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NATURAL AXIOMS FOR CLASSICAL MEREOLOGY

  • A. J. COTNOIR (a1) and ACHILLE C. VARZI (a2)
Abstract

We present a new axiomatization of classical mereology in which the three components of the theory—ordering, composition, and decomposition principles—are neatly separated. The equivalence of our axiom system with other, more familiar systems is established by purely deductive methods, along with additional results on the relative strengths of the composition and decomposition axioms of each system.

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Corresponding author
*DEPARTMENT OF LOGIC AND METAPHYSICS UNIVERSITY OF ST ANDREWS EDGECLIFFE, THE SCORES ST ANDREWS, FIFE KY16 9AR, UK E-mail: ac117@st-andrews.ac.uk
DEPARTMENT OF PHILOSOPHY COLUMBIA UNIVERSITY NEW YORK, NY 10027, USA E-mail: av72@columbia.edu
References
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[1]Hovda, P. (2009). What is classical mereology? Journal of Philosophical Logic, 38, 5582.
[2]Leonard, H. S. & Goodman, N. (1940). The calculus of individuals and its uses. Journal of Symbolic Logic, 5, 4555.
[3]Leśniewski, S. (1916). Podstawy ogólnej teoryi mnogości. I, Moskow, Prace Polskiego Koła Naukowego w Moskwie, Sekcya matematyczno-przyrodnicza; Eng. trans. by Barnett, D. I. (1991). Foundations of the general theory of sets. I. In Surma, S. J., Srzednicki, J. T., Barnett, D. I., and Rickey, F. V., editors. Stanislaw Lesniewski: Collected Works, Vol. 1. Dordrecht: Kluwer Academic Publishers, pp. 129173.
[4]Simons, P. M. (1987). Parts. A Study in Ontology. Oxford: Clarendon Press.
[5]Varzi, A. C. (2016). Mereology. In Zalta, E. N., editor. The Standford Encyclopedia of Philsophy (Spring 2016 edition). Available at http://plato.stanford.edu/archives/spr2016/entries/mereology.
[6]Varzi, A. C. On three axiom systems for classical mereology. Logic and Logical Philosophy, in press.
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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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