Revision Without Revision Sequences: Circular Definitions

Journal of Philosophical Logic:1-29 (forthcoming)
Authors
Edoardo Rivello
Università di Torino
Abstract
The classical theory of definitions bans so-called circular definitions, namely, definitions of a unary predicate P, based on stipulations of the form $$Px =_{\mathsf {Df}} \phi,$$where ϕ is a formula of a fixed first-order language and the definiendum P occurs into the definiensϕ. In their seminal book The Revision Theory of Truth, Gupta and Belnap claim that “General theories of definitions are possible within which circular definitions [...] make logical and semantic sense” [p. IX]. In order to sustain their claim, they develop in this book one general theory of definitions based on revision sequences, namely, ordinal-length iterations of the operator which is induced by the definition of the predicate. Gupta-Belnap’s approach to circular definitions has been criticised, among others, by D. Martin and V. McGee. Their criticisms point to the logical complexity of revision sequences, to their relations with ordinary mathematical practice, and to their merits relative to alternative approaches. I will present an alternative general theory of definitions, based on a combination of supervaluation and ω-length revision, which aims to address some criticisms raised against revision sequences, while preserving the philosophical and mathematical core of revision.
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DOI 10.1007/s10992-018-9481-2
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References found in this work BETA

Outline of a Theory of Truth.Saul A. Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
Revision Without Revision Sequences: Self-Referential Truth.Edoardo Rivello - forthcoming - Journal of Philosophical Logic:1-29.
Notes on Naive Semantics.Hans G. Herzberger - 1982 - Journal of Philosophical Logic 11 (1):61 - 102.
On Rigorous Definitions.Nuel Belnap - 1993 - Philosophical Studies 72 (2-3):115 - 146.

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