W. V. (1980). From a Logical Point of View (second edition). Chapter New Foundations for Mathematical Logic. Cambridge, MA: Harvard University Press.
Rea M., editor. (1997). Material Constitution: A Reader. Lanham, MD: Rowan and Littlefield.
Sanford D. H. (1993). The problem of the many, many composition questions, and naïve mereology. Noûs, 27(2), 219228.
Sharvey R. (1983). Mixtures. Philosophy and Phenomenological Research, 44(2), 227239.
Sider T. (1993). van Inwagen and the possibility of gunk. Analysis, 53, 285289.
Sider T. (2003). Four-dimensionalism: An Ontology of Persistence and Time. Oxford: Oxford University Press.
Simons P. M. (1987). Parts: A Study In Ontology. Oxford, UK: Clarendon.
Smith D. (2009). Mereology without weak supplementation. Australasian Journal of Philosophy, 87, 505511.
Tarski A. (1956). Foundations of the geometry of solids. In Corcoran J., editor. Logic, Semantics, Metamathematics. Indianapolis, IN: Hackett.
Thomson J. J. (1983). Parthood and identity across time. Journal of Philosophy, 80(4), 201220.
Thomson J. J. (1998). The statue and the clay. Noûs, 32(2), 149173.
van Inwagen P. (1993). Naïve mereology, admissible valuations, and other matters. Noûs, 27(2), 229234.
Varzi A. (2009). Universalism entails extensionalism. Analysis, 69, 599604.
Varzi A. (2006). Mereology. In Zalta E. N., editor. The Stanford Encyclopedia of Philosophy. Winter.
Wiggins D. (1968). On being at the same place at the same time. Philosophical Review, 77, 9095.
Zimmerman D. (1996). Could extended objects be made out of simple parts? An argument for atomless gunk. Philosophy and Phenomenological Research, 56, 129.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 25 *
Loading metrics...

Abstract views

Total abstract views: 242 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 20th November 2017. This data will be updated every 24 hours.