Completeness in the theory of properties, relations, and propositions

Journal of Symbolic Logic 48 (2):415-426 (1983)
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Abstract

Higher-order theories of properties, relations, and propositions are known to be essentially incomplete relative to their standard notions of validity. It turns out that the first-order theory of PRPs that results when first-order logic is supplemented with a generalized intensional abstraction operation is complete. The construction involves the development of an intensional algebraic semantic method that does not appeal to possible worlds, but rather takes PRPs as primitive entities. This allows for a satisfactory treatment of both the modalities and the propositional attitudes, and it suggests a general strategy for developing a comprehensive treatment of intensional logic

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George Bealer
Yale University

Citations of this work

Property Theories.George Bealer & Uwe Mönnich - 1983 - In Dov M. Gabbay & Franz Guenthner (eds.), Handbook of Philosophical Logic. Dordrecht, Netherland: Kluwer Academic Publishers. pp. 133-251.
Property Theories.George Bealer & Uwe Monnich - 2003 - In Dov Gabbay & Frans Guenthner (eds.), Handbook of Philosophical Logic, Volume 10. Kluwer Academic Publishers. pp. 143-248.
Fine-Grained Type-Free Intensionality.George Bealer - 1989 - In Gennero Chierchia, Barbara H. Partee & Raymond Turner (eds.), Properties, Types, and Meaning, Volume 1. Kluwer Academic Publishers. pp. 177-230.
Property theory: The Type-Free Approach v. the Church Approach.George Bealer - 1994 - Journal of Philosophical Logic 23 (2):139 - 171.

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References found in this work

Quality and concept.George Bealer - 1982 - New York: Oxford University Press.
Intensional isomorphism and identity of belief.Alonzo Church - 1954 - Philosophical Studies 5 (5):65 - 73.
Theories of properties, relations, and propositions.George Bealer - 1979 - Journal of Philosophy 76 (11):634-648.

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