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Russell's paradox — Part of the foundations of mathematics, Russell s paradox (also known as Russell s antinomy), discovered by Bertrand Russell in 1901, showed that the naive set theory of Frege leads to a contradiction.It might be assumed that, for any formal… … Wikipedia
Intuitionistic logic — Intuitionistic logic, or constructive logic, is a symbolic logic system differing from classical logic in its definition of the meaning of a statement being true. In classical logic, all well formed statements are assumed to be either true or… … Wikipedia
Brouwer-Hilbert controversy — A foundational controversy in twentieth century history of mathematics opposed L. E. J. Brouwer, a supporter of intuitionism, and David Hilbert, the founder of formalism.BackgroundThe background for the controversy was set with David Hilbert s… … Wikipedia
Negation — For other uses, see Negation (disambiguation). In logic and mathematics, negation, also called logical complement, is an operation on propositions, truth values, or semantic values more generally. Intuitively, the negation of a proposition is… … Wikipedia
Heyting algebra — In mathematics, Heyting algebras are special partially ordered sets that constitute a generalization of Boolean algebras, named after Arend Heyting. Heyting algebras arise as models of intuitionistic logic, a logic in which the law of excluded… … Wikipedia
Markov's principle — Markov s principle, named after Andrey Markov Jr, is a classical tautology that is not intuitionistically valid but that may be justified by constructive means. There are many equivalent formulations of Markov s principle. Contents 1 Statements… … Wikipedia
Propositional calculus — In mathematical logic, a propositional calculus or logic (also called sentential calculus or sentential logic) is a formal system in which formulas of a formal language may be interpreted as representing propositions. A system of inference rules… … Wikipedia
Metaphysics — This article is about the branch of philosophy dealing with theories of existence and knowledge. For the work of Aristotle, see Metaphysics (Aristotle). For the occult field, see Metaphysics (supernatural). Philosophy … Wikipedia
Intuitionism — This article is about Intuitionism in mathematics and philosophical logic. For other uses, see Ethical intuitionism. In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach to mathematics as … Wikipedia
Combinatory logic — Not to be confused with combinational logic, a topic in digital electronics. Combinatory logic is a notation introduced by Moses Schönfinkel and Haskell Curry to eliminate the need for variables in mathematical logic. It has more recently been… … Wikipedia
