On 01/08/2013 10:39 PM, Tanner Swett wrote:
On Jul 29, 2013, at 8:13 PM, Fool wrote:
You're right, intuitionistic logic is too weird.
Heck no. Classical logic is weird.
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.
Keeping it on topic:
We don't _assume_ the law of the excluded middle, but many special cases
of it are _provable_ constructively. E.g. by induction, any two natural
numbers are either equal or not equal.
So in the strictly finite world, intuitionistic reasoning collapses to
classical anyway. I don't think there are any "essential" infinities on
Agora, so I doubt the distinction will matter here in the end.
So most likely, if omd or others wish to appeal to intuitionistic logic
to escape some sort of classical conclusion, there's going to be a way
to get to that conclusion anyway.
