This article examines the concept of contradiction، law of non-contradiction and dialetheism in non-classical logic. The main purpose of this paper is examining different definitions of the concept of contradiction and the influence of such differences in accepting or rejecting the low of non-contradiction. Here I try to show، by appealing to an especial conception of contradiction، that how it is possible to make dialetheism plausible. In section 1، basic terms are introduced. Section 2 covers different definitions of contradiction. This section shows that according to diverse conceptions of contradiction، we could have different notions of dialetheism. In section 3، I review most important arguments of the proponents of the low of non-contradiction and try to refute them on the basis of the definitions of section 2. Finally it will be showed that new approaches to dialetheism is due to using semantic instead of ontology، multi-valued logic، vagueness and alternates theory of truth.

Dialetheism is the view that some (and not all) contradictions are true. Since in classical logic the principle of impossibility of contradiction (the Law of Non-Contradiction, i.e., LNC) is widely accepted, the challenge between dialetheism and classical logic surely occurs. In this paper we have tried to explain the main problem of dialetheim and also examined Graham Priest’s arguments against LNC and his advocating to paraconsistent logic. Accordingly, Priest’s examples of dialetheic propositions in some systems such as Law, Natual and Formal Languages and Actual world are examined and criticized. The result is that if Priest’s argument be sound dialetheism may be acceptable. Dialetheism is the view that some (and not all) contradictions are true. Since in classical logic the principle of impossibility of contradiction (the Law of Non-Contradiction, i.e., LNC) is widely accepted, the challenge between dialetheism and classical logic surely occurs. In this paper we have tried to explain the main problem of dialetheim and also examined Graham Priest’s arguments against LNC and his advocating to paraconsistent logic. Accordingly, Priest’s examples of dialetheic propositions in some systems such as Law, Natual and Formal Languages and Actual world are examined and criticized. The result is that if Priest’s argument be sound dialetheism may be acceptable.

Dialetheism is the claim that some contradictions are true (or justified). Dialetheist tries to deduce these contradictions from valid arguments. The critics, on the other hand, try to prove, firstly, that such arguments are unsound, and secondly, they present some general arguments against dialetheism. This paper examines disletheism, while focusing on Graham Priest’s views.

Dialetheism is the view that some contradictions are true. Being usually associated with the name of Graham Priest, this theory rejects the principle of non contradiction which, according to most philosophers following Aristotle, is the most fundamental principle in human thought. According to Priest, there is no good reason to accept the principle of non-contradiction and thus one can, in some cases, agree with the idea of the existence of contradiction. To prove his claim, he turns to some evidence that can be divided into three groups: historical, empirical and intellectual. The present article deals with empirical and intellectual evidence and relates and assesses the criticisms leveled against dialetheism.

In this paper, we will try to reconstruct Hegel’s logic and metaphysics through the modern logic. Graham Priest has claimed that we can read Hegel’s logic with the paraconsistent approach to logic, specially Dialetheism; he calls Hegel a Dialetheist. At first, we report Priest’s account on Hegel’s dialectic and his notion of dialectical contradiction; also, we try to analyze Priest’s argument for calling Hegel a Dialetheist. To achieve the proper comparison between Hegel’s logic and Dialetic one, we explain, non-technically, the simple semantics of a Dialetic logic. And finally, we establish a criticism of Priest’s account in order to reopening the question about Hegel’s being Dialetheist.

In this paper, I will argue for this claim that Hegel's logic implies Trivialism. In recent decades among scholars, there is a special interest in rereading classic philosophers through the modern logic, also about Hegel this story is true. Graham Priest, a contemporary philosopher and logician, had claimed that we can find Hegel's logic in a paraconsistent way. More specifically, Priest said Hegel's logic is committed to Dialetheism. His claim has some opponents(such as Michela Bordignon) who say Hegel's being dialetheist has some requirements such as commitment to the third truth-value (Glutty value) and this is a dubious presupposition. Bordignon had claimed that in Hegel's logic, there is only one truth-value: true. In three-part of this paper, I will report and criticize accounts of Priest and his opponents, then I will establish an argument for Hegel's being Trivialist, respectively. And finally, I will try to explain what Trivialism is and I will give a reason for defense of it.

Defending the truth of some contradictions in the actual world by means of Graham Priest’s views, “To Welcome Contradiction” written by Rahman Sharifzadeh is rarely problematic in the appearance - i.e in the edition. In addition to some suggestions, we have evaluated the content of the book and criticized the views of the author and/or the dialetheists in some cases. We have shown, for example, that the preface paradox and some borderline cases cannot be regarded as true contradictions. Again, there is no need to accept such counterintuitive affairs as negative facts to believe dialetheism. In evaluating the logic of paradox, we have corrected the truth table for the logical negation and implication: instead of saying t = f, p = p and f = t, we must say: t = f ˅ p, p = t ˅ f and f = t ˅ p; and instead of the truth value of p for t→p, p→p and p→f, we must say: t ˅ f. On the basis of such corrections, the objection to the validity of modus ponens rule in the logic of paradox is answered. All in all, the book is a necessary one in Persian.

The article by Graham Priest, the contemporary logician and writer, seeks not only to deny the widely-held logical principle of non- contradiction (the principle that the conjunction of a proposition and its negation is impossible), but also to assert both the possibility and existence of contradictions. To affirm his position, he brings to light some paradoxical cases (propositions), which belong neither to any specific time nor place. He gives some examples from both western and eastern philosophies. On the other hand, he states that all arguments for the principle in question are prone to objections, and concludes that some contradictions are possible, or in other words, some propositions are both true and false. The author makes some remarks on Priest's view of contradictions, insisting that the conjunction of a proposition and is negation is impossible. To prove this, he examines some arguments given by Aristotle and considers them as hints at a self-evident matter instead of technical arguments. Elaborating on some propositions Priest uses to establish his position, the author concludes his discussion by stating that the impossibility of contradictions is self-evident to any mind or common sense, at any time or place. The only difficulty arises from the fact that it has been misconceived by some thinkers and much of its denial comes from the very misunderstanding.

Mullā Ṣadrā’s attempt to reconcile philosophy and mysticism has faced him with several difficulties, of which some are noticed by him and some could be explained according to his taste and principles. One of the difficulties is the incompatibility of the mystical theory of Unity of Existence with the law of contradiction. This perception of presence, which claims the oneness of creatures with the Creator and at the same time their duality, challenges the logical-philosophical law of noncontradiction.The purpose of this paper is to answer the question of what solution could Mullā Ṣadrā have for such a problem. Although he has emphasized on the theory of Personal Unity of Existence in his late works, it seems that the theory of Analogical Unity of Existence –despite Ṣadrā’s lack of clarification– was a solution from his side to get rid of this problem. The authors’ descriptive method and critical analysis, however, indicates the insufficiency of this theory for solving this paradox. The logic of belief, also, cannot be a a solution for this problem. The authors, finally, have shown that on the basis of Mullā Ṣadrā’s principles in the issue of mental existence, the rule of impossibility of coexistence of two contradictories in immaterial worlds has been narrowed down and the possibility of coexistence of some incommensurable things is available in that arena. This way, he can solve the paradox of the unity of existence. All in all, it is clear that Mullā Ṣadrā neither wanted nor - –considering his intellectual foundations– was capable of accepting dialetheism and the violation of the law of noncontradiction.

Although the problem of motion has created various challenges in the history of philosophy by itself, the trans-substantial motion as the turning point of the Transcendent philosophy is prone to some additional challenges that can be followed in the manifest of dialetheism. One of these challenges is the loss of the identity of subject in the context of motion and, following this, the realization of borderline-states and the appearance of a paradox known as the problem of ambiguity in philosophical literature. Such debates themselves lead to paradoxes that contemporary dialetheists consider as evidence for the existence of contradiction in the outside world. The manifestation of such challenges and their relationship with the trans-substantial motion is the focal problem of the present paper. Since any change in archetypal forms in the cradle of trans-substantial motion is of the gradual and continuous type rather than the sudden type, the absence of a borderline at various stages of motion paves the way for the truth of two different quiddities at the same time for one subject, which necessitates contradiction by itself. Following a critical descriptive analytic method, this study reveals that Mullā Ṣadrā has responded to both challenges. He has answered the identity challenge based on the idea of “matter with form” and referred the challenge of ambiguity to our perception’s negligence in matching quiddity to all modes of being.