FOM: Re: [HM] Leibniz and the actual infinity

Julio Gonzalez Cabillon jgc at
Sun Sep 27 13:48:44 EDT 1998

At 09:15 PM 24/09/1998 +0100, Moshe' Machover wrote:
| ...
| But in 1701, also writing in French, he makes his position even clearer.
| He says that if one doesn't believe in infinite or infinitesimal lines
| in methaphysical rigour and as real things (a\ la rigeur metaphysique
| et comme des choses re'elles) one can surely still use them *as ideal
| notions* which shorten argumentation (qui abre\gent raisonnement) *in a
| similar way that one uses imaginary roots in ordinary analysis, as for
| example the sqrt of -2.*
| ...

Moshe' Machover is referring to the famous Leibniz's reply (February 2,
1702) to Varignon's letter. As to the *social* context in which these
letters were exchanged it should be worth examining the debates which
took place within the Paris Academy of Sciences at the time. Paolo
Mancosu has touched this topic in Chapter 6 ("Leibniz's Differential
Calculus and its Opponents") of his well-know book of mathematical
practice in the 17th century.


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