Abstract
In this paper we present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non-contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue that in order to philosophically justify paraconsistency there is no need to endorse dialetheism, the thesis that there are true contradictions. Furthermore, we show that mbC, a logic of formal inconsistency based on classical logic, may be enhanced in order to express the basic ideas of an intuitive interpretation of contradictions as conflicting evidence.
Highlights
We want to present a philosophical motivation for the logics of formal inconsistency (LFIs), a family of paraconsistent logics whose distinctive feature is that of having
With respect to mbC, an LFI based on classical logic presented in Carnielli et al (2007)1, we show how its syntax and semantics can be enhanced in order to express the basic features of the following intuitive reading for the paraconsistent negation: the acceptance of ¬A means that there is some evidence that A is not the case
We defend the view that logics of formal inconsistency are well suited to the epistemological side of logic and fit an intuitive justification of paraconsistency that is not committed to dialetheism
Summary
This is because it endorses the validity of the principle of non-contradiction, (A A), but more importantly because, classically, everything follows from a contradiction This is the inference rule called ex falso quodlibet, or law of explosion,. Classical logic is invariably the logic we first study in introductory logic books, and the law of explosion holds in it, where consistency is tantamount to freedom from contradiction Let us put these things a bit more precisely. Two accepted principles of classical logic are the aforementioned laws of excluded middle and non-contradiction. Note (and this is a point we want to emphasize) that the principle of explosion can be understood as a still more incisive way of saying that there can be no contradiction in reality – otherwise everything is the case, and we know this cannot be so. The central question for an intuitive interpretation for paraconsistency is the following: What does it mean to accept a pair of contradictory propositions A and ¬A?
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