Ripley's inferentialist approach to the solution of semantic paradoxes

The authors of this paper consider a new approach to the notion of truth and to the solution of semantic paradoxes suggested by David Ripley - a contemporary Australian logician and philosopher. The object of the paper is a critical analysis of the logical conception of Ripley and an elicitation of substantial features of his approach to the solution of the paradox problem. Ripley suggests an inferen-tialist and bilateralist approach to the solution of semantic paradoxes underlying in works of Ian Rum-fitt, Greg Restall and Robert Brandom. Bilateralism as a particular form of inferentialism states that a meaning of a sentence depends on validity of its inferences based in terms of conditions of assertion and denial. Bilateralism and inferentialism are influenced by the coherent theory of truth as it opposites denotationalism which is based on the traditional correspondence view. Ripley changes the classical first-order logic by eliminating the rule of cut and adding the predicate of transparent truth but keeping all other axioms of the classical logical system. He considers that paradoxes are such sentences that cannot be either asserted or denied; as a bilateralist, Ripley argues that one should consider some sentences as paradoxes only if we have extra information about elements of the sentence: some paradoxes might not be considered as ones. He proposes two distinct ways of solving paradoxes - strict and tolerant approaches. The difference between these two ways is that if we choose the tolerant way, we can either assert or deny a paradox and if we choose the strict one, we must estimate paradoxes as senseless sentences. The question is how we are able to deal with semantic paradoxes if we cannot actually solve them: Ripley's approach supposes at least a more suitable way to deal with paradoxes considering their contradictional nature. The authors of the paper drew a conclusion that Ripley's inferentialist approach is one of possible ways of solving semantic paradoxes.

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