Los Infinitesimales Actuales de Leibniz

Resumen

En esta presentación intentaremos dilucidar los sentidos de lo infinitesimal
que operan en el pensamiento juvenil de Leibniz a propósito
del problema del continuo. En primer lugar veremos las características
que Leibniz le atribuye a los infinitesimales cuando defendió que componen
actualmente el continuo en 1672. Luego, veremos que por 1676
parecería haber cambiado de opinión al afirmar que hay cantidades
infinitamente pequeñas que son ficticias. Intentaremos mostrar que,
detrás de esto, hay dos sentidos distintos de lo infinitesimal que no se
contradicen, de manera tal que Leibniz podría haber defendido infinitesimales
actuales que componen el continuo al mismo tiempo que
concibió que ciertas cantidades infinitamente pequeñas son ficticias.

In this presentation we will try to elucidate the senses of the infinitesimal
in Leibniz’ early thought on the problem of the continuum.
We will first see the characteristics that Leibniz has assigned to infinitesimals
when in 1672 he defended that they actually compose the
continuum. We will then see that in 1676 he seems to change his mind
when he claimed that there are infinitely small quantities that are fictitious.
We will try to show that beyond this there are two different senses
of the infinitesimal which are not contradictory, in such a way that
Leibniz could have defended infinitesimals that actually compose the
continuum while he conceived that there are certain infinitely small
quantities that are fictitious.