intuitionistic logic

(logic, mathematics)Brouwer's foundational theory ofmathematics which says that you should not count a proof of(There exists x such that P(x)) valid unless the proofactually gives a method of constructing such an x. Similarly,a proof of (A or B) is valid only if it actually exhibitseither a proof of A or a proof of B.

In intuitionism, you cannot in general assert the statement (Aor not-A) (the principle of the excluded middle); (A ornot-A) is not proven unless you have a proof of A or a proofof not-A. If A happens to be undecidable in your system(some things certainly will be), then there will be no proofof (A or not-A).

This is pretty annoying; some kinds of perfectlyhealthy-looking examples of proof by contradiction just stopworking. Of course, excluded middle is a theorem ofclassical logic (i.e. non-intuitionistic logic).

History.

单词	intuitionistic logic
释义	intuitionistic logic intuitionistic logic (logic, mathematics)Brouwer's foundational theory ofmathematics which says that you should not count a proof of(There exists x such that P(x)) valid unless the proofactually gives a method of constructing such an x. Similarly,a proof of (A or B) is valid only if it actually exhibitseither a proof of A or a proof of B. In intuitionism, you cannot in general assert the statement (Aor not-A) (the principle of the excluded middle); (A ornot-A) is not proven unless you have a proof of A or a proofof not-A. If A happens to be undecidable in your system(some things certainly will be), then there will be no proofof (A or not-A). This is pretty annoying; some kinds of perfectlyhealthy-looking examples of proof by contradiction just stopworking. Of course, excluded middle is a theorem ofclassical logic (i.e. non-intuitionistic logic). History.
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