From: "Anthony Crifasi" <crifasi-AT-flash.net>
Date: Wed, 27 May 1998 10:14:46 -0500
Subject: Re: math/meta/truth/...


Jim wrote:

> Thus, if we accept H's Aritotle and H's theory of T, we are in the clear
> with respect to math; that is a big plus I think.

Aristotle's theory of truth does allow for truth in mathematics in a way that 
modern views of causality do not, but there are reasons why Aristotle's theory 
was eventually rejected, and those reasons are the same ones that eventually 
led to the modern view. So I don't think that simply "going back to Aristotle" is 
a viable alternative. Aristotle had four causes - formal, material, moving, and 
final. The latter two have nothing to do with *truth* in mathematics, and the 
former two depend on certain long-since refuted views of physics presented by 
Aristotle (specifically, substantial change, and the resulting separation of form 
and matter). 

> (as for Anthony's position on 'axiomatization', the verdict isn't in yet;
> however, I don't think that accepting Anthony's postion will be to H's
> demerit; thought I've been suggesting that it might, I am still arguing
> back and forth over the 'whether-or-not' of it (I can't sleep at nights)).

I'm not sure what any alternative to what I presented would be like. A non-
axiomatic science or mathematics? Even a study of the "history" of axioms still 
assumes that there are axioms to study, even if those axioms are no longer 
considered "absolutely true." So I don't see how this is an alternative to 
axiomatic science. It is only an alternative to *absolute* science.

Anthony Crifasi


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