# Category: Intuitionism

Constructive analysis
In mathematics, constructive analysis is mathematical analysis done according to some principles of constructive mathematics.This contrasts with classical analysis, which (in this context) simply mean
Intuitionistic type theory
Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory) is a type theory and an alternative foundation of mathematics.Intuitionistic type theory was created by P
Brouwer–Hilbert controversy
In a controversy over the foundations of mathematics, in twentieth-century mathematics, L. E. J. Brouwer, a proponent of the constructivist school of intuitionism, opposed David Hilbert, a proponent o
Constructive set theory
Constructive set theory is an approach to mathematical constructivism following the program of axiomatic set theory.The same first-order language with "" and "" of classical set theory is usually used
Heyting arithmetic
In mathematical logic, Heyting arithmetic is an axiomatization of arithmetic in accordance with the philosophy of intuitionism. It is named after Arend Heyting, who first proposed it.
Peirce's law
In logic, Peirce's law is named after the philosopher and logician Charles Sanders Peirce. It was taken as an axiom in his first axiomatisation of propositional logic. It can be thought of as the law
Henri Lebesgue
Henri Léon Lebesgue ForMemRS (French: [ɑ̃ʁi leɔ̃ ləbɛɡ]; June 28, 1875 – July 26, 1941) was a French mathematician known for his theory of integration, which was a generalization of the 17th-century c
In intuitionistic mathematics, a species is a collection (similar to a classical set in that a species is determined by its members). A spread is a particular kind of species of infinite sequences def
Dialectica interpretation
In proof theory, the Dialectica interpretation is a proof interpretation of intuitionistic arithmetic (Heyting arithmetic) into a finite type extension of primitive recursive arithmetic, the so-called
Arend Heyting
Arend Heyting (Dutch: [ˈɦɛi̯tɪŋ]; 9 May 1898 – 9 July 1980) was a Dutch mathematician and logician.
Carl Friedrich Gauss
Johann Carl Friedrich Gauss (/ɡaʊs/; German: Gauß [kaʁl ˈfʁiːdʁɪç ˈɡaʊs]; Latin: Carolus Fridericus Gauss; 30 April 1777 – 23 February 1855) was a German mathematician and physicist who made significa
L. E. J. Brouwer
Luitzen Egbertus Jan Brouwer (/ˈbraʊ.ər/; Dutch: [ˈlœy̯tsə(n) ɛɣˈbɛrtəs jɑn ˈbrʌu̯ər]; 27 February 1881 – 2 December 1966), usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a
George F. C. Griss
George François Cornelis Griss (30 January 1898, Amsterdam – 2 August 1953, Blaricum), usually cited as G. F. C. Griss, was a Dutch mathematician and philosopher, who was occupied with Hegelian ideali
Inquisitive semantics
Inquisitive semantics is a framework in logic and natural language semantics. In inquisitive semantics, the semantic content of a sentence captures both the information that the sentence conveys and t
Stephen Cole Kleene
Stephen Cole Kleene (/ˈkleɪni/ KLAY-nee; January 5, 1909 – January 25, 1994) was an American mathematician. One of the students of Alonzo Church, Kleene, along with Rózsa Péter, Alan Turing, Emil Post
Harrop formula
In intuitionistic logic, the Harrop formulae, named after , are the class of formulae inductively defined as follows: * Atomic formulae are Harrop, including falsity (⊥); * is Harrop provided and ar
Leopold Kronecker
Leopold Kronecker (German: [ˈkʁoːnɛkɐ]; 7 December 1823 – 29 December 1891) was a German mathematician who worked on number theory, algebra and logic. He criticized Georg Cantor's work on set theory,
Intuitionistic logic
Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion
Michael Dummett
Sir Michael Anthony Eardley Dummett FBA (27 June 1925 – 27 December 2011) was an English academic described as "among the most significant British philosophers of the last century and a leading campai
Double-negation translation
In proof theory, a discipline within mathematical logic, double-negation translation, sometimes called negative translation, is a general approach for embedding classical logic into intuitionistic log
Intuitionism
In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach where mathematics is considered to be purely the result of the constructive mental activ
Émile Borel
Félix Édouard Justin Émile Borel (French: [bɔʁɛl]; 7 January 1871 – 3 February 1956) was a French mathematician and politician. As a mathematician, he was known for his founding work in the areas of m