Re: [HM] well-known saying
David Reed (dreed@math.duke.edu)
Tue, 25 May 1999 08:45:15 -0400 (EDT)
Dedekind invented his statement. The arithmetizdei verb is not
"well-attested" and the contrast with the Platonic geometrizdei is half
the point. The other point is that it is man not god who is doing these
things. Dedekind is a radical "humanist" - in ancient terms, a "sophist"
a la Protagoras (man is the measure of all things). 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. The aei
part - the "always", is also interesting. In the Platonic picture it goes
along with eternity. But if "man" is always "doing arithmetic" this has a
more
anthropological flavor i.e. "man has always done arithmetic and always
will". Today we would take this as ethno-mathematics. 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).
David Reed
warm and sunny Chapel Hill