On 18 Dec 2012, at 01:50, Stephen P. King wrote:

On 12/17/2012 4:31 PM, meekerdb wrote:On 12/17/2012 1:15 PM, Quentin Anciaux wrote:ISTM that consistency is the fact that you can't have contradiction.In some logics you're allowed to have contradictions, but the rulesof inference don't permit you to prove everything from acontradiction. I think they are then called 'para-consistent'.Incompletness that you can't prove every proposition.No, incompleteness is you can't prove every true proposition. Whichimplies there is some measure of 'true' other than 'provable'.BrentIs there a logic that does not recognize a proposition to be trueor false unless there is an accessible proof for it? Accessible ishard for me to define canonically, but one could think of it asbeing able to build a model (via constructive or none constructivemeans) of the proposition with a theory (or some extension thereof)that includes the proposition.I am trying to see if we can use the way that towers of theoriesare allowed by the incompleteness theorems...

`This is studied in recursion theory. Turing shows that incompleteness`

`continue to all effective transfinite tower, on the constructive`

`ordinals.`

Bruno

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