I tried to identify the meaning of "axiom" and found a funny solution:
as it looks, "AXIOM" is an unprovable idea underlining a theory otherwise
non-provable.
In most cases: an unjustified statement, that, however, DOES work in the
contest of the particular theory it is serving.

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Better definitions??????
John M
On Tue, Dec 18, 2012 at 12:50 PM, meekerdb <meeke...@verizon.net> wrote:
> On 12/17/2012 11:53 PM, Quentin Anciaux wrote:
>
> 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
>
>
> It seems like just defining a new predicate "accessible" which means
> "provable or disprovable" which you attach to propositions. Then it
> doesn't need be an axiom and it still allows an excluded middle.
>
> Brent
>
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