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Distinguished Sir, --My statement concerning the
infinite,
that an infinity of parts cannot be inferred from a multitude of
parts, is plain when we consider that, if such a conclusion could
be drawn from a multitude of parts, we should not be able to
imagine a greater multitude of parts; the first-named
multitude, whatever it was, would have to be the greater, which
is contrary to fact. For in the whole space between two
non-concentric circles we conceive a greater multitude of parts than
in half that space, yet the number of parts in the half, as in the
whole of the space, exceeds any assignable number. Again, from
extension, as Descartes conceives it, to wit, a quiescent mass, it
is not only difficult, as you say, but absolutely impossible to
prove the existence of bodies. For matter at rest, as it is in
itself, will continue at rest, and will only be determined to
motion by some more powerful external cause; for this reason I
have not hesitated on a former occasion to affirm, that the
Cartesian principles of natural things are useless, not to say
absurd.
The Hague, 5 May, 1676.
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