[FOM] Concerning Ultraformalism-to Slater&Ozkural

[Hartley Slater]

At 12:00 PM -0500 9/11/06,  Timothy Chow wrote:

>Hartley Slater wrote:
>>The main point for the moment, though, is: how many FOMers, reading
>>this message, even noticed the 'that's in the 'that such and such, or
>>that such and such' just then?
>
>This question is almost equivalent to asking how many FOMers care about
>this particular philosophical question enough to have studied it and
>developed a sensitivity to this distinction.
>
>Working mathematicians don't particularly care about the Liar or about
>Truth.  They don't particularly care if they can't prove that 2+3=5, as
>long as they can produce proofs of "2+3=5".  If you want to convince them
>that they *should* care, then you need to demonstrate what difference it
>would make to the daily practice of mathematics.

I should think that, in the 'daily practice of mathematics', the 
formula '2+3=5' is written and uttered with its standard 
interpretation in mind, whereas in the debate here it has been the 
theoretical difficulty of locating the standard interpretation of 
such formulae, and removing non-standard interpretations, that has 
been of concern.

The issue about the identity of mathematical truths - and more 
generally the identity of facts of any description, and the crucial 
categorical difference between facts and formulae - has arisen in a 
debate about Formalism, the status of semantic interpretations of 
meta-mathematical syntax, and specifically whether Hilbert's 
programme could even prove that 2+3=5 rather than just organise 
systems of (uninterpreted) formulae, like '2+3=5'.  The debate on 
this matter goes back to Frege.  It seems to me, therefore, to be 
entirely appropriate for discussion of the FOM list, as it stands.

-- 
Barry Hartley Slater
Honorary Senior Research Fellow
Philosophy, M207 School of Humanities
University of Western Australia
35 Stirling Highway
Crawley WA 6009, Australia
Ph: (08) 6488 1246 (W), 9386 4812 (H)
Fax: (08) 6488 1057
Url: http://www.philosophy.uwa.edu.au/staff/slater