The Berry paradox is a self-referential paradox arising from an expression like "The smallest positive integer not definable in under sixty letters".
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 or apparently 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".
A quine is a computer program that takes no input and produces a copy of its own source code as its only output. The standard terms for these programs in the computability theory and computer science literature are "self-replicating programs", "self-reproducing programs", and "self-copying programs".
Self-reference is a concept that involves referring to oneself or one's own attributes, characteristics, or actions. It can occur in language, logic, mathematics, philosophy, and other fields.
Willard Van Orman Quine was an American philosopher and logician in the analytic tradition, recognized as "one of the most influential philosophers of the twentieth century". He served as the Edgar Pierce Chair of Philosophy at Harvard University from 1956 to 1978.
In mathematical logic, Russell's paradox is a set-theoretic paradox published by the British philosopher and mathematician Bertrand Russell in 1901. Russell's paradox shows that every set theory that contains an unrestricted comprehension principle leads to contradictions. The paradox had already been discovered independently in 1899 by the German mathematician Ernst Zermelo. However, Zermelo did not publish the idea, which remained known only to David Hilbert, Edmund Husserl, and other academics at the University of Göttingen. At the end of the 1890s, Georg Cantor – considered the founder of modern set theory – had already realized that his theory would lead to a contradiction, as he told Hilbert and Richard Dedekind by letter.
A strange loop is a cyclic structure that goes through several levels in a hierarchical system. It arises when, by moving only upwards or downwards through the system, one finds oneself back where one started. Strange loops may involve self-reference and paradox. The concept of a strange loop was proposed and extensively discussed by Douglas Hofstadter in Gödel, Escher, Bach, and is further elaborated in Hofstadter's book I Am a Strange Loop, published in 2007.
Gödel, Escher, Bach: an Eternal Golden Braid, also known as GEB, is a 1979 book by Douglas Hofstadter.
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible.
In logic, Richard's paradox is a semantical antinomy of set theory and natural language first described by the French mathematician Jules Richard in 1905. The paradox is ordinarily used to motivate the importance of distinguishing carefully between mathematics and metamathematics.
Curry's paradox is a paradox in which an arbitrary claim F is proved from the mere existence of a sentence C that says of itself "If C, then F". The paradox requires only a few apparently-innocuous logical deduction rules. Since F is arbitrary, any logic having these rules allows one to prove everything. The paradox may be expressed in natural language and in various logics, including certain forms of set theory, lambda calculus, and combinatory logic.
In analytic philosophy, a fundamental distinction is made between the use of a term and the mere mention of it. Many philosophical works have been "vitiated by a failure to distinguish use and mention". The distinction can sometimes be pedantic, especially in simple cases where it is obvious.
In mathematical logic, the diagonal lemma establishes the existence of self-referential sentences in certain formal theories of the natural numbers—specifically those theories that are strong enough to represent all computable functions. The sentences whose existence is secured by the diagonal lemma can then, in turn, be used to prove fundamental limitative results such as Gödel's incompleteness theorems and Tarski's undefinability theorem. It is named in reference to Cantor's diagonal argument in set and number theory.
In philosophy and logic, a deflationary theory of truth is one of a family of theories that all have in common the claim that assertions of predicate truth of a statement do not attribute a property called "truth" to such a statement.
Quine's paradox is a paradox concerning truth values, stated by Willard Van Orman Quine. It is related to the liar paradox as a problem, and it purports to show that a sentence can be paradoxical even if it is not self-referring and does not use demonstratives or indexicals. The paradox can be expressed as follows:
Self-referential humor, also known as self-reflexive humor, self-aware humor, or meta humor, is a type of comedic expression that—either directed toward some other subject, or openly directed toward itself—is self-referential in some way, intentionally alluding to the very person who is expressing the humor in a comedic fashion, or to some specific aspect of that same comedic expression. Here, meta is used to describe that the joke explicitly talks about other jokes, a usage similar to the words metadata, metatheatrics and metafiction. Self-referential humor expressed discreetly and surrealistically is a form of bathos. In general, self-referential humor often uses hypocrisy, oxymoron, or paradox to create a contradictory or otherwise absurd situation that is humorous to the audience.
A truth-bearer is an entity that is said to be either true or false and nothing else. The thesis that some things are true while others are false has led to different theories about the nature of these entities. Since there is divergence of opinion on the matter, the term truth-bearer is used to be neutral among the various theories. Truth-bearer candidates include propositions, sentences, sentence-tokens, statements, beliefs, thoughts, intuitions, utterances, and judgements but different authors exclude one or more of these, deny their existence, argue that they are true only in a derivative sense, assert or assume that the terms are synonymous, or seek to avoid addressing their distinction or do not clarify it.
Logophoricity is a phenomenon of binding relation that may employ a morphologically different set of anaphoric forms, in the context where the referent is an entity whose speech, thoughts, or feelings are being reported. This entity may or may not be distant from the discourse, but the referent must reside in a clause external to the one in which the logophor resides. The specially-formed anaphors that are morphologically distinct from the typical pronouns of a language are known as logophoric pronouns, originally coined by the linguist Claude Hagège. The linguistic importance of logophoricity is its capability to do away with ambiguity as to who is being referred to. A crucial element of logophoricity is the logophoric context, defined as the environment where use of logophoric pronouns is possible. Several syntactic and semantic accounts have been suggested. While some languages may not be purely logophoric, logophoric context may still be found in those languages; in those cases, it is common to find that in the place where logophoric pronouns would typically occur, non-clause-bounded reflexive pronouns appear instead.
The inscrutability or indeterminacy of reference is a thesis by 20th century analytic philosopher Willard Van Orman Quine in his book Word and Object. The main claim of this theory is that any given sentence can be changed into a variety of other sentences where the parts of the sentence will change in what they reference, but they will nonetheless maintain the meaning of the sentence as a whole. The referential relation is inscrutable, because it is subject to the background language and ontological commitments of the speaker.
