Date: Jun 21, 2013 8:42 AM
Author: LudovicoVan
Subject: Re: Matheology § 288

"Julio Di Egidio" <julio@diegidio.name> wrote in message 
news:kq1b10$e9m$1@dont-email.me...

> Following links from non-well-founded set theory, I get to the axiom of
> superuniversality and axiomatic nonstandard analysis


This is an article that may be of interest to a justification and then
instantiation of a non-standard approach:

Juha Ruokolainen
"Constructive nonstandard analysis without actual infinity"
<https://www.doria.fi/bitstream/handle/10024/2865/construc.pdf>

<< At least from the computational point of view we can only possess and
process a finite amount of finitely precise information in a finitely long
period of time. If we do not take into account any physical or other
limitations to available space and time resources, then we may allow us to
possess and process indefinitely large yet finite amount of indefinitely yet
finitely precise information in an indefinitely yet finitely long period of
time. But can we make any sense of this? Moreover, if we require that
mathematical objects also be on a par with the above description, how can we
then deal with infinite objects, like real numbers and the continuum, at
all? It is clear that some nonstandard ideas are needed here. >>

It seems to me that such an approach satisfies strict finitism:

<http://en.wikipedia.org/wiki/Finitism#Classical_finitism_vs._strict_finitism>

Julio