Revision without revision sequences: Circular definitions

The classical theory of denitions bans so-called circular definitions, namely, denitions of (say) a unary predicate P, based on stipulations of the form P(x) =Df phi(P; x); where phi is a formula of a fixed first-order language and the definiendum P oc- curs into the definiens . In their seminal book The Revision Theory of Truth [8], Gupta and Belnap claim that "General theories of denitions 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 [13] and McGee [14]. 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. I will present an alternative general theory of definitions, based on a combination of supervaluation and omega-length revision, which aims to address some criticisms raised against revision sequences, while preserving the philosophical and mathematical core of revision.