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Metamathematics of Mereology

Andrzej Pietruszczak

Pages 361 - 367

We will briefly examine mathematical properties of mereological structures as defined by Stanisław Leśniewski and Alfred Tarski (Leśniewski 1991, Tarski 1956a). By a mereological structure we mean a pair (M, ⊏) (or (M, ⊑) resp.), where M is a non-empty set and ⊏ (or ⊑, resp.) is a binary relation in M, and such that for some complete Boolean algebra (A, +, •, –, 0, 1) we have M = A\{0} and for all x, yM: xy iff xy and xy (resp. xy iff xy, or), where the relation ≤ is defined as follows (see section 3 below):

1Department of Logic, Nicolaus Copernicus University

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2 Grzegorczyk, A., (1955), “The System of Leśniewski in Relation to Contemporary Logical Research”, Studia Logica 3: 77-95.

3 Leonard, H. S.; N. Goodman, (1940), “The Calculus of Individuals and its Uses”, Journal of Symbolic Logic 5: 45-55.

4 Leśniewski, S., (1991) (in Polish: 1927–1931), “On the Foundations of Mathematics”, in Collected Works (Surma, S. J. and others, editors), number 44 in Nijhoff International Philosophy Series, pages 174–382. Kluwer Academic Publishers, Dordrecht.

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

6 Pietruszczak, A., (2005), “Pieces of Mereology”, Logic and Logical Philosophy 14: 345-450.

7 Simons, P., (1987), Parts. A Study in Ontology, Oxford: Oxford University Press.

8 Tarski, A., (1956a), “Foundations of the Geometry of Solids” in Logic, Semantics, Metamathematics, Oxford: Oxford University Press.

9 Tarski, A., (1956b), “On the Foundations of Boolean Algebra” in Logic, Semantics, Metamathematics, Oxford: Oxford University Press.


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