References
Bostock, David: 1974, Logic and Arithmetic, Volume I, Oxford Press, New York and Oxford.
Burge, Tyler: 1980, ‘Truth and Singular Terms’, reprinted in Mark Platts (ed.), Reference, Truth and Reality, Routledge & Kegan Paul, London, Boston, and Henley.
Dummett, Michael: 1973, Frege: The Philosophy of Language, Duckworth, London.
Dummett, Michael: 1981, The Interpretation of Frege's Philosophy, Harvard University Press, Cambridge, Massachussetts.
Frege, Gottlob: 1964, The Basic Laws of Arithmetic, University of California Press, Berkeley.
Frege, Gottlob: 1979, Posthumous Writings, The University of Chicago Press, Chicago.
Furth, Montgomery: 1968, ‘Two Types of Denotation’, in N. Rescher (ed.), Studies in Logical Theory, The American Philosophical Quarterly Monograph Series, Oxford, pp. 9–39.
Grossman, Reinhardt: 1973, Ontological Reduction, Indiana University Press, Bloomington, Indiana.
Hodes, Harold: 1976, ‘Review of D. Bostock's Logic and Arithmetic, Volume I’, The Journal of Philosophy 73(6), pp. 149–57.
Hodes, Harold: 1984a, ‘Logicism and the Ontological Commitments of Arithmetic’, The Journal of Philosophy 81(3), pp. 123–49.
Hodes, Harold: 1984b, ‘Axioms for Actuality’, The Journal of Philosophical Logic 13(1), pp. 27–34.
Hodes, Harold: 1984c, ‘On Modal Logics Which Enrich First-Order S5’, The Journal of Philosophical Logic 13, pp. 423–54.
Hodes, Harold: 1986–1987, ‘Individual-Actualism and Three-Valued Modal Logics’, The Journal of Philosophical Logic 15, pp. 369–401, and 16, pp. 17–63.
Hodes, Harold: 1989, ‘Three-Valued Logics: An Introduction, A Comparison of Various Logical Lexica, and Some Philosophical Remarks’, Annals of Pure and Applied Logic 43, pp. 99–145.
Hodes, Harold: 1988a, ‘Cardinality Logics I: Inclusions Between Languages Based on “exactly”’, Annals of Pure and Applied Logic 39, pp. 199–238.
Hodes, Harold: 1988b, ‘Cardinality Logics II: Definability’, The Journal for Symbolic Logic 53(3), pp. 765–84.
Hodes, Harold: 1990, ‘Ontological Commitment, Thick and Thin’, in George Boolos (ed.), Meaning and Method: Essays in Honor of Hilary Putnam, Cambridge University Press, Cambridge.
Hodes, Harold: (forthcoming), ‘Where Do Sets Come From?’, The Journal for Symbolic Logic.
Kaplan, David: 1979, ‘How to Russell a Frege-Church’, reprinted in Michael Loux (ed.), The Possible and The Actual, Cornell University Press, Ithaca, New York.
Wright, Crispin: 1983, Frege's Conception of Numbers as Objects, Aberdeen University Press, Aberdeen.
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I read an ancestor of this paper at the December 1983 meeting of the Eastern Division of the American Philosophical Association. I'd like to thank the commentator Glen Helman for helpful comments; similar thanks go to John G. Bennett.
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Hodes, H.T. Where do the natural numbers come from?. Synthese 84, 347–407 (1990). https://doi.org/10.1007/BF00485187
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DOI: https://doi.org/10.1007/BF00485187