A fully classical logic characterized by substructural means

PAILOS, FEDERICO MATÍAS

Buenos Aires

Workshop; VI Workshop on Philosophical Logic; 2017

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

I have presented a metainferential consequence relation calledTSST. TSST not only recovers every classically valid inference, as ST does,but also every classically valid metainference. Moreover, TSST can be safely expanded with a transparent truth predicate. Nevertheless, it seems not easy to develop a sequent calculus for TSST expanded with a transparent truth predicate.Nevertheless, TS/ST cannot recover every classically valid metainference of levels higher than 1. But we can build a hierarchy of consequence relations CMn such that for every level n, a metainference of level n Gamma 1, ..., Gamma n therefor Delta is valid in CL iff it is valid in CMn. Moreover, with the help of the hierarchy we can design CMomega, that recovers any classically valid metainference of any level, and can be safely expanded with a transparent truth predicate.