The evidence approach to paraconsistency versus the paraconsistent approach to evidence

Abstract

In this paper, we analyze the epistemic approach to paraconsistency. This approach is advanced as an alternative to dialetheism on what concerns interpreting paraconsistency and contradictions; instead of having to accept that there are true contradictions (as dialetheists argue), it is suggested that we may understand such situations as involving only conflicting evidence, which restricts contradictions to a notion of evidence weaker than truth. In this paper, we first distinguish two conflicting programs entangled in the proposal: (1) interpreting paraconsistency in general through the notion of evidence, and (2) modeling reasoning with evidence by using paraconsistent logic. The first part of the program, we argue, does not succeed, on the grounds that it does not lead to a uniform proposal to the understanding of paraconsistency, and fails to engage with dialetheism in a legitimate dispute about interpretation of paraconsistency. Also, when seen through the lights of the second kind of approach, a 'logic as modeling' approach, weaknesses of dealing with evidence through paraconsistency come to light, basically because evidence does not seem to suggest the need of a paraconsistent treatment. As a result, one can neither approach paraconsistency in general through evidence, nor approach evidence with the use of paraconsistent logics.

Logical Pluralism and Interpretations of Logical Systems

“…The epistemic interpretation of N4 defended by Carnielli and Rodrigues faces some difficulties that call doubts on its adequacy. First Lo Guercio and Szmuc [2018] and then also Arenhart [2021] remarked that N4 validates the principle of Adjunction, viz. A, B/A ∧ B.…”

“…The notions of 'interpretation' and 'philosophical interpretation' of a logical system have featured prominently in some recent articles [e.g. Arenhart, 2021;Barrio and Da Ré, 2018;Carnielli and Rodrigues, 2019a;Lo Guercio and Szmuc, 2018]. However, there does not seem to be a clear consensus as regards what exactly these notions mean.…”

“…To finish, we should briefly mention that according to Arenhart [2021], the notion of philosophical interpretation of a logical system is often misleading and, thus, should be avoided. The author advances two main complaints, but they are both related to the epistemic interpretation of paraconsistency in Carnielli and Rodrigues [2019a], and none of them affects the claims we made so far.…”

The Liar Paradox: Between Evidence and Truth

“…Given this situation, the philosophical challenge is: how should these designated values simultaneously attributed to α and ¬α be informally understood? This is an issue that has recently attracted much attention on the philosophy of paraconsistency, and the idea of a philosophical interpretation of paraconsistency has spawned a literature that is currently developing [see, e.g., Barrio and da Re, 2018;Barrio, 2018;Carnielli and Rodrigues, 2015, 2019, 2021Arenhart, 2021].…”

“…The epistemic approach to paraconsistency is a recent proposal to deal with this question, advancing the claim that one should interpret the contradictions allowed in such logics in epistemic terms, thus avoiding commitment to true contradictions and the accompanying doctrine of dialetheism [see Carnielli and Rodrigues, 2015, 2019, 2021. The proposal, in a nutshell, suggests that contradictions are to be interpreted in terms of non-conclusive evidence: α and ¬α, in the context of a paraconsistent system, indicate that there is evidence, of a non-conclusive kind, for us to hold both of these propositions, at least for the time being.…”