Notes on models of first-order mereological theories

Hsing-chien Tsai

doi:10.12775/LLP.2015.009

Authors

Hsing-chien Tsai National Chung-Cheng University, Taiwan

DOI:

https://doi.org/10.12775/LLP.2015.009

Keywords

mereology, models, first-order mereological theories

Abstract

This paper will consider some interesting mereological models and, by looking into them carefully, will clarify some important metalogical issues, such as definability, atomicity and decidability. More precisely, this paper will inquire into what kind of subsets can be defined in certain mereological models, what kind of axioms can guarantee that any member is composed of atoms and what kind of axioms are crucial, by regulating the models in a certain way, for an axiomatized mereological theory to be decidable.

Author Biography

Hsing-chien Tsai, National Chung-Cheng University, Taiwan

Department of Philosophy

References

Casati, R., and A. Varzi, Parts and Places, Cambridge: MIT Press, 1999.

Forrest, P., “How innocent is mereology?”, Analysis, 56 (1996): 127–131. DOI:10.1093/analys/56.3.127

Hodges, W., Model Theory, Cambridge: Cambridge University Press, 1993. DOI:10.1017/CBO9780511551574

Lewis, D., On the Plurality of Worlds, Oxford: Basil Blackwell, 1986.

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

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

Tsai, H., “Decidability of mereological thoeries”, Logic and Logical Philosophy, 18 (2009): 46–63. DOI:10.12775/LLP.2009.004

Tsai, H., “Decidability of General Extensional Mereology”, Studia Logica, 101, 3 (2013): 619–636. DOI:10.1007/s11225-012-9400-4

Tsai, H., “A comprehensive picture of the decidability of mereological theories”, Studia Logica 101, 5 (2013): 987–1012. DOI:10.1007/s11225-012-9405-z

Tsai, H., “On the decidability of axiomatized mereotopological theories”, Notre Dame Journal of Formal Logic, 56, 2 (2015): 287–306. DOI:10.1215/00294527-2864307

Tsai, H. and A. Varzi, “Atoms, gunk, and the limits of ‘composition’”, to appear in Erkenntnis.

van Inwagen, P., Material Beings, Ithaca (NY), 1990.

Varzi, A., “Spatial reasoning and ontology: Parts, wholes, and locations”, pp. 945–1038 in Handbook of Spatial Logics, Berlin: Springer Verlag, 2007. DOI:10.1007/978-1-4020-5587-4_15