By Walter A. Carnielli, Marcelo E. Coniglio, Itala M. Loffredo D'Ottaviano (Editors)
Provided on the moment global Congress on Paraconsistency held in Juquehy-Sao Sebastiao, Sao Paulo, Brazil, this name represents an built-in dialogue of all significant issues within the sector of paraconsistent common sense. It highlights philosophical and old elements, significant advancements and real-world purposes.
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Extra resources for Paraconsistency: The Logical Way to the Inconsistent: Proceedings of the World Congress Held in São Paulo
C. A. da Costa (), the founders of paraconsistent logic, proposed, independently, the study of logics which could accommodate contradictory yet non-trivial theories. Accordingly, a paraconsistent logic (a denomination which would be coined only in the seventies, by Miro Quesada) would be initially defined as a logic such that: 3r3A3£ (F Ih A and T II- -,A and T ¥ B). (PL1) Attention: This definition says not that (PNC) is not to hold in such a logic, for it says nothing about all theories of a paraconsistent logic being contradictory, but only that some of them should be contradictory, and yet non-trivial.
Just as a guiding note to the reader, however, we could remark that usually, but not obligatorily, linguistic extensions are also deductive ones, but it is quite easy to find in the realm of non-classical logics, on the other hand, deductive fragments which are not linguistic ones (like intuitionistic logic is a deductive fragment of classical logic). Most paraconsistent logics in the literature are also deductive fragments of classical logic themselves, but the ones we shall be working on here, the C-systems, are in general deductive fragments only of a conservative extension of classical logic —by the addition of (explicitly definable) connectives expressing consistency / inconsistency).
On what concerns this story about regarding consistency as a primitive notion, the status of points, lines and planes in geometry may immediately be thought of, but the case of (imaginary) complex numbers seems to make an even better comparison: even if we do not know what they are, and may even suspect there is little sense in insisting on which way they can exist in the 'real' world, the most important aspect is that it is possible to calculate with them. Girolamo Cardano, who first had the idea of computing with such numbers, seems to have seen this point clearly —he failed, however, to acknowledge the importance of this; in 1545 he wrote in his Ars Magna (cf.
Paraconsistency: The Logical Way to the Inconsistent: Proceedings of the World Congress Held in São Paulo by Walter A. Carnielli, Marcelo E. Coniglio, Itala M. Loffredo D'Ottaviano (Editors)