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In this paper, I will argue that Logics of Formal Inconsistency $$ can be used as very sophisticated and powerful methods of classical recapture. I will compare $LFIs$ with the well-known non-monotonic logics by Batens and Priest and the ‘shrieking’ rules of Beall. I will show that these proposals can be represented in $LFIs$ and that $LFIs$ give room to more complex and varied recapturing strategies. |
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Infectious logics are systems that have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated as a way to treat different pathological sentences differently, namely, by allowing some of them to be truth-value gluts and some others to be truth-value gaps and as a way to treat the semantic pathology suffered by at least (...) |
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Priest, argues that classical reasoning can be made compatible with his preferred logical theory by proposing a methodological maxim authorizing the use of classical logic in consistent situations. Although Priest has abandoned this proposal in favour of the one in G. Priest, I shall argue that due to the fact that the derivability adjustment theorem holds for several logics of formal consistency, these paraconsistent logics are particularly well suited to accommodate classical reasoning by means of a version of that maxim, (...) |
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Weakening classical logic is one of the most popular ways of dealing with semantic paradoxes. Their advocates often claim that such weakening does not affect non-semantic reasoning. Recently, however, Halbach and Horsten have shown that this is actually not the case for Kripke’s fixed-point theory based on the Strong Kleene evaluation scheme. Feferman’s axiomatization $\textsf{KF}$ in classical logic is much stronger than its paracomplete counterpart $\textsf{PKF}$, not only in terms of semantic but also in arithmetical content. This paper compares the (...) |
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One of the oldest systems of paraconsistent logic is the set of so-called C-systems of Newton da Costa, and this has been generalized into a family of systems now known as logics of formal inconsistencies by Walter Carnielli, Marcelo Coniglio and João Marcos. The characteristic notion in these systems is the so-called consistency operator which, roughly speaking, indicates how gluts are behaving. One natural question then is to ask if we can let not only gluts but also gaps be around (...) |
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In this article, we defend that incorporating a rejection operator into a paraconsistent language involves fully specifying its inferential characteristics within the logic. To do this, we examine a recent proposal by Berto for a paraconsistent rejection, which — according to him — avoids paradox, even when introduced into a language that contains self-reference and a transparent truth predicate. We will show that this proposal is inadequate because it is too incomplete. We argue that the reason it avoids trouble is (...) |
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In different papers, Carnielli, W. & Rodrigues, A., Carnielli, W. Coniglio, M. & Rodrigues, A. and Rodrigues & Carnielli, present two logics motivated by the idea of capturing contradictions as conflicting evidence. The first logic is called BLE and the second—that is a conservative extension of BLE—is named LETJ. Roughly, BLE and LETJ are two non-classical logics in which the Laws of Explosion and Excluded Middle are not admissible. LETJ is built on top of BLE. Moreover, LETJ is a Logic (...) |
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In some recent articles, Cobreros, Egré, Ripley, & van Rooij have defended the idea that abandoning transitivity may lead to a solution to the trouble caused by semantic paradoxes. For that purpose, they develop the Strict-Tolerant approach, which leads them to entertain a nontransitive theory of truth, where the structural rule of Cut is not generally valid. However, that Cut fails in general in the target theory of truth does not mean that there are not certain safe instances of Cut (...) |