Property theory and the revision theory of definitions

Journal of Symbolic Logic 65 (1):212-246 (2000)
Abstract
Russell’s type theory has been the standard property theory for years, relying on rigid type distinctions at the grammatical level to circumvent the paradoxes of predication. In recent years it has been convincingly argued by Bealer, Cochiarella, Turner and others that many linguistic and ontological data are best accounted for by using a type-free property theory. In the spirit of exploring alternatives and “to have as many opportunities as possible for theory comparison”, this paper presents another type-free property theory, to be called P*, intended for applications in Montague-style natural language semantics and formal ontology. The theory is philosophically grounded on Gupta’s and Belnap’s revision theory of definitions and its basic idea is viewing predication (exemplification) as a ‘circular concept’ that can be captured by circular definitions. The paper has the following fourteen sections: (1) Introduction; (2) Formal type-free property theory; (3) Applying RTD [revision theory of definitions] to exemplification; (4) The system P*; (5) Some features of P*; (6) A comparison with Turner’s system; (7) Entailment and P*; (8) P* and natural language semantics; (9) Noun phrases; (10) The need for type-freedom in semantics; (11) Arithmetic in P*; (12) Arithmetic in PN*; (13) Complexity of P*; (14) Conclusion, and acknowledgments.
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DOI 10.2307/2586533
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References found in this work BETA
Truth and Paradox.Anil Gupta - 1982 - Journal of Philosophical Logic 11 (1):1-60.
Notes on Naive Semantics.Hans G. Herzberger - 1982 - Journal of Philosophical Logic 11 (1):61 - 102.
Gupta's Rule of Revision Theory of Truth.Nuel D. Belnap - 1982 - Journal of Philosophical Logic 11 (1):103-116.
Semantics and Property Theory.Gennaro Chierchia & Raymond Turner - 1988 - Linguistics and Philosophy 11 (3):261 - 302.

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Citations of this work BETA
Conditionals in Theories of Truth.Anil Gupta & Shawn Standefer - 2017 - Journal of Philosophical Logic 46 (1):27-63.
Solovay-Type Theorems for Circular Definitions.Shawn Standefer - 2015 - Review of Symbolic Logic 8 (3):467-487.
Meaning and Circular Definitions.Francesco Orilia - 2000 - Journal of Philosophical Logic 29 (2):155-169.
Stability and Paradox in Algorithmic Logic.Wayne Aitken & Jeffrey A. Barrett - 2006 - Journal of Philosophical Logic 36 (1):61 - 95.

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