Paracoherence and Co-constructive Logic

This paper motivates a view called paracoherence, in which paraconsistency and paracompleteness are understood as forms of instability. This is clarified by considering logic and paradox by means of duality so as to provide an account of coherence. Paradoxical statements such as the liar breaks coherence in a classical logic, where (self) duality is mediated by negation. Resultantly, both paraconsistency and paracompleteness represent a break with classical duality, but coherence is reinstated at the level of assertion and denial, where a strengthened version of paradox re-emerges. In response, I suggest a paracoherent structure consisting of an intuitionistic logic of proof, together with co-intuitionistic logic of refutation. By analogy with typical epistemological motivation for intuitionism, this lends itself to an epistemological motivation for paracoherence, which is compatible with a broadly classical view of truth.