The mereology of structural universals

Peter Forrest



This paper explores the mereology of structural universals, using the structural richness of a non-classical mereology without unique fusions. The paper focuses on a problem posed by David Lewis, who using the example of methane, and assuming classical mereology, argues against any purely mereological theory of structural universals. The problem is that being a methane molecule would have to contain being a hydrogen atom four times over, but mereology does not have the concept of the same part occurring several times. This paper takes up the challenge by providing mereological analysis of three operations sufficient for a theory of structural universals: (1) Reflexive binding, i.e. identifying two of the places of a universal; (2) Existential binding, i.e. the language-independent correlate of an existential quantification; and (3) Conjunction.


mereology; conjunction; existential binding; David Lewis; reflexive binding; structural universals; unique fusion

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Armstrong, D., Universals and Scientific Realism, Vol. II. A Theory of Universals, Cambridge: Cambridge University Press, 1978.

Bigelow, J., “Towards structural universals”, Australasian Journal of Philosophy, 64 (1986): 94–96. DOI:10.1080/00048408612342291

Caplan, B., Ch. Tillman, and P. Reeder, “Parts of singletons”, Journal of Philosophy, 107 (2010): 501–533.

Cotnoir, A.J., “Anti-symmetry and non-extensional mereology”, The Philosophical Quarterly, 60 (2010): 396–405. DOI:10.1111/j.1467-9213.2009.649.x

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

Forrest, P., The Necessary Structure of the All-pervading Aether: Discrete or Continuous? Simple or Symmetric?, Ontos, 2012. DOI:10.1515/9783110325928

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

Franklin, J., An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure, Palgrave MacMillan, 2014. DOI:10.1057/9781137400734

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

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

Obojska, L., “Some remarks on supplementation principles in the absence of antisymmetry”, Review of Symbolic Logic, 6 (2013): 343–347. DOI:10.1017/S1755020312000330

Sober, E., “Why logically equivalent predicates may pick out different properties”, American Philosophical Quarterly, 19 (1982): 183–189.

Thompson, J.J., “The statue and the clay”, Nous, 32 (1998): 149–173. DOI:10.1111/0029-4624.00094

Tillman, Ch., and G. Fowler, “Propositions and parthood: The universe and antisymmetry”, Australasian Journal of Philosophy, 90 (2012): 525–539. DOI:10.1080/00048402.2011.611812

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

Financed by MNiSW on the basis of agreement no. 706/P-DUN/2018 (dated 10/05/18). Project 1: “Preparation of articles in English for eight editions of the journal Logic and Logical Philosophy over the period 2018–19; Vol. 27, No. 1–4 (2018), Vol. 28, No. 1–4 (2019)”; amount from the DUN grant: 64800 zł. Project 4: “Digitalisation of eight editions of the journal Logic and Logical Philosophy over the period 2018-19; Vol. 27, No. 1–4 (2018), Vol. 28, No. 1–4 (2019)”; amount from the DUN grant: 18600 zł.

ISSN: 1425-3305 (print version)
ISSN: 2300-9802 (electronic version)

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