Subject: Re: [HM] Kant and non-Euclidean geometry
From: William Tait (wwtx@midway.uchicago.edu)
Date: Sat Mar 11 2000 - 11:32:01 EST
Dirk Schlimm (Fri, 10 Mar 2000 ) wrote
> This reminds me of the following quote I recently came across:
>
> "It is a commonplace of newer Kantian scholarship that he already knew
> about non-euclidean geometry from his friend Lambert."
>
> In: Judson Chambers Webb: Tracking contradictions in geometry: the
> idea of a model from Kant to Hilbert. p.1. In Jaakko Hintikka, editor,
> From Dedekind to Goedel: Essays on the Development of the Foundations
> of Mathematics, number 251 in Synthese Library Series, pages 1-20.
> Kluwer Academic Publishers, Dordrecht, 1995.
>
> As I don't know much about newer Kantian scholarship I'd be interested
> to know what people on this list think about the above claim.
There is evidence, e.g. in Kant's examples of geometric propositions
that he took to be synthetic a priori as opposed to analytic, that he
had the model of spherical geometry in mind. For example, "Two lines
cannot enclose a space" (e.g. A220-221/B268), "The interior angles
of a triangle equal two right angles", and more. Given his
association with Lambert, it makes sense that it was spherical
geometry that influenced his view, contrary to that of Leibniz and
some of his followers, that geometry is not analytic. The earliest
statement of this view of Kant that I know is in G. Martin, *Kant's
Metaphysics and Theory of Science* (1951), trans. P. Lucas
(Manchester 1952). I don't have available the reference to the
original German. This point of view is also taken up in G. Britton's
*Kant's Philosophy of Science* (Princeton 1978). The question is
discussed in Michael Friedman's *Kant and the Exact Sciences (Harvard
1992).
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
William W. Tait
Professor Emeritus of Philosophy
University of Chicago
wwtx@midway.uchicago.edu
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