A dialectical contradiction can be appropriately described within the framework of classical formal logic. It is in harmony with the law of noncontradiction. According to our definition, two theories make up a dialectical contradiction if each of them is consistent and their union is inconsistent. It can happen that each of these two theories has an intended model. Plenty of examples are to be found in the history of science.

There are two ways of understanding the notion of a contradiction: as a conjunction of a statement and its negation, or as a pair of statements one of which is the negation of the other. Correspondingly, there are two ways of understanding the Law of Non-Contradiction (LNC), i.e., the law that says that no contradictions can be true. In this paper I offer some arguments to the effect that on the first (collective) reading LNC is non-negotiable, but on the second (...) (distributive) reading it is perfectly plausible to suppose that LNC may, in some rather special and perhaps undesirable circumstances, fail to hold. (shrink)

Philosophical dialetheism, whose main exponent is Graham Priest, claims that some contradictions hold, are true, and it is rational to accept and assert them. Such a position is naturally portrayed as a challenge to the Law of Non-Contradiction (LNC). But all the classic formulations of the LNC are, in a sense, not questioned by a typical dialetheist, since she is (cheerfully) required to accept them by her own theory. The goal of this paper is to develop a formulation of the (...) Law which appears to be unquestionable, in the sense that the Priestian dialetheist is committed to accept it without also accepting something inconsistent with it, on pain of trivialism—that is to say, on pain of lapsing into the position according to which everything is the case. This will be achieved via (a) a discussion of Priest's dialetheic treatment of the notions of rejection and denial; and (b) the characterization of a negation via the primitive intuition of content exclusion. Such a result will not constitute a cheap victory for the friends of consistency. We may just learn that different things have been historically conflated under the label of 'Law of Non-Contradiction'; that dialetheists rightly attack some formulations of the Law, and orthodox logicians and philosophers have been mistaken in assimilating them to the indisputable one. (shrink)

It is widely believed that some a priori necessary truths are not analytic in the sense of transformable by substitution of synonyms into logical truths. One much-cited example comes from the supposed incompatibility between colour predicates. The idea is that sentences like “Nothing is both blue all over (or uniformly or at a point) and also red” are not transformable into a logical truth in the same way as “Nothing is both a bachelor and married” because the requisite conceptual link (...) between “bachelor” and “not married” is absent between “blue” and “not red”. This paper examines whether colour exclusion may be more like the bachelor case than it initially appears. It transpires that the most promising line of thought is not, however, as has been argued at length in the literature, that “blue” in some more or less convoluted way manages to mean “not red”. Instead it is suggested that the requisite conceptual link may reside in the oft-ignored qualifications (“all over”, “uniformly”, etc.), without which there is no incompatibility in the first place. (shrink)

Historical Discourse’s Truth Matrix was first posited by Michel Foucault to describe the emergence of a discourse of historical events subsequent to the cessation of war and established by the most powerful arbiters of those events. This paper adapts the implements of Foucault’s toolbox to conceptualise the dimensions of subjectivity that historical events pass through from the original event to the subsequent depictions of those events in historical writing or other media. The Corpus of Irish Historical Narratives (COIHN) is a (...) one-million-word representative corpus of oral-history witness testimonies taken from the Bureau of Military History Archive (BMH) which depict the events surrounding the Irish struggle for independence from the lead up to the 1916 rising to the signing of the Anglo-Irish treaty in 1921. The archive provides a rich source of both historical, social and cultural data and has been the source of many publications pertaining to events of this pivotal time in Irish history. This study takes a hybrid corpus-driven and corpus-based approach to the analysis of epistemic modality in these statements through hedged expressions using mental process verbs and, in doing so, offers a framework for the analysis of a core dimension of historical discourse’s truth matrix. The notion of ‘paradoxical authority’ is proposed, stating that the authority of a witness is boosted rather than mitigated by expressing weak commitment to the truth of a proposition. (shrink)

The paper addresses the situation of a dispute in which one speaker says ϕ and a second speaker says not-ϕ. Proceeding on an idealising distinction between "basic" and "interesting" claims that may be formulated in a given idiolectal language, I investigate how it might be sorted out whether the dispute reflects a genuine disagreement, or whether the speakers are only having a merely verbal dispute, due to their using different interesting concepts. I show that four individually plausible principles for the (...) determination of the nature of a dispute are incompatible. As an example, I discuss the question whether Sarai lied in the story told in Genesis 12. (shrink)

The application of paraconsistent logics to theological contradictions is a fascinating move. Jc Beall’s (J Anal Theol, 7(1): 400–439, 2019) paper entitled ‘Christ—A Contradiction: A Defense of ‘Contradictory Christology’ is a notable example. Beall proposes a solution to the fundamental problem of Christology. His solution aims at making the case, and defending the viability of, what he has termed, ‘Contradictory Christology’. There are at least two essential components of Beall’s ‘Contradictory Christology’. These include the dogmatic statements of Chalcedon and FDE (...) logic. The first is the theological contradiction in question. The second is the type of paraconsistent logic. Both components are integral to a contradictory theology in general. I argue that there can be no such thing as an Islamic contradictory theology. I make the case by establishing two points. These points correspond to both integral components of a contradictory theology in general. The first is that an Islamic theological contradiction does not entail an actual (logical) contradiction. The second is that FDE logic, including alternative sub-classical systems of logic, are not adequate in tolerating an Islamic theological contradiction. (shrink)

This paper engages with a specific problem concerning the relationship between descriptive and normative claims. Namely, if we understand that descriptive claims frequently contain normative assertions, and vice versa, how then do we interpret the traditionally rigid distinction that is made between the two, as ’Hume’s law’ or Moore’s ’naturalistic fallacy’ argument offered. In particular, Kripke’s interpretation of Wittgenstein’s ’rule-following paradox’ is specially focused upon in order to re-consider the rigid distinction. As such, the paper argues that if descriptive and (...) normative claims are not mutually exclusive, then we need a new framework with which to understand this relationship. In this regard, the paper borrows from concerns with vagueness, particularly using a degree-theoretic approach in terms of subjective probability, in an attempt to graphically figure out these differences. Consequently, the paper tentatively proposes the hyperbola model in which degrees of normativity and degrees of descriptivity could be expressed and measured. It is hoped, as a result, that this tentative proposal will contribute to deepening the debate on vagueness in general. (shrink)

The application of paraconsistent logics to theological contradictions is a fascinating move. Jc Beall’s (J Anal Theol, 7(1): 400–439, 2019) paper entitled ‘Christ—A Contradiction: A Defense of ‘Contradictory Christology’ is a notable example. Beall proposes a solution to the fundamental problem of Christology. His solution aims at making the case, and defending the viability of, what he has termed, ‘Contradictory Christology’. There are at least two essential components of Beall’s ‘Contradictory Christology’. These include the dogmatic statements of Chalcedon and FDE (...) logic. The first is the theological contradiction in question. The second is the type of paraconsistent logic. Both components are integral to a contradictory theology in general. I argue that there can be no such thing as an Islamic contradictory theology. I make the case by establishing two points. These points correspond to both integral components of a contradictory theology in general. The first is that an Islamic theological contradiction does not entail an actual (logical) contradiction. The second is that FDE logic, including alternative sub-classical systems of logic, are not adequate in tolerating an Islamic theological contradiction. (shrink)

I aim to bring the idea of “degree of free will or freedom” into philosophical debates on free will by rejecting the formulation, ‘we are either free or not’. This idea is based upon my viewpoint of regarding freedom as a realistic phenomena actually occurring. First of all, I focus on the fact that it is vague whether an agent is free or not. This vagueness is interpreted as ontic vagueness, corresponding with the status of freedom as real. However, Evans’s (...) argument regarding ontic vagueness must be considered as, according to his argument, ontic vagueness about identity and objects are impossible. I indicate that this argument assumes the truth-value gap position in borderline cases, hence we can avoid Evans’s argument by adopting truth-value glut position. Of course, the truth-value glut approach has serious difficulties, but I conclude with sketching out a possibility to develop this approach in the free will debate via the introduction of probabilistic valuation. (shrink)