The Ethics | Page 9

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 Coroll. 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 can exist without the other, and can remain in its original
condition. As, then, there does not exist a vacuum in nature (of which
anon), but all parts are bound to come together to prevent it,