Decidability of mereological theories

Hsing-chien Tsai

DOI: http://dx.doi.org/10.12775/LLP.2009.004

Abstract


Mereological theories are theories based on a binary predicate ‘being a part of’. It is believed that such a predicate must at least define a partial ordering. A mereological theory can be obtained by adding on top of the basic axioms of partial orderings some of the other axioms posited based on pertinent philosophical insights. Though mereological theories have aroused quite a few philosophers’ interest recently, not much has been said about their meta-logical properties. In this paper, I will look into whether those theories are decidable or not. Besides, since theories of Boolean algebras are in some sense upper bounds of mereological theories which can be found in the literature, I shall also make some observations about the possibility of getting mereological theories beyond Boolean algebras.

Keywords


mereology; mereological theories; part-whole relation; decidability; undecidability

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References


Casati, R., and A.C. Varzi, 1999, Parts and Places, The MIT Press.

Clay, R.E., 1974, “Relation of Leśniewski’s mereology to Boolean algebras”, Journal of Symbolic Logic 39: 638–648.

Enderton, H.B., 1972, A Mathematical Introduction to Logic, Academic Press, San Diego.

Grzegorczyk, A., 1955, “The systems of Leśniewski in relation to contemporary logical research”, Studia Logica 3: 77–97.

Koppelberg, S., 1989, Handbook of Boolean Algebras, vol. 1, North-Holland, Amsterdam.

Leśniewski, S., 1992, “Foundations of the general theory of sets I”, trans. By D.I. Barnett, in: S. Leśniewski, Collected Works, vol. 1, Kluwer, Dordrecht.

Monk, J.D., 1976, Mathematical Logic, Springer-Verlag, New York.

Pietruszczak, A., 2005, “Pieces of Mereology”, Logic and Logical Philosophy 14: 211–234.

Shoenfield, J.R., 1967, Mathematical Logic, Addison-Wesley, London.

Simons, P., 1987, Parts: A Study in Ontology, Clarendon Press, Oxford.

Tarski, A., 1956, “On the foundations of Boolean algebra”, in: Logic, Semantics, Metamathematics, Oxford University Press, Oxford.

van Inwagen, P., 1990, Material Beings, Cornell University Press, Ithaca.




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