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Topic: mathematical infinite as a matter of method
Replies: 25   Last Post: May 4, 2013 11:24 PM

 Messages: [ Previous | Next ]
 Graham Cooper Posts: 4,495 Registered: 5/20/10
Re: mathematical infinite as a matter of method
Posted: May 3, 2013 9:20 PM

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
>
>
>
>
>
>
>
>
>

> > 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!

Herc
--
www.BLoCKPROLOG.com

Date Subject Author
4/21/13 fom
4/21/13 Virgil
5/2/13 Hercules ofZeus
5/2/13 fom
5/2/13 Virgil
5/3/13 Graham Cooper
5/3/13 fom
5/3/13 Brian Q. Hutchings
5/3/13 Graham Cooper
5/3/13 fom
5/3/13 Graham Cooper
5/3/13 fom
5/3/13 fom
5/4/13 Graham Cooper
5/3/13 Graham Cooper
5/3/13 fom
5/3/13 Graham Cooper
5/4/13 fom
5/4/13 Graham Cooper
5/4/13 fom
5/4/13 Graham Cooper
5/4/13 fom
5/4/13 Graham Cooper
5/4/13 fom
5/4/13 Graham Cooper
5/3/13 Graham Cooper