| slovo | definícia |
intuitionism
(encz) | intuitionism, n: |
Intuitionism
(gcide) | Intuitionism \In`tu*i"tion*ism\, n.
Same as Intuitionalism.
[1913 Webster] |
intuitionism
(wn) | intuitionism
n 1: (philosophy) the doctrine that knowledge is acquired
primarily by intuition |
intuitionism
(foldoc) | intuitionistic logic
intuitionism
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)
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| | podobné slovo | definícia |
intuitionism
(encz) | intuitionism, n: |
intuitionism
(wn) | intuitionism
n 1: (philosophy) the doctrine that knowledge is acquired
primarily by intuition |
intuitionism
(foldoc) | intuitionistic logic
intuitionism
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)
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