Philosophy of non-classical logics: Toward problems of paraconsistency & paracompleteness

Workshop on Philosophy of non-classical logics:

Toward problems of paraconsistency & paracompleteness

Keynote speaker: Graham Priest (CUNY)

There is an ongoing philosophical and logical debate about motivations in accepting or rejecting the principle (law) of (non-)contradiction and the principle (law) of excluded middle. A logic rejecting the principle of non-contradiction is called paraconsistent and a logic rejecting the principle of excluded middle is called paracomplete. If both principles are duals of each other we have some reason to reject both principles and get paranormalsystems. But what does it really mean to reject a classical principle (law)? And what are the philosophical consequences for this refusal? In which sense would it still be possible to defend nowadays that there is just one true logic, if we have such a great diversity of logics?

Among the famous logical systems which are paraconsistent but not paracomplete are, for instance, the da Costa systems. Intuitionist logics are paracomplete but not paraconsistent. And a lot of systems of relevant logic are paraconsistent as well as paracomplete. To evaluate these systems’ philosophical relevance, we have to inter alia examine the logical form of their atomic formulas, the logical behavior of their negation, conjunction and disjunction as well as the properties of logical consequence relations. From a philosophical point of view it is very important to understand which elements are responsible for such deviations from classical logic. E.g., do we have only local reasons? In the case of Jaśkowski's version of paraconsistent logic we have to change the conjunction. In the da Costa systems mainly negation is under attack. Or do we have global reasons like in systems of first degree entailments? (Belnap, Dunn, Priest). What is the position of paracomplete, intuitionist approaches (Brouwer, Heyting and their followers)?

This workshop shall represent a privileged platform to evaluate proposals for a more integrated and general approach to philosophical motivations and consequences in the emergence of non-classical logics.

Workshop organized by Marcos Silva (Federal University of Ceará, Fortaleza, Brazil) and Ingolf Max (University of Leipzig, Germany).

Our workshop will be held at the V World Congress on Universal Logic.

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