The Ethics | Page 6

demonstration, we must premise :- 1. The true definition of a
thing neither involves nor expresses anything beyond the nature of the
thing defined. From this it follows that- 2. No definition implies or
expresses a certain number of individuals, inasmuch as it expresses
nothing beyond the nature of the thing defined. For instance, the
definition of a triangle expresses nothing beyond the actual nature of a
triangle : it does not imply any fixed number of triangles. 3. There is
necessarily for each individual existent thing a cause why it should
exist. 4. This cause of existence must either be contained in the nature
and definition of the thing defined, or must be postulated apart from
such definition. It therefore follows that, if a given number of
individual things exist in nature, there must be some cause for the
existence of exactly that number, neither more nor less. For example, if
twenty men exist in the universe (for simplicity's sake, I will suppose
them existing simultaneously, and to have had no predecessors), and
we want to account for the existence of these twenty men, it will not be
enough to show the cause of human existence in general ; we must also
show why there are exactly twenty men, neither more nor less : for a
cause must be assigned for the existence of each individual. Now this
cause cannot be contained in the actual nature of man, for the true
definition of man does not involve any consideration of the number
twenty. Consequently, the cause for the existence of these twenty men,
and, consequently, of each of them, must necessarily be sought
externally to each individual. Hence we may lay down the absolute rule,
that everything which may consist of several individuals must have an

external cause. And, as it has been shown already that existence
appertains to the nature of substance, existence must necessarily be
included in its definition ; and from its definition alone existence must
be deducible. But from its definition (as we have shown, notes ii., iii.),
we cannot infer the existence of several substances ; therefore it follows
that there is only one substance of the same nature. Q.E.D.
PROP. IX. The more reality or being a thing has, the greater the
number of its attributes (Def. iv.).
PROP. X. Each particular attribute of the one substance must be
conceived through itself. Proof.-An attribute is that which the intellect
perceives of substance, as constituting its essence (Def. iv.), and,
therefore, must be conceived through itself (Def. iii.). Q.E.D. Note-It is
thus evident that, though two attributes are, in fact, conceived as
distinct-that is, one without the help of the other-yet we cannot,
therefore, conclude that they constitute two entities, or two different
substances. For it is the nature of substance that each of its attributes is
conceived through itself, inasmuch as all the attributes it has have
always existed simultaneously in it, and none could be produced by any
other ; but each expresses the reality or being of substance. It is, then,
far from an absurdity to ascribe several attributes to one substance : for
nothing in nature is more clear than that each and every entity must be
conceived under some attribute, and that its reality or being is in
proportion to the number of its attributes expressing necessity or
eternity and infinity. Consequently it is abundantly clear, that an
absolutely infinite being must necessarily be defined as consisting in
infinite attributes, each of which expresses a certain eternal and infinite
essence. If anyone now ask, by what sign shall he be able to distinguish
different substances, let him read the following propositions, which
show that there is but one substance in the universe, and that it is
absolutely infinite, wherefore such a sign would be sought in vain.
PROP. XI. God, or substance, consisting of infinite attributes, of which
each expresses eternal and infinite essentiality, necessarily exists.
Proof.-If this be denied, conceive, if possible, that God does not exist :
then his essence does not involve existence. But this (Prop. vii.) is

absurd. Therefore God necessarily exists. Another proof.-Of everything
whatsoever a cause or reason must be assigned, either for its existence,
or for its non-existence-e.g. if a triangle exist, a reason or cause must be
granted for its existence ; if, on the contrary, it does not exist, a cause
must also be granted, which prevents it from existing, or annuls its
existence. This reason or cause must either be contained in the nature of
the thing in question, or be external to it. For instance, the reason for
the non-existence of a square circle is indicated in its nature, namely,
because it would involve a contradiction. On the other hand, the
existence of substance follows also solely from its nature,