[FOM] reply to s.s. kuteladze
S. S. Kutateladze
sskut at math.nsc.ru
Sat Nov 17 13:04:58 EST 2007
Gabriel Stolzenberg> But Robinson said that Leibniz treated talk of infinitesmals merely
Gabriel Stolzenberg> as a convenient "facon de parler."
Robinson was not that definite, neither Leibniz.
Leibniz wrote for instance as follows (a letter to Varignion
on February 2, 1702):
"If any opponent tries to contradict this proposition,
it follows from our calculus that the error will be less
than any possible assignable error, since it is in our
power to make this incomparably small magnitude small
enough for this purpose, inasmuch as we can always take
a magnitude as small as we wish.
Perhaps this is what you mean, Sir, when you speak on the
inexhaustible, and the rigorous demonstration of the
infinitesimal calculus which we use undoubtedly is to
be found here....
So it can also be said that infinites
and infinitesimals are grounded in such a way that everything
in geometry, and even in nature, takes place as if they
were perfect realities. Witness not only our geometrical
analysis of transcendental curves but also my law
of continuity, in virtue of which it is permitted to consider
rest as infinitely small motion (that is,
as equivalent to a species of its own contradictory),
and coincidence as infinitely small distance, equality
as the last inequality, etc."
Gabriel Stolzenberg> Also, does your use of"nonassignable" have something to do with the
Gabriel Stolzenberg> Name Worshippers??
Name worshippers imply Luzin and his spiritual advisor Florensky. Luzin was in favor of
infinitesimals by the way. However, "nonassignable" is much older. Wallis, for instance,
wrote in 1685 that "those magnitudes (or quantitites) whose difference may be proved to
be less than any assignable are equal" and attributed this to Euclid.
In fact the infinitesimals and indivisibles are instances of the
monads. Monads were not invented by Leibniz, but belong to Ancient
Sobolev Institute of Mathematics
Novosibirsk State University
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