Erkenntnis

, Volume 53, Issue 1–2, pp 219–265 | Cite as

Neo-Logicism? An Ontological Reduction of Mathematics to Metaphysics

  • Edward N. Zalta

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REFERENCES

  1. Balaguer, M.: 1998, Platonism and Anti-Platonism in Mathematics, Oxford University Press, Oxford.Google Scholar
  2. Balaguer, M.: 1995, ‘A Platonist Epistemology', Synthese 10, MA.Google Scholar
  3. Carnap, R.: 1967, The Logical Structure of the World, R. George (trans.), University of California Press, Berkeley.Google Scholar
  4. Carnap, R.: 1950, ‘Empiricism, Semantics, and Ontology', Revue Internationale de Philosophie, 4, 20–40.Google Scholar
  5. Feferman, S.: 1998, In the Light of Logic, Oxford University Press, Oxford.Google Scholar
  6. Feferman, S.: 1998a, ‘What Rests on What? The Proof-Theoretic Analysis of Mathematics', in Feferman (1998), pp. 187–208.Google Scholar
  7. Feferman, S.: 1988, ‘Hilbert's Program Relativized: Proof-Theoretical and Foundational Reductions', Journal of Symbolic Logic 53, 364–384.Google Scholar
  8. Feferman, S.: 1960, ‘Arithmetization of Metamathematics in a General Setting', Fundamenta Mathematicae XLIX, 35–92.Google Scholar
  9. 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
  10. 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
  11. 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
  12. Field, H. 1993, ‘The Conceptual Contingency of Mathematical Objects', Mind, 102(406), 285–299.Google Scholar
  13. Field, H.: 1989, Realism, Mathematics, and Modality, Blackwell, Oxford.Google Scholar
  14. 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
  15. Field, H.: 1980, Science Without Numbers, Blackwell, Oxford.Google Scholar
  16. Frege, Gottlob: 1884, The Foundations of Arithmetic, translated by J. L. Austin, Blackwell, Oxford, 1974, second revised edition.Google Scholar
  17. Frege, Gottlob: 1893/1903, Grundgesetze der Arithmetik, Band I/II, Jena: Verlag Hermann Pohle.Google Scholar
  18. 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
  19. Jubien, M.: 1969, ‘Two Kinds of Reduction', The Journal of Philosophy, 66(17), 533–541.Google Scholar
  20. Kripke, S.: 1959, ‘A Completeness Theorem in Modal Logic', Journal of Symbolic Logic 24, 1–15.Google Scholar
  21. Lewis, D.: 1986, On the Plurality of Worlds, Blackwell, Oxford.Google Scholar
  22. Linsky, B. and Zalta, E.: 1995, ‘Naturalized Platonism vs. Platonized Naturalism', The Journal of Philosophy, xcii(10), 525–555.Google Scholar
  23. Maddy, P.: 1997, Naturalism in Mathematics, Clarendon, Oxford.Google Scholar
  24. Mundy, B.: unpublished manuscript, ‘Zalta's Logic of Encoding', version #3, January 1996.Google Scholar
  25. Niebergall, K. G.: this volume, ‘On the Logic of Reducibility: Axioms and Examples'.Google Scholar
  26. Pelletier, J. and Zalta, E.: 2000, ‘How to Say Goodbye to the Third Man', Noûs, forthcoming.Google Scholar
  27. Resnik, M.: 1997, Mathematics as a Science of Patterns, Clarendon, Oxford.Google Scholar
  28. Resnik, M.: 1981, ‘Mathematics as a Science of Patterns: Ontology and Reference', Noûs, 15, 529–550.Google Scholar
  29. Rosen, G.: 1993, ‘The Refutation of Nominalism(?)', Philosophical Topics, 21(2), 149–186.Google Scholar
  30. 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
  31. Shapiro, S.: 1997, Philosophy of Mathematics: Structure and Ontology, Oxford University Press, Oxford.Google Scholar
  32. Shapiro, S.: 1989, ‘Structure and Ontology', Philosophical Topics, 17, 145–171.Google Scholar
  33. Tarski, A., Mostowski, A., and Robinson, R.: 1953, Undecidable Theories, North Holland, Amsterdam.Google Scholar
  34. 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
  35. Wagner, S.: 1982, ‘Arithmetical Fiction', Pacific Philosophical Quarterly, 63, 255–269.Google Scholar
  36. Wright, C.: 1983, Frege's Conception of Numbers as Objects, Aberdeen University Press, Aberdeen, Scotland, UK.Google Scholar
  37. Zalta, E.: 2000, ‘A (Leibnizian) Theory of Concepts', Philosophiegeschichte und logische Analyse/Logical Analysis and History of Philosophy, forthcoming.Google Scholar
  38. 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
  39. Zalta, E.: 1993, ‘Twenty-Five Basic Theorems in Situation and World Theory', Journal of Philosophical Logic, 22, 385–428.Google Scholar
  40. Zalta, E.: 1988, Intensional Logic and the Metaphysics of Intentionality, MIT/Bradford, Cambridge, MA.Google Scholar
  41. Zalta, E.: 1983, Abstract Objects: An Introduction to Axiomatic Metaphysics, D. Reidel, Dordrecht.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Edward N. Zalta
    • 1
  1. 1.Center for the Study of Language and InformationStanford UniversityStanfordU.S.A.

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