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Non-wellfounded Mereology


A.J. Cotnoir


Pages 383 - 387



Non-wellfounded Mereology A binary relation R is said to be wellfounded on a domain if and only if every non- empty subset of that domain has an R-minimal element; equivalently, iff every descending R chain is finite. A proper parthood relation can be non-wellfounded in various ways; here are three: (i) gunk: for all x there is a y such that y is a proper part of x; (ii) bounded infinite descent: there is an infinite chain of distinct proper parts x1>x2>x3>... which (after infinitely many steps) terminates in a smallest element y; (iii) loops: there are x and y such that x is a proper part of y and y is a proper part of x.




1Department of Philosophy, University of St Andrews



1 Bohn, E., (2009), “An Argument against the Necessity of Unrestricted Composition”, Analysis, 69(1): 27-31.

2 Caplan, B., Tillman, C.; Reeder, P., (2010), “Parts of Singletons”, Journal of Philosophy 107: 501-533.

3 Cotnoir, A. J., (2010), “Anti-Symmetry and Non-Extensional Mereology”, The Philosophical Quarterly 60 (239): 396-405.

4 Cotnoir, A. J., (2013), “Beyond Atomism”, Thought, 2(1): 67-72.

5 Cotnoir, A. J., (2014), “Universalism and Junk”, Australasian Journal of Philosophy 4(92), 649-664.

6 Cotnoir, A. J., (2016), “Does Universalism Entail Extensionalism?”, Nous 50(1): 121-132.

7 Cotnoir, A. J.; Bacon, A., (2012), “Non-Wellfounded Mereology”, Review of Symbolic Logic 5 (2): 187-204.

8 Donnelly, M., (2010), “Parthood and Multi-Location”, in Zimmerman, D. (ed.), Oxford Studies in Metaphysics, Vol. 5, Oxford University Press, 203-243.

9 Donnelly, M., (2011), “Using Mereological Principles to Support Metaphysics”, The Philosophical Quarterly 61: 225-246.

10 Eagle, A., (2007), “Location and Perdurance” in Zimmerman, D. (ed.) Oxford Studies in Metaphysics, Vol. 5, Oxford University Press, 53-94.

11 Effingham, N., (2010), “Mereological Explanation and Time Travel”, Australasian Journal of Philosophy 88 (2): 333-345.

12 Effingham, N.; Robson, J., (2007), “A Mereological Challenge to Endurantism”, Australasian Journal of Philosophy 85: 633-640.

13 Forrest, P., (2002), “Non-Classical Mereology and its Application to Sets”, Notre Dame Journal of Formal Logic 43: 79-94.

14 Gilmore, C., (2007), “Time Travel, Coinciding Objects, and Persistence” in Zimmerman, D. (ed.), Oxford Studies in Metaphysics, Vol. 3, Oxford University Press, 177-198.

15 Gilmore, C., (2010), “Coinciding Objects and Duration Properties: Reply to Eagle”, in Zimmerman, D. (ed.), Oxford Studies in Metaphysics, Vol. 5, Oxford University Press, 95–111.

16 Gilmore, C., (2014a), “Parts of Propositions” in S. Kleinschmidt, ed. Mereology and Location, Oxford: Oxford University Press.

17 Gilmore, C., (2014b), “Quasi-Supplementation, Plenitudinous Coincidentalism, and Gunk” in Substance: New Essays, Munich: Philosophia Verlag.

18 Kearns, S., (2011), “Can a Thing Be Part of itself?”, American Philosophical Quarterly 48 (1): 87-93.

19 Kleinschmidt, S., (2011), “Multilocation and Mereology”, Philosophical Perspectives 25: 253-276.

20 Rea, M., (2010), “Universalism and Extensionalism: A Reply to Varzi”, Analysis, 70 (3): 490-496.

21 Rossberg, M., (2009), “Leonard, Goodman, and the Development of the Calculus of Individuals” in Ernst. G. et al. (eds.) From Logic to Art: Themes from Nelson Goodman, Ontos: Frankfurt, 51-69.

22 Sanford, D., (1993), “The Problem of the Many, Many Composition Questions, and Naïve Mereology”, Nous, 27 (2): 219-228.

23 Simons, P. M., (1987), Parts: A Study in Ontology, Oxford: Clarendon.

24 Smith, D., (2009), “Mereology without Weak Supplementation”, Australasian Journal of Philosophy 87: 505-511.

25 Spencer, J., (2012), “All Things Must Pass away”, in Oxford Studies in Metaphysics: Vol. 7, Bennett, K.; Zimmerman, D. (eds.), Oxford: Oxford University Press, 67-92.

26 Tarski, A., (1956), “Foundations of the Geometry of Solids” in Corcoran, J. (ed.), Logic, Semantics, Metamathematics, Indianapolis: Hackett, 24-29.

27 Thomson, J. J., (1983), “Parthood and Identity across Time”, Journal of Philosophy 80 (4): 201-220.

28 Thomson, J. J., (1998), “The Statue and the Clay”, Nous 32 (2): 149-173.

29 Tillman, C.; Fowler, G., (2012), “Propositions and Parthood: The Universe and Antisymmetry”, Australasian Journal of Philosophy 90: 525-539.

30 Uzquiano, G., (2011), “Mereological Harmony” in Zimmerman, D.; Bennett, K. (eds.), Oxford Studies in Metaphysics. Vol. 6, Oxford University Press, 199-224.

31 van, Inwagen, P., (1993), “Naïve Mereology, Admissible Valuations, and Other Matters”, Nous (2): 229-234.

32 Varzi, A., (2006), “Mereology” in Zalta, E. N. (ed.), The Stanford Encyclopedia of Philosophy_http://plato.stanford.edu/archives/win2006/entries/mereology/.

33 Varzi, A., (2008), “The Extensionality of Parthood and Composition”, The Philosophical Quarterly 58: 108-133.

34 Varzi, A., (2009), “Universalism entails Extensionalism”, Analysis 69: 599-604.

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