Benedict de Spinoza, THE ETHICS
(Ethica Ordine Geometrico Demonstrata)

Translated 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 ("affectiones") 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.

 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. I.  Substance is by nature prior to its
modifications.

>>>>>Proof--This is clear from Deff. iii. and v.

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.

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.

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.

V.  There cannot exist in the universe two or more substances
having the same nature or attribute.

>>>>>Proof--If several distinct substances be granted, they must
be distinguished one from the other, either by the difference of
their attributes, or by the difference of their modifications
(Prop. iv.).  If only by the difference of their attributes, it
will be granted that there cannot be more than one with an
identical attribute.  If by the difference of their
modifications--as substance is naturally prior to its
modifications (Prop. i.)--it follows that setting the
modifications aside, and considering substance in itself, that is
truly, (Deff. iii  and vi.), there cannot be conceived one
substance different from another--that is (by Prop. iv.), there
cannot be granted several substances, but one substance only.
Q.E.D.

VI.  One substance cannot be produced by another substance.

>>>>>Proof--It is impossible that there should be in the universe
two substances with an identical attribute, i.e. which have
anything common to them both (Prop ii.), and,  therefore (Prop.
iii.), one cannot be the cause of the other, neither can one be
produced by the other.  Q.E.D.

<<<<>>>>Proof--Substance cannot be produced by anything external
(Cor., Prop vi.), it must, therefore, be its own cause--that is,
its essence necessarily involves existence, or existence belongs
to its nature.

VIII.  Every substance is necessarily infinite.

>>>>>Proof--There can only be one substance with an identical
attribute, and existence follows from its nature (Prop. vii.);
its nature, therefore, involves existence, either as finite  or
infinite.  It does not exist as finite, for (by Deff. ii.) it
would then be limited by something else of the same kind, which
would also necessarily exist (Prop. vii.); and there would be two
substances with an identical attribute, which is absurd (Prop.
v.).  It therefore exists as infinite.  Q.E.D.

*****Note I.--As finite existence involves a partial negation,
and infinite existence is the  absolute affirmation of the given
nature, it follows (solely from Prop. vii.) that every substance
is necessarily infinite.

*****Note II.--No doubt it will be difficult for those who think
about things loosely, and have not been accustomed to know them
by their primary causes, to comprehend the  demonstration of
Prop. vii.:  for such persons make no distinction between the
modifications of substances and the substances themselves, and
are ignorant of the manner in which things are produced; hence
they may attribute to substances the beginning which they observe
in natural objects.  Those who are ignorant of true causes make
complete confusion--think that trees might talk just as well as
men--that men might be formed from stones as well as from seed;
and imagine that any form might be changed into any other. So,
also, those who confuse the two natures, divine and human,
readily attribute human  passions to the deity, especially so
long as they do not know how passions originate in the mind.
But, if people would consider the nature of substance, they would
have no doubt about the truth of Prop. vii.  In fact, this
proposition would be a universal axiom, and accounted a truism.
For, by substance, would be understood that which is in itself,
and is conceived through itself--that is, something of which the
conception requires not the  conception of anything else; whereas
modifications exist in something external to themselves, and a
conception of them is formed by means of a conception of the
things in  which they exist.  Therefore, we may have true ideas
of non-existent modifications; for, although they may have no
actual existence apart from the conceiving intellect, yet their
essence is so involved in something external to themselves that
they may through it be conceived.  Whereas the only truth
substances can have, external to the intellect, must  consist in
their existence, because they are conceived through themselves.
Therefore, for a person to say that he has a clear and
distinct--that is, a true--idea of a substance, but that he is
not sure whether such substance exists, would be the same as if
he said that he had a true idea, but was not sure whether or no
it was false (a little consideration will make this plain); or if
anyone affirmed that substance is created, it would be the same
as saying that a false idea was true--in short, the height of
absurdity.  It must, then, necessarily be admitted that the
existence of substance as its essence is an eternal truth.  And
we can hence conclude by another process of reasoning--that there
is but one such substance.  I think that this may profitably be
done at once; and, in order to proceed regularly with the
demonstration, we must premise:--

+++++1.  The true definition of a thing neither involves nor
expresses anything beyond the nature of the thing defined.  From
this it follows that--

+++++2.  No definition implies or expresses a certain number of
individuals, inasmuch as it expresses nothing beyond the nature
of the thing defined.  For instance, the definition of a triangle
expresses nothing beyond the actual nature of a triangle:  it
does not imply any fixed number of triangles.

+++++3.  There is necessarily for each individual existent thing
a cause why it should  exist.

+++++4.  This cause of existence must either be contained in the
nature and definition of the thing defined, or must be postulated
apart from such definition.

It therefore follows that, if a given number of individual things
exist in nature, there must be some cause for the existence of
exactly that number, neither more nor less.  For example, if
twenty men exist in the universe (for simplicity's sake, I will
suppose them existing simultaneously, and to have had no
predecessors), and we want to account for the existence of these
twenty men, it will not be enough to show the cause of human
existence in general; we must also show why there are exactly
twenty men, neither more nor less:  for a cause must be assigned
for the existence of each individual.  Now this cause cannot be
contained in the actual nature of man, for the true definition of
man does not involve any consideration of the number twenty.
Consequently, the cause for the existence of these twenty men,
and, consequently, of each of them, must necessarily be sought
externally to each individual. Hence we may lay down the absolute
rule, that everything which may consist of several individuals
must have an external cause.  And, as it has been shown already
that existence appertains to the nature of substance, existence
must necessarily be included in its definition; and from its
definition alone existence must be deducible.  But from its
definition (as we have shown, Notes ii., iii.), we cannot infer
the existence of several substances; therefore it follows that
there is only one substance of the same nature.  Q.E.D.

IX.  The more reality or being a thing has, the greater the
number of its attributes (Def. iv.).

X.  Each particular attribute of the one substance must be
conceived through itself.

>>>>>Proof--An attribute is that which the intellect perceives of
substance, as  constituting its essence (Def. iv.), and,
therefore, must be conceived through itself (Def. iii.).  Q.E.D.

*****Note--It is thus evident that, though two attributes are, in
fact, conceived as distinct--that is, one without the help of the
other--yet we cannot, therefore, conclude  that they constitute
two entities, or two different substances.  For it is the nature
of substance that each of its attributes is conceived through
itself, inasmuch as all the attributes it has have always existed
simultaneously in it, and none could be produced by any other;
but each expresses the reality or being of substance.  It is,
then, far from an absurdity to ascribe several attributes to one
substance:  for nothing in nature is more clear than that each
and every entity must be conceived under some attribute, and that
its  reality or being is in proportion to the number of its
attributes expressing necessity or eternity and infinity.
Consequently it is abundantly clear, that an absolutely infinite
being must necessarily be defined as consisting in infinite
attributes, each of which expresses a  certain eternal and
infinite essence.

If anyone now ask, by what sign shall he be able to distinguish
different substances, let him read the following propositions,
which show that there is but one substance in the universe, and
that it is absolutely infinite, wherefore such a sign would be
sought in vain.

XI.  God, or substance, consisting of infinite attributes, of
which each expresses eternal and infinite essentiality,
necessarily exists.

>>>>>Proof--If this be denied, conceive, if possible, that God
does not exist:  then his essence does not involve existence.
But this (Prop. vii.) is absurd.  Therefore God necessarily
exists.

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

 But the reason for the existence of a triangle or a circle does
not follow from the nature of those figures, but from the order
of universal nature in extension.  From the latter it must
follow, either that a triangle necessarily exists, or that it is
impossible that it should exist.  So much is self-evident.  It
follows therefrom that a thing necessarily exists, if no cause or
reason be granted which prevents its existence.

If, then, no cause or reason can be given, which prevents the
existence of God, or which destroys his existence, we must
certainly conclude that he necessarily does exist.  If such a
reason or cause should be given, it must either be drawn from the
very nature of God, or be external to him--that is, drawn from
another substance of another nature.  For if it were of the same
nature, God, by that very fact, would be admitted to exist.  But
substance of another nature could have nothing in common with God
(by Prop. ii.), and therefore would be unable either to cause or
to destroy his existence.

As, then, a reason or cause which would annul the divine
existence cannot be drawn from  anything external to the divine
nature, such cause must perforce, if God does not exist, be drawn
from God's own nature, which would involve a contradiction.  To
make such an affirmation about a being absolutely infinite and
supremely perfect is absurd; therefore, neither in the nature of
God, nor externally to his nature, can a cause or reason be
assigned which would annul his existence.  Therefore, God
necessarily exists.  Q.E.D.

>>>>>Another proof--The potentiality of non-existence is a
negation of power, and contrariwise the potentiality of existence
is a power, as is obvious.  If, then, that which necessarily
exists is nothing but finite beings, such finite beings are more
powerful than a being absolutely infinite, which is obviously
absurd; therefore, either nothing exists, or else a being
absolutely infinite necessarily exists also.  Now we exist either
in ourselves, or in  something else which necessarily exists (see
Ax. i. and Prop. vii.).  Therefore a being absolutely
infinite--in other words, God (Def. vi.)--necessarily exists.
Q.E.D.

*****Note--In this last proof, I have purposely shown God's
existence 'a posteriori,' so that the proof might be more easily
followed, not because, from the same premises, God's existence
does not follow 'a priori.'  For, as the potentiality of
existence is a power, it follows that, in proportion as reality
increases in the nature of a thing, so also will it increase its
strength for existence.  Therefore a being absolutely infinite,
such as God, has from himself an absolutely infinite power of
existence, and hence he does absolutely exist. Perhaps there will
be many who will be unable to see the force of this proof,
inasmuch as they are accustomed only to consider those things
which flow from external causes.  Of  such things, they see that
those which quickly come to pass--that is, quickly come into
existence--quickly also disappear; whereas they regard as more
difficult of accomplishment --that is, not so easily brought into
existence--those things which they conceive as more complicated.

However, to do away with this misconception, I need not here show
the measure of truth in the proverb, "What comes quickly, goes
quickly," nor discuss whether, from the point of view of
universal nature, all things are equally easy, or otherwise:  I
need only remark that I am not here speaking of things, which
come to pass through causes external to themselves, but only of
substances which (by Prop. vi.) cannot be produced by any
external cause.   Things which are produced by external causes,
whether they consist of many parts or few, owe whatsoever
perfection or reality they possess solely to the efficacy of
their external  cause; wherefore the existence of substance must
arise solely from its own nature, which is nothing else but its
essence.  Thus, the perfection of a thing does not annul its
existence,  but, on the contrary, asserts it.  Imperfection, on
the other hand, does annul it; therefore we cannot be more
certain of the existence of anything, than of the existence of a
being absolutely infinite or perfect--that is, of God.  For
inasmuch as his essence excludes all imperfection, and involves
absolute perfection, all cause for doubt concerning his existence
is done away, and the utmost certainty on the question is given.
This, I think, will be evident to every moderately attentive
reader.

XII.  No attribute of substance can be conceived from which it
would follow that substance can be divided.

>>>>>Proof--The parts into which substance as thus conceived
would be divided either  will retain the nature of substance, or
they will not.  If the former, then (by Prop. viii.) each part
will necessarily be infinite, and (by Prop vi.) self-caused, and
(by Prop. v.) will perforce consist of a different attribute, so
that, in that case, several substances could be formed out of one
substance, which (by Prop. vi.) is absurd.  Moreover, the parts
(by Prop. ii.) would have nothing in common with their whole, and
the whole (by Def. iv. and Prop. X) could both exist and be
conceived without its parts, which everyone will admit to be
absurd.  If we adopt the second alternative--namely, that the
parts will not retain the  nature of substance--then, if the
whole substance were divided into equal parts, it would  lose the
nature of substance, and would cease to exist, which (by Prop.
vii.) is absurd.

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.

<<<<>>>>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.

<<<<>>>>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 (Cor. 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 Cor. 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.

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.

<<<<>>>>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.

<<<<>>>>Proof--All things which are, are in God, and must be
conceived through God (by Prop. xv.), therefore (by Prop. xvi.,
Cor. 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.

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. vii.).  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.

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.

<<<<>>>>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., Cor. 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.

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.

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.

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.

<<<<>>>>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.

<<<<>>>>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.

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 Ax. iii.

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., Cor.)

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.