Re: [HM] well-known saying

Olivier Souan (zalmoxis@cybercable.fr)
Thu, 27 May 1999 12:33:06 +0200

> To me, it sounds like Dedekind is paraphrasing a "well-known" saying of
> Plato: 'God geometrizes'. So Dedekind is answering by 'Man arithmetizes'.
> Does anybody know if that paraphrase originates with Dedekind, or is it
> earlier? And please remind us of the reference for Plato's saying.

There is a footnote worth mentioning in Husserl's "Philosophie der
Arithmetik (1891)" (Husserliana Bd XII, p. 214) where Husserl deals with the
question, while discussing the symbolical nature of arithmetic :

Context : Since Husserl defines number as being a reflexive operation made
on concrete intuition (a flock of sheep and so on), he concludes that we
cannot have an intuition of big numbers and insists on the symbolical,
non-intuitive nature of arithmetics, the whole subject matter being "only a
sum of artificial means overcoming the essential imperfections of our
intellect"(p.214). (Of course, Frege will severely critic this viewpoint,
but that's another story).

It reads : "To that respect, the famous saying of Gauss 'o theos
arithmetizei" do not fit the concept of an infinitely perfect being. [since
arithmetics is related to our sole imperfection] Dedekind paraphrases it
(vgl the at the beginning of 'Was sind und was sollen die Zahlen'?) when he
writes : 'aei o anthropos arithmetizei', which can not be approved for
other reasons [since we have indeed a concrete intuition of the first
numbers : two, three..The 'aei' (always) becomes superfluous]. I would only
say : 'o anthropos arithmetizei'"(p.214 note 1)