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Title In Latin: Ethica Ordine
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This
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(Ethica
Ordine Geometrico Demonstrata)
by
Benedict de Spinoza
Translated
from the Latin by R. H. M. Elwes
DEFINITIONS.
I.
By that which is self-caused, I mean that of which the essence involves
existence, or that of which the nature is only conceivable as existent.
II.
A thing is called finite after its kind, when it can be limited by
another thing of the same nature ; for instance, a body is called finite
because we always conceive another greater body.
So, also, a thought is limited by another thought, but a body is not
limited by thought, nor a thought by body.
III.
By substance, I mean that which is in itself, and is conceived through
itself : in other words, that of which a conception can be formed
independently of any other conception.
IV.
By attribute, I mean that which the intellect perceives as constituting
the essence of substance.
V.
By mode, I mean the modifications1 of substance, or that which exists
in, and is conceived through, something other than itself.
VI.
By God, I mean a being absolutely infinite-that is, a substance
consisting in infinite attributes, of which each expresses eternal and
infinite essentiality.
Explanation-I
say absolutely infinite, not infinite after its kind : for, of a thing
infinite only after its kind, infinite attributes may be denied ; but that
which is absolutely infinite, contains in its essence whatever expresses
reality, and involves no negation.
VII.
That thing is called free, which exists solely by the necessity of its
own nature, and of which the action is determined by itself alone.
On the other hand, that thing is necessary, or rather constrained,
which is determined by something external to itself to a fixed and definite
method of existence or action.
VIII.
By eternity, I mean existence itself, in so far as it is conceived
necessarily to follow solely from the definition of that which is eternal.
Explanation-Existence
of this kind is conceived as an eternal truth, like the essence of a thing,
and, therefore, cannot be explained by means of continuance or time, though
continuance may be conceived without a beginning or end.
I.
Everything which exists, exists either in itself or in something else.
II.
That which cannot be conceived through anything else must be conceived
through itself.
III.
From a given definite cause an effect necessarily follows ; and, on the
other hand, if no definite cause be granted, it is impossible that an effect
can follow.
IV.
The knowledge of an effect depends on and involves the knowledge of a
cause.
V.
Things which have nothing in common cannot be understood, the one by
means of the other ; the conception of one does not involve the conception of
the other.
VI.
A true idea must correspond with its ideate or object.
VII.
If a thing can be conceived as non-existing, its essence does not
involve existence.
PROP.
I. Substance is by nature prior
to its modifications.
Proof.-This
is clear from Deff. iii. and v.
PROP.
II. Two substances, whose
attributes are different, have nothing in common.
Proof.-Also
evident from Def. iii. For each
must exist in itself, and be conceived through itself ; in other words, the
conception of one does not imply the conception of the other.
PROP.
III. Things which have nothing in
common cannot be one the cause of the other.
Proof.-If
they have nothing in common, it follows that one cannot be apprehended by
means of the other (Ax. v.), and, therefore, one cannot be the cause of the
other (Ax. iv.).
PROP.
IV. Two or more distinct things
are distinguished one from the other, either by the difference of the
attributes of the substances, or by the difference of their modifications.
Proof.-Everything
which exists, exists either in itself or in something else (Ax. i.),-that is
(by Deff. iii. and v.), nothing is granted in addition to the understanding,
except substance and its modifications. Nothing
is, therefore, 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.
PROP.
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.
PROP.
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.
Corollary.-Hence
it follows that a substance cannot be 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
Def. iii.) it would itself not be substance.
PROP.
VII. Existence belongs to the
nature of substances.
Proof.-Substance
cannot be produced by anything external (Corollary, Prop vi.), it must,
therefore, be its own cause-that is, its essence necessarily involves
existence, or existence belongs to its nature.
PROP.
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 Def. 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 thing 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.
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, 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 Axiom. i. and Prop. vii.).
Therefore a being absolutely infinite-in other words, God (Def.
vi.)-necessarily exists.
Note.-In
this last proof, I have purposely shown God’s existence à posteriori, so
that the proof might be more easily followed, not because, from the same
premises, God’s existence does not follow à 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 ; and therefore their existence arises solely from the
perfection of their external cause, not from their own.
Contrrariwise, whatsoever perfection is possessed by substance is due
to no 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.
PROP.
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.
PROP.
XIII. Substance absolutely
infinite is indivisible.
Proof.-If
it could be divided, the parts into which it was divided would either retain
the nature of absolutely infinite substance, or they would not.
If the former, we should have several substances of the same nature,
which (by Prop. v.) is absurd. If
the latter, then (by Prop. vii.) substance absolutely infinite could cease to
exist, which (by Prop. xi.) is also absurd.
Corollary.-It
follows, that no substance, and consequently no extended substance, in so far
as it is substance, is divisible.
Note.-The
indivisibility of substance may be more easily understood as follows.
The nature of substance can only be conceived as infinite, and by a
part of substance, nothing else can be understood than finite substance, which
(by Prop. viii) involves a manifest contradiction.
PROP.
XIV. Besides God no substance can
be granted or conceived.
Proof.-As
God is a being absolutely infinite, of whom no attribute that expresses the
essence of substance can be denied (by Def. vi.), and he necessarily exists
(by Prop. xi.) ; if any substance besides God were granted, it would have to
be explained by some attribute of God, and thus two substances with the same
attribute would exist, which (by Prop. v.) is absurd ; therefore, besides God
no substance can be granted, or, consequently, be conceived.
If it could be conceived, it would necessarily have to be conceived as
existent ; but this (by the first part of this proof) is absurd.
Therefore, besides God no substance can be granted or conceived. Q.E.D.
Corollary
I.-Clearly, therefore : 1. God is
one, that is (by Def. vi.) only one substance can be granted in the universe,
and that substance is absolutely infinite, as we have already indicated (in
the note to Prop. x.).
Corollary
II.-It follows : 2.
That extension and thought are either attributes of God or (by Ax. i.)
accidents (affectiones) of the attributes of God.
PROP.
XV. Whatsoever is, is in God, and
without God nothing can be, or be conceived.
Proof.-Besides
God, no substance is granted or can be conceived (by Prop. xiv.), that is (by
Def. iii.) nothing which is in itself and is conceived through itself.
But modes (by Def. v.) can neither be, nor be conceived without substance ;
wherefore they can only be in the divine nature, and can only through it be
conceived. But substances and
modes form the sum total of existence (by Ax. i.), therefore, without God
nothing can be, or be conceived. Q.E.D.
Note.-Some
assert that God, like a man, consists of body and
mind,
and is susceptible of passions. How
far such persons have
strayed
from the truth is sufficiently evident from what has been
said.
But these I pass over. For
all who have in anywise
reflected
on the divine nature deny that God has a body.
Of this
they
find excellent proof in the fact that we understand by body
a
definite quantity, so long, so broad, so deep, bounded by a
certain
shape, and it is the height of absurdity to predicate
such
a thing of God, a being absolutely infinite.
But meanwhile
by
other reasons with which they try to prove their point, they
show
that they think corporeal or extended substance wholly apart
from
the divine nature, and say it was created by God.
Wherefrom
the
divine nature can have been created, they are wholly ignorant
;
thus they clearly show, that they do not know the meaning of
their
own words. I myself have proved
sufficiently clearly, at
any
rate in my own judgment (Coroll. Prop. vi, and 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 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, it follows from this that the parts
cannot really be distinguished, and that extended substance in so far as it is
substance cannot be divided.
If
anyone asks me the further question, Why are we naturally so prone to divide
quantity? I answer, that quantity
is conceived by us in two ways ; in the abstract and superficially, as we
imagine it ; or as substance, as we conceive it solely by the intellect. If, then, we regard quantity as it is represented in our
imagination, which we often and more easily do, we shall find that it is
finite, divisible, and compounded of parts ; but if we regard it as it is
represented in our intellect, and conceive it as substance, which it is very
difficult to do, we shall then, as I have sufficiently proved, find that it is
infinite, one, and indivisible. This
will be plain enough to all who make a distinction between the intellect and
the imagination, especially if it be remembered, that matter is everywhere the
same, that its parts are not distinguishable, except in so far as we conceive
matter as diversely modified, whence its parts are distinguished, not really,
but modally. For instance, water,
in so far as it is water, we conceive to be divided, and its parts to be
separated one from the other ; but not in so far as it is extended substance ;
from this point of view it is neither separated nor divisible.
Further, water, in so far as it is water, is produced and corrupted ;
but, in so far as it is substance, it is neither produced nor corrupted.
I
think I have now answered the second argument ; it is, in fact, founded on the
same assumption as the first-namely, that matter, in so far as it is
substance, is divisible, and composed of parts.
Even if it were so, I do not know why it should be considered unworthy
of the divine nature, inasmuch as besides God (by Prop. xiv.) no substance can
be granted, wherefrom it could receive its modifications.
All things, I repeat, are in God, and all things which come to pass,
come to pass solely through the laws of the infinite nature of God, and follow
(as I will shortly show) from the necessity of his essence. Wherefore it can in nowise be said, that God is passive in
respect to anything other than himself, or that extended substance is unworthy
of the Divine nature, even if it be supposed divisible, so long as it is
granted to be infinite and eternal. But
enough of this for the present.
PROP.
XVI. From the necessity of the
divine nature must follow an infinite number of things in infinite ways-that
is, all things which can fall within the sphere of infinite intellect.
Proof.-This
proposition will be clear to everyone, who remembers that from the given
definition of any thing the intellect infers several properties, which really
necessarily follow therefrom (that is, from the actual essence of the thing
defined) ; and it infers more properties in proportion as the definition of
the thing expresses more reality, that is, in proportion as the essence of the
thing defined involves more reality. Now,
as the divine nature has absolutely infinite attributes (by Def. vi.), of
which each expresses infinite essence after its kind, it follows that from the
necessity of its nature an infinite number of things (that is, everything
which can fall within the sphere of an infinite intellect) must necessarily
follow. Q.E.D.
Corollary
I.-Hence it follows, that God is the efficient cause of all that can fall
within the sphere of an infinite intellect.
Corollary
II.-It also follows that God is a cause in himself, and not through an
accident of his nature.
Corollary
III.-It follows, thirdly, that God is the absolutely first cause.
PROP.
XVII. God acts solely by the laws
of his own nature, and is not constrained by anyone.
Proof.-We
have just shown (in Prop. xvi.), that solely from the necessity of the divine
nature, or, what is the same thing, solely from the laws of his nature, an
infinite number of things absolutely follow in an infinite number of ways ;
and we proved (in Prop. xv.), that without God nothing can be nor be conceived
; but that all things are in God. Wherefore
nothing can exist outside himself, whereby he can be conditioned or
constrained to act. Wherefore God
acts solely by the laws of his own nature, and is not constrained by anyone.
Q.E.D.
Corollary
I.-It follows : 1. That there can
be no cause which, either extrinsically or intrinsically, besides the
perfection of his own nature, moves God to act.
Corollary
II.-It follows : 2. That God is
the sole free cause. For God
alone exists by the sole necessity of his nature (by Prop. xi. and Prop. xiv.,
Coroll. i.), and acts by the sole necessity of his own nature, wherefore God
is (by Def. vii.) the sole free cause. Q.E.D.
Note.-Others
think that God is a free cause, because he can, as they think, bring it about,
that those things which we have said follow from his nature-that is, which are
in his power, should not come to pass, or should not be produced by him.
But this is the same as if they said, that God could bring it about,
that it should follow from the nature of a triangle that its three interior
angles should not be equal to two right angles ; or that from a given cause no
effect should follow, which is absurd.
Moreover,
I will show below, without the aid of this proposition, that neither intellect
nor will appertain to God’s nature. I
know that there are many who think that they can show, that supreme intellect
and free will do appertain to God’s nature ; for they say they know of
nothing more perfect, which they can attribute to God, than that which is the
highest perfection in ourselves. Further,
although they conceive God as actually supremely intelligent, they yet do not
believe that he can bring into existence everything which he actually
understands, for they think that they would thus destroy God’s power.
If, they contend, God had created everything which is in his intellect,
he would not be able to create anything more, and this, they think, would
clash with God’s omnipotence ; therefore, they prefer to asset that God is
indifferent to all things, and that he creates nothing except that which he
has decided, by some absolute exercise of will, to create.
However, I think I have shown sufficiently clearly (by Prop. xvi.),
that from God’s supreme power, or infinite nature, an infinite number of
things-that is, all things have necessarily flowed forth in an infinite number
of ways, or always flow from the same necessity ; in the same way as from the
nature of a triangle it follows from eternity and for eternity, that its three
interior angles are equal to two right angles.
Wherefore the omnipotence of God has been displayed from all eternity,
and will for all eternity remain in the same state of activity.
This manner of treating the question attributes to God an omnipotence,
in my opinion, far more perfect. For,
otherwise, we are compelled to confess that God understands an infinite number
of creatable things, which he will never be able to create, for, if he created
all that he understands, he would, according to this showing, exhaust his
omnipotence, and render himself imperfect.
Wherefore, in order to establish that God is perfect, we should be
reduced to establishing at the same time, that he cannot bring to pass
everything over which his power extends ; this seems to be a hypothesis most
absurd, and most repugnant to God’s omnipotence.
Further
(to say a word here concerning the intellect and the will which we attribute
to God), if intellect and will appertain to the eternal essence of God, we
must take these words in some significance quite different from those they
usually bear. For intellect and
will, which should constitute the essence of God, would perforce be as far
apart as the poles from the human intellect and will, in fact, would have
nothing in common with them but the name ; there would be about as much
correspondence between the two as there is between the Dog, the heavenly
constellation, and a dog, an animal that barks.
This I will prove as follows. If
intellect belongs to the divine nature, it cannot be in nature, as ours is
generally thought to be, posterior to, or simultaneous with the things
understood, inasmuch as God is prior to all things by reason of his causality
(Prop. xvi., Coroll. i.). On the
contrary, the truth and formal essence of things is as it is, because it
exists by representation as such in the intellect of God.
Wherefore the intellect of God, in so far as it is conceived to
constitute God’s essence, is, in reality, the cause of things, both of their
essence and of their existence. This
seems to have been recognized by those who have asserted, that God’s
intellect, God’s will, and God’s power, are one and the same.
As, therefore, God’s intellect is the sole cause of things, namely,
both of their essence and existence, it must necessarily differ from them in
respect to its essence, and in respect to its existence.
For a cause differs from a thing it causes, precisely in the quality
which the latter gains from the former.
For
example, a man is the cause of another man’s existence, but not of his
essence (for the latter is an eternal truth), and, therefore, the two men may
be entirely similar in essence, but must be different in existence ; and hence
if the existence of one of them cease, the existence of the other will not
necessarily cease also ; but if the essence of one could be destroyed, and be
made false, the essence of the other would be destroyed also.
Wherefore, a thing which is the cause both of the essence and of the
existence of a given effect, must differ from such effect both in respect to
its essence, and also in respect to its existence. Now the intellect of God is the cause both of the essence and
the existence of our intellect ; therefore, the intellect of God in so far as
it is conceived to constitute the divine essence, differs from our intellect
both in respect to essence and in respect to existence, nor can it in anywise
agree therewith save in name, as we said before.
The reasoning would be identical in the case of the will, as anyone can
easily see.
PROP.
XVIII. God is the indwelling and
not the transient cause of all things.
Proof.-All
things which are, are in God, and must be conceived through God (by Prop.
xv.), therefore (by Prop. xvi., Coroll. i.) God is the cause of those things
which are in him. This is our
first point. Further, besides God
there can be no substance (by Prop. xiv.), that is nothing in itself external
to God. This is our second point.
God, therefore, is the indwelling and not the transient cause of all
things. Q.E.D.
PROP.
XIX. God, and all the attributes
of God, are eternal.
Proof.-God
(by Def. vi.) is substance, which (by Prop. xi.) necessarily exists, that is
(by Prop. vii.) existence appertains to its nature, or (what is the same
thing) follows from its definition ; therefore, God is eternal (by Def.
viii.). Further, by the
attributes of God we must understand that which (by Def.
iv.) expresses the essence of the divine substance-in other words, that
which appertains to substance : that, I say, should be involved in the
attributes of substance. Now
eternity appertains to the nature of substance (as I have already shown in
Prop. vii.) ; therefore, eternity must appertain to each of the attributes,
and thus all are eternal. Q.E.D.
Note.-This
proposition is also evident from the manner in which (in Prop. xi.) I
demonstrated the existence of God ; it is evident, I repeat, from that proof,
that the existence of God, like his essence, is an eternal truth.
Further (in Prop. xix. of my “Principles of the Cartesian Philosophy”),
I have proved the eternity of God, in another manner, which I need not here
repeat.
PROP.
XX. The existence of God and his
essence are one and the same.
Proof.-God
(by the last Prop.) and all his attributes are eternal, that is (by Def.
viii.) each of his attributes expresses existence.
Therefore the same attributes of God which explain his eternal essence,
explain at the same time his eternal existence-in other words, that which
constitutes God’s essence constitutes at the same time his existence.
Wherefore God’s existence and God’s essence are one and the same.
Q.E.D.
Coroll.
I.-Hence it follows that God’s existence, like his essence, is an eternal
truth.
Coroll.
II-Secondly, it follows that God, and all the attributes of God, are
unchangeable. For if they could
be changed in respect to existence, they must also be able to be changed in
respect to essence-that is, obviously, be changed from true to false, which is
absurd.
PROP.
XXI. All things which follow from
the absolute nature of any attribute of God must always exist and be infinite,
or, in other words, are eternal and infinite through the said attribute.
Proof.-Conceive,
if it be possible (supposing the proposition to be denied), that something in
some attribute of God can follow from the absolute nature of the said
attribute, and that at the same time it is finite, and has a conditioned
existence or duration ; for instance, the idea of God expressed in the
attribute thought. Now thought,
in so far as it is supposed to be an attribute of God, is necessarily (by
Prop. xi.) in its nature infinite. But, in so far as it possesses the idea of
God, it is supposed finite. It
cannot, however, be conceived as finite, unless it be limited by thought (by
Def. ii.) ; but it is not limited by thought itself, in so far as it has
constituted the idea of God (for so far it is supposed to be finite) ;
therefore, it is limited by thought, in so far as it has not constituted the
idea of God, which nevertheless (by Prop. xi.) must necessarily exist.
We
have now granted, therefore, thought not constituting the idea of God, and,
accordingly, the idea of God does not naturally follow from its nature in so
far as it is absolute thought (for it is conceived as constituting, and also
as not constituting, the idea of God), which is against our hypothesis.
Wherefore, if the idea of God expressed in the attribute thought, or,
indeed, anything else in any attribute of God (for we may take any example, as
the proof is of universal application) follows from the necessity of the
absolute nature of the said attribute, the said thing must necessarily be
infinite, which was our first point.
Furthermore,
a thing which thus follows from the necessity of the nature of any attribute
cannot have a limited duration. For
if it can, suppose a thing, which follows from the necessity of the nature of
some attribute, to exist in some attribute of God, for instance, the idea of
God expressed in the attribute thought, and let it be supposed at some time
not to have existed, or to be about not to exist.
Now
thought being an attribute of God, must necessarily exist unchanged (by Prop.
xi., and Prop. xx., Coroll. ii.) ; and beyond the limits of the duration of
the idea of God (supposing the latter at some time not to have existed, or not
to be going to exist) thought would perforce have existed without the idea of
God, which is contrary to our hypothesis, for we supposed that, thought being
given, the idea of God necessarily flowed therefrom.
Therefore the idea of God expressed in thought, or anything which
necessarily follows from the absolute nature of some attribute of God, cannot
have a limited duration, but through the said attribute is eternal, which is
our second point. Bear in mind
that the same proposition may be affirmed of anything, which in any attribute
necessarily follows from God’s absolute nature.
PROP.
XXII. Whatsoever follows from any
attribute of God, in so far as it is modified by a modification, which exists
necessarily and as infinite, through the said attribute, must also exist
necessarily and as infinite.
Proof.-The
proof of this proposition is similar to that of the preceding one.
PROP.
XXIII. Every mode, which exists
both necessarily and as infinite, must necessarily follow either from the
absolute nature of some attribute of God, or from an attribute modified by a
modification which exists necessarily, and as infinite.
Proof.-A
mode exists in something else, through which it must be conceived (Def. v.),
that is (Prop. xv.), it exists solely in God, and solely through God can be
conceived. If therefore a mode is conceived as necessarily existing and
infinite, it must necessarily be inferred or perceived through some attribute
of God, in so far as such attribute is conceived as expressing the infinity
and necessity of existence, in other words (Def. viii.) eternity ; that is, in
so far as it is considered absolutely. A
mode, therefore, which necessarily exists as infinite, must follow from the
absolute nature of some attribute of God, either immediately (Prop. xxi.) or
through the means of some modification, which follows from the absolute nature
of the said attribute ; that is (by Prop. xxii.), which exists necessarily and
as infinite.
PROP.
XXIV. The essence of things
produced by God does not involve existence.
Proof.-This
proposition is evident from Def. i. For
that of which the nature (considered in itself) involves existence is
self-caused, and exists by the sole necessity of its own nature.
Corollary.-Hence
it follows that God is not only the cause of things coming into existence, but
also of their continuing in existence, that is, in scholastic phraseology, God
is cause of the being of things (essendi rerum). For whether things exist, or do not exist, whenever we
contemplate their essence, we see that it involves neither existence nor
duration ; consequently, it cannot be the cause of either the one or the
other. God must be the sole
cause, inasmuch as to him alone does existence appertain. (Prop. xiv. Coroll. i.) Q.E.D.
PROP.
XXV. God is the efficient cause
not only of the existence of things, but also of their essence.
Proof.-If
this be denied, then God is not the cause of the essence of things ; and
therefore the essence of things can (by Ax. iv.) be conceived without God.
This (by Prop. xv.) is absurd. Therefore,
God is the cause of the essence of things.
Note.-This
proposition follows more clearly from Prop. xvi. For it is evident thereby that, given the divine nature, the
essence of things must be inferred from it, no less than their existence-in a
word, God must be called the cause of all things, in the same sense as he is
called the cause of himself. This
will be made still clearer by the following corollary.
Corollary.-Individual
things are nothing but modifications of the attributes of God, or modes by
which the attributes of God are expressed in a fixed and definite manner.
The proof appears from Prop. xv. and Def. v.
PROP.
XXVI. A thing which is
conditioned to act in a particular manner, has necessarily been thus
conditioned by God ; and that which has not been conditioned by God cannot
condition itself to act.
Proof.-That
by which things are said to be conditioned to act in a particular manner is
necessarily something positive (this is obvious) ; therefore both of its
essence and of its existence God by the necessity of his nature is the
efficient cause (Props. xxv. and
xvi.) ; this is our first point. Our
second point is plainly to be inferred therefrom.
For if a thing, which has not been conditioned by God, could condition
itself, the first part of our proof would be false, and this, as we have shown
is absurd.
PROP.
XXVII. A thing, which has been
conditioned by God to act in a particular way, cannot render itself
unconditioned.
Proof.-This
proposition is evident from the third axiom.
PROP.
XXVIII. Every individual thing,
or everything which is finite and has a conditioned existence, cannot exist or
be conditioned to act, unless it be conditioned for existence and action by a
cause other than itself, which also is finite, and has a conditioned existence
; and likewise this cause cannot in its turn exist, or be conditioned to act,
unless it be conditioned for existence and action by another cause, which also
is finite, and has a conditioned existence, and so on to infinity.
Proof.-Whatsoever
is conditioned to exist and act, has been thus conditioned by God (by Prop.
xxvi. and Prop. xxiv., Coroll.).
But
that which is finite, and has a conditioned existence, cannot be produced by
the absolute nature of any attribute of God ; for whatsoever follows from the
absolute nature of any attribute of God is infinite and eternal (by Prop.
xxi.). It must, therefore, follow
from some attribute of God, in so far as the said attribute is considered as
in some way modified ; for substance and modes make up the sum total of
existence (by Ax. i. and Def.
iii., v.), while modes are merely modifications of the attributes of God. But from God, or from any of his attributes, in so far as the
latter is modified by a modification infinite and eternal, a conditioned thing
cannot follow. Wherefore it must
follow from, or be conditioned for, existence and action by God or one of his
attributes, in so far as the latter are modified by some modification which is
finite, and has a conditioned existence.
This is our first point. Again,
this cause or this modification (for the reason by which we established the
first part of this proof) must in its turn be conditioned by another cause,
which also is finite, and has a conditioned existence, and, again, this last
by another (for the same reason) ; and so on (for the same reason) to
infinity.
Note.-As
certain things must be produced immediately by God, namely those things which
necessarily follow from his absolute nature, through the means of these
primary attributes, which, nevertheless, can neither exist nor be conceived
without God, it follows :-1. That God is absolutely the proximate cause of
those things immediately produced by him.
I say absolutely, not after his kind, as is usually stated. For the effects of God cannot either exist or be conceived
without a cause (Prop. xv. and Prop. xxiv.
Coroll.). 2. That God cannot
properly be styled the remote cause of individual things, except for the sake
of distinguishing these from what he immediately produces, or rather from what
follows from his absolute nature. For,
by a remote cause, we understand a cause which is in no way conjoined to the
effect. But all things which are,
are in God, and so depend on God, that without him they can neither be nor be
conceived.
PROP.
XXIX. Nothing in the universe is
contingent, but all things are conditioned to exist and operate in a
particular manner by the necessity of the divine nature.
Proof.-Whatsoever
is, is in God (Prop. xv.). But
God cannot be called a thing contingent.
For (by Prop. xi.) he exists necessarily, and not contingently.
Further, the modes of the divine nature follow therefrom necessarily,
and not contingently (Prop. xvi.) ; and they thus follow, whether we consider
the divine nature absolutely, or whether we consider it as in any way
conditioned to act (Prop. xxvii.). Further, God is not only the cause of these modes, in so far
as they simply exist (by Prop. xxiv,
Coroll.), but also in so far as they are considered as conditioned for
operating in a particular manner (Prop. xxvi.). If they be not conditioned by God (Prop. xxvi.), it is
impossible, and not contingent, that they should condition themselves ;
contrariwise, if they be conditioned by God, it is impossible, and not
contingent, that they should render themselves unconditioned. Wherefore all
things are conditioned by the necessity of the divine nature, not only to
exist, but also to exist and operate in a particular manner, and there is
nothing that is contingent. Q.E.D.
Note.-Before
going any further, I wish here to explain, what we should understand by nature
viewed as active (natura naturans), and nature viewed as passive (natura
naturata). I say to explain, or
rather call attention to it, for I think that, from what has been said, it is
sufficiently clear, that by nature viewed as active we should understand that
which is in itself, and is conceived through itself, or those attributes of
substance, which express eternal and infinite essence, in other words (Prop.
xiv., Coroll. i., and Prop. xvii., Coroll. ii) God, in so far as he is
considered as a free cause.
By
nature viewed as passive I understand all that which follows from the
necessity of the nature of God, or of any of the attributes of God, that is,
all the modes of the attributes of God, in so far as they are considered as
things which are in God, and which without God cannot exist or be conceived.
PROP.
XXX. Intellect, in function
(actu) finite, or in function infinite, must comprehend the attributes of God
and the modifications of God, and nothing else.
Proof.-A
true idea must agree with its object (Ax. vi.) ; in other words (obviously),
that which is contained in the intellect in representation must necessarily be
granted in nature. But in nature
(by Prop. xiv., Coroll. i.) there is no substance save God, nor any
modifications save those (Prop. xv.) which are in God, and cannot without God
either be or be conceived. Therefore
the intellect, in function finite, or in function infinite, must comprehend
the attributes of God and the modifications of God, and nothing else. Q.E.D.
PROP.
XXXI. The intellect in function,
whether finite or infinite, as will, desire, love, &c., should be referred
to passive nature and not to active nature.
Proof.-By the intellect we do not (obviously) mean absolute thought, but only a certain mode of thinking, differing from other modes, such as love, desire, &c., and therefore (Def. v.) requiring to be conceived through absolute thought. It must (by Prop. xv. and Def. vi.), through some attribute of God which expresses the eternal and infinite essence of thought, be so conceived, that without such attribute it could neither be nor be conceived. It must therefore be ref