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.
Better definitions?????? John M On Tue, Dec 18, 2012 at 12:50 PM, meekerdb <[email protected]> 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 > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
