On May 4, 10:38 am, fom <fomJ...@nyms.net> wrote: > 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 dot-com 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? >
Right! Infinite Set calculations by Induction are not required to work on Natural Language processing, but a core theorem proving kernal is... e.g. detecting a contradiction when planning a robot movement..
You don't just 'choose' a foundational theory, none of ZFC holds up to Induction, when it's derived proofs are more closely examined there is a lot of convoluted circular reasoning...
Imagine a 1900 astronomer..
OBSERVATION: CANT SEE ANY DETAIL ON VENUS! INFERENCE: 100% CLOUD COVER INFERENCE: RAIN INFERENCE: RAINFORRESTS INFERENCE: JUNGLE WILDLIFE INFERENCE: DINASAURS
Compare this to ZFC and CANTOR
OBSERVATION: change ALL(n) DIGIT(n,n) INFERENCE: ALL(n) ANTID(n) is different to DIGIT(n,n) INFERENCE: ALL(n) ANTID(n) is different to ROW(n) INFERENCE: ALL(n) ANTID is different to ROW(n) INFERENCE: ANTID is missing infinite string from LIST INFERENCE: Pigeon Hole Principle - |LIST+ANTID| > |LIST| INFERENCE: |R| > |N| INFERENCE: X is Bigger Than INFINITY! ....
*this goes on for miles, |OMEGA| is uncomputable, incomplete mathematics....*
Perhaps it's time you exercised some CONTRADICTION CHECKING yourselves on that conclusion!