On Aug 2, 2013, at 6:38 AM, Fool wrote: > On 01/08/2013 10:39 PM, Tanner Swett wrote: >> But classical logic is the system obeyed by truth-bearing statements! >> >> —"Of course, who cares about truth-bearing statements, anyway" Machiavelli > > It's common enough to hear that classical logic is "about truth" while > intuitionistic is "about provability" or something like that, but I don't buy > it.
Yeah, clearly everything provable in intuitionistic logic is true (isn't it?), whereas not everything provable in classical logic is provable in intuitionistic logic. It does make sense to me to say that intuitionistic logic is about demonstrability. If you prove that assuming the negation of a statement leads to a contradiction, you haven't really demonstrated the truth of that statement, but you have demonstrated the statement's truth if you can give an actual example. —Machiavelli
