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# 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)

Tagged:

• Intuitionistic probability

logic Florentin Smarandache’s representation of the probability of an event occuring, given by T, I, F which are real subsets representing the truth, indeterminacy, and falsity percentages respectively, and n_sup = sup(T) + sup(I) + sup(F) < 100 Related to intuitionistic logic. [Florentin Smarandache, "A Unifying Field in Logics. / Neutrosophy: Neutrosophic Probability, Set, and […]

• Intuitionist logic

spelling Incorrect term for “intuitionistic logic”. (1999-11-24)

• Intuitive

[in-too-i-tiv, -tyoo-] /ɪnˈtu ɪ tɪv, -ˈtyu-/ adjective 1. perceiving directly by without rational thought, as a person or the mind. 2. perceived by, resulting from, or involving intuition: intuitive knowledge. 3. having or possessing intuition: an intuitive person. 4. capable of being perceived or known by intuition. 5. easy to understand or operate without explicit […]

• Intuitively

[in-too-i-tiv, -tyoo-] /ɪnˈtu ɪ tɪv, -ˈtyu-/ adjective 1. perceiving directly by without rational thought, as a person or the mind. 2. perceived by, resulting from, or involving intuition: intuitive knowledge. 3. having or possessing intuition: an intuitive person. 4. capable of being perceived or known by intuition. 5. easy to understand or operate without explicit […]

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