The Revision System

Abstract

Abstract The last phase of our defense of the revision theory of truth is to confirm its material adequacy. We said in the preceding chapter that we shall achieve this goal by developing a formal semantical system that correctly models the revision theory of truth, and then showing that it delivers the intuitively correct verdicts in a representative sample of cases. In this chapter, we make good our promise: we advance a system of stability semantics whose limit rule assignment is designed to deal successfully with the problem of ,-unstable sentences and the problem of initial excessive arbitrariness. We call this system the revision system. In Section 4.2 we describe the limit rule assignment that generates the revision system and explain its approach to these two problems. We show there that this system does not produce any of the CRASS or CHOP errors discussed in Chapter 3. Given the type oflimit rule that the system employs, it is very likely that this system is free from all artifacts. Hence, we conclude that the revision system of stability semantics confirms the material adequacy of the revision theory of truth. In Section 4.3, we carry this confirmation one step further. We define a notion of logical consequence that is appropriate for any formal language whose semantics is of the type described in Section 4.2, and we show that this logical consequence relation validates all modes of deductive reasoning that ought to be preserved.