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>.

   (2001-03-18)