On 11/5/2012 7:43 AM, Roger Clough wrote:
Hi Bruno Marchal

OK, you say propositions might have a contradiction but you might not
yet have found the contradictions. That's a profound point.
In other words, one can't ever be sure if a proposition is
necessarily true, because, as Woody Allen says, forever
is a long time. And the variety and number of possible copntradictions
is possibly vast. Shades of Nietzsche ! Tell me it isn't so !

I guess that's the same as saying that you can never be sure
of contingency either. I need to lie down for a while. This
is beginning to look like existentialism.

Roger Clough, rclo...@verizon.net <mailto:%20rclo...@verizon.net>
"Forever is a long time, especially near the end." -Woody Allen
Hi Roger,

Great question! If we are allowed to take forever to pay back a debt, then we have an effective free lunch! What you are thinking about with the concept of "propositions might have a contradiction but you might not yet have found the contradictions" is what is known as omega-inconsistent logical systems <http://math.stackexchange.com/questions/110635/how-it-is-posible-that-omega-inconsistency-does-not-lead-to-inconsistency>. ;-) Theories that are consistent right up until they produce a statement that is not consistent. By the way, the usual rules of logical inference in math assumes that truth theories are never inconsistent. What about theories that are only 'almost' never inconsistent? This might help us think about the shade of Nietzche a bit more.



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