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Theoretical Mereology


Peter Forrest


Pages 554 - 562



Mereology is widely defined as the theory of parthood, but as I shall explain it is better described as the theory of materiall parthood, where I use the adjective ‘material’ to mean concerned with the stuff of which things are made. Mereology was introduced by Leśniewski (1916) following his equally rigorous theories of protothetic and ontology (Simons 1987: 60–65) and, in a somewhat different and more accessible form as the Calculus of Individuals by Leonard and Goodman (1940), based on Leonard’s 1930 thesis ‘Singular Terms’. These systems are different ways of developing what I call classical mereology, which is mathematically equivalent to a complete Boolean algebra with the minimum element deleted – deleted because there is no null thing. There are many expositions of classical mereology but not as much has been written on alternatives. (See, however, Simons 1987: 81-92)). So in this article I shall briefly expound the classical theory, and then consider what sort of case can be made for or against classical mereology.




1School of Humanities, University of New England in Armidale, NSW, Australia



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2 Burkhardt, H.; Dufour, C. A., (1991), “Part/Whole I: History”, in Burkhardt, H.; Smith, B. (eds.), Handbook of Metaphysics and Ontology, Munich: Philosophia, 663-673.

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5 Dennett, D., (1979), “Where am I”, in Brainstorms: Philosophical Essays in Mind and Psychology, Hassocks: Harvester Press, 310-323.

6 Eberle, R. A., (1970), Nominalistic Systems, Dordrecht: Reidel.

7 Forrest, P., (2004), “Grit or Gunk: Implications of the Banach-Tarski Paradox”, The Monist 87: 351-370.

8 Hudson, H., (2004), “Simples”, The Monist 87: 3030-351.

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

10 Leśniewski, S., (1916), “Podstawy ogólnej teoryi mnogości I”, (Foundations of a General Theory of Manifolds), Prace Polskiego Kola Naukowe w Moskwie.

11 Lewis, D. K., (1991), Parts of Classes, Oxford: Blackwell.

12 Luschei, E. C., (1965), The Logical Systems of Leśniewski, Amsterdam: North-Holland.

13 Rescher, N, (1955), “Axioms for the Part Relation”, Philosophical Studies, 6: 8-11.

14 Sanford, D., (1993), “The Problem of the Many, Many Composition Questions, and Naive Mereology”, Noûs 27: 219-228.

15 Simons, P. M., (1987), Parts. A Study in Ontology, Oxford: Clarendon.

16 Simons, P. M., (1991), “Part/Whole II: Mereology Since 1900”, in Burkhardt, H.; Smith, B. (eds.), Handbook of Metaphysics and Ontology, Munich: Philosophia: 209-210.

17 Smith, B., (1982), “Annotated Bibliography of Writings on Part-Whole Relations since Brentano”, in B. Smith (ed.), Parts and Moments. Studies in Logic and Formal Ontology, Munich: Philosophia: 481-552.

18 Smith, B., (1985), “Addenda to: Annotated Bibliography of Writings on Part-Whole Relations since Brentano”, in Sällström, P. (ed.), An Inventory of Present Thinking about Parts and Wholes, vol. 3, Stockholm: Forskningsrådsnämnden: 74-86.

19 Tarski, A., (1956), “Foundation of the Geometry of Solids” in Logic, Semantics, Metamathematics, Tr. J. H. Woodger, Oxford: Clarendon Press: 24-9.

20 Varzi, A.“Mereology”, Stanford Encyclopedia of Philosophy.

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