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.

Last updated: 2001-03-18

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 Logic", American Research Press, Rehoboth 1999].

Last updated: 2001-03-18

Nearby terms:

intuitionism ♦ intuitionistic logic ♦ intuitionistic probability

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