[FOM] A formalism for Ultrafinitism

Vladimir Sazonov V.Sazonov at csc.liv.ac.uk
Wed May 26 14:10:09 EDT 2004

Andrew Boucher wrote:
> Recall the first-order system of Bill Taylor (Thu May 20).  Call it W.

> Indeed without sequences W does not even seem to have access to 
> recursion and e.g. is unable to define the exponentiation relationship 
> from addition and multiplication.  

I hope you have seen my posting both on recursion and second-order
quantification in what I call Box-Arithmetic.

> I do agree with Bill's assessment that these approaches, by W or in SOL, 
> are more "honest" approaches to ultrafinitism.

What would this "honest" mean? There are various and diverging
views on numbers even from the point of view of a strict finitism
or ultrafinitism (I am not sure about terms). Realizing that big
finite, even like 2^1000 is a kind of infinity is one of such views.
Is it possible to convert this highly informal idea to something
mathematical? Will this give us some new insight?

How important are various considerations and formalisms will be
clear later.

Kind regards,

Vladimir Sazonov

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