Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-24T21:23:51.807Z Has data issue: false hasContentIssue false
  • English
  • Français

NON-WELLFOUNDED MEREOLOGY

Published online by Cambridge University Press:  09 December 2011

AARON J. COTNOIR  and
ANDREW BACON
AARON J. COTNOIR*
Affiliation:
Northern Institute of Philosophy, University of Aberdeen
ANDREW BACON*
Affiliation:
Oxford University, Magdalen College
*
*NORTHERN INSTITUTE OF PHILOSOPHY, UNIVERSITY OF ABERDEEN, OLD BREWERY, ABERDEEN, AB24 3UB, UNITED KINGDOM E-mail:[email protected]
†MAGDALEN COLLEGE, OXFORD, OX1 4AU, UNITED KINGDOM
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 5 , Issue 2 , June 2012 , pp. 187 - 204
Copyright
Copyright © Association for Symbolic Logic 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BIBLIOGRAPHY

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. 296–303.Google Scholar
Barwise, J., & Etchemendy, J. (1987). The Liar. Oxford: Oxford University Press.Google Scholar
Casati, R., & Varzi, A. C. (1999). Parts and Places: The Structures of Spatial Representation. Cambridge, MA: MIT Press.Google Scholar
Cotnoir, A. J. (2010). Anti-symmetry and non-extensional mereology. The Philosophical Quarterly, 60(239), 396–405.CrossRefGoogle Scholar
Eagle, A. (2010). Location and perdurance. Oxford Studies in Metaphysics, 5, 53–94.Google Scholar
Effingham, N. (2010). Mereological explanation and time travel. Australasian Journal of Philosophy, 88, 333–345.CrossRefGoogle Scholar
Effingham, N., & Robson, J. (2007). A mereological challenge to endurantism. Australasian Journal of Philosophy, 85, 633–640.CrossRefGoogle Scholar
Forrest, P. (2002). Non-classical mereology and its application to sets. Notre Dame Journal of Formal Logic, 43, 79–94.CrossRefGoogle Scholar
Geach, P. T. (1962). Reference and Generality. Ithaca, NY: Cornell University Press.Google Scholar
Gilmore, C. (2007). Time travel, coinciding objects, and persistence. Oxford Studies in Metaphysics, 3, 177–198.Google Scholar
Gilmore, C. (2010). Coinciding objects and duration properties: Reply to Eagle. Oxford Studies in Metaphysics, 5, 95–111.Google Scholar
Hawthorne, J. (2006). Three dimensionalism. Metaphysical Essays, 85–111.CrossRefGoogle Scholar
Hovda, P. (2009). What is classical mereology? Journal of Philosophical Logic, 38(1), 55–82.CrossRefGoogle Scholar
Kearns, S. (2011). Can a thing be part of itself? American Philosophical Quarterly, 48(1).Google Scholar
Lewis, D. (1991). Parts of Classes. Oxford, UK: Basil Blackwell.Google Scholar
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. 303–323.Google Scholar
Mascaró, J., editor. (1965). Upanishads. London: Penguin.Google Scholar
Niebergall, K. (2009). On 2nd order variants of calculi of individuals. Theoria, 24, 169–202.CrossRefGoogle Scholar
Noonan, H. (2009). Identity. In Zalta, E. N., editor. The Stanford Encyclopedia of Philosophy. Winter 2009 edition.Google Scholar
Quine, W. V. (1980). From a Logical Point of View (second edition). Chapter New Foundations for Mathematical Logic. Cambridge, MA: Harvard University Press.CrossRefGoogle Scholar
Rea, M., editor. (1997). Material Constitution: A Reader. Lanham, MD: Rowan and Littlefield.Google Scholar
Sanford, D. H. (1993). The problem of the many, many composition questions, and naïve mereology. Noûs, 27(2), 219–228.CrossRefGoogle Scholar
Sharvey, R. (1983). Mixtures. Philosophy and Phenomenological Research, 44(2), 227–239.CrossRefGoogle Scholar
Sider, T. (1993). van Inwagen and the possibility of gunk. Analysis, 53, 285–289.CrossRefGoogle Scholar
Sider, T. (2003). Four-dimensionalism: An Ontology of Persistence and Time. Oxford: Oxford University Press.Google Scholar
Simons, P. M. (1987). Parts: A Study In Ontology. Oxford, UK: Clarendon.Google Scholar
Smith, D. (2009). Mereology without weak supplementation. Australasian Journal of Philosophy, 87, 505–511.CrossRefGoogle Scholar
Tarski, A. (1956). Foundations of the geometry of solids. In Corcoran, J., editor. Logic, Semantics, Metamathematics. Indianapolis, IN: Hackett.Google Scholar
Thomson, J. J. (1983). Parthood and identity across time. Journal of Philosophy, 80(4), 201–220.CrossRefGoogle Scholar
Thomson, J. J. (1998). The statue and the clay. Noûs, 32(2), 149–173.CrossRefGoogle Scholar
van Inwagen, P. (1993). Naïve mereology, admissible valuations, and other matters. Noûs, 27(2), 229–234.CrossRefGoogle Scholar
Varzi, A. (2009). Universalism entails extensionalism. Analysis, 69, 599–604.CrossRefGoogle Scholar
Varzi, A. (2006). Mereology. In Zalta, E. N., editor. The Stanford Encyclopedia of Philosophy. Winter.Google Scholar
Wiggins, D. (1968). On being at the same place at the same time. Philosophical Review, 77, 90–95.CrossRefGoogle Scholar
Zimmerman, D. (1996). Could extended objects be made out of simple parts? An argument for atomless gunk. Philosophy and Phenomenological Research, 56, 1–29.CrossRefGoogle Scholar