Ethics, part 1 | Page 8

Note 2, Prop. viii.), that no
substance can be produced or created by anything other than itself.
Further, I showed (in Prop. xiv.) that besides God no substance can be
granted or conceived. Hence we drew the conclusion that extended
substance is one of the infinite attributes of God. However, in order to
explain more fully, I will refute the arguments of my adversaries, which
all start from the following points:--
Extended substance, in so far as it is substance, consists, as they think,

in parts, wherefore they deny that it can be infinite, or consequently,
that it can appertain to God. This they illustrate with many examples, of
which I will take one or two. If extended substance, they say, is infinite,
let it be conceived to be divided into two parts; each part will then be
either finite or infinite. If the former, then infinite substance is
composed of two finite parts, which is absurd. If the latter, then one
infinite will be twice as large as another infinite, which is also absurd.
Further, if an infinite line be measured out in foot lengths, it will
consist of an infinite number of such parts; it would equally consist of
an infinite number of parts, if each part measured only an inch:
therefore, one infinity would be twelve times as great as the other.
Lastly, if from a single point there be conceived to be drawn two
diverging lines which at first are at a definite distance apart, but are
produced to infinity, it is certain that the distance between the two lines
will be continually increased, until at length it changes from definite to
indefinable. As these absurdities follow, it is said, from considering
quantity as infinite, the conclusion is drawn that extended substance
must necessarily be finite, and, consequently, cannot appertain to the
nature of God.
The second argument is also drawn from God's supreme perfection.
God, it is said, inasmuch as he is a supremely perfect being, cannot be
passive; but extended substance, insofar as it is divisible, is passive. It
follows, therefore, that extended substance does not appertain to the
essence of God.
Such are the arguments I find on the subject in writers, who by them try
to prove that extended substance is unworthy of the divine nature, and
cannot possibly appertain thereto. However, I think an attentive reader
will see that I have already answered their propositions; for all their
arguments are founded on the hypothesis that extended substance is
composed of parts, and such a hypothesis I have shown (Prop. xii., and
Cor. Prop. xiii.) to be absurd. Moreover, anyone who reflects will see
that all these absurdities (if absurdities they be, which I am not now
discussing), from which it is sought to extract the conclusion that
extended substance is finite, do not at all follow from the notion of an
infinite quantity, but merely from the notion that an infinite quantity is
measurable, and composed of finite parts: therefore, the only fair
conclusion to be drawn is that infinite quantity is not measurable, and

cannot be composed of finite parts. This is exactly what we have
already proved (in Prop. xii.). Wherefore the weapon which they aimed
at us has in reality recoiled upon themselves. If, from this absurdity of
theirs, they persist in drawing the conclusion that extended substance
must be finite, they will in good sooth be acting like a man who asserts
that circles have the properties of squares, and, finding himself thereby
landed in absurdities, proceeds to deny that circles have any center,
from which all lines drawn to the circumference are equal. For, taking
extended substance, which can only be conceived as infinite, one, and
indivisible (Props. viii., v., xii.) they assert, in order to prove that it is
finite, that it is composed of finite parts, and that it can be multiplied
and divided.
So, also, others, after asserting that a line is composed of points, can
produce many arguments to prove that a line cannot be infinitely
divided. Assuredly it is not less absurd to assert that extended substance
is made up of bodies or parts, than it would be to assert that a solid is
made up of surfaces, a surface of lines, and a line of points. This must
be admitted by all who know clear reason to be infallible, and most of
all by those who deny the possibility of a vacuum. For if extended
substance could be so divided that its parts were really separate, why
should not one part admit of being destroyed, the others remaining
joined together as before? And why should all be so fitted into one
another as to leave no vacuum? Surely in the case of things, which are
really distinct one from the other, one