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

Hi Bruno MarchalOK, 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> 11/5/2012 "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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