Advertisement

Mathematical descriptions

  • Bernard Linsky
  • Edward N. Zalta
Article
  • 70 Downloads

Abstract

In this paper, the authors briefly summarize how object theory uses definite descriptions to identify the denotations of the individual terms of theoretical mathematics and then further develop their object-theoretic philosophy of mathematics by showing how it has the resources to address some objections recently raised against the theory. Certain ‘canonical’ descriptions of object theory, which are guaranteed to denote, correctly identify mathematical objects for each mathematical theory T, independently of how well someone understands the descriptive condition. And to have a false belief about some particular mathematical object is not to have a true belief about some different mathematical object.

Keywords

Philosophy of mathematics Abstract objects Definite descriptions Denotation of individual terms 

References

  1. Benacerraf, P. (1981). Frege: The last logicist. In P. French et al. (Ed.), Midwest studies in philosophy: VI (pp. 17–35). Minneapolis: University of Minnesota Press [reference is to the reprint in Demopoulos, W. (1995). Frege’s philosophy of mathematics (pp. 44–67). Cambridge, MA: Harvard University Press.Google Scholar
  2. Buijsman, S. (2017). Referring to mathematical objects via definite descriptions. Philosophia Mathematica, 3(25), 128–138.Google Scholar
  3. Linsky, B., & Zalta, E. (1995). Naturalized platonism versus platonized naturalism. Journal of Philosophy, 92, 525–555.CrossRefGoogle Scholar
  4. Nodelman, U., & Zalta, E. (2014). Foundations for mathematical structuralism. Mind, 123, 39–78.CrossRefGoogle Scholar
  5. Russell, B. (1905). On denoting. Mind (n.s.), 14, 479–493.CrossRefGoogle Scholar
  6. Zalta, E. (1983). Abstract objects: An introduction to axiomatic metaphysics. Dordrecht: D. Reidel.CrossRefGoogle Scholar
  7. Zalta, E. (1988). Intensional logic and the metaphysics of intentionality. Cambridge, MA: MIT Press.Google Scholar
  8. Zalta, E. (2000). Neo-logicism? An ontological reduction of mathematics to metaphysics. Erkenntnis, 53, 219–265.CrossRefGoogle Scholar
  9. Zalta, E. (2001). Fregean senses, modes of presentation, and concepts. Philosophical Perspectives (Noûs Supplement), 15, 335–359.Google Scholar
  10. Zalta, E. (2003). Referring to fictional characters. Dialectica, 57, 243–254.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of AlbertaEdmontonCanada
  2. 2.Center for the Study of Language and InformationStanford UniversityStanfordUSA

Personalised recommendations