On the Metatheory of Field’s ‘Solving the Paradoxes, Escaping Revenge’
Hannes Leitgeb · 2007
Abstract In a sequence of recent publications ([3],[4],[5],[6],[2]), Hartry Field has developed a new and sophisticated account of how to approach the problem of semantic paradoxes. The core of his theory is a theory of truth for languages that contain their own truth predicate, but Field has also shown how analogous type-free theories for satisfaction ([2]), property instantiation ([5]), and definability ([2]) can be introduced. Moreover, the theory can perhaps also be used to give consistent syntactic treatments of modalities in terms of modal predicates of sentences (cf. section 9 on designatedness in [2]). Field’s theory (together with related ones such as Yablo[12]) is now one of the main contenders in this area of philosophical logic and deserves critical attention from both philosophers and logicians who — like Field — are prepared to give up classical logic in view of the benefits from accepting Tarski’s T-scheme unrestrictedly, as well as from those who are willing to abandon the full strength of the T-scheme while not constraining the laws or rules of classical reasoning (I count myself among the latter).