intuitionistic logic
intuitionistic logic
(logic, mathematics)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.