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.
(2001-03-18)
Nearby terms:
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