Advertisement

The Measure of Scottish Neo-Logicism

  • Stewart Shapiro
Part of the Synthese Library book series (SYLI, volume 341)

Keywords

Natural Number Cardinal Number Logical Truth Basic Proposition Abstraction 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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Blackburn, S. [1994], The Oxford dictionary of philosophy, Oxford, Oxford University Press.Google Scholar
  2. 2.
    Blanchette, P. [1996], “Frege and Hilbert on consistency”, Journal of Philosophy 93, 317–336.CrossRefMathSciNetGoogle Scholar
  3. 3.
    Boolos, G. [1987], “The consistency of Frege’s Foundations of arithmetic” in On being and saying: Essays for Richard Cartwright, edited by Judith Jarvis Thompson, Cambridge, Massachusetts, The MIT Press, 3–20; reprinted in [5], 183–201.Google Scholar
  4. 4.
    Boolos, G. [1997], “Is Hume’s principle analytic?”, in Language, thought, and logic, edited by Richard G. Heck, Jr., New York, Oxford University Press, 245–261; reprinted in [5].Google Scholar
  5. 5.
    Boolos, G. [1998], Logic, logic, and logic, Cambridge, Massachusetts, Harvard University Press.zbMATHGoogle Scholar
  6. 6.
    Burge, T. [1998], “Frege on knowing the foundation”, Mind 107, 305–347.CrossRefMathSciNetGoogle Scholar
  7. 7.
    Coffa, A. [1991], The semantic tradition from Kant to Carnap, Cambridge, Cambridge University Press.Google Scholar
  8. 8.
    Cook, R. and P. Ebert [2005], “Abstraction and identity”, Dialectica 59, 1–19.Google Scholar
  9. 9.
    Dedekind, R. [1888], Was sind und was sollen die Zahlen?, Brunswick, Vieweg; translated as The nature and meaning of numbers, in Essays on the theory of numbers, edited by W. W. Beman, New York, Dover Press, 1963, 31–115.Google Scholar
  10. 10.
    Dummett, M. [1991], Frege: Philosophy of mathematics, Cambridge, Massachusetts, Harvard University Press.Google Scholar
  11. 11.
    Ebert, P. [2005], The context principle and implicit definitions: Towards an account of our a priori knowledge of arithmetic, Ph.D. thesis, University of St. Andrews.Google Scholar
  12. 12.
    Fine, K. [2002], The limits of abstraction, Oxford, Oxford University Press.zbMATHGoogle Scholar
  13. 13.
    Frege, G. [1884], Die Grundlagen der Arithmetik, Breslau, Koebner; The foundations of arithmetic, translated by J. Austin, second edition, New York, Harper, 1960.Google Scholar
  14. 14.
    Frege, G. [1893], Grundgesetze der Arithmetik 1, Olms, Hildescheim.Google Scholar
  15. 15.
    Hale, B. [1987], Abstract objects, Oxford, Basil Blackwell.Google Scholar
  16. 16.
    Hale, B. [2000a], “Reals by abstraction”, Philosophia Mathematica (3) 8, 100–123; reprinted in [18], 399–420.zbMATHMathSciNetGoogle Scholar
  17. 17.
    Hale, B. [2000b], “Abstraction and set theory”, Notre Dame Journal of Formal Logic 41, 379–398.zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Hale, B. and Wright, C. [2001], The reason’s proper study, Oxford, Oxford University Press.zbMATHGoogle Scholar
  19. 19.
    Heck, R. [1997], “Finitude and Hume’s principle”, Journal of Philosophical Logic 26, 589–617.zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Hodes, H. [1984], “Logicism and the ontological commitments of arithmetic”, Journal of Philosophy 81, 123–149.CrossRefMathSciNetGoogle Scholar
  21. 21.
    Jeshion, R. [2001], “Frege’s notions of self-evidence”, Mind 110, 937–976.CrossRefMathSciNetGoogle Scholar
  22. 22.
    Linnebo, Ø. [2004], “Predicative fragments of Frege arithmetic”, Bulletin of Symbolic Logic 10, 153–174.zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Parsons, C. [1964], “Frege’s theory of number”, Philosophy in America, edited by Max Black, Ithaca, New York, Cornell University Press, 180–203; reprinted in Mathematics in Philosophy, by C. Parsons, Ithaca, New York, Cornell University Press, 1983, 150–175.Google Scholar
  24. 24.
    Resnik, M. [1997], Mathematics as a science of patterns, Oxford, Oxford University Press.zbMATHGoogle Scholar
  25. 25.
    Shapiro, S. [1991], Foundations without foundationalism: A case for second-order logic, Oxford, Oxford University Press.zbMATHGoogle Scholar
  26. 26.
    Shapiro, S. [1997], Philosophy of mathematics: Structure and ontology, New York, Oxford University Press.zbMATHGoogle Scholar
  27. 27.
    Shapiro, S. [2000], “Frege meets Dedekind: A neo-logicist treatment of real analysis”, Notre Dame Journal of Formal Logic 41, 335–364.zbMATHCrossRefMathSciNetGoogle Scholar
  28. 28.
    Shapiro, S. [2003], “Prolegomenon to any future neo-logicist set theory: Abstraction and indefinite extensibility”, British Journal for the Philosophy of Science 54, 59–91.zbMATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Shapiro, S. [2006], “Structure and identity”, in Identity and modality, edited by Fraser MacBride, Oxford, Oxford University Press, 164–173.Google Scholar
  30. 30.
    Shapiro, S. and A. Weir [2000], “Neo-logicist’ logic is not epistemically innocent”, Philosophia Mathematica (3) 8, 163–189.MathSciNetGoogle Scholar
  31. 31.
    Tarski, A. [1933], “Der Warheitsbegriff in dem formalisierten Sprachen”, Studia philosophica 1, 261–405; translated as “The concept of truth in formalized languages”, [33], 152–278.Google Scholar
  32. 32.
    Tarski, A. [1935], “On the concept of logical consequence”, in [33], 417–429.Google Scholar
  33. 33.
    Tarski, A. [1956], Logic, semantics and metamathematics, Oxford, Clarendon Press; second edition, edited by John Corcoran, Indianapolis, Hackett Publishing Company, 1983.Google Scholar
  34. 34.
    Tennant, N. [1987], Anti-realism and logic, Oxford, Oxford University Press.Google Scholar
  35. 35.
    Wright, C. [1983], Frege’s conception of numbers as objects, Aberdeen, Aberdeen University Press.zbMATHGoogle Scholar
  36. 36.
    Wright, C. [1997], “On the philosophical significance of Frege’s theorem”, Language, thought, and logic, edited by Richard Heck, Jr., Oxford, Oxford University Press, 201–244; reprinted in [18], 272–306.Google Scholar
  37. 37.
    Wright, C. [1998], “On the harmless impredicativity of N= (Hume’s principle)”, The philosophy of mathematics today, edited by Mathias Schirn, Oxford, Oxford University Press, 339–368; reprinted in [18], 229–255.Google Scholar
  38. 38.
    Wright, C. [1999], “Is Hume’s Principle analytic”, Notre Dame Journal of Formal Logic 40, 6–30; reprinted in [18], 307–332.zbMATHCrossRefMathSciNetGoogle Scholar
  39. 39.
    Wright, C. [2000], “Neo-Fregean foundations for real analysis: Some reflections on Frege’s constraint”, Notre Dame Journal of Formal Logic 41, 317–334.zbMATHCrossRefMathSciNetGoogle Scholar
  40. 40.
    Wright, C. and Bob Hale [2000], “Implicit definition and the a priori”, in New essays on the a priori, edited by P. Boghossian and C. Peacocke, Oxford, Oxford University Press, 286–319; reprinted in [18], 117–150.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Stewart Shapiro
    • 1
  1. 1.Department of PhilosophyThe Ohio State UniversityColumbusUSA

Personalised recommendations