2012/12/18 Stephen P. King <stephe...@charter.net>

> 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.
>

If you include the proposition as an axiom, then it is trivially true, but
you don't work anymore in the same theory as the one without that
proposition as axiom.

Quentin

>
>     I am trying to see if we can use the way that towers of theories are
> allowed by the incompleteness theorems...
>
> --
> Onward!
>
> Stephen
>
>
>
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