Dialetheism

Contradictions in Dōgen

by Koji Tanaka

This is my contribution to the discussion forum on Contradictions in Buddhism to be published in Philosophy East & West, 2013.

In their article ‘The Way of the Dialetheist: Contradictions in Buddhism’, Deguchi, Garfield and Priest argue that... more In their article ‘The Way of the Dialetheist: Contradictions in Buddhism’, Deguchi, Garfield and Priest argue that some (though not all) of the contradictions that appear in Buddhist texts should be accepted. An examination of their argument depends on what sort(s) of negation is (are) used in the texts. In order to see apparently contradictory statements as affirmations of true contradictions, we must assume that ‘not' (or its variance) is used as a contradiction forming operator. In this paper, I examine the conception of negation(s) that is (are) salient in the writings of Dōgen and argue that he would not agree that his sentences are to be considered, and accepted, as contradictory.

Hegel e la filosofia contemporanea del tempo [Hegel and the contemporary philosophy of time]

by Federico PERELDA

Draft version of "Hegel e la filosofia contemporanea del tempo", published in  "Verifiche" XXXIX, 1-4, 2010, pp. 135-85.

In this essay I compare Hegel’s theory of time and becoming with the contemporary debate, aiming on the one hand (A)... more In this essay I compare Hegel’s theory of time and becoming with the contemporary debate, aiming on the one hand (A) at presenting Hegel’s thought in contemporary terms, and on the other, (B) at offering new inputs to the present metaphysical debate from a Hegelian point of view. From a close reading of selected Hegelian texts I argue (1) that Hegel advocates a form of presentism and shares McTaggart’s thesis that the B-series (chronological time) presupposes the A-series (dynamical time); (2) that his position is pe-culiar because, although he admits that change is inconsistent, he puts in jeopardy the law of non contradiction (at least in its universality), instead of denying the reality of time and change, like McTaggart did. These considerations will then lead to Hegel’s speculative logic. According to the so called coherentistic reading of Hegel’s thought, he never seriously questioned the principle of non contradiction: he would be just a very sophisticated Aristo-telian, after all. I oppose this view, arguing (3) that Hegel was a proponent of an articulated form of dialetheism.

Gaps and Gluts in Semantic Models of Vagueness

by David Van Bruwaene

Adynaton and Material Exclusion

by Francesco Berto

Philosophical dialetheism, whose main exponent is Graham Priest, claims that some contradictions hold, are true, and... more 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.

Dialetheism

by Francesco Berto

Co-authored with Graham Priest.

A dialetheia is a sentence, A, such that both it and its negation, ¬A, are true (we shall talk of sentences throughout... more A dialetheia is a sentence, A, such that both it and its negation, ¬A, are true (we shall talk of sentences throughout this entry; but one could run the definition in terms of propositions, statements, or whatever one takes as her favourite truth-bearer: this would make little difference in the context). Assuming the fairly uncontroversial view that falsity just is the truth of negation, it can equally be claimed that a dialetheia is a sentence which is both true and false...

Che cos' è la dialettica hegeliana?: un'interpretazione analitica del metodo

by Francesco Berto

Strong Paraconsistency and Exclusion Negation

by Francesco Berto

Is Dialetheism an Idealism? The Russellian Fallacy and the Dialetheist's Dilemma

by Francesco Berto

In his famous work on vagueness, Russell named “fallacy of verbalism” the fallacy that consists in mistaking the... more In his famous work on vagueness, Russell named “fallacy of verbalism” the fallacy that consists in mistaking the properties of words for the properties of things. In this paper, I examine two (clusters of) mainstream paraconsistent logical theories – the non-adjunctive and relevant approaches –, and show that, if they are given a strongly paraconsistent or dialetheic reading, the charge of committing the Russellian Fallacy can be raised against them in a sophisticated way, by appealing to the intuitive reading of their underlying semantics. The meaning of “intuitive reading” is clarified by exploiting a well-established distinction between pure and applied semantics. If the proposed arguments go through, the dialetheist or strong paraconsistentist faces the following Dilemma: either she must withdraw her claim to have exhibited true contradictions in a metaphysically robust sense – therefore, inconsistent objects and/or states of affairs that make those contradictions true; or she has to give up realism on truth, and embrace some form of anti-realistic (idealistic, or broadly constructivist) metaphysics. Sticking to the second horn of the Dilemma, though, appears to be promising: it could lead to a collapse of the very distinction, commonly held in the literature, between a weak and a strong form of paraconsistency – and this could be a welcome result for a dialetheist.

Teorie dell'assurdo: i rivali del principio di non-contraddizione

by Francesco Berto

Meaning, metaphysics, and contradiction

by Francesco Berto

How to Sell a Contradiction: The Logic and Metaphysics of Inconsistency

by Francesco Berto

There is a principle in things, about which we cannot be deceived, but must always, on the contrary, recognize the... more There is a principle in things, about which we cannot be deceived, but must always, on the contrary, recognize the truth – viz. that the same thing cannot at one and the same time be and not be": with these words of the Metaphysics, Aristotle introduced the Law of Non-Contradiction, which was to become the most authoritative principle in the history of Western thought. However, things have recently changed, and nowadays various philosophers, called dialetheists, claim that this Law does not hold unrestrictedly – that in peculiar circumstances the same thing may at the same time be and not be, and contradictions may obtain in the world. This book opens with an examination of the famous logical paradoxes that appear to speak on behalf of contradictions (e.g., the Liar paradox, the set-theoretic paradoxes such as Cantor’s and Russell’s), and of the reasons for the failure of the standard attempts to solve them. It provides, then, an introduction to paraconsistent logics – non-classical logics in which the admission of contradictions does not lead to logical chaos –, and their astonishing applications, going from inconsistent data base management to contradictory arithmetics capable of circumventing Gödel’s celebrated Incompleteness Theorem. The final part of the book discusses the philosophical motivations and difficulties of dialetheism, and shows how to extract from Aristotle’s ancient words a possible reply to the dialetheic challenge. How to Sell a Contradiction will appeal to anyone interested in non-classical logics, analytic metaphysics, and philosophy of mathematics, and especially to those who consider challenging our most entrenched beliefs the main duty of philosophical inquiry.