Skip to main content
Log in

Neo-Logicism? An Ontological Reduction of Mathematics to Metaphysics

  • Published:
Erkenntnis 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

  • Balaguer, M.: 1998, Platonism and Anti-Platonism in Mathematics, Oxford University Press, Oxford.

    Google Scholar 

  • Balaguer, M.: 1995, ‘A Platonist Epistemology', Synthese 10, MA.

  • Carnap, R.: 1967, The Logical Structure of the World, R. George (trans.), University of California Press, Berkeley.

    Google Scholar 

  • Carnap, R.: 1950, ‘Empiricism, Semantics, and Ontology', Revue Internationale de Philosophie, 4, 20–40.

    Google Scholar 

  • Feferman, S.: 1998, In the Light of Logic, Oxford University Press, Oxford.

    Google Scholar 

  • Feferman, S.: 1998a, ‘What Rests on What? The Proof-Theoretic Analysis of Mathematics', in Feferman (1998), pp. 187–208.

  • Feferman, S.: 1988, ‘Hilbert's Program Relativized: Proof-Theoretical and Foundational Reductions', Journal of Symbolic Logic 53, 364–384.

    Google Scholar 

  • Feferman, S.: 1960, ‘Arithmetization of Metamathematics in a General Setting', Fundamenta Mathematicae XLIX, 35–92.

    Google Scholar 

  • Field, H.: 1998a, ‘Which Undecidable Mathematical Sentences Have Determinate Truth Values?', in H. Dales and G. Olivieri (eds), Truth and Mathematics, Oxford University Press, Oxford, pp. 291–310.

    Google Scholar 

  • Field, H.: 1998b, ‘Mathematical Objectivity and Mathematical Objects', in S. Laurence and C. Macdonald (eds), Contemporary Readings in the Foundations of Metaphysics, Blackwell, Oxford, pp. 387–403.

    Google Scholar 

  • Field, H.: 1994, ‘Are Our Logical and Mathematical Concepts Highly Indeterminate?', in P. French, T. Uehling, H. Wettstein (eds), Midwest Studies in Philosophy, Volume 19, Notre Dame University Press, Nortre Dame, pp. 391–429.

    Google Scholar 

  • Field, H. 1993, ‘The Conceptual Contingency of Mathematical Objects', Mind, 102(406), 285–299.

    Google Scholar 

  • Field, H.: 1989, Realism, Mathematics, and Modality, Blackwell, Oxford.

    Google Scholar 

  • Field, H.: 1984, ‘Critical Notice of Crispin Wright: Frege's Conception of Numbers as Objects', Canadian Journal of Philosophy, 14, 637–662; reprinted in Field (1989), pp. 147–170, with the new title ‘Platonism for Cheap? CrispinWright on Frege's Context Principle'.

    Google Scholar 

  • Field, H.: 1980, Science Without Numbers, Blackwell, Oxford.

    Google Scholar 

  • Frege, Gottlob: 1884, The Foundations of Arithmetic, translated by J. L. Austin, Blackwell, Oxford, 1974, second revised edition.

    Google Scholar 

  • Frege, Gottlob: 1893/1903, Grundgesetze der Arithmetik, Band I/II, Jena: Verlag Hermann Pohle.

    Google Scholar 

  • Hempel, C.: 1945, ‘On the Nature of Mathematical Truth', American Mathematical Monthly 52, 543–556; reprinted in H. Putnam and P. Benacerraf, (eds), The Philosophy of Mathematics: Selected Readings, second edition, Cambridge University Press, Cambridge pp. 377–393.

    Google Scholar 

  • Jubien, M.: 1969, ‘Two Kinds of Reduction', The Journal of Philosophy, 66(17), 533–541.

    Google Scholar 

  • Kripke, S.: 1959, ‘A Completeness Theorem in Modal Logic', Journal of Symbolic Logic 24, 1–15.

    Google Scholar 

  • Lewis, D.: 1986, On the Plurality of Worlds, Blackwell, Oxford.

    Google Scholar 

  • Linsky, B. and Zalta, E.: 1995, ‘Naturalized Platonism vs. Platonized Naturalism', The Journal of Philosophy, xcii(10), 525–555.

    Google Scholar 

  • Maddy, P.: 1997, Naturalism in Mathematics, Clarendon, Oxford.

    Google Scholar 

  • Mundy, B.: unpublished manuscript, ‘Zalta's Logic of Encoding', version #3, January 1996.

  • Niebergall, K. G.: this volume, ‘On the Logic of Reducibility: Axioms and Examples'.

  • Pelletier, J. and Zalta, E.: 2000, ‘How to Say Goodbye to the Third Man', Noûs, forthcoming.

  • Resnik, M.: 1997, Mathematics as a Science of Patterns, Clarendon, Oxford.

    Google Scholar 

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

    Google Scholar 

  • Rosen, G.: 1993, ‘The Refutation of Nominalism(?)', Philosophical Topics, 21(2), 149–186.

    Google Scholar 

  • Quine, W.: 1976, ‘Ontological Reduction and the World of Numbers', in The Ways of Paradox and Other Essays, rev. ed., Harvard University Press, Harvard, pp. 212–220.

    Google Scholar 

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

    Google Scholar 

  • Shapiro, S.: 1989, ‘Structure and Ontology', Philosophical Topics, 17, 145–171.

    Google Scholar 

  • Tarski, A., Mostowski, A., and Robinson, R.: 1953, Undecidable Theories, North Holland, Amsterdam.

    Google Scholar 

  • Visser, A.: 1998, ‘An Overview of Interpretability Logic', in M. Kracht, M. de Rijke, H. Wansing, and M. Zakharyaschev (eds), Advances in Modal Logic, Volume 1, CSLI Lecture Notes No. 87, Stanford: Center for the Study of Language and Information Publications, pp. 307–359.

    Google Scholar 

  • Wagner, S.: 1982, ‘Arithmetical Fiction', Pacific Philosophical Quarterly, 63, 255–269.

    Google Scholar 

  • Wright, C.: 1983, Frege's Conception of Numbers as Objects, Aberdeen University Press, Aberdeen, Scotland, UK.

    Google Scholar 

  • Zalta, E.: 2000, ‘A (Leibnizian) Theory of Concepts', Philosophiegeschichte und logische Analyse/Logical Analysis and History of Philosophy, forthcoming.

  • Zalta, E.: 1999, ‘Natural Numbers and Natural Cardinals as Abstract Objects: A Partial Reconstruction of Frege's Grundgesetze in Object Theory', Journal of Philosophical Logic, 28(6), 619–660.

    Google Scholar 

  • Zalta, E.: 1993, ‘Twenty-Five Basic Theorems in Situation and World Theory', Journal of Philosophical Logic, 22, 385–428.

    Google Scholar 

  • Zalta, E.: 1988, Intensional Logic and the Metaphysics of Intentionality, MIT/Bradford, Cambridge, MA.

    Google Scholar 

  • Zalta, E.: 1983, Abstract Objects: An Introduction to Axiomatic Metaphysics, D. Reidel, Dordrecht.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zalta, E.N. Neo-Logicism? An Ontological Reduction of Mathematics to Metaphysics. Erkenntnis 53, 219–265 (2000). https://doi.org/10.1023/A:1005614102033

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1005614102033

Keywords

Navigation