Advertisement

Suggestions for Further Pluralist Research

  • Michèle Friend
Chapter
Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 32)

Abstract

In this chapter I do three quite different things. One is to give some indication of how to extend Maddy’s idea of making mathematician’s aspirations explicit, thereby marrying philosophy and mathematics. The second is to elaborate on the discussion of Lobachevsky by comparing intentional perspectives on Lobachevsky’s work. This is best done by a pluralist, since he has no agenda. The third is to demonstrate working in a trivial setting, in particular the work concerns Frege’s formal trivial system. A speculation is made about how we can learn more about the notion of cardinality. This is important since only the pluralist can see how to do this explicitly, consciously and seriously. Each of these developments suggests further directions for pluralist research.

Keywords

Euclidean Geometry Cardinal Number Hyperbolic Geometry Paraconsistent Logic Regulatory Principle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Arrigoni, T. (2007). What is meant by V? Reflections on the universe of all sets. Paderborn: Mentis.Google Scholar
  2. Boolos, G. (1986). Saving Frege from contradiction. Proceedings of the Aristotelian Society, LXXXVII, 137–151.Google Scholar
  3. Buldt, B., & Schlimm, D. (2010). Loss of vision: How mathematics turned blind while it learned to see more clearly. In B. Löwe & T. Muller (Eds.), PhiMSAMP philosophy of mathematics: Aspects and mathematical practice (Texts in philosophy, 11, pp. 39–58). London: Individual Author/College Publications.Google Scholar
  4. Davis, P. J., & Hersh, R. (1998). The mathematical experience. Boston: A Mariner Book, Houghton Mifflin Company.Google Scholar
  5. Frege, G. (1893, 1903). Grundgesetze der Arithmetik I, II. Jena: Pohle. Partly translated in Black, M., & Geach, P. (Trans.). (1980). Translations from the philosophical writings of Gottlob Frege (3rd ed.). Oxford: Blackwell.Google Scholar
  6. Friend, M., Goethe, N. B., & Harizanov, V. (Eds.). (2007). Induction, algorithmic learning theory and philosophy: Vol. IX. Logic epistemology and the unity of science. Dordrecht: Springer.Google Scholar
  7. Heck, R. G., Jr. (1993). The development of arithmetic in Frege’s Grundgesetze der Arithmetik. The Journal of Symbolic Logic, 58(2), 579–601.CrossRefGoogle Scholar
  8. Kagan, V. F. (1957). N. Lobachevsky and his contribution to science. Moscow: Foreign Languages Publishing House.Google Scholar
  9. Maddy, P. (1997). Naturalism in mathematics. Oxford: Clarendon Press.Google Scholar
  10. Marker, D. (2000). Model theory: An introduction (Graduate texts in mathematics). New York: Springer.Google Scholar
  11. Shapiro, S. (1991). Foundations without foundationalism. In A case for second-order logic (Oxford logic guides 17). Oxford: Oxford University Press.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Michèle Friend
    • 1
  1. 1.The George Washington UniversityWashington, DCUSA

Personalised recommendations