Notes on models of first-order mereological theories

• Authors: Tsai Hsing-chien
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

mereology; models; first-order mereological theorie

• Publisher: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Journal: Logic and Logical Philosophy
• Year: 2015
• Volume: 24
• Issue: 4 Mereology and Beyond
• Pages: 469–482

Dates

online

2015-04-28

Contributors

author

Tsai Hsing-chien

• Department of Philosophy, National Chung-Cheng University, Taiwan

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

Identifiers

DOI

10.12775/LLP.2015.009