Ethics, part 1 | Page 4

given besides the understanding, by which
several things may be distinguished one from the other, except the
substances, or, in other words (see Ax. iv.), their attributes and
modifications. Q.E.D.
V. There cannot exist in the universe two or more substances having
the same nature or attribute.
>>>>>Proof--If several distinct substances be granted, they must be
distinguished one from the other, either by the difference of their
attributes, or by the difference of their modifications (Prop. iv.). If only
by the difference of their attributes, it will be granted that there cannot

be more than one with an identical attribute. If by the difference of their
modifications--as substance is naturally prior to its modifications (Prop.
i.)--it follows that setting the modifications aside, and considering
substance in itself, that is truly, (Deff. iii and vi.), there cannot be
conceived one substance different from another--that is (by Prop. iv.),
there cannot be granted several substances, but one substance only.
Q.E.D.
VI. One substance cannot be produced by another substance.
>>>>>Proof--It is impossible that there should be in the universe two
substances with an identical attribute, i.e. which have anything
common to them both (Prop ii.), and, therefore (Prop. iii.), one cannot
be the cause of the other, neither can one be produced by the other.
Q.E.D.
<<<< produced by anything external to itself. For in the universe nothing is
granted, save substances and their modifications (as appears from Ax. i.
and Deff. iii. and v.). Now (by the last Prop.) substance cannot be
produced by another substance, therefore it cannot be produced by
anything external to itself. Q.E.D. This is shown still more readily by
the absurdity of the contradictory. For, if substance be produced by an
external cause, the knowledge of it would depend on the knowledge of
its cause (Ax. iv.), and (by Deff. iii.) it would itself not be substance.
VII. Existence belongs to the nature of substances.
>>>>>Proof--Substance cannot be produced by anything external (Cor.,
Prop vi.), it must, therefore, be its own cause--that is, its essence
necessarily involves existence, or existence belongs to its nature.
VIII. Every substance is necessarily infinite.
>>>>>Proof--There can only be one substance with an identical
attribute, and existence follows from its nature (Prop. vii.); its nature,
therefore, involves existence, either as finite or infinite. It does not exist
as finite, for (by Deff. ii.) it would then be limited by something else of
the same kind, which would also necessarily exist (Prop. vii.); and there
would be two substances with an identical attribute, which is absurd
(Prop. v.). It therefore exists as infinite. Q.E.D.
*****Note I.--As finite existence involves a partial negation, and
infinite existence is the absolute affirmation of the given nature, it
follows (solely from Prop. vii.) that every substance is necessarily

infinite.
*****Note II.--No doubt it will be difficult for those who think about
things loosely, and have not been accustomed to know them by their
primary causes, to comprehend the demonstration of Prop. vii.: for such
persons make no distinction between the modifications of substances
and the substances themselves, and are ignorant of the manner in which
things are produced; hence they may attribute to substances the
beginning which they observe in natural objects. Those who are
ignorant of true causes make complete confusion--think that trees
might talk just as well as men--that men might be formed from stones
as well as from seed; and imagine that any form might be changed into
any other. So, also, those who confuse the two natures, divine and
human, readily attribute human passions to the deity, especially so long
as they do not know how passions originate in the mind. But, if people
would consider the nature of substance, they would have no doubt
about the truth of Prop. vii. In fact, this proposition would be a
universal axiom, and accounted a truism. For, by substance, would be
understood that which is in itself, and is conceived through itself--that
is, something of which the conception requires not the conception of
anything else; whereas modifications exist in something external to
themselves, and a conception of them is formed by means of a
conception of the things in which they exist. Therefore, we may have
true ideas of non-existent modifications; for, although they may have
no actual existence apart from the conceiving intellect, yet their essence
is so involved in something external to themselves that they may
through it be conceived. Whereas the only truth substances can have,
external to the intellect, must consist in their existence, because they
are conceived through themselves. Therefore, for a person to say that
he has a clear and distinct--that is, a true--idea of a substance, but that
he is not sure whether such substance exists, would be the same as