09-05-2018, 07:31 AM
Propositions
1: A substance is prior in nature to its states.
This is evident from D3 and D5.
2: Two substances having different attributes have nothing
in common with one another.
This is also evident from D3. For each ·substance·
must be in itself and be conceived through itself,
which is to say that the concept of the one doesn’t
involve the concept of the other.
3: If things have nothing in common with one another,
one of them can’t be the cause of the other.
If they have nothing in common with one another,
then (by A5) they can’t be understood through one
another, and so (by A4) one can’t be the cause of the
other.
4: Two or more things are made distinct from one another
either by a difference in their attributes or by a
difference in their states.
Whatever exists is either •in itself or •in something else
(by A1), which is to say (by D3 and D5) that outside
the intellect there is nothing except •substances and
•their states. So there is nothing outside the intellect
through which things can be distinguished from one
another except •substances (which is to say (by D4)
their attributes) and •their states.
5: In Nature there cannot be two or more substances
having the same nature or attribute.
If there were two or more distinct substances, they
would have to be distinguished from one another by a
difference either •in their attributes or •in their states
(by 4). If they are distinguished only by a difference
in their attributes, then any given attribute can be
possessed by only one of them. Suppose, then, that
they are distinguished by a difference in their states.
But a substance is prior in nature to its states (by
1), so we can set the states aside and consider the
substance in itself; and then there is nothing left
through which one substance can be conceived as
distinguished from another, which by 4 amounts to
saying that we don’t have two or more substances
·with a single attribute·, but only one.
6: One substance can’t be produced by another substance.
In Nature there can’t be two substances that share
an attribute (by 5), that is (by 2), there can’t be two
substances that have something in common with each
other. Therefore (by 3) one substance can’t be the
cause of another, or be caused by it.
Corollary: A substance can’t be produced by anything else.
In Nature there are only substances and their states
(as is evident from A1, D3, and D5). But a substance
can’t be produced by a·nother· substance (by 6).
Therefore, a substance can’t be produced by anything
else at all.
This corollary is demonstrated even more easily from the
absurdity of its contradictory. If a substance could be
produced by something else, the knowledge of it would have
to depend on the knowledge of its cause (by A4). And so (by
D3) it wouldn’t be a substance.
7: It pertains to the nature of a substance to exist.
A substance can’t be produced by anything else (by
the corollary to 6), so it must be its own cause; and
that, by D1, is to say that its essence necessarily
involves existence, i.e. it pertains to its nature to exist.
8: Every substance is necessarily infinite.
[The difficult demonstration of 8 has this at its core: if
x is finite then it is limited by something of the same
kind as itself, i.e. something that shares an attribute
with it; but no substance shares an attribute with any
other substance, so no substance can be limited in
this way, so every substance is infinite.]
First note on 7 and 8: Since finiteness is partly negative,
while being infinite is an unqualifiedly ·positive· affirmation
of the existence of some nature, it follows from 7 alone that
every substance must be infinite; for in calling a substance
‘finite’ we partly, because of the negative element in finiteness,
deny existence to its nature, and according to 7 that is
absurd.
Second note on 7 and 8: I’m sure that the proof of 7 will be
found difficult to grasp by people who judge things confusedly
and haven’t been accustomed to understanding things
through their first causes. Such people don’t distinguish
the qualities of substances from the substances themselves,
and they don’t know how things are produced. This brings it
about that they fictitiously ascribe to •substances the ·sort
of· beginning that they see •natural things to have; for those
who don’t know the true causes of things confuse everything,
and have no difficulty supposing that both trees and men
speak, that men are formed both from stones and from seed,
and that anything can be changed into anything else! So,
also, those who confuse the divine nature with human nature
easily ascribe human character-traits to God, particularly
must be an external cause of its existing. Now since it
pertains to the nature of a substance to exist (already shown
in this note), its definition must involve necessary existence,
and so its existence must be inferred from its definition alone.
But, as we have shown in 2 and 3, the existence of a number
of substances can’t follow from a definition. So it follows that
there can exist only one substance having a given nature.
9: The more reality or being each thing has, the more
attributes belong to it.
This is evident from D4.
10: Each attribute of a substance must be conceived
through itself.
An attribute is what the intellect perceives concerning
a substance, as constituting its essence (by D4); so
(by D3) it must be conceived through itself.
Note on 10: From these propositions it is evident that
although two attributes can be conceived to be really distinct
(each conceived without the aid of the other), we still can’t
infer from that that they constitute—·that is, constitute
the natures of, i.e. are possessed by·—two different substances.
. . . It is far from absurd to ascribe many attributes
to one substance. Indeed, nothing in Nature is clearer
than that each thing must be conceived under some attribute,
and the more reality a thing has the more attributes
it has—attributes that express necessity, or eternity and
infinity. So it is utterly clear that an absolutely infinite
thing must be defined (as in D6) as a thing that consists of
infinite attributes, each of which expresses a certain eternal
and infinite essence. If you want to know how we can tell
when there are many substances, read on: in the following
propositions I shall show that in Nature there exists only one
substance, which is absolutely infinite. So there is nothing
to ‘tell’.
11: God, or a substance consisting of infinite attributes
each of which expresses eternal and infinite essence,
necessarily exists.
If God didn’t exist, then (by A7) God’s essence would
not involve existence; and (by 7) that is absurd. Therefore
God necessarily exists.
A second proof: For each thing there must be assigned
a cause or reason for its existence (if it exists) and for its
nonexistence (if it doesn’t). . . . This reason or cause must be
either contained in, or lie outside of, the nature of the thing.
For example, the very nature of a square circle indicates the
reason why it doesn’t exist, namely because it involves a
contradiction; and the very nature of a substance explains
why it does exist, because that nature involves existence (see
7). But the reason why [changing Spinoza’s example] a coin exists,
or why it doesn’t exist, does not follow from its nature but
from the order of the whole of the physical world. For from
this ·order· it must follow either that the coin necessarily
exists now or that it is impossible for it to exist now.
These things are self-evident. From them it follows that
a thing necessarily exists if there is no reason or cause that
prevents it from existing. So if there is no reason or cause
that prevents God from existing or takes God’s existence
away, it certainly follows that God necessarily exists.
But if there were such a reason or cause, it would have to
be either •in God’s very nature or •outside it and in another
substance of a different nature. It couldn’t be in a substance
of the same nature as God’s, for the supposition that there is
such a substance is, itself, the supposition that God exists.
So it would have to be a substance of a nature different from
God’s; but such a substance would have nothing in common
with God (by 2) and so could neither give existence to God
nor take it away. So a reason or cause that takes away God’s
existence couldn’t lie outside the divine nature.
It would, then, have to be in God’s nature itself. That
would mean that God’s nature involved a contradiction, ·like
the square circle·. But it is absurd to affirm this of a thing
that is absolutely infinite and supremely perfect. (·That is
because •a contradiction must involve something of the form
‘P and not-P—a ‘square circle’ would be something that was
‘square and not square’ because ‘not square is contained
in the meaning of ‘circle’—and •a thing that is infinite and
perfect is one whose nature involves nothing negative, so
nothing of the contradictory form·.) So there is no cause
or reason—either in God or outside God—that takes God’s
existence away. Therefore God necessarily exists.
A third proof: [slightly expanded from Spinoza’s very compact
statement of it] To be unable to exist is to lack power, and
conversely to be able to exist is to have power (this is
self-evident). Now, suppose that God doesn’t exist but some
finite things do exist necessarily. In that case, these finite
things are more powerful than an absolutely infinite thing
(because they can exist and the absolutely infinite thing
can’t). But this is self-evidently absurd. So either nothing
exists or an absolutely infinite thing also exists. But we
exist, either in ourselves as substances that necessarily exist
or as qualities of something else that necessarily exists (see
A1 and 7). Therefore an absolutely infinite thing—that is (by
D6) God—necessarily exists.
Note on the third proof of 11: In this last demonstration
I wanted to show God’s existence a posteriori (·bringing in
the contingent fact that we exist·), so as to make the demonstration
easier to grasp—but not because God’s existence
doesn’t follow a priori from the same premises. For since
being able to exist is power, it follows that the more reality
belongs to the nature of a thing the more powers it has, of
itself, to exist. Therefore an absolutely infinite thing (God)
has of itself an absolutely infinite power of existing. For that
reason, God exists absolutely. Still, there may be many who
won’t easily see the force of this proof because they have
been accustomed to think only about things that flow from
external causes. And of those things they see that •the ones
that quickly and easily come into existence also easily perish.
And conversely, they judge that •complicated and intricately
structured things are harder to produce, i.e. that they don’t
exist so easily. I might free them from these prejudices
by looking into •what truth there is in the proposition that
what quickly comes to be quickly perishes, and considering
whether •all things are equally easy in respect to the whole
of Nature (·I think they are·). But I shan’t go into any of that.
All I need here is to point out that I am here speaking not
of things that come into existence from external causes but
only of substances, which (by 6) can’t be produced by any
external cause. For things that come to exist from external
causes—whether they have many parts or few—owe all their
perfection or reality to the power of the external cause; and
therefore their existence arises only from the perfection of
their external cause and not from their own perfection. On
the other hand, whatever perfection a substance has is not
due to any external cause; so its existence must follow from
its nature alone; so its existence is nothing but its essence.
So perfection doesn’t take away the existence of a thing, but
on the contrary asserts it. But imperfection takes it away. So
there is nothing of whose existence we can be more certain
than we are of the existence of an absolutely infinite thing, i.e.
a perfect thing, i.e. God. For since God’s essence •excludes
all imperfection and •involves absolute perfection, by that
very fact it removes every cause of doubting God’s existence
and gives the greatest certainty concerning it. I think this
will be clear to you even if you are only moderately attentive!
12: No attribute of a substance can be truly conceived
from which it follows that the substance can be divided.
Suppose that a substance can be conceived as being
divisible; then either its parts will also have the nature
of the substance or they won’t. If they •do, then (by
8) each part will be infinite, and (by 7) will be its own
cause; and (by 5) each part will have to consist of a
different attribute. And so many substances can be
formed from one, which is absurd (by 6). Furthermore,
the parts would have nothing in common with their
whole (by 2), and the whole (by D4 and 10) could
exist without its parts and be conceived without them;
and no-one can doubt that that is absurd. But if on
the other hand the parts •do not retain the nature
of substance, then dividing the whole substance into
equal parts would deprive it of the nature of substance,
meaning that it would cease to exist; and (by 7) that
is absurd.
13: A substance that is absolutely infinite is indivisible.
If it were divisible, its parts would either retain the
nature of an absolutely infinite substance or they
wouldn’t. If they did, then there would be a number
of substances of the same nature, which (by 5) is
absurd. If they didn’t, then (as in 12) an absolutely
infinite substance could ·be divided into such parts
and thereby· cease to exist, which (by 11) is also
absurd.
Corollary: No substance is divisible, and thus no corporeal
substance, insofar as it is a substance, is divisible. [This use
of ‘insofar as’ is explained on page 9 just above the start of section V.]
Note on 12–13: That substance is indivisible can be understood
more simply merely from this: the nature of substance
can’t be conceived other than as infinite, whereas ‘a part of
a substance’ can only mean a finite substance, which (by 8)
implies a plain contradiction.
14: God is the only substance that can exist or be
conceived.
Since God is an absolutely infinite thing, of whom no
attribute expressing an essence of substance can be
denied (by 6), and God necessarily exists (by 11), if
there were a substance other than God it would have
to be explained through some attribute of God; ·but
explanations can flow only within attributes, not from
one attribute to another·; and so two substances with
an attribute in common would exist, which (by 5) is
absurd. So no substance other than God can exist;
and none such can be conceived either, for if it could
be conceived it would have to be conceived as existing,
and the first part of this demonstration shows that to
be absurd. Therefore, God is the only substance that
can exist or be conceived.
First corollary: God is unique, i.e. (by 6) in Nature there is
only one substance, and it is absolutely infinite.
Second corollary: An extended thing and a thinking thing
are either attributes of God or (by A1) states of God’s attributes.
15: Whatever exists is in God, and nothing can exist or
be conceived without God.
14 secures that apart from God there cannot exist (or
be conceived) any substance, i.e. (by D3) any thing
that is in itself and is conceived through itself. But
(by D5) modes can’t exist or be conceived without a
substance ·that they are modes of ·. So modes can
exist only in the divine nature, and can be conceived
only through that nature. But (by A1) substances and
modes are all there is. Therefore, everything is in God
and nothing can be or be conceived without God.
Note on 15: [This text follows Curley in numbering sections of this
note, and of the note on 17 and the Appendix, as an aid to reference.]
I. Some people imagine a God who is like a man, consisting
of a body and a mind, and subject to passions. But
how far they wander from the true knowledge of God is
shown well enough by what I have already demonstrated,
and I shan’t talk about them any more. Everyone who has
to any extent contemplated the divine nature denies that
God is corporeal. This is best proved from the fact that by
‘a body’ we understand a quantity that has length, breadth,
and depth, • by some specific shape. Nothing could be more
absurd than to say this about God, i.e. about a thing that is
infinite [= •’unlimited’.]
In trying to demonstrate this same conclusion by different
arguments from mine, some people clearly show that ·as
well as denying that God is or has •a body· they conclude
that the divine nature doesn’t in any way involve corporeal
or •extended substance. They maintain that the corporeal
world, ·rather than being part of God’s nature·, has been
created by God. But by what divine power could it be
created? They have no answer to that, which shows clearly
that they don’t understand what they are saying.
At any rate, I have demonstrated clearly enough—in my
judgment, at least—that no substance can be produced or
created by any other (see the corollary to 6 and the second
note on 8). Next, I have shown (14) that God is the only
substance that can exist or be conceived, and from this I
have inferred in the second corollary to 14 that extended
substance is one of God’s infinite attributes. To explain
all this more fully, I shall refute my opponents’ arguments,
which all come down to these two.
II. First, they think that corporeal substance, insofar
as it is substance, consists of parts. From this they infer
that it cannot be infinite, and thus cannot pertain to God.
They explain this through many examples, of which I shall
mention three.
•If corporeal substance is infinite, they say, let us conceive
it to be divided into two parts. If each part is finite, then an
infinite is composed of two finite parts, which is absurd. If
each part is infinite, then there is one infinite twice as large
as another, which is also absurd. •Again, if an infinite quantity
is measured by parts each equal to a foot, it will consist
of infinitely many of them, as it will also if it is measured by
parts each equal to an inch. So one infinite number will be
twelve times as great as another, which is no less absurd.
•Finally, suppose that from one point in something of infinite
extent two lines are extended to infinity. Although near
the beginning they are a certain determinate distance apart,
the distance between them is continuously increased ·as
they lengthen·, until finally it stops being determinate and
becomes indeterminable; ·which is also absurd·. Since these
absurdities follow—so they think—from the supposition of an
infinite quantity, they infer that corporeal substance must
be finite and consequently cannot pertain to God’s essence.
III. Their second argument is also drawn from God’s
supreme perfection. For, they say, God as a supremely
perfect thing cannot be acted on. But corporeal substance,
since it is divisible, can be acted on; ·anything that is
divisible can be pulled apart by outside forces·. So it follows
that corporeal substance does not pertain to God’s essence.
IV. These are the arguments that I find being used by
authors who want to show that corporeal substance is
unworthy of the divine nature, and cannot have anything to
do with it. But anyone who is properly attentive will find that
I have already replied to them, since these arguments are
based wholly on the supposition that corporeal substance is
composed of parts, which I have already (12 and corollary to
13) shown to be absurd. Anyone who wants to consider the
matter rightly will see that all those absurdities (if indeed
that’s what they are) from which they infer that extended
substance is finite don’t at all follow from •the supposition
of an infinite quantity, but from •supposing that an infinite
quantity might be measurable and composed of finite parts.
All they are entitled to infer from the absurdities they have
uncovered is that infinite quantity is not measurable and is
not composed of finite parts. This is just what I have already
demonstrated above (12, etc.). So the weapon they aim at
me turns against themselves. . . .
Others, imagining that a line is composed of points, know
how to invent many arguments showing that a line can’t be
divided to infinity. And indeed it is just as absurd to say that
corporeal substance is composed of bodies, or parts, as it is
to say that a body is composed of surfaces, the surfaces of
lines, and the lines of points.
This must be admitted by all those who know that clear
reason is infallible, and especially those who deny that there
is a vacuum. For if corporeal substance could be divided
into parts that were really distinct, why couldn’t one part be
annihilated while the rest remained inter-related as before
(·thus creating a vacuum·)? Why must they all be so fitted
together that there is no vacuum? If two things are really
distinct from one another ·rather than being different modes
or aspects of a single substance·, one of them can stay
where it is whatever the other does. But there isn’t any
vacuum in Nature (a subject I discuss elsewhere, ·namely
in my Descartes’s Principles, part 2, propositions 2 and
3·); all the parts of Nature do have to hang together so
that there is no vacuum; so it follows that those parts are
not really distinct from one another, ·i.e. that they are not
distinct things·, which is to say that corporeal substance,
insofar as it is a substance, cannot be divided
1: A substance is prior in nature to its states.
This is evident from D3 and D5.
2: Two substances having different attributes have nothing
in common with one another.
This is also evident from D3. For each ·substance·
must be in itself and be conceived through itself,
which is to say that the concept of the one doesn’t
involve the concept of the other.
3: If things have nothing in common with one another,
one of them can’t be the cause of the other.
If they have nothing in common with one another,
then (by A5) they can’t be understood through one
another, and so (by A4) one can’t be the cause of the
other.
4: Two or more things are made distinct from one another
either by a difference in their attributes or by a
difference in their states.
Whatever exists is either •in itself or •in something else
(by A1), which is to say (by D3 and D5) that outside
the intellect there is nothing except •substances and
•their states. So there is nothing outside the intellect
through which things can be distinguished from one
another except •substances (which is to say (by D4)
their attributes) and •their states.
5: In Nature there cannot be two or more substances
having the same nature or attribute.
If there were two or more distinct substances, they
would have to be distinguished from one another by a
difference either •in their attributes or •in their states
(by 4). If they are distinguished only by a difference
in their attributes, then any given attribute can be
possessed by only one of them. Suppose, then, that
they are distinguished by a difference in their states.
But a substance is prior in nature to its states (by
1), so we can set the states aside and consider the
substance in itself; and then there is nothing left
through which one substance can be conceived as
distinguished from another, which by 4 amounts to
saying that we don’t have two or more substances
·with a single attribute·, but only one.
6: One substance can’t be produced by another substance.
In Nature there can’t be two substances that share
an attribute (by 5), that is (by 2), there can’t be two
substances that have something in common with each
other. Therefore (by 3) one substance can’t be the
cause of another, or be caused by it.
Corollary: A substance can’t be produced by anything else.
In Nature there are only substances and their states
(as is evident from A1, D3, and D5). But a substance
can’t be produced by a·nother· substance (by 6).
Therefore, a substance can’t be produced by anything
else at all.
This corollary is demonstrated even more easily from the
absurdity of its contradictory. If a substance could be
produced by something else, the knowledge of it would have
to depend on the knowledge of its cause (by A4). And so (by
D3) it wouldn’t be a substance.
7: It pertains to the nature of a substance to exist.
A substance can’t be produced by anything else (by
the corollary to 6), so it must be its own cause; and
that, by D1, is to say that its essence necessarily
involves existence, i.e. it pertains to its nature to exist.
8: Every substance is necessarily infinite.
[The difficult demonstration of 8 has this at its core: if
x is finite then it is limited by something of the same
kind as itself, i.e. something that shares an attribute
with it; but no substance shares an attribute with any
other substance, so no substance can be limited in
this way, so every substance is infinite.]
First note on 7 and 8: Since finiteness is partly negative,
while being infinite is an unqualifiedly ·positive· affirmation
of the existence of some nature, it follows from 7 alone that
every substance must be infinite; for in calling a substance
‘finite’ we partly, because of the negative element in finiteness,
deny existence to its nature, and according to 7 that is
absurd.
Second note on 7 and 8: I’m sure that the proof of 7 will be
found difficult to grasp by people who judge things confusedly
and haven’t been accustomed to understanding things
through their first causes. Such people don’t distinguish
the qualities of substances from the substances themselves,
and they don’t know how things are produced. This brings it
about that they fictitiously ascribe to •substances the ·sort
of· beginning that they see •natural things to have; for those
who don’t know the true causes of things confuse everything,
and have no difficulty supposing that both trees and men
speak, that men are formed both from stones and from seed,
and that anything can be changed into anything else! So,
also, those who confuse the divine nature with human nature
easily ascribe human character-traits to God, particularly
must be an external cause of its existing. Now since it
pertains to the nature of a substance to exist (already shown
in this note), its definition must involve necessary existence,
and so its existence must be inferred from its definition alone.
But, as we have shown in 2 and 3, the existence of a number
of substances can’t follow from a definition. So it follows that
there can exist only one substance having a given nature.
9: The more reality or being each thing has, the more
attributes belong to it.
This is evident from D4.
10: Each attribute of a substance must be conceived
through itself.
An attribute is what the intellect perceives concerning
a substance, as constituting its essence (by D4); so
(by D3) it must be conceived through itself.
Note on 10: From these propositions it is evident that
although two attributes can be conceived to be really distinct
(each conceived without the aid of the other), we still can’t
infer from that that they constitute—·that is, constitute
the natures of, i.e. are possessed by·—two different substances.
. . . It is far from absurd to ascribe many attributes
to one substance. Indeed, nothing in Nature is clearer
than that each thing must be conceived under some attribute,
and the more reality a thing has the more attributes
it has—attributes that express necessity, or eternity and
infinity. So it is utterly clear that an absolutely infinite
thing must be defined (as in D6) as a thing that consists of
infinite attributes, each of which expresses a certain eternal
and infinite essence. If you want to know how we can tell
when there are many substances, read on: in the following
propositions I shall show that in Nature there exists only one
substance, which is absolutely infinite. So there is nothing
to ‘tell’.
11: God, or a substance consisting of infinite attributes
each of which expresses eternal and infinite essence,
necessarily exists.
If God didn’t exist, then (by A7) God’s essence would
not involve existence; and (by 7) that is absurd. Therefore
God necessarily exists.
A second proof: For each thing there must be assigned
a cause or reason for its existence (if it exists) and for its
nonexistence (if it doesn’t). . . . This reason or cause must be
either contained in, or lie outside of, the nature of the thing.
For example, the very nature of a square circle indicates the
reason why it doesn’t exist, namely because it involves a
contradiction; and the very nature of a substance explains
why it does exist, because that nature involves existence (see
7). But the reason why [changing Spinoza’s example] a coin exists,
or why it doesn’t exist, does not follow from its nature but
from the order of the whole of the physical world. For from
this ·order· it must follow either that the coin necessarily
exists now or that it is impossible for it to exist now.
These things are self-evident. From them it follows that
a thing necessarily exists if there is no reason or cause that
prevents it from existing. So if there is no reason or cause
that prevents God from existing or takes God’s existence
away, it certainly follows that God necessarily exists.
But if there were such a reason or cause, it would have to
be either •in God’s very nature or •outside it and in another
substance of a different nature. It couldn’t be in a substance
of the same nature as God’s, for the supposition that there is
such a substance is, itself, the supposition that God exists.
So it would have to be a substance of a nature different from
God’s; but such a substance would have nothing in common
with God (by 2) and so could neither give existence to God
nor take it away. So a reason or cause that takes away God’s
existence couldn’t lie outside the divine nature.
It would, then, have to be in God’s nature itself. That
would mean that God’s nature involved a contradiction, ·like
the square circle·. But it is absurd to affirm this of a thing
that is absolutely infinite and supremely perfect. (·That is
because •a contradiction must involve something of the form
‘P and not-P—a ‘square circle’ would be something that was
‘square and not square’ because ‘not square is contained
in the meaning of ‘circle’—and •a thing that is infinite and
perfect is one whose nature involves nothing negative, so
nothing of the contradictory form·.) So there is no cause
or reason—either in God or outside God—that takes God’s
existence away. Therefore God necessarily exists.
A third proof: [slightly expanded from Spinoza’s very compact
statement of it] To be unable to exist is to lack power, and
conversely to be able to exist is to have power (this is
self-evident). Now, suppose that God doesn’t exist but some
finite things do exist necessarily. In that case, these finite
things are more powerful than an absolutely infinite thing
(because they can exist and the absolutely infinite thing
can’t). But this is self-evidently absurd. So either nothing
exists or an absolutely infinite thing also exists. But we
exist, either in ourselves as substances that necessarily exist
or as qualities of something else that necessarily exists (see
A1 and 7). Therefore an absolutely infinite thing—that is (by
D6) God—necessarily exists.
Note on the third proof of 11: In this last demonstration
I wanted to show God’s existence a posteriori (·bringing in
the contingent fact that we exist·), so as to make the demonstration
easier to grasp—but not because God’s existence
doesn’t follow a priori from the same premises. For since
being able to exist is power, it follows that the more reality
belongs to the nature of a thing the more powers it has, of
itself, to exist. Therefore an absolutely infinite thing (God)
has of itself an absolutely infinite power of existing. For that
reason, God exists absolutely. Still, there may be many who
won’t easily see the force of this proof because they have
been accustomed to think only about things that flow from
external causes. And of those things they see that •the ones
that quickly and easily come into existence also easily perish.
And conversely, they judge that •complicated and intricately
structured things are harder to produce, i.e. that they don’t
exist so easily. I might free them from these prejudices
by looking into •what truth there is in the proposition that
what quickly comes to be quickly perishes, and considering
whether •all things are equally easy in respect to the whole
of Nature (·I think they are·). But I shan’t go into any of that.
All I need here is to point out that I am here speaking not
of things that come into existence from external causes but
only of substances, which (by 6) can’t be produced by any
external cause. For things that come to exist from external
causes—whether they have many parts or few—owe all their
perfection or reality to the power of the external cause; and
therefore their existence arises only from the perfection of
their external cause and not from their own perfection. On
the other hand, whatever perfection a substance has is not
due to any external cause; so its existence must follow from
its nature alone; so its existence is nothing but its essence.
So perfection doesn’t take away the existence of a thing, but
on the contrary asserts it. But imperfection takes it away. So
there is nothing of whose existence we can be more certain
than we are of the existence of an absolutely infinite thing, i.e.
a perfect thing, i.e. God. For since God’s essence •excludes
all imperfection and •involves absolute perfection, by that
very fact it removes every cause of doubting God’s existence
and gives the greatest certainty concerning it. I think this
will be clear to you even if you are only moderately attentive!
12: No attribute of a substance can be truly conceived
from which it follows that the substance can be divided.
Suppose that a substance can be conceived as being
divisible; then either its parts will also have the nature
of the substance or they won’t. If they •do, then (by
8) each part will be infinite, and (by 7) will be its own
cause; and (by 5) each part will have to consist of a
different attribute. And so many substances can be
formed from one, which is absurd (by 6). Furthermore,
the parts would have nothing in common with their
whole (by 2), and the whole (by D4 and 10) could
exist without its parts and be conceived without them;
and no-one can doubt that that is absurd. But if on
the other hand the parts •do not retain the nature
of substance, then dividing the whole substance into
equal parts would deprive it of the nature of substance,
meaning that it would cease to exist; and (by 7) that
is absurd.
13: A substance that is absolutely infinite is indivisible.
If it were divisible, its parts would either retain the
nature of an absolutely infinite substance or they
wouldn’t. If they did, then there would be a number
of substances of the same nature, which (by 5) is
absurd. If they didn’t, then (as in 12) an absolutely
infinite substance could ·be divided into such parts
and thereby· cease to exist, which (by 11) is also
absurd.
Corollary: No substance is divisible, and thus no corporeal
substance, insofar as it is a substance, is divisible. [This use
of ‘insofar as’ is explained on page 9 just above the start of section V.]
Note on 12–13: That substance is indivisible can be understood
more simply merely from this: the nature of substance
can’t be conceived other than as infinite, whereas ‘a part of
a substance’ can only mean a finite substance, which (by 8)
implies a plain contradiction.
14: God is the only substance that can exist or be
conceived.
Since God is an absolutely infinite thing, of whom no
attribute expressing an essence of substance can be
denied (by 6), and God necessarily exists (by 11), if
there were a substance other than God it would have
to be explained through some attribute of God; ·but
explanations can flow only within attributes, not from
one attribute to another·; and so two substances with
an attribute in common would exist, which (by 5) is
absurd. So no substance other than God can exist;
and none such can be conceived either, for if it could
be conceived it would have to be conceived as existing,
and the first part of this demonstration shows that to
be absurd. Therefore, God is the only substance that
can exist or be conceived.
First corollary: God is unique, i.e. (by 6) in Nature there is
only one substance, and it is absolutely infinite.
Second corollary: An extended thing and a thinking thing
are either attributes of God or (by A1) states of God’s attributes.
15: Whatever exists is in God, and nothing can exist or
be conceived without God.
14 secures that apart from God there cannot exist (or
be conceived) any substance, i.e. (by D3) any thing
that is in itself and is conceived through itself. But
(by D5) modes can’t exist or be conceived without a
substance ·that they are modes of ·. So modes can
exist only in the divine nature, and can be conceived
only through that nature. But (by A1) substances and
modes are all there is. Therefore, everything is in God
and nothing can be or be conceived without God.
Note on 15: [This text follows Curley in numbering sections of this
note, and of the note on 17 and the Appendix, as an aid to reference.]
I. Some people imagine a God who is like a man, consisting
of a body and a mind, and subject to passions. But
how far they wander from the true knowledge of God is
shown well enough by what I have already demonstrated,
and I shan’t talk about them any more. Everyone who has
to any extent contemplated the divine nature denies that
God is corporeal. This is best proved from the fact that by
‘a body’ we understand a quantity that has length, breadth,
and depth, • by some specific shape. Nothing could be more
absurd than to say this about God, i.e. about a thing that is
infinite [= •’unlimited’.]
In trying to demonstrate this same conclusion by different
arguments from mine, some people clearly show that ·as
well as denying that God is or has •a body· they conclude
that the divine nature doesn’t in any way involve corporeal
or •extended substance. They maintain that the corporeal
world, ·rather than being part of God’s nature·, has been
created by God. But by what divine power could it be
created? They have no answer to that, which shows clearly
that they don’t understand what they are saying.
At any rate, I have demonstrated clearly enough—in my
judgment, at least—that no substance can be produced or
created by any other (see the corollary to 6 and the second
note on 8). Next, I have shown (14) that God is the only
substance that can exist or be conceived, and from this I
have inferred in the second corollary to 14 that extended
substance is one of God’s infinite attributes. To explain
all this more fully, I shall refute my opponents’ arguments,
which all come down to these two.
II. First, they think that corporeal substance, insofar
as it is substance, consists of parts. From this they infer
that it cannot be infinite, and thus cannot pertain to God.
They explain this through many examples, of which I shall
mention three.
•If corporeal substance is infinite, they say, let us conceive
it to be divided into two parts. If each part is finite, then an
infinite is composed of two finite parts, which is absurd. If
each part is infinite, then there is one infinite twice as large
as another, which is also absurd. •Again, if an infinite quantity
is measured by parts each equal to a foot, it will consist
of infinitely many of them, as it will also if it is measured by
parts each equal to an inch. So one infinite number will be
twelve times as great as another, which is no less absurd.
•Finally, suppose that from one point in something of infinite
extent two lines are extended to infinity. Although near
the beginning they are a certain determinate distance apart,
the distance between them is continuously increased ·as
they lengthen·, until finally it stops being determinate and
becomes indeterminable; ·which is also absurd·. Since these
absurdities follow—so they think—from the supposition of an
infinite quantity, they infer that corporeal substance must
be finite and consequently cannot pertain to God’s essence.
III. Their second argument is also drawn from God’s
supreme perfection. For, they say, God as a supremely
perfect thing cannot be acted on. But corporeal substance,
since it is divisible, can be acted on; ·anything that is
divisible can be pulled apart by outside forces·. So it follows
that corporeal substance does not pertain to God’s essence.
IV. These are the arguments that I find being used by
authors who want to show that corporeal substance is
unworthy of the divine nature, and cannot have anything to
do with it. But anyone who is properly attentive will find that
I have already replied to them, since these arguments are
based wholly on the supposition that corporeal substance is
composed of parts, which I have already (12 and corollary to
13) shown to be absurd. Anyone who wants to consider the
matter rightly will see that all those absurdities (if indeed
that’s what they are) from which they infer that extended
substance is finite don’t at all follow from •the supposition
of an infinite quantity, but from •supposing that an infinite
quantity might be measurable and composed of finite parts.
All they are entitled to infer from the absurdities they have
uncovered is that infinite quantity is not measurable and is
not composed of finite parts. This is just what I have already
demonstrated above (12, etc.). So the weapon they aim at
me turns against themselves. . . .
Others, imagining that a line is composed of points, know
how to invent many arguments showing that a line can’t be
divided to infinity. And indeed it is just as absurd to say that
corporeal substance is composed of bodies, or parts, as it is
to say that a body is composed of surfaces, the surfaces of
lines, and the lines of points.
This must be admitted by all those who know that clear
reason is infallible, and especially those who deny that there
is a vacuum. For if corporeal substance could be divided
into parts that were really distinct, why couldn’t one part be
annihilated while the rest remained inter-related as before
(·thus creating a vacuum·)? Why must they all be so fitted
together that there is no vacuum? If two things are really
distinct from one another ·rather than being different modes
or aspects of a single substance·, one of them can stay
where it is whatever the other does. But there isn’t any
vacuum in Nature (a subject I discuss elsewhere, ·namely
in my Descartes’s Principles, part 2, propositions 2 and
3·); all the parts of Nature do have to hang together so
that there is no vacuum; so it follows that those parts are
not really distinct from one another, ·i.e. that they are not
distinct things·, which is to say that corporeal substance,
insofar as it is a substance, cannot be divided