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