Paraconsistent set theory by predicating on consistency
Carnielli Walter, Marcelo Coniglio
ARTIGO
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This article intends to contribute to the debate about the uses of paraconsistent reasoning in the foundations of set theory, by means of using the logics of formal inconsistency and by considering consistent and inconsistent sentences, as well as consistent and inconsistent sets. We establish the...
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This article intends to contribute to the debate about the uses of paraconsistent reasoning in the foundations of set theory, by means of using the logics of formal inconsistency 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.
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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQ
FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP
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Paraconsistent set theory by predicating on consistency
Carnielli Walter, Marcelo Coniglio
Paraconsistent set theory by predicating on consistency
Carnielli Walter, Marcelo Coniglio
Fontes
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Journal of logic and computation Vol. 26, no. 1 (Fev, 2016), p. 97-116 |