The Ethics
(Ethica Ordine Geometrico Demonstrata)

by Benedict de Spinoza




Translated from the Latin by R. H. M. Elwes




PART I. CONCERNING GOD.

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 modifications[1] of substance, or that
which exists in, and is conceived through, something other than
itself.

[1] "Affectiones"

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.


AXIOMS.

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.


PROPOSITIONS.

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.).
Q.E.D.

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.
Q.E.D.

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.
Q.E.D.
    Note.-In this last proof, I have purposely shown God's
existence Г  posteriori, so that the proof might be more easily
followed, not because, from the same premises, God's existence
does not follow Г  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.
Q.E.D.
    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.
Q.E.D.
    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.