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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Paraconsistent set theory by predicating on consistency

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Author(s):
Carnielli, Walter [1] ; Coniglio, Marcelo E. [1]
Total Authors: 2
Affiliation:
[1] Univ Estadual Campinas, UNICAMP, Ctr Log Epistemol & Hist Sci CLE, Rua Sergio Buarque de Holanda 251, BR-13083859 Campinas, SP - Brazil
Total Affiliations: 1
Document type: Journal article
Source: JOURNAL OF LOGIC AND COMPUTATION; v. 26, n. 1, SI, p. 97-116, FEB 2016.
Web of Science Citations: 5
Abstract

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. (AU)

FAPESP's process: 10/51038-0 - Logical consequence, reasoning and computation - LOGCONS
Grantee:Walter Alexandre Carnielli
Support type: Research Projects - Thematic Grants