The Ethics, Benedictus de Spinoza [best reads txt] 📗

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