Classical mereology is not elementarily axiomatizable

Andrzej Pietruszczak

DOI: http://dx.doi.org/10.12775/LLP.2015.017

Abstract


By the classical mereology I mean a theory of mereological structures in the sense of [10]. In [7] I proved that the class of these structures is not elementarily axiomatizable. In this paper a new version of this result is presented, which according to my knowledge is the first such presentation in English. A relation of this result to a certain Hsing-chien Tsai’s theorem from [13] is emphasized.

Keywords


classical mereology; mereological structures; the absence of elementary definability of classical mereology

Full Text:

PDF

References


Koppelberg, S., “Elementary arithmetic”, Chapter 1 in Handbook of Boolean Algebras. Vol. 1, J.D. Monk (ed.), North-Holland: Amsterdam, New York, Oxford, Tokyo, 1989.

Koppelberg, S., “Metamathematics” , Chapter 7 in Handbook of Boolean Algebras. Vol. 1, J.D.Monk (ed.), North-Holland: Amsterdam, New York, Oxford, Tokyo, 1989.

Leonard, H. S., and N. Goodman, “The calculus of individuals and its uses”, Journal of Symbolic Logic, 5 (1940): 45–55. DOI: 10.2307/2266169

Leśniewski, S., “O podstawach matematyki. Rozdział IV”, Przegląd Filozoficzny, XXXI (1928): 261–291. English version: “On the foundations of mathematics. Chapter IV”, pages 226–263 in Collected Works, S. J. Surma et al. (eds.), PWN and Kluwer Academic Publishers: Dordrecht, 1991.

Leśniewski, S., “O podstawach matematyki. Rozdziały VI–IX”, Przegląd Filozoficzny, XXXIII (1930): 77–105. English version: “On the foundations of mathematics. Chapters VI–IX”, pages 313–349 in Collected Works, S. J. Surma et al. (eds.), PWN and Kluwer Academic Publishers: Dordrecht, 1991.

Pietruszczak A., 2000, “Kawałki mereologii” (“Pieces of mereology”; In Polish), pages 357–374 in Logika & Filozofia Logiczna. FLFL 1996–1998, J. Perzanowski and A. Pietruszczak (eds.), Nicolaus Copernicus University Press: Toruń, 2000.

Pietruszczak A., Metamereologia (Metamereology; in Polish), Nicolaus Copernicus University Press: Toruń, 2000.

Pietruszczak A., “Pieces of mereology”, Logic and Logical Philosophy, 14 (2005): 211–234. DOI: 10.12775/LLP.2005.014

Pietruszczak A., Podstawy teorii części (Foundations of the theory of parts; in Polish), Nicolaus Copernicus University Scientific Publishing Hause: Toruń, 2013.

Tarski, A., “Les fondemements de la geometrie des corps”, pages 29–30 in Księga Pamiątkowa Pierwszego Zjazdu Matematycznego, Krakow, 1929. Eng. trans.: “Foundations of the geometry of solids”, pages 24–29 in Logic, Semantics, Metamathematics. Papers from 1923 to 1938, Oxford University Press: Oxford, 1956.

Tarski, A., “Zur Grundlegund der Booleschen Algebra. I”, Fundamenta Mathematicae, 24: 177–198. Eng. trans.: “On the foundations of Boolean Algebra”, pages 320–341 in Logic, Semantics, Metamathematics. Papers from 1923 to 1938, Oxford University Press: Oxford, 1956.

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

Tsai, H., “Notes on models of first-order mereological theories”, Logic and Logical Philosophy (published online: April 28, 2015). DOI: 10.12775/LLP.2005.009




Bookmark and Share




ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

Partnerzy platformy czasopism