4 ms·
Anything can be derived from p or not p, not from false.
by silasdavis 7y ago
Anything can be derived from p or not p, not from false.
- thegeomaster 7y agoThis is just a corollary of the fact that "p or not p" is false (for any value of p).
- pretty_lorelei 7y ago"p and not p" is false, "p or not p" is always true.
- thegeomaster 7y agoOops. Went a bit on autopilot with that one.
- rq1 7y agoThen everything is true. :)
- H8crilA 7y agoThe sentence "p or not p" is a tautology ("true", ⊤) in classical logic, so you can't derive anything useful from it. It can carry some power in non-classical logics, like the intuitionistic logic, where it's not true that "p or not p" for any sentence p. You can derive anything from false, this is known as the principle of explosion: "ex falso quodlibet", "from false anything": https://en.wikipedia.org/wiki/Principle_of_explosion https://en.wikipedia.org/wiki/Principle_of_explosion