Towards a Philosophical Understanding of the Logics of Formal Inconsistency

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.

Contra o dogmatismo realista: notas sobre acordos e jogos

“…Em algumas discussões racionais ou em alguns domínios importantes de nossas vidas, quando nós lidamos com crenças e informações, por exemplo, nós, de fato, encontramos contradições e mesmo assim continuamos raciocinando, sem a demanda irreal de nos comprometermos com qualquer outra crença, especialmente com as estapafúrdias (CARNIELLI; RODRIGUES, 2015RODRIGUES, , 2016RODRIGUES, , 2017RODRIGUES, , 2019aRODRIGUES, , 2019b. Além disso, vale notar que algumas teorias na ciência poderiam ser inconsistentes, sem serem triviais (PRIEST; TANAKA; WEBER, 2015).…”

Recovery operators, paraconsistency and duality

“…This section reviews the logics mbC and mbCD proposed respectively in [9] and [11], and introduces their new variants mbD and mbCDE. We begin by defining the languages to be used in the remainder of this paper.…”

“…Definition 17 (Paraconsistent and paracomplete logic mbCD) The logic mbCD, defined over the language F or(Σ ), is obtained from CPL + by adding the following (see [11]):…”

Contradiction and (in)Consistency

“…According to (1), there is no model M such that α ∧ ∼α holds in M. (2) says that for every model M, α ∨ ∼α holds in M. Now, given the definition of classical consequence, α ∨ ∼α follows from anything, and anything follows from α ∧ ∼α. 7 We say that a negation is paracomplete if it disobeys (2), and that a negation is paraconsistent if it disobeys (1).…”

“…As outlined in [4], the logic of antiquity did not endorse the validity of ECSQ, and the principle only became a topic of debate in the Middle Ages or Medieval era. It is a plausible, though debatable, conjecture that what is now known as ECSQ, sometimes confused 2 with Ex Falso Sequitur Quodlibet, or Ex Impossibile Sequitur Quodlibet 3 might have been originated in the 14th century ideas of John of Cornwall (quite possibly the 'Pseudo-Duns Scotus' himself).…”