On Barrio, Lo Guercio, and Szmuc on Logics of Evidence and Truth

Abstract

The aim of this text is to reply to criticisms of the logics of evidence and truth and the epistemic approach to paraconsistency advanced by Barrio [2018], and Lo Guercio and Szmuc [2018]. We also clarify the notion of evidence that underlies the intended interpretation of these logics and is a central point of Barrio’s and Lo Guercio & Szmuc’s criticisms.

Paraconsistency, Evidence and Semantic Incompleteness

“…Of course, formal systems themselves may prevent certain informal interpretations, as in the case of intuitionistic logic to classical truth. Carnielli and Rodrigues certainly agree with the latter statement, and some textual evidence shows it (Rodrigues & Carnielli, 2022). However, as we argued, this does 8 One can find a study of LP o in Barrio et al (2017).…”

“…Roughly speaking, DAT states that classical inferences hold when we have conclusive evidence for the sentences involved in the inference. According to Rodrigues and Carnielli (2022), such a recovering device highlights the anti-dialetheist perspective of their approach because "the simultaneous truth and falsity of A is expressed by A∧¬A∧oA, and the latter leads to triviality" (Rodrigues & Carnielli, 2022, p. 325). So, according to them, paraconsistency does not rival classical logic.…”

“…9 It is a matter of fact that a single formal logical system can receive different interpretations, because the formal definitions of consequence relations are not able to uniquely point to a single informal notion of validity, and the case BLE and LET J are not exceptions. 10 Although Rodrigues and Carnielli (2022) accept that both BLE and LET J can receive alternative interpretations, they claim that it is the combination of BLE with its evidence informal interpretation that is anti-dialetheist by nature. So, it is not these systems alone that are incompatible with dialetheism, but we also must consider the evidence informal interpretation.…”

Valuation semantics for first-order logics of evidence and truth (and some related logics)

“…In Section 3 we provide sound and complete semantics for the first-order versions of F DE, K3, and LP, which are particular cases of the method of anti-extensions + valuations. Section 4 wraps up the text with some historical remarks about valuation 1 For a more detailed discussion of the notion of evidence, see [26,Sect. 2].…”

“…Evidence is thus just information that comes together with a justification that may fail to justify that information it is intended to justify [cf. 26,Sect. 2.3].…”