Believing and asserting contradictions

Manuel Bremer

Abstract


The debate around 'strong' paraconsistency or dialetheism (the view that there are true contradictions) has - apart from metaphysical concerns - centred on the questions whether dialetheism itself can be definitely asserted or has a unique truth value, and what it should mean, if it is possible at all, to believe a contradiction one knows to be contradictory (i.e. an explicit contradiction). And what should it mean, if it is possible at all, to assert a sentence one knows to be contradictory?
The investigation of believing and asserting the two sides of a contradiction involves considering the semantic and pragmatic distinctions between asserting, believing, denying, rejecting, disbelieving a sentence, abstaining from an opinion and affirming the opposite. Standard logic with its treatment of negation and denial levels some important distinctions. Given a paraconsistent logic with bivalent truth operators and given an account when to assert a sentence there may be occasions on which it is rational not only to believe a sentence one knows to be contradictory, but also to assert it. Dialetheism turns out to be unambiguously affirmable and avoids sliding into trivialism (that anything is true and false and might be believed or asserted).

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