A revision-theoretic general theory of definitions

The classical theory of definitions bans so-called circular definitions, namely, definitions of, say, a unary predicate P based on stipulations of the form P(x) =Df Φ(P, x), where Φ is a formula of a fixed first-order language and the definiendum P occurs into the definiens Φ. In their seminal book The Revision Theory of Truth [1], 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 (in some variants) based on revision sequences, namely, ordinal-length iterations of the operator which is induced by the (possibly circular) definition of the predicate. Gupta–Belnap’s approach to circular definitions has been criticised, among others, by Martin [2] and McGee [3]. Their criticisms point on the logical complexity of revision sequences, on their relations with ordinary mathematical practice, and on their merits relative to alternative approaches. In my talk I will present an alternative general theory of definitions, based on a combination of supervaluation and omega-length revision, which aims to address some issues raised by Martin and McGee while preserving the philosophical and mathematical core of revision. [1] A.Gupta and N. Belnap, The Revision Theory of Truth,A Bradford Book, MIT Press, 1993. [2] D. A. Martin, Revision and its rivals. Philosophical Issues, vol. 8 (1997), pp. 387–406. [3] V. McGee, Revision. Philosophical Issues, vol. 8 (1997), pp. 407–418.