Abstract
The proof-theoretic results on axiomatic theories oftruth obtained by different authors in recent years are surveyed.In particular, the theories of truth are related to subsystems ofsecond-order analysis. On the basis of these results, thesuitability of axiomatic theories of truth for ontologicalreduction is evaluated.
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REFERENCES
Belnap, N. and A. Gupta: 1993, The Revision Theory of Truth, MIT Press, Cambridge, MA.
Bonevac, D.: 1982, Reduction in the Abstract Sciences, Hackett, Indianapolis, IN.
Buchholz, W., S. Feferman, W. Pohlers, and W. Sieg: 1981, Iterated Inductive Definitions: Recent Proof-Theoretical Studies, Springer, Berlin.
Burgess, J.: 1986, ‘The Truth is Never Simple', Journal of Symbolic Logic 51, 663–681.
Burgess, J. and Rosen, G.: 1997, A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics, Clarendon, Oxford.
Cantini, A.: 1989, ‘Notes on Formal Theories of Truth', Zeitschrift für mathematische Logik und Grundlagen der Mathematik 35, 97–130.
Cantini, A.: 1990, ‘A Theory of Truth Formally Equivalent to ID1, Journal of Symbolic Logic 55, 244–259.
Cantini, A.: 1996, Logical Frameworks for Truth and Abstraction. An Axiomatic Study, Vol. 135 of Studies in Logic and the Foundations of Mathematics, Elsevier, Amsterdam.
David, M.: 1994, Correspondence and Disquotation: an Essay on the Nature of Truth, Oxford University Press.
Feferman, S.: 1962, ‘Transfinite Recursive Progressions of Axiomatic Theories', Journal of Symbolic Logic 27, 259–316.
Feferman, S.: 1964, ‘Systems of Predicative Analysis', Journal of Symbolic Logic 29, 1–30.
Feferman, S.: 1988, ‘Hilbert's Program Relativized: Proof-Theoretical and Foundational Reductions', Journal of Symbolic Logic 53, 364–384.
Feferman, S.: 1991, ‘Reflecting on Incompleteness', Journal of Symbolic Logic 56, 1–49.
Field, H.: 1986, ‘The Deflationary Conception of Truth', in G. MacDonald and C. Wright (eds), Fact, Science and Morality, Blackwell, Oxford, pp. 55–117.
Friedman, H. and M. Sheard: 1987, ‘An Axiomatic Approach to Self-Referential Truth', Annals of Pure and Applied Logic 33, 1–21.
Gupta, A.: 1982, ‘Truth and Paradox', Journal of Philosophical Logic 11, 1–60.
Halbach, V.: 1994, ‘A System of Complete and Consistent Truth', Notre Dame Journal of Formal Logic 35, 311–327.
Halbach, V.: 1996, Axiomatische Wahrheitstheorien, Akademie Verlag, Berlin.
Halbach, V.: 1999a, ‘Conservative Theories of Classical Truth', Studia Logica 62, 353–370.
Halbach, V.: 1999b, ‘Disquotationalism and Infinite Conjunctions', Mind 108, 1–22.
Halbach, V.: 1999c, ‘Disquotationalism Fortified', in A. Chapuis and A. Gupta (eds), Circularity, Definitions, and Truth, Indian Council of Philosophical Research, New Delhi, to appear.
Halbach, V.: n.d., ‘Modalized Disquotationalism', to appear in proceedings of the conference, ‘Truth, Necessity and Provability’ (V. Halbach and L. Horsten, eds).
Herzberger, H.: 1982, ‘Notes on Naive Semantics', Journal of Philosophical Logic 11, 61–102.
Kahle, R.: 1997, Applikative Theorien und Frege-Strukturen, PhD thesis, Universität Bern, Institut für Informatik und angewandte Mathematik.
Ketland, J.: 1999, ‘Deflationism and Tarski's Paradise', Mind 108, 69–94.
Kotlarski, H., S. Krajewski, and A. Lachlan: 1981, ‘Construction of Satisfaction Classes for Nonstandard Models', Canadian Mathematical Bulletin 24, 283–293.
Kotlarski, H. and Z. Ratajczyk: 1990a, ‘Inductive Full Satisfaction Classes', Annals of Pure and Applied Logic 47, 199–223.
Kotlarski, H. and Z. Ratajczyk: 1990b, ‘More on Induction in the Language with a Satisfaction Class', Zeitschrift für mathematische Logik und Grundlagen der Mathematik 36, 441–454.
Kripke, S.: 1975, ‘Outline of a Theory of Truth', Journal of Philosophy 72, 690–712.
Lachlan, A.: 1981, ‘Full Satisfaction Classes and Recursive Saturation', Canadian Mathematical Bulletin 24, 295–297.
McGee, V.: 1985, ‘How Truthlike can a Predicate Be?', Journal of Philosophical Logic 14, 399–410.
McGee, V.: 1991, Truth, Vagueness and Paradox, Hackett, Indianapolis, IN.
Myczielski, J., P. Pudlak, and A. Stern: 1990, A Lattice of Chapters of Mathematics (Interpretations between Theorems), Vol. 84 of Memoirs of the American Mathematical Society, American Mathematical Society, Providence, Rhode Island.
Niebergall, K.-G.: n.d., 'stärkevergleich und beweistheoretische Ordinalzahlen', manuscript, Munich.
Niebergall, K.-G.: 2000, ‘The Logic of Reducibility: Axioms and Examples', this issue, 97–126.
Orey, S.: 1961, ‘Relative Interpretations', Journal of Symbolic Logic 7, 146–53.
Quine, W. V. O.: 1969, 'Ontological Relativity', Ontological Relativity and Other Essays, Columbia University Press, New York, pp. 26–68.
Schütte, K.: 1977, Proof Theory, Springer, Berlin.
Shapiro, S.: 1985, ‘Second-Order Languages and Mathematical Practice', Journal of Symbolic Logic 50, 714–742.
Shapiro, S.: 1998, ‘Proof and Truth: Through Thick and Thin', Journal of Philosophy 95, 493–521.
Simpson, S.: 1998, Subsystems of Second Order Arithmetic, Springer, Berlin.
Smory?ski, C.: 1985, Self-Reference and Modal Logic, Universitext, Springer.
Tarski, A.: 1956, ‘The Concept of Truth in Formalized Languages', Logic, Semantics, Metamathematics, Clarendon Press, Oxford, pp. 152–278.
Tarski, A., A. Mostowski, and R. M. Robinson: 1953, Undecidable Theories, North Holland, Amsterdam.
Turner, R.: 1990, Truth and Modality, Pitman, London.
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Halbach, V. Truth and Reduction. Erkenntnis 53, 97–126 (2000). https://doi.org/10.1023/A:1005662017962
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DOI: https://doi.org/10.1023/A:1005662017962