The paper explains how a paraconsistent logician can appropriate all classical reasoning. This is to take consistency as a default assumption, and hence to work within those models of the theory at hand which are minimally inconsistent. The paper spells out the formal application of this strategy to one paraconsistent logic, first-order LP. (See, Ch. 5 of: G. Priest, In Contradiction, Nijhoff, 1987.) The result is a strong non-monotonic paraconsistent logic agreeing with classical logic in consistent situations. It is shown (...) that the logical closure of a theory under this logic is trivial only if its closure under LP is trivial. (shrink)

In this paper we present a comparison of certain inconsistencyadaptive logics and Jaśkowski’s logic.

In this paper, I argue that logic hasan important role to play in the methodological studyof creativity. I also argue, however, that onlyspecial kinds of logic enable one to understand thereasoning involved in creative processes. I show thatdeductive and ampliative adaptive logics areappropriate tools in this respect.

In this paper we propose substructural propositional logic obtained by da Costa weakening of the intuitionistic negation. We show that the positive fragment of the da Costa system is distributive lattice logic, and we apply a kind of da Costa weakening of negation, by preserving, differently from da Costa, its fundamental properties: antitonicity, inversion, and additivity for distributive lattices. The other stronger paraconsistent logic with constructive negation is obtained by adding an axiom for multiplicative property of weak negation. After that, (...) we define Kripke-style semantics based on possible worlds and derive from it many-valued semantics based on truth-functional valuations for these two paraconsistent logics. Finally, we demonstrate that this model-theoretic inference system is adequate—sound and complete with respect to the axiomatic da Costa-like systems for these two logics. (shrink)

Philosophically, the study of argumentation is important because it holds out the prospect of an interpretation of rationality. For this we need to identify a transcendent perspective on the argumentative interaction. We need a normative theory of argumentation that provides an answer to the question: should the hearer accept the argument of the speaker. In this article I argue that formal logic implies a notion of transcendence that is not suitable for the study of argumentation, because, from a logical point (...) of view, argumentation ’disappears from sight‘. We should therefore not expect formal logic to provide an interesting interpretation of the rationality intrinsic in argument and discussion. (shrink)

The pluralist sheds the more traditional ideas of truth and ontology. This is dangerous, because it threatens instability of the theory. To lend stability to his philosophy, the pluralist trades truth and ontology for rigour and other ‘fixtures’. Fixtures are the steady goal posts. They are the parts of a theory that stay fixed across a pair of theories, and allow us to make translations and comparisons. They can ultimately be moved, but we tend to keep them fixed temporarily. Apart (...) from considering rigour of proof as a fixture, I discuss fixed models, invariant notions and fixed information about objects across theories. There are other fixtures, but it is enough to start with these. (shrink)

The aim of this paper is to lay bare the roots of dialetheism in discussions about dialectics and dialectical logic at the time of the first development of paraconsistent logics. In other words, th...

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)

In the service of paraconsistent (indeed, ‘dialetheic’) theories, Graham Priest has long advanced a non-monotonic logic (viz., MiLP) as our ‘universal logic’ (at least for standard connectives), one that enjoys the familiar logic LP (for ‘logic of paradox’) as its monotonic core (Priest, G. In Contradiction , 2nd edn. Oxford: Oxford University Press. First printed by Martinus Nijhoff in 1987: Chs. 16 and 19). In this article, I show that MiLP faces a dilemma: either it is (plainly) unsuitable as a (...) universal logic or its role as a ‘universal logic’ (indeed, its role full stop) is a mystery. While familiarity with the basic ideas of dialetheism is assumed, formal details of the target logics are relegated to an appendix; the basic problem is evident without them. (shrink)

A logic of diagnosis proceeds in terms of a set of data and one or more (prioritized) sets of expectancies. In this paper we generalize the logics of diagnosis from [27] and present some alternatives. The former operate on the premises and expectancies themselves, the latter on their consequences.

The paper highlights the import of the paraconsistent movement, list some motivations for its origin, and distinguishes some stands with respect to para-consistency. It then discusses some sources of inconsistency that are specific for worldviews, and the import of the paraconsistent turn for the worldviews enterprise.

In an adaptive logic APL, based on a (monotonic) non-standardlogic PL the consequences of can be defined in terms ofa selection of the PL-models of . An important property ofthe adaptive logics ACLuN1, ACLuN2, ACLuNs1, andACLuNs2 logics is proved: whenever a model is not selected, this isjustified in terms of a selected model (Strong Reassurance). Theproperty fails for Priest's LP m because its way of measuring thedegree of abnormality of a model is incoherent – correcting thisdelivers the property.

Creativity is commonly seen as beyond the scope of rationality. In the present paper, it is argued that available insights in epistemology and available results in logic enable us to incorporate creativity within an independently sensible view on human rationality.

This paper studies the question: How should one handle inconsistencies that derive from the inadequacy of the criteria by which one approaches the world. I compare several approaches. The adaptive logics defined from CLuN appear to be superior to the others in this respect. They isolate inconsistencies rather than spreading them, and at the same time allow for genuine deductive steps from inconsistent and mutually inconsistent premises. Yet, the systems based on CLuN seem to introduce an asymmetry betweennegated and non-negated (...) formulas, and this seems hard to justify. To clarify and understand the source of the asymmetry, the epistemological presuppositions of CLuN, viz. inadequate criteria, are investigated. This leads to a new type of paraconsistent logic that involves gluts with respect to all logical symbols. The larger part of the paper is devoted to this logic, to the adaptive logics defined from it, and to the properties of these systems. While the resulting logics are sensible and display interesting features, the search for variants of the justification leads to an unexpected justification for CLuN. (shrink)