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What is Nominalistic Mereology?

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Abstract

Hybrid languages are introduced in order to evaluate the strength of “minimal” mereologies with relatively strong frame definability properties. Appealing to a robust form of nominalism, I claim that one investigated language \(\mathcal {H}_{\textsf {m}}\) is maximally acceptable for nominalistic mereology. In an extension \(\mathcal {H}_{\textsf {gem}}\) of \(\mathcal {H}_{\textsf {m}}\), a modal analog for the classical systems of Leonard and Goodman (J Symb Log 5:45–55, 1940) and Leśniewski (1916) is introduced and shown to be complete with respect to 0-deleted Boolean algebras. We characterize the formulas of first-order logic invariant for \(\mathcal {H}_{\textsf {gem}}\)-bisimulations.

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References

  1. Armstrong, D.M. (1978). Universals and scientific realism Vol. I and II. Cambridge: Cambridge University Press.

    Google Scholar 

  2. Armstrong, D.M. (1986). In defence of structural universals. Australasian Journal of Philosophy, 64, 85–88.

    Article  Google Scholar 

  3. Blackburn, P., de Rijke, M., Venema, Y. (2001). Modal logic: Cambridge University Press.

  4. Balbiani, P., Tinchev, T., Vakarelov, D. (2007). Modal logics for region based theory of space. Fundamenta Informaticae, 81(1–3), 29–82.

    Google Scholar 

  5. Blackburn, P. (1993). Nominal tense logic. Notre Dame Journal of Formal Logic, 14, 56–83.

    Google Scholar 

  6. van Benthem, J. (1976). Modal correspondence theory. PhD Thesis Mathematisch Instituut en Instituut voor Grondslagenonderzoed, Universiteit van Amsterdam.

  7. Casati, R., & Varzi, A.C. (1999). Parts and places. Cambride MA: MIT Press.

    Google Scholar 

  8. Chang, C.C., & Keisler, H.J. (1973). Model theory. Amsterdam: North-Holland Publishing Company.

    Google Scholar 

  9. Erschov, Y. (1964). Decidablity of the elementary theory of distributive lattices with relative complements and the theory of filters. Algebra i Logika, 3, 17–38.

    Google Scholar 

  10. Goodman, N. (1972). A world of individuals (pp. 155–172). Indianapolis and New York: The Bobbs-Merrill Company, Inc.

    Google Scholar 

  11. Goodman, N. (1986). Nominalisms. In L.E. Hahn, & P.A. Schilpp (Eds.), The philosophy of W. V. Quine (pp. 159–161). La Salle, Illinois: Open Court.

    Google Scholar 

  12. Goodman, N., & Quine, W.V.O. (1947). Steps toward a constructive nominalism. The Journal of Symbolic Logic, 12, 105–122.

    Article  Google Scholar 

  13. Goncharov, S. (1997). Countable Boolean algebras and decidability. Consultants Bureau, New York: Siberian School of Algebra and Logic.

    Google Scholar 

  14. Goranko, V., & Vakarelov, D. (1999). Hyperboolean algebras and hyperboolean modal logic. Journal of Applied Non-classical Logics, 9(2–3), 345–368.

    Article  Google Scholar 

  15. Hudson, H. (2007). Simples and gunk. Philosophy Compass, 2, 291–302.

    Article  Google Scholar 

  16. Kontchakov, R., Pratt-Hartmann, I., Wolter, F., Zakharyaschev, M. (2010). Spatial logics with connectedness predicates. Logical Methods in Computer Science, 6(3 3:5, 43), 958–962.

    Google Scholar 

  17. Koppelberg, S. (2006). Boolean algebras as unions of chains of subalgebras. Algebra Universalis, 1, 195–203.

    Google Scholar 

  18. Kozen, D. (1980). Complexity of Boolean algebra. Theoretical Computer Science, 10, 221–247.

    Article  Google Scholar 

  19. Kuusisto, A. (2008). A modal perspective on monadic second-order alternation hierarchies. In Proceedings of Advances in Modal Logic (AiML) Vol. 7.

  20. Leśniewski, S. (1916). Podstawy ogólnej teoryi mnogości. I. Moskow. Prace Polskiego Kola Naukowego w Moskwie.

  21. Leonard, H., & Goodman, N. (1940). A calculus of individuals and its uses. Journal of Symbolic Logic, 5, 45–55.

    Article  Google Scholar 

  22. Lewis, D. (1983). New work for a theory of universals. Australian Journal of Philosophy, 61, 343–377.

    Article  Google Scholar 

  23. Lewis, D. (1991). Parts of classes. Oxford: Blackwell.

    Google Scholar 

  24. Lewis, D. (1986). On the plurality of worlds. Oxford: Blackwell.

    Google Scholar 

  25. Maddy, P. (1990). Realism in mathematics. Oxford: Clarendon Press.

    Google Scholar 

  26. Markosian, N. (1998). Brutal composition. Philosophical Studies, 92, 211–249.

    Article  Google Scholar 

  27. Mason, F.C. (2000). How not to prove the existence of “Atomless Gunk”. Ratio, 13, 175–185.

    Article  Google Scholar 

  28. Monk, D. (Ed.) (1989). Handbook of Boolean algebras, 3 Vols. Amsterdam: North-Holland Publishing Co.

    Google Scholar 

  29. Nenov, Y., & Vakarelov, D. (2008). Modal logics for mereotopological relations. Advances in Modal Logic, 7, 249–272.

    Google Scholar 

  30. Prior, A. (1968). Papers on time and tense: Oxford University Press.

  31. Prior A. N. (1968). Egocentric logic. Nous, 2, 101–119.

    Article  Google Scholar 

  32. Prior A. N. (1969). Worlds, times and selves. L’Age de la Science’, 3, 179–191.

    Google Scholar 

  33. Prior A. N., & Fine K. (1977). Worlds, times and selves. London: Duckworth.

    Google Scholar 

  34. Quine, W.V.O. (1964). On what there is. In From a logical point of view. Second edition, revised. Harvard University Press, Cambridge, Massachusetts (pp. 1–19).

    Google Scholar 

  35. Quine, W.V. (1976). Worlds away. The Journal of Philosophy, 73, 859–863. Reprinted in Quine, W. V. (1981). Theories and things. Cambridge, Mass.: Harvard University Press.

    Article  Google Scholar 

  36. Quine, W.V. (1985). The time of my life: An autobiography: MIT Press.

  37. Sider, T. (2001). Four-dimensionalism: An ontology of persistence and time. Oxford: Oxford University Press.

    Book  Google Scholar 

  38. Sider, T. (1993). Parthood. Philosophical Review, 116, 51–91.

    Article  Google Scholar 

  39. Sider, T. (2011). Writing the Book of the World. Oxford.

  40. Simons, P. (1987). Parts. Oxford.

  41. Simons, P. (2011). Stanislaw Leśniewski. In E. Zalta (Ed.), The Stanford Encyclopedia of philosophy. http://plato.stanford.edu/entries/lesniewski.

  42. Tarski, A. (1956). Foundations of the geometry of solids. In J. Woodger, & J. Corcoran (Eds.), Logic, semantics, metamathematics: Papers 1923-38: Trans. Hackett.

  43. Tarski, A. (1935). Zur Grundlegung der Booleschen Algebra. I. Fundamenta Mathematicae, 24, 177–198.

    Google Scholar 

  44. Tarski, A. (1949). Arithmetical classes and types of Boolean algebras. Bulletin of the American Mathematical Society, 55, 64.

    Google Scholar 

  45. Vakarelov, D. (1995) . A modal logic for set relations. In 10th international congress of logic, methodology, and philosophy of science, Florence, Italy Abstracts (p. 183).

  46. van Inwagen, P. (1990). Material beings. Ithaca NY: Cornell University Press.

    Google Scholar 

  47. Varzi, A. (2011). Mereology. In E. Zalta (Ed.), The Stanford Encyclopedia of philosophy. http://plato.stanford.edu/entries/mereology.

  48. Waszkiewicz, J. (1974). \(\forall \)n-theories of Boolean algebras. Colloquium Mathematicum, 30, 171–175.

    Google Scholar 

  49. Whitehead, A.N. (1929). Process and reality. New York: MacMillan.

    Google Scholar 

  50. Zimmerman, D.W. (1996). Could extended objects be made out of simple parts? An argument for “Atomless Gunk”. Philosophy and Phenomenological Research, 56, 1–29.

    Article  Google Scholar 

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  1. Stanford University, Stanford, CA, 94305, USA

    Jeremy Meyers

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  1. Jeremy Meyers
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Meyers, J. What is Nominalistic Mereology?. J Philos Logic 43, 71–108 (2014). https://doi.org/10.1007/s10992-012-9252-4

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