3 ms·

Is that still true constructively?

• sid0 16y ago
  By "constructively" do you mean in a constructivist logic like intuitionist logic? I'm too lazy to work it out right now, but I'd place my money on that statement not being valid in intuitionist logic.
  • moultano 16y ago
    Yes. That's what I meant. That was my feeling too, but I know myself too well than to place any bets on what is provable or not constructively unless I work it out. :)
• vilhelm_s 16y ago
  No. Intuitionistic logic has the pleasing property that whenever G |- P \/ Q is provable, then either G |- P is provable or G |- Q is provable. I think this gets to the heart of what is confusing about this example: (London -> England) /\ (Paris -> France) |- (London -> France) \/ (Paris -> England) is classically valid, even though neither (London -> England) /\ (Paris -> France) |- (London -> France) nor (London -> England) /\ (Paris -> France) |- (Paris -> England) is