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.

The main aim of this paper is to introduce first-order versions of logics of evidence and truth, together with corresponding sound and complete Kripke semantics with variable and constant domains. According to the intuitive interpretation proposed here, these logics intend to represent possibly inconsistent and incomplete information bases over time. The paper also discusses the connections between Belnap-Dunn’s and da Costa’s approaches to paraconsistency, and argues that the logics of evidence and truth combine them in a very natural way.

The idea at the basis of this special issue is that reopening the old debate about the logical status of Hegel’s dialectics is extremely interesting, for various reasons.1 The first reason is that...

In 2023, Beall and Ficara present what they call Hegelian conjunctions. A Hegelian conjunction is a true conjunction of contradictory opposites in which the conjuncts, separately taken, are untrue and for which simplification fails. The analysis in Beall & Ficara History and Philosophy of Logic 44 (2) 119-131, 2023 is important for various reasons. First, for overcoming the deleterious state of estrangement between two ways of conceiving and practicing logic, the “dialectical” or “continental” and the “analytical” one. Second, for strengthening (...) a new, promising way of conceiving conjunction in paraconsistency (d’Agostini Synthese 199, 6845 6874, 2021). Yet it needs an enlargement, mainly in two dimensions, a hermeneutical and a logical one. The former concerns the textual basis used by Beall and Ficara for motivating their account (the focus of their analysis is a small part of the early Hegelian fragment on Vereinigung – unification/conjunction). The latter is the semantics proposed by Beall and Ficara. In this paper, I focus on the first dimension, in the conviction that the condition for making the chief formal characteristics of dialectics (the logical dimension) clearer is a grasp of the Hegelian fragment in its entirety and complexity. The fragment is crucial for thinking about the logic, metaphysics and epistemology of true contradictions. Yet it counts as obscure. My aim is to make its content more accessible, and to present its relevance for conjunctive paraconsistency. (shrink)

1. The label conjunctive paraconsistency has been adopted to mean a consequence relation whereby ‘p and not p’ does not imply ‘p’ and ‘not p’ separately, so that Simplification in case of contradic...

In his Lectures on the History of Philosophy, Hegel develops a subtle analysis of Megarian paradoxes: the Liar, the Veiled Man and the Sorites. In this paper, we focus on Hegel's interpretation of...

Stratified properties such as ‘happy unhappiness’, ‘ungrounded ground’, ‘fortunate misfortune’, and evidently ‘true falsity’ may generate dialetheias (true contradictions). The aim of the article is to show that if this is the case, then we will have a special, conjunctive, kind of dialetheia: a true state description of the form ‘Fa and not Fa’ (for some property F and object a), wherein the two conjuncts, separately taken, are to be held untrue. The particular focus of the article is on happy (...) unhappiness: people suffering from (or enjoying) happy unhappiness (if there is some situation or state of mind of this kind) cannot be truly said ‘happy’ or ‘unhappy’, but we can say they are both. In the first section three cases of conjunctive stratification are presented; in the second section the logic of stratified contradictions is explored. The last section focuses on eudemonistic ascriptions: stated that a is happy to be unhappy (or unhappy to be happy), should we say a is happy? unhappy? both? neither? (shrink)

This article is a preliminary presentation of conjunctive paraconsistency, the claim that there might be non-explosive true contradictions, but contradictory propositions cannot be considered separately true. In case of true ‘p and not p’, the conjuncts must be held untrue, Simplification fails. The conjunctive approach is dual to non-adjunctive conceptions of inconsistency, informed by the idea that there might be cases in which a proposition is true and its negation is true too, but the conjunction is untrue, Adjunction fails. While (...) non-adjunctivism is a well-known option, the other view is not so much studied nowadays, but it was not unknown in the tradition, and there are some positive suggestions, in recent literature, that the position is plausible and deserves to be developed. The article compares conjunctivism, non-adjunctivism and dialetheism, then focuses on some possible justifications, costs and benefits of the conjunctive view. (shrink)

Systems of paraconsistent logics violate the law of explosion: from contradictory premises not every formula follows. One of the philosophical options for interpreting the contradictions allowed as premises in these cases was put forward recently by Carnielli and Rodrigues, with their epistemic approach to paraconsistent logics. In a nutshell, the plan consists in interpreting the contradictions in epistemic terms, as indicating the presence of non-conclusive evidence for both a proposition and its negation. Truth, in this approach, is consistent and is (...) dealt with by classical logic. In this paper we discuss the fate of the Liar paradox in this picture. While this is a paradox about truth, it cannot be accommodated by the classical part of the approach, due to trivialization problems. On the other hand, the paraconsistent part does not seem fit as well, due to the fact that its intended reading is in terms of non-conclusive evidence, not truth. We discuss the difficulties involved in each case and argue that none of the options seems to accommodate the paradox in a satisfactory manner. (shrink)

There are a considerable number of logics that do not seem to share the same inferential principles. Intuitionistic logics do not include the law of the exclude.

In different papers, Carnielli, W. & Rodrigues, A., Carnielli, W. Coniglio, M. & Rodrigues, A. and Rodrigues & Carnielli, present two logics motivated by the idea of capturing contradictions as conflicting evidence. The first logic is called BLE and the second—that is a conservative extension of BLE—is named LETJ. Roughly, BLE and LETJ are two non-classical logics in which the Laws of Explosion and Excluded Middle are not admissible. LETJ is built on top of BLE. Moreover, LETJ is a Logic (...) of Formal Inconsistency. This means that there is an operator that, roughly speaking, identifies a formula as having classical behavior. Both systems are motivated by the idea that there are different conditions for accepting or rejecting a sentence of our natural language. So, there are some special introduction and elimination rules in the theory that are capturing different conditions of use. Rodrigues & Carnielli’s paper has an interesting and challenging idea. According to them, BLE and LETJ are incompatible with dialetheia. It seems to show that these paraconsistent logics cannot be interpreted using truth-conditions that allow true contradictions. In short, BLE and LETJ talk about conflicting evidence avoiding to talk about gluts. I am going to argue against this point of view. Basically, I will firstly offer a new interpretation of BLE and LETJ that is compatible with dialetheia. The background of my position is to reject the one canonical interpretation thesis: the idea according to which a logical system has one standard interpretation. Then, I will secondly show that there is no logical basis to fix that Rodrigues & Carnielli’s interpretation is the canonical way to establish the content of logical notions of BLE and LETJ. Furthermore, the system LETJ captures inside classical logic. Then, I am also going to use this technical result to offer some further doubts about the one canonical interpretation thesis. (shrink)

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, 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: interpreting paraconsistency in general through the notion (...) of evidence, and 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. (shrink)

In this paper, we critically discuss the idea of a ‘philosophical interpretation’ of paraconsistent logics. We do so by considering the epistemic approach to paraconsistency, by Carnielli and Rodrigues, according to which paraconsistent logics should be interpreted exclusively in terms of non-conclusive evidence, and also, by considering counter-arguments by Barrio and Barrio and Da Re, according to whom paraconsistent logics are not specially tied to any specific interpretation. We begin by presenting the positions involved, and by arguing that the debate (...) may be profitably understood in terms of the distinction between pure and applied logics. We argue that dialetheism is not an interpretation of paraconsistent logics, but rather a view on truth and negation which requires use of paraconsistent logics. Something similar may be said about the epistemic approach itself. The result is that there is nothing distinctive to be called a philosophical interpretation of paraconsistent logics, but rather what we have are distinct applications of paraconsistent logics. Arguments by Barrio and Barrio and Da Re may be then re-framed more effectively. (shrink)

Dialetheism is the view that some contradictions are true. One common motivation to the view concerns cases of contradictory concepts obtaining together. Allegedly, in these cases, such concepts lead to a true contradiction. In this paper, we argue that this path is closed as a motivation for dialetheism. There are two basic difficulties to articulate the view: i) once contradictory or incompatible concepts are granted to obtain together, there is no longer any reason to claim that they were incompatible to (...) begin with, and ii) it is not easy to go from such concepts to clear cases of negation-involving contradictions without already assuming the truth of dialetheism. Further difficulties discussed here concern the maintenance of the meaning of important concepts such as “contradiction” in a dialetheist setting. Those difficulties make the case for dialetheism hard to motivate via contradictory concepts. (shrink)