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40. Logicians Setting Together Contradictories: A Perspective on Relevance, Paraconsistency, and Dialetheism


Subject Logic and Language » Logic

DOI: 10.1111/b.9781405145756.2002.00044.x


You shall never be good logician, that would set together two contradictories: for that, the schoolmen say, God cannot do. (Thomas Cranmer, cited in the entry for “contradictory” in Little et al., 1973 ) There were doubtlessly many notable features of philosophy in the twentieth century. Perhaps we will have to wait for the perspective afforded by the passage of time to see clearly what they all were. But I think it true to say that one very notable feature is already visible. This is the final breaking of the taboo against inconsistency – the “superstitious dread and veneration in face of contradiction” as Wittgenstein put it (1978: 122). In Western philosophy since Aristotle onwards, as the quotation from Archbishop Cranmer illustrates, inconsistency has been the ultimate ‘no-no.’ Accounts of truth, validity, rationality, have all taken it for granted. True, a few enterprising philosophical spirits, notably Hegel, have challenged the orthodoxy. But this was secure whilst its heartland in formal logic lay unchallenged. It is precisely this heartland that was challenged in the twentieth century, and which allowed the unthinkable to become thinkable. The challenge was laid down by paraconsistent formal logics. These logics allow for a discriminating handling of inconsistencies, not the crude ‘contradictions entail everything’ beloved by the latter – day friends of consistency. This ... log in or subscribe to read full text

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