Re: [HM] Bettazzi's theorem

Avinoam Mann (MANN@vms.huji.ac.il)
Sun, 25 Apr 1999 11:00:19 +0200 (IST)

On Sat, 24 Apr 1999, Bill Everdell wrote:

> In a message dated 4/23/99 3:44:50 PM, walter.felscher@uni-tuebingen.de
> writes:
>
> <<An early reference to Bettazzi's work can be found in a footnote of
>
> Alfred Pringsheim et Jules Molk: Nombres irrationels et notion de
> limite. Encyclop. de Sci. Math. Pures et Appl., I, 3, Paris 1908.
>
> The following is a translation from my German "Naive Mengen und Abstrakte
> Zahlen", vol. II , Mannheim 1968 , pp.201-202 :
>
> Bettazzi's book from 1890, written already in 1888, remained widely
> unknown. >>

(Rest of WF's message deleted)
>
> This reminds me that in October, 1900, Bertrand Russell was at Fernhurst,
> just back from the momentous meeting with Peano at the Paris World's Fair
> Mathematics Conference, and working happily on his first book on foundations,
> _The Principles of Mathematics_.He wrote in margin of the third state of
> his manuscript (1899-1900), as published in _Collected Papers of Bertrand
> Russell_, vol. 3, p. xxviii:
>
> ----------------------------- begin quote -----------------------------
> "Note. I have been wrong in regarding the Logical Calculus as having
> especially to do with whole and part. Whole is distinct from Class, and
> occurs nowhere in the Logical Calculus, which depends on these notions: 1)
> implication, 2) and, 3) negation. Whole and part require the Teoria della
> grandezza (Bettazzi 1890), i.e. a special form of addition, not that of the
> Logical Calculus."
> ----------------------------- end quote -------------------------------
>
> Can Walter Felscher help me understand how Russell might have found this in
> Bettazzi?
>
> Bill Everdell, Brooklyn
>

And also how Russell have found Bettazzi? His reference to him seems to
contradict to some extent the "largely unknown" claim above.

Avinoam Mann