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Was (wer) ist intuitionistic - definition

APPROACH IN PHILOSOPHY OF MATHEMATICS AND LOGIC

MathematicalIntuitionism; Neointuitionism; Mathematical intuitionism; Intuitionism (philosophy of mathematics); Intuitionistic; Intuitionist; Intuitionist mathematics; Intuitionistics mathemtatics; Intuitionistic mathemtatics; Intuitionistic mathematics; Intuitionistic math

Intuitionist

·noun ·same·as Intuitionalist.

intuitionist logic

VARIOUS SYSTEMS OF SYMBOLIC LOGIC

Constructivist logic; Constructive logic; Intuitionist logic; Intuitionistic propositional calculus; Intuitionistic Prop Calc; Intuitionistic Logic; Semantics of intuitionistic logic; Semantics for intuitionistic logic

<spelling> Incorrect term for "intuitionistic logic". (1999-11-24)

intuitionistic logic

VARIOUS SYSTEMS OF SYMBOLIC LOGIC

Constructivist logic; Constructive logic; Intuitionist logic; Intuitionistic propositional calculus; Intuitionistic Prop Calc; Intuitionistic Logic; Semantics of intuitionistic logic; Semantics for intuitionistic logic

<logic, mathematics> Brouwer's foundational theory of mathematics which says that you should not count a proof of (There exists x such that P(x)) valid unless the proof actually gives a method of constructing such an x. Similarly, a proof of (A or B) is valid only if it actually exhibits either a proof of A or a proof of B. In intuitionism, you cannot in general assert the statement (A or not-A) (the principle of the excluded middle); (A or not-A) is not proven unless you have a proof of A or a proof of not-A. If A happens to be undecidable in your system (some things certainly will be), then there will be no proof of (A or not-A). This is pretty annoying; some kinds of perfectly healthy-looking examples of proof by contradiction just stop working. Of course, excluded middle is a theorem of classical logic (i.e. non-intuitionistic logic). {History (http://britanica.com/bcom/eb/article/3/0,5716,118173+14+109826,00.html)}. (2001-03-18)

Wikipedia

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 activity of humans rather than the discovery of fundamental principles claimed to exist in an objective reality. That is, logic and mathematics are not considered analytic activities wherein deep properties of objective reality are revealed and applied, but are instead considered the application of internally consistent methods used to realize more complex mental constructs, regardless of their possible independent existence in an objective reality.

https://en.wikipedia.org/wiki/Intuitionism