Leibniz's New Essays Concerning the Human Understanding: A Critical ExpositionDewey, John
Philosophy
Leibniz's New Essays Concerning the Human Understanding: A Critical Exposition
Dewey, John
Leibniz, Gottfried Wilhelm, Freiherr von, 1646-1716
Leibniz's reply consists simply in carrying out this same thought
somewhat further. It is granted that the idea of an infinite quantity
of any kind is absurd and self-contradictory. But what does this prove,
except that the notions of quantity and infinity are incompatible with
each other, that they contradict each other? Hence, instead of the
infinite being a mode of quantity, it must be conceived as essentially
distinct from and even opposed to quantity. Locke's argument is
virtually a _reductio ad absurdum_ of the notion that the infinite
is capable of parts. In the few pages of comment which Leibniz in
1696 wrote upon Locke, this topic of the infinite is one of the few
touched upon. His words upon that occasion were as follows: "I agree
with Mr. Locke that, properly speaking, there is no space, time, nor
number which is infinite; and that it is only true that however great
be a space, a time, or a number, there is always another which is still
greater, and this without end; and that, _therefore_, the infinite
is not to be found in a whole made up of parts. But it does not cease
to exist: it is found in the absolute, which is without parts, and of
which compound things [phenomena in space and time, or facts which may
be numbered] are only limitations. The positive infinite being nothing
else than the absolute, it may be said that there is, in this sense,
a positive idea of the infinite, and that it is anterior to the idea
of the finite." In other words, while the infinite is to Locke an
indefinite extension of the finite, which alone is positively "given,"
to Leibniz the infinite is the positive and real, and the finite is
only in and by it. The finite is the negative.
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