Mereology then and now

Rafał Gruszczyński, Achille C. Varzi

DOI: http://dx.doi.org/10.12775/LLP.2015.024

Abstract


This paper offers a critical reconstruction of the motivations that led to the development of mereology as we know it today, along with a brief description of some questions that define current research in the field.

Keywords


mereology; parthood; formal ontology; foundations of mathematics

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References


Aczel, P., Non-Well-Founded Sets, CSLI Lecture Notes, Stanford, 1988.

Armstrong, D.M., “In defence of structural universals”, Australasian Journal of Philosophy, 64, 1 (1986): 85–88. DOI: 10.1080/00048408612342261

Bennett, B., and I. Düntsch, “Axioms, algebras and topology”, pages 99–159 in Handbook of Spatial Logics, M. Aiello, I. Pratt-Hartmann, and J. Van Benthem (eds.), Springer-Verlag, Berlin, 2007. DOI: 10.1007/978-1-4020-5587-4_3

Bennett, K., “Having a part twice over”, Australasian Journal of Philosophy, 91, 1 (2013): 83–103. DOI: 10.1080/00048402.2011.637936

Black, M., “The identity of indiscernibles”, Mind, 61, 242 (1952): 153–164. DOI: 10.1093/mind/LXI.242.153

Caplan, B., C. Tillman, and P. Reeder, “Parts of singletons”, Journal of Philosophy, 107, 10 (2010): 501–533. DOI: 10.5840/jphil20101071036

Casari, E., “On Husserl’s theory of wholes and parts”, History and Philosophy of Logic, 21, 1 (2000): 1–43. DOI:10.1080/01445340050044628

Casati, R. and A.C. Varzi, Parts and Places. The Structures of Spatial Representation, MIT Press, Cambridge (MA), 1999.

Clay, R.E., “Relation of Leśniewski’s mereology to Boolean algebra”, Journal of Symbolic Logic, 39, 4 (1974): 638–648. DOI: 10.2307/2272847

Cotnoir, A.J., “Strange parts: The metaphysics of non-classical mereologies”, Philosophy Compass, 8, 9 (2013): 834–845. DOI: 10.1111/phc3.12061

Cotnoir, A.J., “Beyond atomism”, Thought, 2, 1 (2013): 67–72. DOI: 10.1002/tht3.64

Cotnoir, A.J., “Composition as identity. Framing the debate”, pages 3–23 in Composition as identity, A.J. Cotnoir and D. Baxter (eds.), Oxford University Press, Oxford, 2014. DOI: 10.1093/acprof:oso/9780199669615.003.0001

Cotnoir, A.J. and A. Bacon, “Non-wellfounded mereology”, Review of Symbolic Logic, 5, 2 (2012): 187–204. DOI: 10.1017/S1755020311000293

de Laguna, T., “Point, line, and surface, as sets of solids”, Journal of Philosophy, 19, 17 (1922): 449–461. DOI: 10.2307/2939504

Donnelly, M., “Using mereological principles to support metaphysics”, Philosophical Quarterly, 61, 243 (2011): 225–246. DOI: 10.1111/j.1467-9213.2010.683.x

Fine, K., “Part-whole”, pages 463–485 in The Cambridge Companion to Husserl, B. Smith and D.W. Smith (eds.), Cambridge University Press, Cambridge, 1995. DOI: 10.1017/CCOL0521430232.011

Forrest, P., “Nonclassical mereology and its application to sets”, Notre Dame Journal of Formal Logic, 43, 2 (2002): 79–94. DOI:10.1305/ndjfl/1071509430

French, S., and D. Krause Identity in Physics: A Historical, Philosophical, and Formal Analysis, Oxford University Press, Oxford, 2006. DOI: 10.1093/0199278245.001.0001

Gerla, G., “Pointless geometries”, pages 1015–1031 in Handbook of Incidence Geometry, F. Buekenhout (ed.), Elsevier, Amsterdam, 1995. DOI: 10.1016/B978-044488355-1/50020-7

Goodman, N., “A world of individuals”, pages 13–31 in J.M. Bochenski, A. Church, and N. Goodman, The Problem of Universals. A Symposium, University of Notre Dame Press, Notre Dame, 1956.

Gruszczyński, R., and A. Pietruszczak, “Full development of Tarski’s geometry of solids”, The Bulletin of Symbolic Logic, 14, 4 (2008): 481–540. DOI: 10.2178/bsl/1231081462

Gruszczyński, R., and A. Pietruszczak, “How to define a mereological (collective) set”, Logic and Logical Philosophy, 19, 4 (2010): 309–328. DOI: 10.12775/LLP.2010.011

Gruszczyński, R., and A. Pietruszczak, “The relations of supremum and mereological sum in partially ordered sets”, pages 123–140 in Mereology and the Sciences, C. Calosi and P. Graziani (eds.), Springer-Verlag, Berlin, 2014. DOI: 10.1007/978-3-319-05356-1_6

Grzegorczyk, A., “Axiomatizability of geometry without points”, Synthese, 12, 2–3 (1960): 228–235. DOI: 10.1007/BF00485101

Hellman, G., and S. Shapiro, “The classical continuum without points”, Review of Symbolic Logic, 6, 3 (2013): 488–512. DOI: 10.1017/S1755020313000075

Hovda, P., “What is classical mereology?”, Journal of Philosophical Logic, 38, 1 (2009), 55–82. DOI: 10.1007/s10992-008-9092-4

Husserl, E., Logische Untersuchungen. Zweiter Band. Untersuchungen zur Phänomenologie und Theorie der Erkenntnis, Niemeyer, Halle, 1900/1901; 2nd ed. 1913; cited in the Eng. trans. by J.N. Findlay: Logical investigations. Volume Two, Routledge & Kegan Paul, London, 1970.

Leonard, H.S., and N. Goodman, “The calculus of individuals and its uses”, Journal of Symbolic Logic, 5, 2 (1940): 45–55. DOI: 10.2307/2266169

Leśniewski, S., “Czy klasa klas, nie podporządkowanych sobie, jest podporządkowana sobie?”, Przegląd Filozoficzny, 17: 63–75. Eng. trans. By S.J. Surma and J. Wójcik: “Is the class of classes not subordinated to themselves, subordinated to itself?”, pages 115–128 in [32].

Leśniewski, S., Podstawy ogólnej teoryi mnogości. I, Prace Polskiego Koła Naukowego w Moskwie, Sekcja matematyczno-przyrodnicza, Moscow, 1916. Eng. trans. by D.I. Barnett: “Foundations of the general theory of sets. I”, pages 129–173 in [32].

Leśniewski, S., “O podstawach matematyki”, Przegląd Filozoficzny, 30 (1927): 164–206; 31 (1928): 261–291; 32 (1929): 60–101; 33 (1930): 77–105; 34 (1931): 142–170. Cited in the Eng. trans. by D.I. Barnett: “On the foundations of mathematics”, pages 174–382 in [32].

Leśniewski, S., Collected Works. Volume I, S.J. Surma, J.T. Srzednicki, D.I. Barrnett, and V.F. Rickey (eds.), Kluwer Academic Publishers, Dordrecht, 1991.

Lewis, D.K., “Against structural universals”, Australasian Journal of Philosophy, 64, 1 (1986): 25–46. DOI: 10.1080/00048408612342211

Lewis, D.K., Parts of Classes, Blackwell, Oxford, 1991.

Maffezioli, P., “Analytic rules for mereology”, Studia Logica. DOI: 10.1007/s11225-015-9623-2

Mormann, T., “Structural universals as structural parts: Toward a general theory of parthood and composition”, Axiomathes, 20, 2–3 (2010): 209–227. DOI: 10.1007/s10516-010-9105-0

Null, G., “A first-order axiom system for non-universal part-whole and foundational relations”, pages 463–484 in Essays in memory of Aron Gurwitsch, L. Embree (ed.), UniversityPress of America, Lanham (MD), 1983.

Pietruszczak, A., Metamereologia, Wydawnictwo UMK, Toruń, 2000.

Pietruszczak, A., “Paradoks Russella a początki mereologii”, Ruch Filozoficzny, 59, 1 (2002): 123–129.

Pietruszczak, A., “Pieces of mereology”, Logic and Logical Philosophy, 14, 2 (2005): 211–234. DOI: 10.12775/LLP.2005.014

Pietruszczak, A., Podstawy teorii części, Wydawnictwo Naukowe UMK, Toruń, 2013.

Pietruszczak, A., “A general concept of being a part of a whole”, Notre Dame Journal of Formal Logic, 55, 3 (2014): 359–381. DOI: 10.1215/00294527-2688069

Polkowski, L., Approximate Reasoning by Parts. An Introduction to Rough Mereology, Springer-Verlag, Berlin, 2011. DOI: 10.1007/978-3-642-22279-5

Pontow, C., and R. Schubert, “A mathematical analysis of theories of parthood”, Data & Knowledge Engineering, 59, 1 (2006): 107–138. DOI: 10.1016/j.datak.2005.07.010

Priest, G., “A site for sorites”, pages 9–24 in Liars and Heaps: New Essays on Paradox, J.C. Beall (ed.), Oxford University Press, Oxford, 2003.

Quine, W.V.O., “On what there is”, Review of Metaphysics, 2, 5 (1948): 21–38.

Quine, W.V.O., “Speaking of objects”, Proceedings and Addresses of the American Philosophical Association, 31 (1957/1958): 5–22. DOI:10.2307/3129242

Roeper, P., “Region-based topology”, Journal of Philosophical Logic, 23, 3 (1997): 251–309. DOI: 10.1023/A:1017904631349

Shiver, A., “How do you say ‘everything is ultimately composed of atoms’?”, Philosophical Studies, 172, 3 (2015): 607–614. DOI: 10.1007/s11098-014-0321-0

Simons, P.M., “The formalizationof Husserl’s theory of parts and wholes”, pages 481–552 in Parts and Moments. Studies in Logic and Formal Ontology, B. Smith (ed.), Philosophia, Munich, 1982. DOI: 10.1007/978-94-015-8094-6_4

Simons, P.M., Parts. A study in Ontology, Clarendon Press, Oxford, 1987. DOI: 10.1093/acprof:oso/9780199241460.001.0001

Sinisi, V.F., “Leśniewski’s analysis of Russell’s antinomy”, Notre Dame Journal of Formal Logic, 17, 1 (1976): 19–34. DOI: 10.1305/ndjfl/1093887422

Sobociński, B., “L’analyse de l’antinomie russellienne par Leśniewski”, Methodos, 1 (1949): 94–107, 220–228, 308–316; and 2 (1950): 237–257.

Tarski, A., “Les fondements de la géométrie des corps”, pages 29–33 in Księga Pamiątkowa Pierwszego Polskiego Zjazdu Matematycznego, suppl. to Annales de la Société Polonaise de Mathématique, Vol. 7, 1929. Eng. trans. by J.H. Woodger, “Foundations of the geometry of solids”, pages 24–29 in A. Tarski, Logic, Semantics, Metamathematics. Papers from 1923 to 1938, Oxford, Clarendon Press, 1956.

Tarski, A., “Zur Grundlegung der Booleschen Algebra, I”, Fundamenta Mathematicae 24, 1 (1935): 177–198. Engl. trans. “On the foundations of Boolean algebra”, pages 320–341 in A. Tarski, Logic, Semantics, Metamathematics. Papers from 1923 to 1935, Oxford, Clarendon Press, 1956. http://eudml.org/doc/212745 Mereology then and now 427

Tsai, H., “More on decidability of mereological theories”, Logic and Logical Philosophy, 20, 3 (2011): 251–265. DOI: 10.12775/LLP.2011.015

Tsai, H., “More on decidability of mereological theories”, Logic and Logical Philosophy, 20, 3 (2011): 251–265. DOI: 10.12775/LLP.2011.015

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, Vol. 101, No. 5, pp. 987–1012, 2013. DOI:10.1007/s11225-012-9405-z

Tsai, H. and A.C. Varzi, “Atoms, gunk, and the limits of ‘composition’”, Erkenntnis. DOI: 10.1007/s10670-015-9736-z

Urbaniak, R., Leśniewski’s Systems of Logic and Foundations of Mathematics, Springer-Verlag, Berlin, 2013. DOI: 10.1007/978-3-319-00482-2

Vakarelov, D., “Region-based theory of space: Algebras of regions, representation theory, and logics”, pages 267–348 in Mathematical Problems from Applied Logic II, D. Gabbay, M. Zakharyaschev, and S. Goncharov (eds.), Springer-Verlag, New York, 2007. DOI: 10.1007/978-0-387-69245-6_6

van Inwagen, P., Material Beings, Cornell University Press, Ithaca (NY), 1990.

Varzi, A.C., “Spatial reasoning and ontology: Parts, wholes and locations”, pages 945–1038 in Handbook of Spatial Logics, M. Aiello, I. Pratt-Hartmann, and J. Van Benthem (eds.), Springer-Verlag, Berlin, 2007. DOI: 10.1007/978-1-4020-5587-4_15

Varzi, A.C., “On the boundary between material and formal ontology”, pages 3–8 in Interdisciplinary Ontology, Vol. 3, “Proceedings of the Third Interdisciplinary Ontology Meeting”, B. Smith, R. Mizoguchi, and S. Nakagawa (eds.), Keio University Press, Tokyo, 2010.

Varzi, A.C., “Mereology”, in Stanford Encyclopedia of Philosophy, E.N. Zalta (ed.), 2015. http://plato.stanford.edu/entries/mereology/

Whitehead, A.N., An Enquiry Concerning the Principles of Human Knowledge, Cambridge University Press, Cambridge, 1919.

Whitehead, A.N., The Concept of Nature, Cambridge University Press, Cambridge, 1920.

Whitehead, A.N., Process and Reality, MacMillan, New York, 1929.

Zadeh, L., “Fuzzy sets”, Information and Control, 8, 3 (1965): 338–353. DOI: 10.1016/S0019-9958(65)90241-X








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