On the Methodology of Paraconsistent Logic

Logical theory revision through data underdetermination: an anti-exceptionalist exercise

“…Accordingly, new insights over how to adequately interpret the inferential goal of the theory may lead to different interpretations of the logical vocabulary. As examples, in Wansing & Odintsov (2016) the authors defend information as the relevant data for paraconsistent theories so that paraconsistency can be motivated independently of epistemological or metaphysical commitments. According to this view, negation is understood as an operation of cancellation, and the failure of PE is explained by assuming that from the information of A and ¬A, one cannot infer any information about B.…”

“…The selection of the relevant data is then accompanied by an interpretation of the principle in dispute with the reference theory. In the case of the rivalry between paraconsistent and classical theories, four different views on inconsistencies may be distinguished: epistemic (Carnielli & Rodrigues 2019), semantic (Priest (2014) and Mares (2004)), ontological (Priest 2006), and informational (Wansing & Odintsov 2016). 11 The interpretation of inconsistencies for epistemic purposes is motivated by comprehending classical logic as a set of rationality principles that are useful to organize collections of knowledge and evidence in the process of scientific investigation.…”

“…Authors who favor the epistemic view usually weigh the explanatory power of paraconsistent theories through the description of epistemic faculties such as knowledge, evidence, justification, belief, and others. 12 The informational perspective on contradictions is also similar to the epistemic one, but in the sense of Wansing & Odintsov (2016) it has the purpose of ruling out considerations about epistemic agents. As explained by the authors:…”

“…This one best methodology is usually tied to a fixed interpretation of the relevant logical data. In Wansing & Odintsov (2016) the authors defend a monist perspective over the methodology of paraconsistent logic, according to which paraconsistent systems ought to be produced by accepting the notion of information as the relevant data along with the rejection of classical logic as the reference logic for paraconsistent theories.…”

On Contra-Classical Variants of Nelson Logic N4 and Its Classical Extension

“…The pressing question is probably the following: is ∼ a negation at all? Note first that a very modest requirement for a unary connective to deserve the classification as a negation can be found in [14,2,25]: a unary connective ¬ is a negation in a logic L if there exist L-formulas A and B such that in L, A ¬A and ¬B B. This condition is clearly satisfied by Kamide's ∼.…”