[FOM] Concerning Ultraformalism-to Slater&Ozkural

Hartley Slater slaterbh at cyllene.uwa.edu.au
Wed Nov 8 21:37:07 EST 2006

Mirco Mannucci first says

>The reason why I love that paragraph instead, and why I pointed you 
>and the other FOM
>fellows there, is that it hints at  a view that I find fascinating, 
>and, it seems to me,
>(as yet) not fully explored in all its implications:
>----->  from the (rigorous) formalist standpoint,
>                 THERE ARE NO NUMBERS whatsoever.
>What IS there is simply an "arithmetical game", and "numbers" are just the
>"characters" of such a game.

but later:

>SSSSS0 is just the CANONICAL representative term in the (temporary)
>similarity classes of available terms denoting 5. Indeed is the simplest &
>most rudimentary way of denoting 5, but also an extremely
>expensive and clumsy one. Following the vector space analogy, one could say
>that SSSSS0 is the representation of 5 in the standard basis (i.e. 
>the standard  denotation system).

So here he has something *denoting* the number 5.  Maybe the 
difficulty is that he does not put quotation marks around terms like 
'SSSSS0'.  Without then made explicit then even the '5' might look 
like it is a mentioned term, and so just a 'character in a game'.  In 
short what is true is that
'SSSSS0' denotes 5,
(which presumes there are numbers, or at least the number 5), but one 
cannot say either that
SSSSS0 denotes '5',
or that
'SSSSS0' denotes '5'.

A similar point is involved when he goes on to say:

>Before I leave the section dedicated to you (Hartley Slater), I would like
>to say that I found your sentence
>>if one does not incorporate into one's formal language the ability to say
>  >what it means.
>very intriguing and a bit  mysterious. I assume that you would
>like a language that is both ground-language  and meta-language at the
>same time.
>But PA does that already, via Godelization. What am I missing???

Godelisation enables one to say things like
'n' represents 'p',
i.e. its sets up a 1-1 correlation between certain numerals and 
certain syntactic formulae.  That has nothing to do with saying what 
'p' means, or 'n' refers to.  To say that one has to say things like:
'2+3=5' means that 2+3=5,
'SSO' refers to the number 2.

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

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