Este é um conto sobre visão, pensamento e contradição, bem como sobre o papel que desempenham na primeira metade da Ciência da Lógica de Hegel. A Lógica começa com uma descida, nesse caso, uma queda do Ser ao Nada. Posteriormente, aproximadamente na metade de cada texto, há um certo paradoxo em que tudo está em jogo, a categoria da contradição. Nesse exato momento, o pensamento ao mesmo tempo falha e é renovado em um viés especulativo. Nessa seção, nos debruçamos sobre (...) algumas das interpretações influentes do uso hegeliano da contradição. Para isso, voltamo-nos a uma curiosa obra de arte, Pleiades, de James Turrell, como um exemplo estético dessa primeira queda. Progrediremos, então, através do texto com pensamento e visão como nosso duplo norteador em um passo relativamente rápido, sem desacelerar até encontrarmos a história de Hegel da contradição, onde mostro a natureza explosiva da contradição. Isso nos permitirá ver como Hegel invoca o poder da contradição para gerar a segunda metade da história da Ciência da Lógica. Eu começo com a descida do Ser ao Nada, o momento em que a escuridão emerge. (shrink)

This paper compares two proposed solutions to the liar paradox, both of which involve revisions to classical semantics. The first, that of truth value gaps, denies that all sentences are true or false. The second, that of truth value gluts, asserts that some sentences are true and false. A natural question about these proposals is, ?Do they offer equally good (or bad) solutions, or is one better than the other?? Parsons 1990 suggested an answer to this question, arguing that for (...) every problem for one solution, there is a parallel problem for the other. Since then, several people have given arguments for and against the idea that the two face parallel problems. This paper advances the debate in two ways. First, it answers four attempts by Graham Priest to reject the parallel. In particular, it discusses alleged advantages for the gap solution with regard to the teleological account of truth, an extended liar paradox, Berry's paradox, and inexpressibility. Second, it discusses where, if anywhere, the parallel may be broken. (shrink)

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.

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)

I argue that dialetheists have a problem with the concept of logical consequence. The upshot of this problem is that dialetheists must appeal to a hierarchy of concepts of logical consequence. Since this hierarchy is akin to those invoked by more orthodox resolutions of the semantic paradoxes, its emergence would appear to seriously undermine the dialetheic treatments of these paradoxes. And since these are central to the case for dialetheism, this would represent a significant blow to the position itself.

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. (shrink)

I argue that dialetheists have a problem with the concept of logical consequence. The upshot of this problem is that dialetheists must appeal to a hierarchy of concepts of logical consequence. Since this hierarchy is akin to those invoked by more orthodox resolutions of the semantic paradoxes, its emergence would appear to seriously undermine the dialetheic treatments of these paradoxes. And since these are central to the case for dialetheism, this would represent a significant blow to the position itself.

Intervals in boolean algebras enter into the study of conditional assertions (or events) in two ways: directly, either from intuitive arguments or from Goodman, Nguyen and Walker's representation theorem, as suitable mathematical entities to bear conditional probabilities, or indirectly, via a representation theorem for the family of algebras associated with de Finetti's three-valued logic of conditional assertions/events. Further representation theorems forge a connection with rough sets. The representation theorems and an equivalent of the boolean prime ideal theorem yield an algebraic (...) completeness theorem for the three-valued logic. This in turn leads to a Henkin-style completeness theorem. Adequacy with respect to a family of Kripke models for de Finetti's logic, Łukasiewicz's three-valued logic and Priest's Logic of Paradox is demonstrated. The extension to first-order yields a short proof of adequacy for Körner's logic of inexact predicates. (shrink)

The notion of a proposition is central to philosophy. But it is subject to paradoxes. A natural response is a hierarchical account and, ever since Russell proposed his theory of types in 1908, this has been the strategy of choice. But in this paper I raise a problem for such accounts. While this does not seem to have been recognized before, it would seem to render existing such accounts inadequate. The main purpose of the paper, however, is to provide a (...) new hierarchical account that solves the problem. (shrink)

Liar-like paradoxes are typically arguments that, by using very intuitive resources of natural language, end up in contradiction. Consistent solutions to those paradoxes usually have difficulties either because they restrict the expressive power of the language, or else because they fall prey to extended versions of the paradox. Dialetheists, like Graham Priest, propose that we should take the Liar at face value and accept the contradictory conclusion as true. A logical treatment of such contradictions is also put forward, with the (...) Logic of Paradox, which should account for the manifestations of the Liar. In this paper we shall argue that such a formal approach, as advanced by Priest, is unsatisfactory. In order to make contradictions acceptable, Priest has to distinguish between two kinds of contradictions, internal and external, corresponding, respectively, to the conclusions of the simple and of the extended Liar. Given that, we argue that while the natural interpretation of LP was intended to account for true and false sentences, dealing with internal contradictions, it lacks the resources to tame external contradictions. Also, the negation sign of LP is unable to represent internal contradictions adequately, precisely because of its allowance of sentences that may be true and false. As a result, the formal account suffers from severe limitations, which make it unable to represent the contradiction obtained in the conclusion of each of the paradoxes. (shrink)

Approaches to truth and the Liar paradox seem invariably to face a dilemma: either appeal to some sort of hierarchy, or declare apparently perfectly coherent concepts incoherent. But since both options lead to severe expressive restrictions, neither seems satisfactory. The aim of this paper is a new approach, which avoids the dilemma and the resulting expressive restrictions. Previous approaches tend to appeal to some new sort of semantic value for the truth predicate to take. I argue that such approaches inevitably (...) lead to the dilemma in question. In contrast, the present proposal sticks with classical semantic values, but allows the compositional rules associated with these to admit of exceptions. I show how such an approach can be developed systematically. (shrink)