Dialetheism is a paraconsistent logic typified by its tolerance of at least some contradictions. More specifically, dialetheists believe that some propositions of the form P ∧ ¬P are true. A paraconsistent logic is a logic which attempts to deal with contradictions. ...

Like other paraconsistent logics, the motivations for dialetheism might be split into two groups:

1. Formal semantic concerns brought about by such puzzles as the Liar's and Russell's paradoxes. From the premises of classical logic and naïve set theory one can derive outright contradictions, a result that is traditionally frowned upon. The classical response to this problem is to revise the axioms of set theory in order to make them consistent. Dialetheists respond to the problem by accepting the contradictions as true.
2. It might be argued that our actual thinking is dialetheistic. In other words, it is not completely prima facie implausible that we might affirm both a proposition and its negation. Consider "John is in the room" when John is standing precisely halfway in the room.

It is important to recognize the formal ramifications of accepting a contradiction as true. Using some commonly accepted and intuitively plausible rules of logic, we can easily show that the formula P ∧ ¬P implies everything; taking a contradiction as a premise, we can prove any A. (This is often called the principle of explosion, since the truth of a contradiction makes the number of theorems in your system "explode".) Any system in which any formula is provable is trivial and uninformative; this is the motivation for solving the semantic paradoxes. Dialethesists solve this problem by rejecting the principle of explosion, and, along with it, at least one of the more basic laws of disjunction that lead to it. In general, semantics (from the Greek semantikos, or significant meaning, derived from sema, sign) is the study of meaning, in some sense of that term. ... In philosophy and logic, the liar paradox encompasses paradoxical statements such as: or To avoid having a sentence directly refer to its own truth value, one can also construct the paradox as follows: // Eubulides of Miletus words The oldest version of the liar paradox is attributed to the Greek philosopher... Russells paradox (also known as Russells antinomy) is a paradox discovered by Bertrand Russell in 1901 which shows that the naive set theory of Cantor and Frege is contradictory. ... Prima facie is a Latin expression meaning at first sight, used in common law regions to denote a case that is strong enough to justify further discovery and possibly a full trial. ... Ex falso quodlibet or the principle of explosion is the rule of classical logic that states that anything follows from a contradiction. ... Logical disjunction (usual symbol or) is a logical operator that results in true if either of the operands is true. ...

Perhaps the most penetrating criticism of dialetheism is that it fails to capture something crucial about negation and, consequently, disagreement. Imagine John's utterance of "P". Sally's typical way of disagreeing with John is a consequent utterance of "¬P". Yet, if we accept dialetheism, Sally's so uttering does not prevent her from also accepting P; after all, P may be a dialetheia and therefore it and its negation are both true. The absoluteness of disagreement is lost. A first guess at a defense by the dialetheist is to say that disagreement can be displayed by uttering "¬P and, furthermore, P is not a dialetheia". Again, though, the dialetheist's own theory is his Achilles' heel: the most obvious codification of "P is not a dialetheia" is ¬(P ∧ ¬P). But what if this itself is a dialetheia as well? The dialetheist response is to offer a distinction between two illocutionary speech acts: assertion and rejection (as opposed to the classical view, from Frege, that there is only one such speech act--assertion--that is expressed towards a proposition and its negation). This response pushes the burden of argument from the purely logical realm to the theory of speech acts, which is largely pragmatic. Negation, in its most basic sense, changes the truth value of a statement to its opposite. ... Posterior view of the foot and leg, showing the Achilles tendon (tendo calcaneus). ... Illocutionary force is the effect a speech act has in the world. ... A speech act is an action performed by means of language, such as describing something (), asking a question (Is it snowing?), making a request or order (Could you pass the salt?, Drop your weapon or Ill shoot you!), or making a promise () For much of the history of linguistics... The logical assertion is a statement that asserts that a certain premise is true, and is useful for statements in proof. ... Friedrich Ludwig Gottlob Frege Friedrich Ludwig Gottlob Frege (November 8, 1848 - July 26, 1925) was a German mathematician, logician, and philosopher who is regarded as a founder of both modern mathematical logic and analytic philosophy. ... Pragmatism is a school of philosophy which originated in the United States in the late 1800s. ...

Graham Priest of the University of St. Andrews is dialetheism's most prominent contemporary champion. University of St Andrews The University of St Andrews was founded between 1410-1413 and is the oldest university in Scotland and the third oldest in the United Kingdom. ...

Works Cited

Frege, Gottlob. “Negation.” Logical Investigations. Trans. P. Geach and R. H Stoothoff. New Haven, CT: Yale UP, 1977. 31-53.
Parsons, Terence. “Assertion, Denial, and the Liar Paradox.” Journal of Philosophical Logic 13 (1984): 137-152.
Parsons, Terence. “True Contradictions.” Canadian Journal of Philosophy 20 (1990): 335-354.
Priest, Graham. In Contradiction. Dordrecht: Martinus Nijhoff (1987).
Priest, Graham. “What Is So Bad About Contradictions?” Journal of Philosophy 95 (1998): 410-426.

External Links

• Graham Priest. Dialetheism. In the Stanford Encyclopedia of Philosophy, 2004.