>>>>>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 if
he said that he had a true idea, but was not sure whether or no
it was false (a little consideration will make this plain); or if
anyone affirmed that substance is created, it would be the same
as saying that a false idea was true--in short, the height of
absurdity. It must, then, necessarily be admitted that the
existence of substance as its essence is an eternal truth. And
we can hence conclude by another process of reasoning--that there
is but one such substance. I think that this may profitably be
done at once; and, in order to proceed regularly with the
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.
IX. The more reality or being a thing has, the greater the
number of its attributes (Def. iv.).
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.
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, inasmuch as its
nature involves existence. (See Prop. vii.)
But the reason for the existence of a triangle or a circle does
not follow from the nature of those figures, but from the order
of universal nature in extension. From the latter it must
follow, either that a triangle necessarily exists, or that it is
impossible that it should exist. So much is self-evident. It
follows therefrom that a thing necessarily exists, if no cause or
reason be granted which prevents its existence.
If, then, no cause or reason can be given, which prevents the
existence of God, or which destroys his existence, we must
certainly conclude that he necessarily does exist. If such a
reason or cause should be given, it must either be drawn from the
very nature of God, or be external to him--that is, drawn from
another substance of another nature. For if it were of the same
nature, God, by that very fact, would be admitted to exist. But
substance of another nature could have nothing in common with God
(by Prop. ii.), and therefore would be unable either to cause or
to destroy his existence.
As, then, a reason or cause which would annul the divine
existence cannot be drawn from anything external to the divine
nature, such cause must perforce, if God does not exist, be drawn
from God's own nature, which would involve a contradiction. To
make such an affirmation about a being absolutely infinite and
supremely perfect is absurd; therefore, neither in the nature of
God, nor externally to his nature, can a cause or reason be
assigned which would annul his existence. Therefore, God
necessarily exists. Q.E.D.
>>>>>Another proof--The potentiality of non-existence is a
negation of power, and contrariwise the potentiality of existence
is a power, as is obvious. If, then, that which necessarily
exists is nothing but finite beings, such finite beings are more
powerful than a being absolutely infinite, which is obviously
absurd; therefore, either nothing exists, or else a being
absolutely infinite necessarily exists also. Now we exist either
in ourselves, or in something else which necessarily exists (see
Ax. i. and Prop. vii.). Therefore a being absolutely
infinite--in other words, God (Def. vi.)--necessarily exists.
Q.E.D.
*****Note--In this last proof, I have purposely shown God's
existence 'a posteriori,' so that the proof might be more easily
followed, not because, from the same premises, God's existence
does not follow 'a priori.' For, as the potentiality of
existence is a power, it follows that, in proportion as reality
increases in the nature of a thing, so also will it increase its
strength for existence. Therefore a being absolutely infinite,
such as God, has from himself an absolutely infinite power of
existence, and hence he does absolutely exist. Perhaps there will
be many who will be unable to see the force of this proof,
inasmuch as they are accustomed only to consider those things
which flow from external causes. Of such things, they see that
those which quickly come to pass--that is, quickly come into
existence--quickly also disappear; whereas they regard as more
difficult of accomplishment --that is, not so easily brought into
existence--those things which they conceive as more complicated.
However, to do away with this misconception, I need not here show
the measure of truth in the proverb, "What comes quickly, goes
quickly," nor discuss whether, from the point of view of
universal nature, all things are equally easy, or otherwise: I
need only remark that I am not here speaking of things, which
come to pass through causes external to themselves, but only of
substances which (by Prop. vi.) cannot be produced by any
external cause. Things which are produced by external causes,
whether they consist of many parts or few, owe whatsoever
perfection or reality they possess solely to the efficacy of
their external cause; wherefore the existence of substance must
arise solely from its own nature, which is nothing else but its
essence. Thus, the perfection of a thing does not annul its
existence, but, on the contrary, asserts it. Imperfection, on
the other hand, does annul it; therefore we cannot be more
certain of the existence of anything, than of the existence of a
being absolutely infinite or perfect--that is, of God. For
inasmuch as his essence excludes all imperfection, and involves
absolute perfection, all cause for doubt concerning his existence
is done away, and the utmost certainty on the question is given.
This, I think, will be evident to every moderately attentive
reader.
XII. No attribute of substance can be conceived from which it
would follow that substance can be divided.
>>>>>Proof--The parts into which substance as thus conceived
would be divided either will retain the nature of substance, or
they will not. If the former, then (by Prop. viii.) each part
will necessarily be infinite, and (by Prop vi.) self-caused, and
(by Prop. v.) will perforce consist of a different attribute, so
that, in that case, several substances could be formed out of one
substance, which (by Prop. vi.) is absurd. Moreover, the parts
(by Prop. ii.) would have nothing in common with their whole, and
the whole (by Def. iv. and Prop. X) could both exist and be
conceived without its parts, which everyone will admit to be
absurd. If we adopt the second alternative--namely, that the
parts will not retain the nature of substance--then, if the
whole substance were divided into equal parts, it would lose the
nature of substance, and would cease to exist, which (by Prop.
vii.) is absurd.