Date: Tue, 19 May 1998 13:35:54 -0500
Subject: Re: Math/Metaphysics


> In one of H's articles concerning Maths, there are numerous claims
> about the discipline, e.g., about views concerning its characteristic
> axiomatization, about views concerning its grounding on ultimate, first
> principles, i.e., concerning its having a complete/comprehensive
> (Euclidean) edifice, albeit, yet-to-be formulated, resting on self-evident
> axioms, axioms from which, in accord with some finite set of rules of
> inference, all the 'true' theorems of math, and no 'false' statements of
> math, would be derived.
> 
> I submit that most of these views are now archaic, that they are of
> historical or pedagogical interest only. It was in light of Godel's and
> Godel-related results -- not only his incompleteability results, but his
> independence results also concerning the Ax of Choice (and its various
> equivalents) -- that these views came to be shelved.

I am not intimate with Godel's results, though I know them in general, so 
please forgive any obvious inaccuracies. First, what exactly does Godel prove? 
Is is that every axiomatic system has axioms which cannot be proven within 
that system? If so, then all this implies is that there are no "absolutely true" 
axioms, not that any given mathematical system can lack axiomatic structure. 
Even if they are not the "traditional" axioms, they are still axioms. All 
Heidegger would be saying, then, is that mathematics qua mathematics is 
axiomatic by nature, not that there is any "one true" mathematics in the 
traditional sense.

Anthony Crifasi


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