From: Paul Gallagher <pcg-AT-panix.com>
Subject: Re: On the Kantian Theory of Space
Date: Fri, 5 Jul 1996 03:24:19 -0400 (EDT)


> 
> Completely ignorant about mathematics would be a better description. Shallow
> and dogmatic don't really give all due credit.
> 
> He should first tell us what he thinks "valid" means mathematically. As far
> as I know, it means consistent. Mathematics is neither true nor false.
> 
> The author of that quote, should be made to look up the word "axiom" in a
> dictionary. Also, "theorem". Or maybe, is this a Sokal quote? 
> 
> The whole problem I think is the non-understanding of the relationship with
> epistomology and ontology. As it is with the "chaos" hype.
> 
> Mathematical space is distinct than physical space. Mathematics is "a
> subjective construction". You can choose to use hyperbolic geometry or
> elliptic geometry or Euclidian geometry in your interpretations/applications
> to/of the physical world. 
> 
> Zeynep
>

I have no special knowledge about this subject, but my impression
was the exact opposite of what Zeynep writes. I thought it was Kant
who believed Euclidean geometry and absolute space-time constituted
a priori synthetic knowledge about the world - that it was precisely
not just "a subjective construction." Modern physics has shown that
these ideas do not exactly model the world. Kant was mistaken on
this point. The dissertation writer was correct on this point. Both
Kant and the dissertation guy were writing about the physical world,
not about abstract mathematics. At least, that's my impression.

Paul



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