> A theorem of that logic is
> (p -> q) -> q <-> pvq
Is not true in intuitionistic logic.
Take the following model:
w1:p=0,q=0
w2:p=1,q=1
> NN
> PL IN
> CN
Further I assume that it does only
make sense to talk about different
logics as your PL, NN, IN, CN, if
you start with a logic that is not
classical.
Because in a classical setting you
have NN==PL==CN==IN. In classical
setting it doesn't matter to add
all your axioms:
p -> q -> (p -> ~q) -> ~p
p -> q -> p -> p
p -> (~p -> q)
~p -> q -> (~p -> ~q) -> p
~~p -> p
Because they are anyway already
tautologies.
Re: Do we really need to have models for a theory? ... >>> entirety just goes to infinitely higher order logics.... >> be associated with large cardinal axioms.... > Hi Mitch,... > being the one infinite set.... (sci.logic)
Re: tedious sledding re set existence in FOL ... >>> That involves NO axioms.... It involves inference rules INSTEAD OF ... > classical logics are all sufficiently different from ... the theorem is a proven, no matter what semantics we choose, even if, ... (sci.logic)
Re: Analytic/Synthetic distinction in modern inference engines? ... You asked about the analytic/synthetic distinction,... to ask about logics that treat the a/s distinction in some interesting ... All you have to do is pick appropriate axioms for whatever field ... preexisting axioms) can conflict with that; ... (sci.logic)
Re: tedious sledding re set existence in FOL ... >> That involves NO axioms.... It involves inference rules INSTEAD OF ...classical logics are all sufficiently different from ... not only the avoidance of "level" confusion but something ... (sci.logic)
