From: Zeynep Tufekcioglu <zeynept-AT-turk.net>
Subject: Re: On the Kantian Theory of Space         
Date: Sat, 6 Jul 1996 01:58:19 +0300


Paul writes:

>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
>

Paul, my comment was against the following position:

>The author cited relativity theory and stressed that other forms
>of geometry apart from that of Euclid were equally valid. He 
>perceived Kant as a subjective idealist superseded by the empiric
>materialism of Einstein. He concluded: "The space-time continuum
>does not constitute a reference system on the basis of which one
>can build unvarying natural laws." 

I believe that mathematics is a subjective construction. The axioms are
derived from what we believe to be self-evident, as per observation. What is
called "a priori" knowledge is, imo, derived from our practical experience
and observation. We are small compared to our planet, so the round surface
of the earth looks flat. A straight line drawn on earth looks "straight", it
is not, actually "straight" as defined in the Euclidean sense.

If our planet was small enough so that you could walk a few steps, and see
the sunset again, the infamous fifth postulate would probably have been
first posited as such that all "parallel lines meet", since direct
observation would show "roundness" of the earth. Some smart person centuries
later would perhaps try to prove this axiom by attempting to make it into a
theorem, and then also discover that no contradiction came up if s/he
replaced it with the unbelievable sounding "parallel lines do not meet".

The author of the above quote can claim that "we can't constitute a
reference system on the basis of which one can build unvarying natural laws"
because there are Non-Euclidian and other geometries that are consistent.

That is a problem of epistomology, not ontology. *We* define the
correspondence between mathematical space and physical space. You *can* just
as practically use hyperbolic geometry as long as you stay *within* this.

>>"The space-time continuum
>>does not constitute a reference system on the basis of which one
>>can build unvarying natural laws." 

I swear I don't understand this comment. I also don't see how one can at
once use the relativity theory and non-Euclidean geometries, both, in
connection with the result the author derives. I am no expert in either of
the fields either, especially the physics. But what I do know does not
produce the above result, and someone must clearly show me how they do it
before I'll believe it.

By the way, Euclid was also troubled with the fifth axiom, and many others
for a few thousand years. 

I honestly believe that if the "theory of relativity" was not named
"relativity" but say "theory of pumpkins", "postmodern" thought would not
even be able to really discover it as a source for those kinds of statements
as above. 

Zeynep



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