As Robert Black (6/23) and Stig Andur Pedersen (6/26) note, one question
is answered: Hilbert's quote is in Kant at A702/B730. In response to
Graham White's question whether H or an editor supplied the page
reference, I am not sure. The citation is to *Elementarlehre* T[heil].2,
Abt[heilung].2, which begins with the passage that I quoted in my first
posting. But Robert and Stig have solved the mystery anyway, since it is
easy to see how anyone might cite the one passage while giving page
reference to the other.
Graham White is right that the terms involved all have techical meanings
for Kant; but there remain two questions about this:
a) What *did* Kant mean? I believe that there are rather different
accounts of K's meaning of the term 'pure intuition'. The problem is that
its supposed connection with empirical intuition (which is needed to
support the applicability of geometry to space) is in conflict with its
supposed role in mathematical demonstration. One obtains different views
of K's idea as one attempts to take into account one of the other of
these two poles.
b) Did Hilbert use these terms with a Kantian meaning (as he understood
K) in mind?
It is so that there are passages (one in particular) in ``Ueber das
Unendliche'', describing the finitist position, that sound very Kantian;
but it can at least be questioned whether that should be read back into
*Found Geom*.
Bill Tait