On the foundations (of logic and arithmetic)

From: Tomek (tmyslowski_at_wp.pl)
Date: 09/08/04 

Date: 8 Sep 2004 06:20:09 -0700

Hello,
In his seminal paper Hilbert says:

"[...] We take as a basis of our considerations
the first thought object 1 (one). We call what
we obtain by [putting together] two, three, or more
of this object, for example

 11, 111, 1111

combinations [Kombinationen] of the object 1 with
itself. These combinations, such as

 (1)(11), (11)(11)(11), ((11)(11))(11), ((111)(1))(1)

are again called combinations of object 1 with
itself.

The combinations are likewise just called objects,
and then, to distinguish it, object 1 is called
a simple object. [...]"

No, I am not going to be a nuisance and ask question
after question (I'd rather die). The passage I quoted, however,
_touches_ upon a very delicate issue, which I
most certainly cannot expect myself to work out
on my own vis. [putting together] of geometric
figures (of symbols) as the principal act of

BRINGING MATHEMATICAL OBJECTS INTO EXISTENCE.

Please, does Hilbert himself, or some other genius,
discuss this most profound ontological and epistemological
issue in ALL DETAILS.

Thank you.

Tom