The Fact Semantics for Ramified Type Theory and the Axiom of Reducibility
Edwin D. Mares
Source: Notre Dame J. Formal Logic Volume 48, Number 2
(2007), 237-251.
Abstract
This paper uses an atomistic ontology of universals, individuals, and facts to provide a semantics for ramified type theory. It is shown that with some natural constraints on the sort of universals and facts admitted into a model, the axiom of reducibility is made valid.
First Page:
Show
Hide
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1179323266
Digital Object Identifier: doi:10.1305/ndjfl/1179323266
Mathematical Reviews number (MathSciNet): MR2306395
Zentralblatt MATH identifier: 1137.03004
References
[1] Anderson, C. A., "Russellian intensional logic", pp. 69--103 in Themes from Kaplan, edited by J. Almog, J. Perry, and H. Wettstein, Oxford University Press, Oxford, 1989.
[2] Church, A., "Comparison of Russell's resolution of the semantical antinomies with that of Tarski", The Journal of Symbolic Logic, vol. 41 (1976), pp. 747--60. Reprinted in R. L. Martin, editor, Recent Essays on Truth and the Liar Paradox, Oxford University Press, Oxford,1984, pp. 289--306.
Mathematical Reviews (MathSciNet): MR0441682
Zentralblatt MATH: 0383.03005
Digital Object Identifier: doi:10.2307/2272393
Project Euclid: euclid.jsl/1183739862
[3] Hazen, A. P., and J. M. Davoren, "Russell's 1925 logic", Australasian Journal of Philosophy, vol. 78 (2000), pp. 534--56.
[4] Hazen, A. P., "Predicative logics", pp. 331--408 in Handbook of Philosophical Logic. Vol. 1. Elements of Classical Logic, 2d edition, edited by D. M. Gabbay and F. Guenthner, D. Reidel, Dordrecht, 1983.
Mathematical Reviews (MathSciNet): MR1885180
Zentralblatt MATH: 0875.03037
[5] Jeffrey, R., Formal Logic: Its Scope and Limits, McGraw Hill, New York, 1967.
Zentralblatt MATH: 0925.03002
[6] Kaplan, D., "The ramified theory of types", unpublished manuscript.
[7] Landini, G., Russell's Hidden Substitutional Theory, Oxford University Press, New York, 1998.
Mathematical Reviews (MathSciNet): MR1694614
Zentralblatt MATH: 0933.03002
[8] Leblanc, H., "That Principia Mathematica, first edition, has a predicative interpretation after all", Journal of Philosophical Logic, vol. 4 (1975), pp. 67--70. Reprinted in H. Leblanc, Existence, Truth, and Provability, SUNY Press, Albany, 1982, pp. 236--39.
Mathematical Reviews (MathSciNet): MR0472467
Zentralblatt MATH: 0304.02007
Digital Object Identifier: doi:10.1007/BF00263121
[9] Leblanc, H., and G. Weaver, "Truth-functionality and the ramified theory of types", pp. 148--67 in Truth, Syntax and Modality (Proceedings of the Conference on Alternative Semantics, Temple University, Philadelphia, 1970), vol. 68 of Studies in Logic and the Foundations of Mathematics, North-Holland, Amsterdam, 1973.
Mathematical Reviews (MathSciNet): MR0414313
Zentralblatt MATH: 0273.02010
[10] Lewis, D., On the Plurality of Worlds, Blackwell, Oxford, 1986.
[11] Linsky, B., Russell's Metaphysical Logic, vol. 101 of CSLI Lecture Notes, CSLI Publications, Stanford, 1999.
Mathematical Reviews (MathSciNet): MR1833170
Zentralblatt MATH: 0981.03004
[12] Russell, B., The Problems of Philosophy, Oxford University Press, Oxford, 1959.
[13] Russell, B., An Inquiry into Meaning and Truth, George Allen and Unwin, London, 1980.
[14] Russell, B., ``Theory of knowledge: The 1913 manuscript,'' pp. 1--178 in The Collected Papers of Bertrand Russell. Vol. 7, edited by E. R. Eames, George Allen and Unwin, London, 1984.
[15] Russell, B., The Philosophy of Logical Atomism, Open Court, La Salle, 1985.
[16] Urquhart, A., "The theory of types", pp. 286--309 in The Cambridge Companion to Bertrand Russell, edited by N. Griffin, Cambridge Companions to Philosophy, Cambridge University Press, Cambridge, 2003.
Mathematical Reviews (MathSciNet): MR2021784
Zentralblatt MATH: 1056.03002
Digital Object Identifier: doi:10.1017/CCOL0521631785.009
[17] Whitehead, A. N., and B. Russell, Principia Mathematica, 2d edition, Cambridge University Press, Cambridge, 1925.
Zentralblatt MATH: 51.0046.06
Notre Dame Journal of Formal Logic
