2012/12/18 Stephen P. King <[email protected]> > 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 > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to > everything-list@googlegroups.**com<[email protected]> > . > To unsubscribe from this group, send email to everything-list+unsubscribe@ > **googlegroups.com <everything-list%[email protected]>. > For more options, visit this group at http://groups.google.com/** > group/everything-list?hl=en<http://groups.google.com/group/everything-list?hl=en> > . > > -- All those moments will be lost in time, like tears in rain. -- 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.
