FOM: RE: Transfinite Logic

[Axiomize@aol.com]

Subj:Re: FOM: RE: Transfinite Logic 
Date:6/10/02 11:54:01 AM Eastern Daylight Time
From:martin at eipye.com
To:Dean.Buckner at btopenworld.com, fom at math.psu.edu
CC:heck at fas.harvard.edu
Sent from the Internet (Details)

At 03:59 AM 6/9/2002, Dean Buckner wrote:
>My argument is about
>use of English, not mathematics!

Dear Professor Buckner,

Why are you posting (and repeatedly) issues about the use of English on a 
forum devoted to foundations of mathemaitcs?

Martin Davis

 - - -

I would point out that both mathematics and English are bases of computing - 
or at least should be treated as such, in which case the Liar paradox is 
easily formalized, starting with:

true English sentence = program that halts yes = provable wff = set 
containing a particular element
false English sentence = program that halts no = refutable wff = set not 
containing a particular element
undecidable English sentence (e.g. "This is false.") = program that loops = 
undecidable wff = undecidable (set,element)

Or is this just obvious and uninteresting?

English being the "ultimate superset of mathematics", are we not striving 
toward expanding mathematics to prove as much as what is true in English as 
we consistently/soundly can?

Charlie Volkstorf
Cambridge, MA