Abstract
Priest’s 2014 theory of unity and identity, based on a paraconsistent logic, has a wide range of applications. In this paper, I apply his theory to some puzzles concerning mereology and topology. These puzzles suggest that the classical mereotopology needs to be revised. I compare and contrast the Priest-inspired solution with another, based on classical logic, that requires the co-location of boundaries. I suggest that the co-location view should be preferred on abductive grounds.
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Notes
- 1.
By “classical mereotopology” I mean the system called General Extensional Mereotopology with Closure (GEMTC) by Casati and Varzi (1999, p. 59).
- 2.
These definitions are from Casati and Varzi (1999, p. 80).
- 3.
These are the smt systems of Casati and Varzi (1999).
- 4.
- 5.
Of course the rejection of the antisymmetry of parthood is available. See, e.g., Cotnoir (2010).
- 6.
See, e.g., Hocking and Young (1961, p. 14).
- 7.
Early suggestions along these lines can be found in Priest (2006, Chap. 11).
- 8.
Priest (2014) following his earlier coinage (2002) calls them “gluons”. The name is unfortunate: “gluon” is already the name for a fundamental particle of physics, the gauge boson for the strong force which is responsible for holding matter together by binding quarks into protons and neutrons. Of course, Priest isn’t literally talking about gluons in the physicist sense since his gluons are responsible for the unity of all parts into any whole. Turner (2015) suggests the name is a mischievous wink at current physics. Anyway, I avoid all talk of gluons in what follows.
- 9.
See Sects. 2.6–2.7 of Priest (2014).
- 10.
Typically, only purely qualitative properties are thought to feature in Leibniz’s Law. As locational properties aren’t purely qualitative, they wouldn’t typically be allowed to play a distinguishing role. Priest, however, rejects this restriction (2014, p. 23) allowing locational differences to play a distinguishing role. (See also Priest 2014, Sect. 2.7.)
- 11.
Priest (2014, p. 26) accepts that identities are temporary.
- 12.
See Fact 1, Priest (2014, p. 27).
- 13.
See Fact 2, Priest (2014, p. 27).
- 14.
- 15.
Of course there are other ways of making a donut. We could insist that the correct model involves simply punching out a portion of matter from the middle of the sphere, leaving a donut and its remainder (similar to the lumps of dough sometimes sold as “donut holes”); this method would not be all that different from the model of cutting the sphere in half. The puzzle isn’t that there’s no way of making a donut, but that there’s seemingly no explanation for a very natural way of doing so.
- 16.
In the case of splitting the sphere, we wouldn’t want to apply this solution, which would commit us to say that term “u”, which denotes the u-part for the sphere pre-split comes to denote a and b post-split. But if that were so, then u doesn’t go out of existence even when the sphere does.
- 17.
The following presentation of these ideas owes much to Smith (1997).
- 18.
It should be noted that this reverses the ordinary direction of explanation. Typically we’d want to determine facts about boundaries from facts about what pointy objects there are around. On the Brentano–Chisholm view, we start with the condition that everything has a boundary and work back to the number of points. This aspect of the account is not strictly necessary for the co-location solution to go through. All that is needed is for there to be uncountably many co-located points—the underlying explanation for that fact needn’t be as the Brentano–Chisholm view assumes. (Thanks to an anonymous referee for raising the issue.)
- 19.
See Chisholm (1984).
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Acknowledgements
The research and writing of this paper was supported by a 2017–2018 Leverhulme Research Fellowship from the Leverhulme Trust.
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Cotnoir, A.J. (2019). Unity, Identity, and Topology: How to Make Donuts and Cut Things in Half. In: Başkent, C., Ferguson, T. (eds) Graham Priest on Dialetheism and Paraconsistency. Outstanding Contributions to Logic, vol 18. Springer, Cham. https://doi.org/10.1007/978-3-030-25365-3_11
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