In logic, the law of non-contradiction (LNC) states that contradictory propositions cannot both be true in the same sense at the same time, e. g. the two propositions "p is the case" and "p is not the case" are mutually exclusive. Formally, this is expressed as the tautology ¬(p ∧ ¬p). The law is not to be confused with the law of excluded middle which states that at least one, "p is the case" or "p is not the case", holds.
In philosophy and logic, the classical liar paradox or liar's paradox or antinomy of the liar is the statement of a liar that they are lying: for instance, declaring that "I am lying". If the liar is indeed lying, then the liar is telling the truth, which means the liar just lied. In "this sentence is a lie" the paradox is strengthened in order to make it amenable to more rigorous logical analysis. It is still generally called the "liar paradox" although abstraction is made precisely from the liar making the statement. Trying to assign to this statement, the strengthened liar, a classical binary truth value leads to a contradiction.
A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion. A paradox usually involves contradictory-yet-interrelated elements that exist simultaneously and persist over time. They result in "persistent contradiction between interdependent elements" leading to a lasting "unity of opposites".
The unexpected hanging paradox or surprise test paradox is a paradox about a person's expectations about the timing of a future event which they are told will occur at an unexpected time. The paradox is variously applied to a prisoner's hanging or a surprise school test. It was first introduced to the public in Martin Gardner's March 1963 Mathematical Games column in Scientific American magazine.
Moore's paradox concerns the apparent absurdity involved in asserting a first-person present-tense sentence such as "It is raining, but I do not believe that it is raining" or "It is raining, but I believe that it is not raining." The first author to note this apparent absurdity was G. E. Moore. These 'Moorean' sentences, as they have become known, are paradoxical in that while they appear absurd, they nevertheless
- Can be true;
- Are (logically) consistent; and
- Are not (obviously) contradictions.
Pluralism is a term used in philosophy, referring to a worldview of multiplicity, oft used in opposition to monism or dualism. The term has different meanings in metaphysics, ontology, epistemology and logic. In metaphysics, it is the view that there are in fact many different substances in nature that constitute reality. In ontology, pluralism refers to different ways, kinds, or modes of being. For example, a topic in ontological pluralism is the comparison of the modes of existence of things like 'humans' and 'cars' with things like 'numbers' and some other concepts as they are used in science.
George Stephen Boolos was an American philosopher and a mathematical logician who taught at the Massachusetts Institute of Technology.
A paraconsistent logic is an attempt at a logical system to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that is concerned with studying and developing "inconsistency-tolerant" systems of logic which reject the principle of explosion.
Richard Sylvan was a New Zealand–born philosopher, logician, and environmentalist.
Dialetheism is the view that there are statements that are both true and false. More precisely, it is the belief that there can be a true statement whose negation is also true. Such statements are called "true contradictions", dialetheia, or nondualisms.
In classical logic, intuitionistic logic and similar logical systems, the principle of explosion, or the principle of Pseudo-Scotus, is the law according to which any statement can be proven from a contradiction. That is, from a contradiction, any proposition can be inferred from it; this is known as deductive explosion.
Graham Priest is Distinguished Professor of Philosophy at the CUNY Graduate Center, as well as a regular visitor at the University of Melbourne, where he was Boyce Gibson Professor of Philosophy and also at the University of St Andrews.
Jean-Yves Beziau (French:[bezjo]; born January 15, 1965, in Orléans, France is a Swiss Professor in logic at the University of Brazil, Rio de Janeiro, and Researcher of the Brazilian Research Council. He is permanent member and former president of the Brazilian Academy of Philosophy. Before going to Brazil, he was Professor of the Swiss National Science Foundation at the University of Neuchâtel in Switzerland and researcher at Stanford University working with Patrick Suppes.
Trivialism is the logical theory that all statements are true and that all contradictions of the form "p and not p" are true. In accordance with this, a trivialist is a person who believes everything is true.
Stephen Yablo is a Canadian-born American philosopher. He is David W. Skinner Professor of Philosophy at the Massachusetts Institute of Technology (MIT) and taught previously at the University of Michigan, Ann Arbor. He specializes in the philosophy of logic, philosophy of mind, metaphysics, philosophy of language, and philosophy of mathematics.
Walter Alexandre Carnielli is a Brazilian mathematician, logician, and philosopher, full professor of Logic at the State University of Campinas (UNICAMP). With Bachelor and M.Sc. degrees in mathematics at the State University of Campinas in Campinas he obtained his Ph.D. in 1984 from the same university under the supervision of Newton da Costa and subsequently worked as a postdoc at the University of California at Berkeley as a Research Fellow, following an invitation by Leon Henkin.
Martha Kneale was a British philosopher.
Eduardo Barrio is an Argentine logician.
Graham Nerlich was an Australian philosopher. He was an Emeritus Professor of Philosophy at the University of Adelaide, and his expertise was in the areas of philosophy; existence of God; meaning of life; mind and body; ethics; and philosophy of science.
Forrester's paradox, also known as the paradox of gentle murder, is a paradox of deontic logic attributed to James Forrester. It is a version of the Good Samaritan paradox.