On Tue, 25 May 1999, David Reed wrote:
> In a well known
> letter to Weber he refers to the divine creative power of the human mind
> and uses phrases which were to be picked up later by Einstein.
In the context of Dedekind's remarks about the divine creative powers
there's another quote worth mentioning: Dedekind comments on Weber's
manuscript "Elementare Mengenlehre. Nat\"urliche Zahlen". The manuscript
must have quoted Dedekind as having said "Wir sind g\"ottlicher Natur",
and Dedekind corrects it into "Wir sind g\"ottlichen Geschlechts" making
an explicit reference to the Bible: "Apostelgeschichte Cap. 17,
Abs. 28--29" (Cited from Dugac, 1976, Appendix LI, p. 273.)
However, I'm not quite sure what the difference between 'Natur' and
'Geschlecht' is supposed to be. Any hints?
> For Dedekind, as he
> makes clear in the introd to WsuwsdZ, numbering and arithmetizing are a
> basic aspect of human thought (the more 19c sense of "anthropology"). The
> contrast with Kronecker becomes even clearer, both agree on arithmetic as
> fundamental, but for Dedekind it is part of the basic apparatus of human
> thought and for Kronecker it is part of god's creation (as are men of
> course).
Ewald, 1996, p. 837 quotes an undated fragment from the Dedekind Nachlass
on this issue:
"Of all the aids which the human mind has yet created to simplify its life
- that is, to simplify the work in which thinking consists - none is so
momentuous and so inseparably bound up with the mind's most inward nature
as the concept of {\it number}. Arithmetic, whose sole object is this
concept, is already a science of immeasurable breadth, and there can be no
doubt that there are absolutely no limits to its further development; and
the domain of its application is equally immeasurable, for every thinking
man, even if he does not clearly realize it, is a man of numbers, an
arithmetician."
from windy & rainy Pittsburgh,
Dirk Schlimm