Subject: Re: [HM] Kant and non-Euclidean geometry
From: David Stump (stumpd@usfca.edu)
Date: Sat Mar 11 2000 - 12:26:29 EST
I can add a little to the interesting thread on Kant and non-Euclidean
geometry. The conflict was not really apparent, until Helmholtz made
in explicit in his famous lectures:
Helmholtz, H. von (1866). "Uber die Tatsaechilichen Grundlagen der
Geometrie." Heidelberg, Verhandlungen Naturhistorisch-Medizinischer
Verin 4 & 5: 197-202 & 31-32.
Helmholtz, Hermann von (1870). Uber den Ursprung und de Bedeutung der
Geometrischen Axiome. Pop. Wiss. Vortr.
Helmholtz, Hermann von, Moritz Schlick, et al. (1977). Epistemological
writings: the Paul Hertz/Moritz Schlick centenary edition of 1921 with
notes and commentary by the editors. Dordrecht, Holland
Boston: D. Reidel.
see
Nowak, Gergory (1989). Riemann's Habilitationsvortrag and the Synthetic
A Priori Status of Geometry. The History of Modern Mathematics, Volume I:
Ideas and Their Reception. David E. Rowe and John McCleary, Eds. Boston:
Academic Press: 17-46.
After Helmholtz, there was an "uproar of Boetians". However, Kantians
had a "fix" that became quite popular: Kant could not have thought that
only Euclidean geometry was logically possible, because in that case
geometry would be analytically true, and Kant stated clearly that
geometry is not analytic. So, the neo-Kantians argued, the existence of
non-Euclidean geometries (as logically possible) is completely compatible
with Kant, indeed it even confirms Kant's view. The earliest example of
this line of argument that I have found is in C. Renouvier.
So, it seems to me that the real death-knell of Kant's theory of geometry
did not come until Einstein's GTR. After Einstein, one cannot even say
that Euclid should be used in physics. It is not accidental that
Poincare's conventionalism also dies with Einstein. Poincare, after all,
said precisely that while alternative metric geometries are possible,
Euclid should continue to be used in physics.
Finally, a comment on Bill Tait's last remark. Since Leibniz hold the
bizarre sounding view that every truth is analytic, it seems to me that
there is no special issue about the status of geometry here.
> To me, the real historical puzzle is making sense of Leibniz's view
> that geometry is analytic (as well as Kant's view that the 'axioms',
> i.e. common notions of Euclid, are analytic). 'Analytic' in both cases
> means that the predicate is contained in the subject.
>
> Bill Tait
>
David J. Stump voice: (415) 422-6153
Department of Philosophy FAX: (415) 422-5356
University of San Francisco email: stumpd@usfca.edu
2130 Fulton Street
San Francisco, CA 94117-1080 USA
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