Hegel's Lectures on the History of Philosophy: Volume 1 (of 3)Hegel, Georg Wilhelm Friedrich
Philosophy
Hegel's Lectures on the History of Philosophy: Volume 1 (of 3)
Hegel, Georg Wilhelm Friedrich
Philosophy -- History
The general explanation which Aristotle gives to this contradiction, is
that space and time are not infinitely divided, but are only divisible.
But it now appears that, because they are divisible—that is, in
potentiality—they must actually be infinitely divided, for else they
could not be divided into infinity. That is the general answer of the
ordinary man in endeavouring to refute the explanation of Aristotle.
Bayle (Tom. IV. art. Zénon, not. E.) hence says of Aristotle’s answer
that it is “pitoyable: C’est se moquer du monde que de se servir de
cette doctrine; car si la matière est divisible à l’infini, elle
contient un nombre infini de parties. Ce n’est donc point un infini en
puissance, c’est un infini, qui existe réellement, actuellement. Mais
quand-même on accorderait cet infini en puissance, qui deviendrait
un infini par la division actuelle de ses parties, on ne perdrait
pas ses avantages; car le mouvement est une chose, qui a la même
vertu, que la division. Il touche une partie de l’espace sans toucher
l’autre, et il les touche toutes les unes après les autres. N’est-ce
pas les distinguer actuellement? N’est-ce pas faire ce que ferait un
géomètre sur une table en tirant des lignes, qui désignassent tous les
demi-pouces? Il ne brise pas la table en demi-pouces, mais il y fait
néanmoins une division, qui marque la distinction actuelle des parties;
et je ne crois pas qu’Aristote eut voulu nier, que _si_ l’on tirait une
infinité de lignes sur un pouce de matière, on n’y introduisît une
division, qui réduirait en infini actuel ce qui n’était selon lui qu’un
infini virtual.” This _si_ is good! Divisibility is, as potentiality,
the universal; there is continuity as well as negativity or the point
posited in it—but posited as moment, and not as existent in and for
itself. I can divide matter into infinitude, but I only can do so; I
do not really divide it into infinitude. This is the infinite, that no
one of its moments has reality. It never does happen that, in itself,
one or other—that absolute limitation or absolute continuity—actually
comes into existence in such a way that the other moment disappears.
There are two absolute opposites, but they are moments, i.e. in the
simple Notion or in the universal, in thought, if you will; for in
thought, in ordinary conception, what is set forth both is and is not
at the same time. What is represented either as such, or as an image
of the conception, is not a thing; it has no Being, and yet it is not
nothing.
Public-domain text, read in full here on John Shaqi.
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