In this paper we explain that the paraconsistent logic LP promoted by Graham Priest can only be supported by trivial dialetheists, i.e., those who believe that all sentences are dialetheias.

In In Contradiction, Graham Priest shows, as clearly as anything like this can be shown, that it is coherent to maintain that some sentences can be both true and false at the same time. As a consequence, some contradictions are true, and an appreciation of this possibility advances our understanding of the nature of logic and language.

The arguments of the dialetheists for the rejection of the traditional law of noncontradiction are not yet conclusive. The reason is that the arguments that they have developed against this law uniformly fail to consider the logic of encoding as an analytic method that can resolve apparent contradictions. In this paper, we use Priest [1995] and [1987] as sample texts to illustrate this claim. In [1995], Priest examines certain crucial problems in the history of philosophy from the point of view (...) of someone without a prejudice in favor of classical logic. For each of these problems, the logic of encoding offers an alternative explanation of the phenomena---this alternative is not considered when Priest describes what options there are in classical logic for analyzing the problem at hand. (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.

This dissertation is a critical examination of dialetheism, the view that there are true contradictions. Dialetheism's proponents argue that adopting the view will allow us to solve hitherto unsolved problems, including the well-known logical paradoxes. ;Dialetheism faces three kinds of challenge. Challenges of the first kind put in doubt the intrinsic coherence of dialetheism. It can be claimed, for example, that it is incoherent for a claim to be both true and false; that claims known to be false cannot be (...) accepted; that claims known to be false cannot be rationally accepted; and that dialetheism entails the falsity of some of its own theoretical claims. The second kind of challenge concerns the use of paraconsistent logics, which dialetheists must adopt on pain of accepting the truth of every proposition. I examine a number of paraconsistent logics, and conclude that either they come at an unacceptably high price or they do not support the dialetheist project. ;I devote most attention to the third kind of challenge, according to which dialetheism fails to provide the promised solutions to the paradoxes and other previously intractable problems, and so we lose the major motivation for the theory. Proponents claim that dialetheism allows for the solution of numerous problems, particularly in metaphysics, law, and logic. In the case of metaphysics, it is claimed that dialetheism allows us to deal with puzzles involving change, vagueness, and motion. However, I argue that the proposed solution does not eliminate the old metaphysical problems, and in fact gives rise to new ones. In the case of law, it is claimed that dialetheism can allow us to deal with legal contradiction. I argue there are more plausible means of solving such conflicts. The strongest case for dialetheism is that it allows us to solve logical and semantic paradoxes of self-reference, some of which have endured for well over two thousand years. I construct a paradox that the dialetheist cannot accommodate, and which shows that dialetheism never provided a solution to the paradoxes at all, even in their more familiar forms. (shrink)

The significance of the semantical paradoxes for natural languages is examined. If Tarski’s reflections on the issue are correct, English is inconsistent. Paul Ziff responds to Tarskian reflections by arguing to the conclusion that no natural language is or can be inconsistent. The authors reject Ziff’s argument, but they defend something similar to its conclusion: no language, natural or otherwise, is or can be inconsistent in the way that Tarski holds languages capable of formulating the Epimenides are inconsistent.

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.

I offer an interpretation of a familiar, but poorly understood portion of Tarskis work on truth – bringing to light a number of unnoticed aspects of Tarskis work. A serious misreading of this part of Tarski to be found in Scott Soames Understanding Truth is treated in detail. Soamesreading vies with the textual evidence, and would make Tarskis position inconsistent in an unsubtle way. I show that Soames does not finally have a coherent interpretation of Tarski. This is unfortunate, since (...) Soames ultimately arrogates to himself a key position that he has denied to Tarski and which is rightfully Tarskis own. (shrink)

Approaches to paraconsistency can be arranged on a spectrum similar to the way in which approaches to vagueness are often understood. On the left are the metaphysical realists; those who think that there are real contradictory facts, that are mind and language independent. On the right are those who think that although we can have inconsistent beliefs and inconsistent theories — and we need a paraconsistent logic to deal with them — the world itself is perfectly consistent. In the middle (...) are the semantic dialetheists, who claim that there are true contradictions, but that these come about because of particular features of our use of language. This chapter outlines a particular version of semantic dialetheism based on a four-valued logic. It contends that although we need such a logic to deal with our current language, we could regiment our uses of predicates (and other expressions) to eliminate all true contradictions. (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)

B. H. Slater has argued that there cannot be any truly paraconsistent logics, because it's always more plausible to suppose whatever "negation" symbol is used in the language is not a real negation, than to accept the paraconsistent reading. In this paper I neither endorse nor dispute Slater's argument concerning negation; instead, my aim is to show that as an argument against paraconsistency, it misses (some of) the target. A important class of paraconsistent logics - the preservationist logics - are (...) not subject to this objection. In addition I show that if we identify logics by means of consequence relations, at least one dialetheic logic can be reinterpreted in preservationist (non-dialetheic) terms. Thus the interest of paraconsistent consequence relations - even those that emerge from dialetheic approaches - does not depend on the tenability of dialetheism. Of course, if dialetheism is defensible, then paraconsistent logic will be required to cope with it. But the existence (and interest) of paraconsistent logics does not depend on a defense of dialetheism. (shrink)

The concept of dialetheia and the claim of dialetheism has been examined and compared to such related concept as contradiction, antinomy, consistency and paraconsistency. Dialetheia is a true contradiction and dialetheism is the claim that there exists at least one dialetheia. It has been observed that dialetheism is equivalent to the negation of the traditional principle of contradiction. Hence, dialetheism itself is no new idea in whatsoever. The novelty of dialetheism consists in the arguments delivered for its case. Key justification (...) the partisans deliver for dialetheism has been examined and evaluated: antinomies, an alleged Gödel’s paradox, and existence of limits of thought. The structure of those arguments has been analyzed. It has been claimed that they share one and the same simple structure which may be called reverse paradox. The vital content dialetheists add to the traditional paradoxes is only the thesis of reliability of the vernacular prima facie knowledge. Three objections have been raised against the justification of dialetheism: firstly, it has been claimed that exactly the same argument supports principle of contradiction, secondly, it has been questioned whether the arguments preserve their value when logic is subject to revision, and thirdly, it has been claimed that the underlying logic of dialetheism is classical. (shrink)

This dissertation is a critical examination of dialetheism, the view that there are true contradictions. Dialetheism's proponents argue that adopting the view will allow us to solve hitherto unsolved problems, including the well-known logical paradoxes. ;Dialetheism faces three kinds of challenge. Challenges of the first kind put in doubt the intrinsic coherence of dialetheism. It can be claimed, for example, that it is incoherent for a claim to be both true and false; that claims known to be false cannot be (...) accepted; that claims known to be false cannot be rationally accepted; and that dialetheism entails the falsity of some of its own theoretical claims. The second kind of challenge concerns the use of paraconsistent logics, which dialetheists must adopt on pain of accepting the truth of every proposition. I examine a number of paraconsistent logics, and conclude that either they come at an unacceptably high price or they do not support the dialetheist project. ;I devote most attention to the third kind of challenge, according to which dialetheism fails to provide the promised solutions to the paradoxes and other previously intractable problems, and so we lose the major motivation for the theory. Proponents claim that dialetheism allows for the solution of numerous problems, particularly in metaphysics, law, and logic. In the case of metaphysics, it is claimed that dialetheism allows us to deal with puzzles involving change, vagueness, and motion. However, I argue that the proposed solution does not eliminate the old metaphysical problems, and in fact gives rise to new ones. In the case of law, it is claimed that dialetheism can allow us to deal with legal contradiction. I argue there are more plausible means of solving such conflicts. The strongest case for dialetheism is that it allows us to solve logical and semantic paradoxes of self-reference, some of which have endured for well over two thousand years. I construct a paradox that the dialetheist cannot accommodate, and which shows that dialetheism never provided a solution to the paradoxes at all, even in their more familiar forms. (shrink)