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Mostert, A.

Theoretical Philosophy

Inconsistency Blown Away: On the principle of explosion in relevant and other paraconsistent logics

In this thesis I explore the way in which relevant and other paraconsistent logics deal with the principle of explosion (EFQ). Central theme to this thesis is the concept of logical consequence. Classically logical consequence is only defined in terms of truth preservation. EFQ follows because any inference using a contradictory (hence impossible) set of premises is valid.

I have found two basic strategies to deal with the problem of EFQ, firstly one could make it possible for a contradictory set of premises to be true. Secondly one could deal with the notion logical consequence. In this thesis I found that all paraconsistent logics adopt the former strategy whereas some but not all school of relevant logics adopt the latter.

In this thesis I argue that the first strategy is a “mechanical” and does not address the core of the problem which lies with the concept of logical consequence itself. I argue that truth preservation is a necessary but not sufficient criterion for logical consequence. In contrast to standard literature, I do not argue for this on the basis of intuitions concerning validity, but, on the basis of pragmatic reasons concerning the sense (sinn) of these inferences. Based on these reasons I defend the so-called Scottish plan involving a non truth-functional definition of logical consequence.

Last modified:11 September 2014 12.15 p.m.