Acta Analytica

, Volume 33, Issue 1, pp 19–33 | Cite as

A Notion of Logical Concept Based on Plural Reference

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Abstract

In To be is to be the object of a possible act of choice (Studia Logica, 96, 289–313, 2010) the authors defended Boolos’ thesis that plural quantification is part of logic. To this purpose, plural quantification was explained in terms of plural reference, and a semantics of plural acts of choice, performed by an ideal team of agents, was introduced. In this paper, following that approach, we develop a theory of concepts that—in a sense to be explained—can be labeled as a theory of logical concepts. Within this theory, we propose a new logicist approach to natural numbers. Then, we compare our logicism with Frege’s traditional logicism.

Keywords

Plural reference Plural quantification Logical concepts Logicism 

References

  1. Balaguer, M. (2009). Fictionalism, theft, and the story of mathematics. Philosophia Mathematica, 17, 131–62.CrossRefGoogle Scholar
  2. Boolos, G. (1984). To be is to be the value of a variable (or to be some values of some variables). Journal of Philosophy, 81, 430–49.CrossRefGoogle Scholar
  3. Boolos, G. (1985). Nominalist platonism. Philosophical Review, 94, 327–44.CrossRefGoogle Scholar
  4. Breckenridge, W., & Magidor, O. (2012). Arbitrary reference. Philosophical Studies, 158, 377–400.CrossRefGoogle Scholar
  5. Bueno, O. (2009). Mathematical fictionalism. In Bueno, O., & Linnebo, Ø. (Eds.) New waves in philosophy of mathematics (pp. 59–79). Palgrave Macmillan, Hampshire.Google Scholar
  6. Carrara, M., & Martino, E. (2010). To be is to be the object of a plural act of choice. Studia Logica, 96, 289–313.CrossRefGoogle Scholar
  7. Carrara, M., & Martino, E. (2014). How to understand arbitrary reference. A proposal. In Moriconi, E. (Ed.), Second Pisa colloquium in logic, language and epistemology (pp. 99–121). ETS, Pisa. Google Scholar
  8. Cocchiarella, N. (1985). Frege’s double correlation thesis and Quine’s set theories NF and ML. Journal of Philosophical Logic, 14, 1–39.CrossRefGoogle Scholar
  9. Cocchiarella, N. (1986). Frege, Russell and logicism: a logical reconstruction. In Haaparanta, L., & Hintikka, J. (Eds.) Frege synthesized (pp. 197–252). Reidel, Dordrecht.Google Scholar
  10. Hilbert, D. (2002). On the infinite. In van Heijenoort, J. (Ed.), From Frege to Goedel. A source book in mathematical logic: 1879-1931. (Originally published in 1925) (pp. 367–392). Cambridge, MA: Harvard University Press.Google Scholar
  11. Linnebo, Ø. (2003). Plural quantification exposed. Noûs, 1, 71–92.CrossRefGoogle Scholar
  12. Linnebo, Ø. (2013). Plural quantification. In Zalta, E.N. (Ed.), The Stanford encyclopedia of philosophy. http://plato.stanford.edu/archives/spr2013/entries/plural-quant/.
  13. Linsky, B., & Zalta, E.N. (2006). What is neologicism? Bulletin of Symbolic Logic, 12, 60–99.CrossRefGoogle Scholar
  14. Parsons, C. (1990). The structuralist view of mathematical objects. Synthese, 84, 303–346.CrossRefGoogle Scholar
  15. Resnik, M.D. (1988). Second-order logic still wild. The Journal of Philosophy, 85, 75–87.CrossRefGoogle Scholar
  16. Wright, C. (1983). Frege’s conception of numbers as objects. Aberdeen: Aberdeen University Press.Google Scholar
  17. Wright, C. (1992). Truth and objectivity. Cambridge, MA: Harvard University Press.Google Scholar
  18. Yablo, S. (2005). The myth of the seven. In Kalderon, M. (Ed.), Fictionalism in metaphysics (pp. 88–115). Oxford: Oxford University Press.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.FISPPA DepartmentUniversity of PaduaPadovaItaly

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