Paraconsistent set theory by predicating on consistency

8 years 7 months ago

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This paper intends to contribute to the debate about the uses of paraconsistent reasoning in the foundations of set theory, by means of employing the logics of formal inconsistency (LFIs) and by considering consistent and inconsistent sentences, as well as consistent and inconsistent sets. We establish the basis for new paraconsistent set-theories (such as ZFmbC and ZFCil) under this perspective and establish their non-triviality, provided that ZF is consistent. By recalling how George Cantor himself, in his eﬀorts towards founding set theory more than a century ago, not only used a form of ‘inconsistent sets’ in his mathematical reasoning, but regarded contradictions as beneﬁcial, we argue that Cantor’s handling of inconsistent collections can be related to ours. 1 A new look at antinomic sets Ever since the discovery of the paradoxes, the history of contemporary set theory has centered around attempts to rescue Cantor’s naive theory from triviality, traditionally by plac...

Walter Alexandre Carnielli, Marcelo E. Coniglio

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