A suitable conditional in a neutral semantics

PAILOS, FEDERICO MATÍAS

C.A.B.A.

Encuentro; The Buenos Aires-Oxford Research Project: Truth, Paradoxes and Inexpresability; 2013

G.A.F./Sociedad Argentina de Análisis Filosófico

I will present a trivalent semantics for a theory of truth with a suitable conditional, according to the criteria fixed by Beall (2009). The conditional will invalidate all forms of Pseudo-Modus Ponens and Contraction (but leave the sub-structural rules untouched). It will also be non-monotonic, and will allow for an unrestricted validation of the T-Schema. The truth conditions from conjunction and disjunction will also be altered. The key feature of the theory is that the truth conditions of these logical constants are partially indeterminate, and so the logic is not compositional. The resulting theory of truth will not also be paracomplete, but paraconsistent.