Mr. Everdell quotes a note of Russell's from 1900
"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."
and asks me how Russell might have found this in Bettazzi.
I am afraid that I have no answer. Because
(1) I cannot easily consult Bettazzi's book: when I read
and excerpted it some 20 years ago, I obtained it through
interlibrary loan from the Universitaetsbibliothek at
Heidelberg.
(2) Italian "grandezze" (sing. grandezza) means 'magnitudes'
and it may well be that Bettazzi, in his earlier paragraphs,
somewhere alludes to the relationship between whole and
part. If so, I did not find it important enough to make
excerpts about it.
(3) Nor do I understand Russell's note intimating that a study
of whole and part requires 'a special form of addition'.
Of course, Bettazzi investigates additively written semigroups,
but I do not see how such addition is related to studies of
whole and part.
Mr. Mann asks me how Russell may have found Bettazzi, a question
for which I have no answer either. As for Mr. Mann's remark
that Russell's reference seems to contradict my "claim"
about Bettazzi's work being largeley unknown, I hold onto it
because of
(4) the fact that nobody seems to have taken notice of
Bettazzi's theorem before 1968 , and
(5) the scarcity of his book in German libraries.
In view of (3) above, it even may be conjectured that Russell,
writing his note, was not quite aware of its content either.
W.F.