Alfred Tarski’s T-Scheme as a Definitional Equivalence

Abstract

The goal of this paper is to present a way of reading Alfred Tarski’s T-scheme as a definitional – and not material – equivalence. Anil Gupta and Nuel Belnap in their book The Revision Theory of Truth (MIT 1993), develop a theory of truth and a theory of definition, which are called Revision Theories – of Truth (RTT) and of Definition (RTD). They accept Tarski’s T-sentences (such as: “snow is white” is true iff snow is white) and their central role for the signification of truth. According to RTT and RTD the centrality of Tarski’s T-sentences can be maintained only by accepting interdependent definitions. Gupta and Belnap claim that it is worthy to read the T-scheme as a definitional equivalence rather than as a material equivalence, for the former understanding allows us to solve the Liar paradox. To obtain this result, it is important to notice a structural similarity between the T-scheme and the general scheme of definition.

Gupta and Belnap reject Tarski’s demand for formal correctness of definitions and claim that it is logically justified to accept circular definitions. This is why they modify a general scheme of definition by adding a predicate which is being defined (definiendum) – e.g. an arbitrary predicate G – to the definiens, i.e. to the defining formula which occurs on the right side of the definitional scheme. A circular definition, which is constructed in such a way, is helpful in showing that different patterns of behaviour of the predicate G are similar to respective patterns of behaviour of the predicate “true”. Such a result suggests that the concept of truth is itself circular.