Validity, dialetheism and self-reference

PAILOS, FEDERICO MATÍAS

SYNTHESE (DORDRECHT)

SPRINGER

Lugar: Berlin; Año: 2018

0039-7857

It has been argued recently (in Beall (2009) and Beall and Murzi (2013)) that dialetheist theories are unable to express the concept of naive validity. In this paper, we will show that LP can be non-trivially expanded with a naive validity predicate. The resulting theory, LPVal reaches this goal by adopting a weak self-referential procedure. We show that LPVal is sound and complete with respect to the three-sided sequent calculus SLPVal. Moreover, LPVal can be safely expanded with a transparent truth predicate. We will also present an alternative theory LPVal∗, which includes a nondeterministic validity predicate.