Subject: Re: [HM] Kant and non-Euclidean geometry
From: Bill Oates (boates1@home.com)
Date: Sat Mar 11 2000 - 11:40:14 EST
Gordon et al
> In related news, Kant has often been accused of being an old
> stick-in-the-mud for having proclaimed Euclidean geometry to the
> only kind there could be, due to the way human minds work.
I tried to locate the information concerning the relationship between
Lambert and Kant, but could find no relevant details quickly. It is
clear that Lambert was a friend of Kant's. Kant actually taught
mathematics from time to time and Lambert was aware of non-Euclidean
geometry. The conclusion seems inevitable but I can not demonstrate
from Kant's own writings. Kant does indicate that non-Euclidean
geometries are wrong, not because of logic, but because they do not
fit into our intuition of space. This is part of the argument that
geometry is synthetic not analytic. So for us to agree that
non-Euclidean geometry is possible and in fact may represent
reality (whatever that means), I would argue is not a refutation of
the synthetic a priori.
I believe that Kant was not per se interested in geometry but in
showing that synthetic a priori are possible. Euclidean geometry is
chosen as an example. If the example fails it does not mean that
synthetic a priori are impossible.
I am no Kant scholar but would be interested to hear comments.
Bill
from chilly Dundas Canada
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