|E1: PROP. 1. Substance is by nature prior to its modifications.|
|Proof.-- This is clear from E1D3 and E1D5.|
|Referenced in: E1P5|
|E1: PROP. 2. Two substances, whose attributes are different, have nothing in common.|
|Proof.--Also evident from E1D3. 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.|
|Referenced in: E1P6,- E1P11,- E1P12|
|E1: PROP. 3. 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 (E1A5), and, therefore, one cannot be the cause of the other (E1A4). Q.E.D.|
|Referenced in: E1P6|
|E1: PROP. 4. 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 (E1A1),--that is (by E1D3 and E1D5), 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 E1D4), their attributes and modifications. Q.E.D.|
|Referenced in: E1P5|
|E1: PROP. 5. 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 (E1P4). 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 (E1P1),--it follows that setting the modifications aside, and considering substance in itself, that is truly, (E1D3 and E1A6), there cannot be conceived one substance different from another,--that is (by E1P4), there cannot be granted several substances, but one substance only. Q.E.D.|
|Referenced in: E1P6,- E1P8,- E1P12,- E1P13,- E1P14,- E1P15N,- E2P10N,- E2P13L1|
|E1: PROP. 6. 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 [E1P5], i.e. which have anything common to them both (E1P2), and, therefore (E1P3), one cannot be the cause of another, neither can one be produced by the other. Q.E.D.|
|Referenced in: E1P6C,- E1P11N,- E1P12|
|E1: PROP. 6, Corollary.--Hence it follows that a substance cannot be produced by anything external to itself.|
|Proof.-- For in the universe nothing is granted, save substances and their modifications (as appears from E1A1 and E1D3 and E1D5). Now (by E1P6) substance cannot be produced by another substance, therefore it cannot be produced by anything external to itself. Q.E.D. This is shown still more readily by the absurdity of the contradictory. For, if substance be produced by an external cause, the knowledge of it would depend on the knowledge of its cause (E1A4), and (by E1D3) it would itself not be substance.|
|Referenced in: E1P7,- E1P15N|
|E1: PROP. 7. Existence belongs to the nature of substance.|
|Proof.-- Substance cannot be produced by anything external (E1P6C), it must, therefore, be its own cause--that is [E1D1], its essence necessarily involves existence, or existence belongs to its nature.|
|Referenced in: E1P8,- E1P8N1,- E1P8N2,- E1P11,- E1P12,- E1P13,- E1P19,- E2P10|
|E1: PROP. 8. Every substance is necessarily infinite.|
|Proof.--There can only be one substance with an identical attribute [E1P5], and existence follows from its nature (E1P7); its nature, therefore, involves existence, either as finite or infinite. It does not exist as finite, for (by E1D2) it would then be limited by something else of the same kind, which would also necessarily exist (E1P7); and there would be two substances with an identical attribute, which is absurd (E1P5). It therefore exists as infinite. Q.E.D.|
|Referenced in: E1P12,- E1P13CN,- E1P15N,- E2P13L1,- Let15-P04|
|E1: PROP. 8, Note 1.--As finite existence involves a partial negation, and infinite existence is the absolute affirmation of the given nature, it follows (solely from E1P7) that every substance is necessarily infinite.|
PROP. 8, Note 2.--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 E1P7: 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 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 E1P7. In fact, this proposition would be a universal axiom, and accounted a truism. For, by substance, would be understood that which is in itself, and is conceived through itself--that is, something of which the conception requires not the conception of anything else; whereas modifications exist in something external to themselves, and a conception of them is formed by means of a conception of the thing in which they exist.
Therefore, we may have true ideas of non-existent modifications; for, although they may have no actual existence apart from the conceiving intellect, yet their essence is so involved in something external to themselves that they may through it be conceived. Whereas the only truth substances can have, external to the intellect, must consist in their existence, because they are conceived through themselves.
Therefore, for a person to say that he has a clear and distinct --that is, a true--idea of a substance, but that he is not sure whether such substance exists, would be the same as if he said that he had a true idea, but was not sure whether or not 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 2., 3.), we cannot infer the existence of several substances; therefore it follows that there is only one substance of the same nature. Q.E.D.
|Referenced in: E1P15N|
|E1: PROP. 10. 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 (E1D4) and, therefore, must be conceived through itself (E1D3). Q.E.D.|
|Referenced in: E1P12,- E2P5,- E2P6,- Let66-P02,- Let68-P01|
PROP. 10, 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
it is the nature of substance that each of its
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
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 [E1D6] 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 for in vain.
|Referenced in: E1P14C1,- Let66-P04|
|E1: PROP. 11. 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 [E1A7] his essence does not involve existence. But this (by E1P7) is absurd. Therefore God necessarily exists.|
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
follows also solely from its
nature, inasmuch as its nature involves
existence. (See E1P7)
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 E1P2), 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 E1A1 and E1P7). Therefore a being absolutely infinite --in other words, God (E1D6) --necessarily exists. Q.E.D.|
|Referenced in: E1P13,- E1P14,- E1P17C2,- E1P19,- E1P19N,- E1P21,- E1P29,- E1P33,- E1P34,- E5P35|
PROP. 11, 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,
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 E1P6) cannot be produced by any external cause.
Things which are produced by external causes, whether they consist of many parts or few, owe whatsoever perfection or reality they possess solely to the efficacy of their external cause, and therefore their existence arises solely from the perfection of their external cause, not from their own. Contrariwise, whatsoever perfection is possessed by substance is due to no external cause; wherefore the existence of substance must arise solely from its own nature, which is nothing else but its essence.
Thus, the perfection of a thing does not annul its existence, but, on the contrary, asserts it. Imperfection, on the other hand, does annul it; therefore we cannot be more certain of the existence of anything, than of the existence of a being absolutely infinite or perfect --that is, of God. For inasmuch as his essence excludes all imperfection, and involves absolute perfection, all cause for doubt concerning his existence is done away, and the utmost certainty on the question is given. This, I think, will be evident to every moderately attentive reader.