A recovery operator for non-transitive approaches

PAILOS, FEDERICO MATÍAS

Buenos Aires

Workshop; V Workshop on Philosophical Logic; 2016

Buenos Aires Logic Group-S.A.D.A.F.

We will present a way to expand non-transitive theories in order to recover gentle versions of Cut and other classically valid meta-rules. We prove two main results, a negative and a positive one. We will show that STTT, that expands the non transitive logic ST with a transparent truth predicate, and uses a Strong self referential procedure, cannot be further expanded with a recovery operator. In order to do that, one need to use a Weak way to achieve self-references, that uses biconditional, and not identities. We will show that the resulting theory, STTTConsW, is non-trivial.