Re: [HM] Aristotle's like-minded persons about Actual Infinity

Julio Gonzalez Cabillon (jgc@adinet.com.uy)
Sun, 13 Sep 1998 19:11:00 -0300

On Sat, 12 Sep 1998, Alexander Zenkin wrote:

: As is known, Aristotle was the first person who explicitly and
: definitely postulated: "Infinitum actu non datur".
: I think it would be interesting (for different goals : -) ) to list all
: his famous like-minded persons. Today, I have the following very
: approximate beginning of such the list:
:
: ARISTOTLE, LEIBNIZ, GAUSS, CAUCHY, POINCARE, BROUWER, WEYL, LUZIN, ...

And on Sunday, 13 Sep 1998, Gregory H. Moore remarked:

| Leibniz does not belong on this list, since he accepted the actual
| infinite. See, for example, the passage from Leibniz (quoted by
| Cantor, Gesammelte Abhandlungen, p.179) beginning "Je suis tellement pour
| l'infini actuel ...".

Leibniz's opinions/beliefs (?) about the infinite seemed to vary according
to 'pompa & circunstancia'. The passage referred to above is that also
quoted on p. 124 of Dauben's "Georg Cantor: His Mathematics and Philosophy
of the Infinite" [Princeton: Princeton University Press, 1979].
Dauben remarks that "... Cantor was happy to claim him [= Leibniz] as a
supporter of the former", but apparently both without recalling of a letter
that Leibniz wrote a couple of months before his death in which he states
without euphemisms "I told them that I did not believe at all in the
existence of magnitudes actually infinite or actually infinitesimal..."
(p. 500) [*]. If my memory serves, Paolo Mancosu has discussed this issue.

[*] "Lettre a\ M. Dangicourt", September 1716, pp. 499-502 in vol. III
(Opera mathematica) of Leibniz's _Opera Omnia_, edited by Louis Dutens,
Genevae: Apud Fratres de Tournes, 1768.

Regards,
Julio Gonzalez Cabillon