Abstract
This paper surveys mereology, the theory of parts and wholes, focussing on its origins in Leśniewski, and noting its intended employment as a surrogate for set theory. We examine parallel and independent work by Whitehead, Leonard and Goodman, and outline the subsequent adventures of mereology, both in its formal guises and in its now intensive application within philosophical ontology.
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References
Leśniewski, S.: Pisma zebrane [Collected writings]. In: Jadacki, J.J. (ed.) vol. 2. Semper, Warsaw (2015)
Leśniewski, S.: Collected works. In: Surma, S.J. et al. (eds.) vol. 2. Kluwer/Polish Scientific Publishers, Dordrecht/Warsaw (1992)
Leśniewski, S.: Lesniewski’s lecture notes in logic. In: Srzednicki, J.T.J., Stachniak, Z. (eds.) Kluwer, Dordrecht (1988)
Sobociński, B.: L’analyse de l’antinomie Russellienne par Leśniewski. Methodos 1, 94–107, 220–228, 308–316 (1949); 2, 237–257 (1950). English translation: Leśniewski’s Analysis of Russell’s Paradox. In: Srzednicki, J.T.J., Rickey, V.F. (eds.) Leśniewski’s Systems: Ontology and Mereology, pp. 11–44. Nijhoff/Ossolineum, The Hague/Wrocław (1984)
Leśniewski, S.: Czy klasa klas nie podporządkowanych sobie jest podporządkowana sobie? Przegląd Filozoficzny. 17, 63–75 (1914). Cf. [1, pp. 223–35, 2015]. Translation: Is the Class of Classes not Subordinated to Themselves, Subordinated to Itself? in [2, pp. 115–28]
Leśniewski, S.: Podstawy ogólnej teorii mnogości. I [No further parts appeared]. Moscow: Popławski (1916). (Prace Polskiego Koła Naukowego w Moskwie. Sekcya matematyczno-przyrodnicza, No. 2.) Cf. [1, pp. 256–94]. Translation: Foundations of the General Theory of Sets. I, in [2, pp. 129–73]
Simons, P.: Parts. A Study in Ontology. Clarendon, Oxford (1987)
Whitehead, A.N.: La théorie relationniste de l’espace. Rev. Metaphys. Morale. 23, 423–454 (1916)
Whitehead, A.N.: An Enquiry Concerning the Principles of Natural Knowledge. Cambridge University Press, Cambridge (1919)
Simons, P.: Whitehead und die Mereologie. In: Hampe, M., Maaßen, H. (eds.) Die Gifford Lectures und ihre Deutung. Materialien zu Whiteheads Prozess and Realität, vol. 2, pp. 369–388. Suhrkamp, Frankfurt am Main (1991); English translation: Whitehead and mereology. In: Durand, G., Weber, M. (eds.) Les principes de la connaissance naturelle d’Alfred North Whitehead, pp. 215–233. Ontos, Frankfurt am Main (2007)
Whitehead, A.N.: Process and Reality. An Essay in Cosmology. Macmillan, New York/London (1929). Corrected edition, Macmillan, New York/London (1978)
Lejewski, C.: Consistency of mereology. J. Symb. Log. 34, 321–328 (1969)
Tarski, A.: Les fondements de la géométrie du corps. Księga Pamiątkowa Pierwszego Polskiego Zjazdu Matematycznego, pp. 29–33. Supplement to Annales de la Société Polonaise de Mathématique, Kraków (1929). Extended translation: Foundations of the geometry of solids, in [29, pp. 24–29]
Betti, A.: Leśniewski, tarski and the axioms of mereology. In: Mulligan, K. et al. (eds.) The History and Philosophy of Polish Logic. Essays in Honour of Jan Woleński, pp. 242–258. Palgrave Macmillan, Basingstoke (2013)
Tarski, A.: Appendix E. In: Woodger, J.H. (ed.) The Axiomatic Method in Biology, pp. 161–172. Cambridge University Press, Cambridge (1937)
Tarski, A.: Zur Grundlegung der Booleschen Algebra I. Fund. Math. 24, 177–98 (1935). Translation: On the Foundations of Boolean Algebra, in [14, pp. 320–41]
Leonard, H.S., Goodman, N.: The calculus of individuals and its uses. J. Symb. Log. 5, 45–54 (1940)
Rossberg, M.: Leonard, Goodman, and the development of the calculus of individuals. In: Ernst, G., et al. (eds.) From Logic to Art: Themes from Nelson Goodman, pp. 51–69. Ontos, Frankfurt am Main (2009)
Eberle, R.: Nominalistic systems. Reidel, Dordrecht (1970)
Breitkopf, A.: Axiomatisierung einiger Begriffe aus Nelson Goodmans the structure of appearance. Erkenntnis. 12, 229–247 (1978)
Bostock, D.: Logic and Arithmetic. Vol. 2. Rational and Irrational Numbers. Oxford, Clarendon (1979)
Simons, P.: The formalisation of Husserl’s theory of wholes and parts. In: Smith, B. (ed.) Parts and Moments, pp. 113–159. Philosophia, Munich (1982)
Ridder, L.: Mereologie. Ein Beitrag zur Ontologie und Erkenntnistheorie. Klostermann, Frankfurt am Main (2002)
Varzi, A.: Mereology. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/archives/spr2016/entries/mereology (2016)
van Inwagen, P.: Material Beings. Cornell University Press, Ithaca (1990)
Lewis, D.K.: Parts of Classes. Blackwell, Oxford (1991)
Casati, R., Varzi, A.: Parts and Places. The Structures of Spatial Representation. MIT Press, Cambridge (1999)
Kleinschmidt, S. (ed.): Mereology and Location. Oxford University Press, Oxford (2014)
Tarski, A.: Logic, Semantics, Metamathematics. Papers from 1923 to 1938. Translated by J. H. Woodger, 2nd ed. edited and introduced by J. Corcoran. Hackett, Philadelphia (1983) (1st edn. Oxford, Clarendon Press, 1956)
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Simons, P. (2018). Leśniewski and Mereology. In: Garrido, Á., Wybraniec-Skardowska, U. (eds) The Lvov-Warsaw School. Past and Present. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-65430-0_26
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