fom
Posts:
1,968
Registered:
12/4/12


Re: mathematical infinite as a matter of method
Posted:
May 3, 2013 8:38 PM


On 5/3/2013 6:19 PM, Graham Cooper wrote: > On May 3, 8:15 pm, fom <fomJ...@nyms.net> wrote: >> > > Well its fine to call it all philosophy anyway, but there > are real world problems here! >
I know. Up until the dotcom crash, I had been a Sun Solaris systems/network administrator and an Oracle database administrator.
> Most of ZFC axioms port across to PROLOG... > > AXIOM OF PAIRING > > e( A , union( S1, S2 ) ) : e( A , S1 ). > e( A , union( S1, S2) ) : e(A , S2 ). > > Now you can WRITE EXPRESSIONS with UNION > > eq( union( odds, evens) , nats ) ? >> YES > > > but the AXIOM OF EXTENSIONALITY > > (set equality) is completely useless on infinite sets. >
Have you considered looking at New Foundations? There is current interest and it has no axiom of infinity.
As a matter of curiosity, why bother with ZFC or any set theory for that matter? There are an immmense number of computationally interesting problems (such as your posts concerning temporal logic). Why bother with problems that are fundamentally impossible for a computer?

