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 rules
of inference don't permit you to prove everything from a
contradiction. 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. Which
implies there is some measure of 'true' other than 'provable'.
Brent
Is there a logic that does not recognize a proposition to be true
or false unless there is an accessible proof for it? Accessible is
hard for me to define canonically, but one could think of it as
being able to build a model (via constructive or none constructive
means) 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 theories
are 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
--
Onward!
Stephen
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