Date: Thu, 28 May 1998 04:28:37 +0900 (JST)
From: Alan Myouka Sondheim <sondheim-AT-gol.com>
Subject: Re: Math/Metaphysics



One can also bring a phenomenological accounting to axiomatization, which
is rarely done.

The fact that an infinite number of axioms are necessary for a system
(extended into the realm of Godel numbering) dosen't mean the system is
not axiomatic, only that it's not finite-axiomatic; I think the direction
of further axioms is also indicated (i.e. what is necessary on every
level).

The 19th century dream via Hertz or for that matter the Tractatus of a
finite natural order drawn from limited axioms, a la Occam or Euclid for
that matter - that's what's changed, dream into drama. Don't forget that
Godel himself remained a platonist of sorts.

Alan

On Wed, 27 May 1998, Anthony Crifasi wrote:

> Date: Wed, 27 May 1998 12:38:12 -0500
> From: Anthony Crifasi <crifasi-AT-flash.net>
> Reply-To: heidegger-AT-lists.village.Virginia.EDU
> To: heidegger-AT-lists.village.Virginia.EDU
> Subject: Re: Math/Metaphysics
> 
> Hen wrote:
> 
> > I'd like to hear a "clean" discourse regarding how this topic connects
> > with heidegger's view that all of the theoretical strainings towards 
> > calculative knowledge (and, therefore, towards theories of calculative
> > methodologies, plus any and all additional layering of that onion) is of 
> > a secondary and derivitive acquisition via being-in-the-world.
> 
> If I remember correctly, the original issue was whether or not Heidegger's view 
> of mathematics as essentially axiomatic is outdated in light of Godel's 
> argument. I replied by arguing that all Godel shows is that there are no 
> "absolute" axioms in mathematics, not that mathematics can actually be non-
> axiomatic, thereby saving Heidegger's interpretation of math. Further, I argued 
> that the only way to escape axiomatization, not only that of mathematics but 
> also that of the objective sciences, was by transcending science altogether, 
> which is exactly what Heidegger does by subordinating calculative knowledge 
> to being-in-the-world.
> 
> Anthony Crifasi
> 
> 
> 
> 
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