Skip to main content
Log in

Logicism, Structuralism and Objectivity

  • Published:
Topoi Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  • Awodey, S.: 1996, ‘Structure in Mathematics and Logic: A Categorical Perspective’, Philosophia Mathematica 4(3), 209–237.

    Google Scholar 

  • Bell, J. L.: 1986, ‘From Absolute to Local Mathematics’, Synthèse 69, 409–426.

    Article  Google Scholar 

  • Carl, W.: 1994, Frege's Theory of Sense and Reference: Its Origins and Scope, Cambridge: Cambridge University Press.

    Google Scholar 

  • Carnap, R.: 1928, (Aufbau) The Logical Structure of the World, R. A. George (Trans.) (1967), London: Routledge & Kegan Paul.

    Google Scholar 

  • Carnap, R.: 1934, The Logical Syntax of Language, A. Smeaton (Trans.) (1937), London: Kegan Paul.

    Google Scholar 

  • Carnap, R.: 1935, Philosophy and Logical Syntax, London: Kegan Paul.

    Google Scholar 

  • Carnap, R.: 1956, ‘Empiricism, Semantics, and Ontology’, in P. Benacerraf and H. Putnam (Eds.) (1991), Philosophy of Mathematics (2nd ed.), Cambridge: Cambridge University Press.

    Google Scholar 

  • Coffa, J. A.: 1991, The Semantic Tradition from Kant to Carnap: To the Vienna Station, Cambridge: Cambridge University Press.

    Google Scholar 

  • Dummett, M.: 1984, Truth and Other Enigmas, Massachusetts: Harvard University Press.

    Google Scholar 

  • Dummett, M.: 1991, Frege: Philosophy of Mathematics, Massachusetts: Harvard University Press.

    Google Scholar 

  • Dummett, M.: 1994, Origins of Analytic Philosophy, Massachusetts: Harvard University Press.

    Google Scholar 

  • Frege, G.: 1879, Begriffsschrift, in Conceptual Notation and Related Articles, T. W. Bynum (Trans. & Ed.) (1972), Oxford: Oxford University Press, pp. 101–203.

    Google Scholar 

  • Frege, G.: 1880/81, ‘Boole's Logical Calculus and the Conceptscript’, in P. Long and R. White (Eds.) (1979), Posthumous Writings, Oxford: Blackwell, pp. 9–46.

    Google Scholar 

  • Frege, G.: 1882a, ‘On the Scientific Justification of a Conceptual Notation’, in T. W. Bynum (Trans. & Ed.) (1972), Conceptual Notation and Related Articles, Oxford: Oxford University Press, pp. 83–89.

    Google Scholar 

  • Frege, G.: 1882b, ‘On the Aim of Conceptual Notation’, in T. W. Bynum (Trans. & Ed.) (1972), Conceptual Notation and Related Articles, Oxford: Oxford University Press, pp. 90–100.

    Google Scholar 

  • Frege, G.: 1882c, ‘Boole's Logical Formula-language and my Concept-script’, in P. Long and R. White (Eds.) (1979), Posthumous Writings, Oxford: Blackwell, pp. 47–52.

    Google Scholar 

  • Frege, G.: 1884, (Die Grundlagen der Arithmetik) The Foundations of Arithmetic, J. L. Austin (Trans.) (1986), Illinois: Northwestern University Press.

    Google Scholar 

  • Frege, G.: 1885, ‘On Formal Theories of Arithmetic’, in B. McGuinness (Ed.) (1984), Collected Papers on Mathematics, Logic, and Philosophy, Oxford: Blackwell, pp. 112–121.

    Google Scholar 

  • Frege, G.: 1893, The Basic Laws of Arithmetic, M. Furth (Trans. & Ed.) (1967), California: University of California Press.

    Google Scholar 

  • Frege, G.: 1897, ‘Logic’, in P. Long and R. White (Eds.) (1979), Posthumous Writings, Oxford: Blackwell, pp. 126–151.

    Google Scholar 

  • Frege, G.: 1906, ‘Reply to Mr. Thomae's Holiday Causerie’, in B. McGuinness (Ed.) (1984), Collected Papers on Mathematics, Logic, and Philosophy, Oxford: Blackwell, pp. 341–345.

    Google Scholar 

  • Frege, G.: 1924/25, ‘Numbers and Arithmetic’, in P. Long and R. White (Eds.) (1979), Posthumous Writings, Oxford: Blackwell, pp. 275–277.

    Google Scholar 

  • Friedman, M.: 1994, Kant and the Exact Sciences, 2nd ed., Massachusetts: Harvard University Press.

    Google Scholar 

  • Goldfarb, W.: 2001, ‘Frege's Conception of Logic’, to appear in J. Floyd and S. Shieh (Eds.), Futures Past: Reflections on the History and Nature of Analytic Philosophy, Massachusetts: Harvard University Press.

    Google Scholar 

  • Hart, W. D. (ed.): 1996, The Philosophy of Mathematics, Oxford: Oxford University Press.

    Google Scholar 

  • Kant, I.: 1781 & 1787, The Critique of Pure Reason, N. Kemp Smith (Trans.) (1992), London: The Macmillian Press Ltd.

    Google Scholar 

  • Lambek J., and Scott, P. J.: 1989, Introduction to Higher Order Categorical Logic, Cambridge: Cambridge University Press.

    Google Scholar 

  • Landry, E.: 1999, ‘Category Theory: The Language of Mathematics’, Philosophy of Science 66 (Proceedings), S14–S27.

    Article  Google Scholar 

  • Lawvere, F. W.: 1966, ‘The Category of Categories as a Foundation of Mathematics’, Proc. Conference Categorical Algebra (LaJolla 1965), New York: Springer, pp. 1–20.

    Google Scholar 

  • Maddy, P.: 1992, Realism in Mathematics, Toronto: Clarendon Press.

    Book  Google Scholar 

  • Mayberry, J.: 1994, ‘What is Required of a Foundation for Mathematics?’, Philosophia Mathematica 2(3). Special Issue, ‘Categories in the Foundations of Mathematics and Language’, J. L. Bell (Ed.), pp. 16–35.

  • McLarty, C.: 1993, ‘Numbers Can Be Just What They Have to Be’, Nous 27, 487–498.

    Article  Google Scholar 

  • McLarty, C.: 1995, Elementary Categories, Elementary Toposes, Toronto: Clarendon Press.

    Google Scholar 

  • Quine, W. V.: 1951, ‘Two Dogmas of Empiricism’, From a Logical Point of View, 2nd Ed., Massachusetts: Harvard University Press, pp. 20–46.

    Google Scholar 

  • Resnik, M. D.: 1980, Frege and the Philosophy of Mathematics, Ithaca: Cornell University Press.

    Google Scholar 

  • Resnik, M. D.: 1981, ‘Mathematics as a Science of Patterns: Ontology and Reference’, Nous 15, 529–550.

    Article  Google Scholar 

  • Resnik, M. D.: 1996, ‘Structural Relativity’, Philosophia Mathematica 4(3), Special Issue, ‘Mathematical Structuralism’, S. Shapiro (Ed.), pp. 83–99.

  • Richardson, A.: 1998, Carnap's Construction of the World, Cambridge: Cambridge University Press.

    Google Scholar 

  • Russell, B.: 1918, The Philosophy of Logical Atomism, D. Pears (Ed.) (1993), Illinois: Open Court.

    Google Scholar 

  • Russell, B., and Whitehead, A. N.: 1925, Principia Mathematica, 2nd ed., Cambridge: Cambridge University Press.

    Google Scholar 

  • Shapiro, S.: 1996, ‘Space, Number and Structure: A Tale of Two Debates’, Philosophia Mathematica 4(3), Special Issue, ‘Mathematical Structuralism’, S. Shapiro (Ed.), pp. 148–173.

  • Shapiro, S.: 1997, Philosophy of Mathematics: Structure and Ontology, Oxford: Oxford University Press.

    Google Scholar 

  • Tait, W. W.: 1986, ‘Truth and Proof: The Platonism of Mathematics’, in W. D. Hart (Ed.) (1996),The Philosophy of Mathematics, Oxford: Oxford University Press, pp. 142–167.

    Google Scholar 

  • Wittgenstein, L.: 1921, Tractatus Logico-Philosophicus, D. F. Pears, and B. F. McGuinness (Trans.) (1992), London: Routledge & Kegan Paul.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Landry, E. Logicism, Structuralism and Objectivity. Topoi 20, 79–95 (2001). https://doi.org/10.1023/A:1010617228485

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1010617228485

Keywords

Navigation