Subject: Re: [HM] Kant and non-Euclidean geometry
From: M.Carmen Hernandez Martin (mchm@cica.es)
Date: Fri Mar 17 2000 - 14:52:21 EST
Dear all,
I think that Kant's idea that geometry is a synthesis a priori, that
is, a construction independent of reality or previous to it, continues
to be valid. And not only for Euclidean geometry but also for
non-Euclidean ones.
As a matter of fact neither Frege nor Russell could begin to reduce
geometry to logic as they both try with arithmetic.
Geometries are in fact constructions a priori whose truth, as
Hilbert stated, lies on their consistency, their coherence.
The question of which of them corresponds to our intuition of space is
an empirical question, as Hilbert said also, and that is the only
point where, in my opinion, Kant's thought is wrong or better
incomplete.
Saludos desde Sevilla
M.Carmen Hernandez Martin
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