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25 September, 2015 - 10:32
  1. Substance is by nature prior to its modifications.
    Proof—This is clear from Definitions 3 and 5.
  2. Two substances, whose attributes are different, have nothing in common.
    Proof—Also evident from Definition 3. 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.
  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
    (Axiom 5), and, therefore, one cannot be the cause of the other (Axiom 4). Q.E.D.
  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 (Axiom 1)—that is (by Definitions 3 and 5), 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 Axiom 4), their attributes and modifications. Q.E.D.
  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 (Proposition 4). 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 (Proposition 1)—it follows that setting the modifications aside, and considering substance in itself, that is truly, (Definitions 3 and 6), there cannot be conceived one substance different from another—that is (by Proposition 4), there cannot be granted several substances, but one substance only. Q.E.D.
  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, i.e., which have anything common to them both (Proposition 2), and, therefore (Proposition 3), one cannot be the cause of the other, neither can one be produced by the other. Q.E.D.
         Corollary—Hence it follows that a substance cannot be produced by anything external to itself. For in the universe nothing is granted, save substances and their modifications (as appears from Axiom 1 and Definitions 3 and 5). Now (by the last Proposition) 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 (Axiom 4), and (by Definition 3) it would itself not be substance.

  7. Existence belongs to the nature of substances.
    Proof—Substance cannot be produced by anything external (Corollary, Proposition 6), it must, therefore, be its own cause—that is, its essence necessarily involves existence, or existence belongs to its nature.
  8. Every substance is necessarily infinite.
    Proof—There can only be one substance with an identical attribute, and existence follows from its nature (Proposition 7); its nature, therefore, involves existence, either as finite or infinite. It does not exist as finite, for (by Definition 2) it would then be limited by something else of the same kind, which would also necessarily exist (Proposition 7); and there would be two substances with an identical attribute, which is absurd (Proposition 5). It therefore exists as infinite. Q.E.D.
    Note 1—As finite existence involves a partial negation, and infinite existence is the absolute affirmation of the given nature, it follows (solely from Proposition 7) that every substance is necessarily infinite.
    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 Proposition 7: 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 Proposition 7 In fact, this proposition would be a universal axiom, and accounted a truism. For, by substance, would be understood that which is in itself, and is conceived through itself—that is, something of which the conception requires not the conception of anything else; whereas modifications exist in something external to themselves, and a conception of them is formed by means of a conception of the thing in which they exist.Therefore, we may have true ideas of non-existent modifications; for, although they may have no actual existence apart from the conceiving intellect, yet their essence is so involved in something external to themselves that they may through it be conceived. Whereas the only truth substances can have, external to the intellect, must consist in their existence, because they are conceived through themselves.
    Therefore, for a person to say that he has a clear and distinct—that is, a true—idea of a substance, but that he is not sure whether such substance exists, would be the same as if he said that he had a true idea, but was not sure whether or no it was false (a little consideration will make this plain); or if anyone affirmed that substance is created, it would be the same as saying that a false idea was true—in short, the height of absurdity. It must, then, necessarily be admitted that the existence of substance as its essence is an eternal truth. And we can hence conclude by another process of reasoning—that there is but one such substance. I think that this may profitably be done at once; and, in order to proceed regularly with the demonstration, we must premise:
    1. The true definition of a thing neither involves nor expresses anything beyond the nature of the thing defined. From this it follows that
    2. No definition implies or expresses a certain number of individuals, inasmuch as it expresses nothing beyond the nature of the thing defined. For instance, the definition of a triangle expresses nothing beyond the actual nature of a triangle: it does not imply any fixed number of triangles.
    3. There is necessarily for each individual existent thing a cause why it should exist.
    4. This cause of existence must either be contained in the nature and definition of the thing defined, or must be postulated apart from such definition.

It therefore follows that, if a given number of individual things exist in nature, there must be some cause for the existence of exactly that number, neither more nor less. For example, if twenty men exist in the universe (for simplicity’s sake, I will suppose them existing simultaneously, and to have had no predecessors), and we want to account for the existence of these twenty men, it will not be enough to show the cause of human existence in general; we must also show why there are exactly twenty men, neither more nor less: for a cause must be assigned for the existence of each individual. Now this cause cannot be contained in the actual nature of man, for the true definition of man does not involve any consideration of the number twenty. Consequently, the cause for the existence of these twenty men, and, consequently, of each of them, must necessarily be sought externally to each individual. Hence we may lay down the absolute rule, that everything which may consist of several individuals must have an external cause. And, as it has been shown already that existence appertains to the nature of substance, existence must necessarily be included in its definition; and from its definition alone existence must be deducible. But from its definition (as we have shown, notes 2 and 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.

  1. The more reality or being a thing has, the greater the number of its attributes (Definition 4).
  2. 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 (Definition4), and, therefore, must be conceived through itself (Definition 3). 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.

  3. 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 (Proposition 7) 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 Proposition 7.)
    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 Proposition 2), and therefore would be unable either to cause or to destroy his existence.
    As, then, a reason or cause which would annul the divine existence cannot be drawn from anything external to the divine nature, such cause must perforce, if God does not exist, be drawn from God’s own nature, which would involve a contradiction. To make such an affirmation about a being absolutely infinite and supremely perfect is absurd; therefore, neither in the nature of God, nor externally to his nature, can a cause or reason be assigned which would annul his existence. Therefore, God necessarily exists. Q.E.D.
    Another proof—The potentiality of non-existence is a negation of power, and contrariwise the potentiality of existence is a power, as is obvious. If, then, that which necessarily exists is nothing but finite beings, such finite beings are more powerful than a being absolutely infinite, which is obviously absurd; therefore, either nothing exists, or else a being absolutely infinite necessarily exists also. Now we exist either in ourselves, or in something else which necessarily exists (see Axiom 1 and Proposition 7). Therefore a being absolutely infinite— in other words, God (Definition 6)—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 Proposition 6) 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, theperfection 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 utmostcertainty on the question is given. This, I think, will be evident to every moderately attentive reader.

  4. 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 Proposition 8) each part will necessarily be infinite, and (by Proposition 6) self-caused, and (by Proposition 5) will perforce consist of a different attribute, so that, in that case, several substances could be formed out of one substance, which (by Proposition 6) is absurd. Moreover, the parts (by Proposition 2) would have nothing in common with their whole, and the whole (by Definition 4 and Proposition 10) 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 Proposition 7) is absurd.

  5. 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 Proposition 5) is absurd. If the latter, then (by Proposition 7) substance absolutely infinite could cease to exist, which (by Proposition 11) 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 Proposition 8) involves a manifest contradiction.

  6. 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 Definition 6), and he necessarily exists (by Proposition 11); 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 Proposition 5) 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 1—Clearly, therefore: God is one, that is (by Definition 6) only one substance can be granted in the universe, and that substance is absolutely infinite, as we have already indicated (in the note to Proposition 10).
    Corollary 2—It follows, second, that extension and thought are either attributes of God or (by Axiom 1) accidents (affectiones) of the attributes of God.

  7. 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 Proposition 14), that is (by Definition 3) nothing which is in itself and is conceived through itself. But modes (by Definition 5) 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 Axiom 1), therefore, without God nothing can be, or be conceived. Q.E.D.

Spinoza now faces an objection. Many will claim that God cannot be an extended thing, since extended things are divisible and Godis supposed to be a unity.

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 (Corollary to Proposition 6 and Note 2 of Proposition 8), that no substance can be produced or created by anything other than itself. Further, I showed (in Proposition 14), 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.

Spinoza discusses two versions of this objection; we’ll look at the second of these.

  • 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 own objections; for all their arguments are founded on the hypothesis that extended substance is composed of parts, and such a hypothesis I have shown (Proposition 12 and Corollary to Proposition 8) to be absurd. Moreover, anyone who reflects will see that all these absurdities (if absurdities they be, which I am not now discussing) … 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 Proposition 12).

Thus the weapon which they aimed at us has in reality recoiled upon themselves. …

Spinoza now argues that extended substance is not in fact divisible. We can see this argument as aimed especially at Descartes. Onsome readings, anyway, Descartes thinks that there are multiple extended substances. But this seems to be at odds with his denial ofthe vacuum, which follows from his identification of extension with space. See if you can reconstruct Spinoza’s argument. Supposethe contrary were true: suppose that extended substance were divisible. What would go wrong?

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, 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 … Assumption 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 Proposition 14) 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.

  1. What would Spinoza make of Descartes’s argument for the real distinction between mind and body? Is there some premise or assumption he would reject?
  2. Complete this sketch of Spinoza’s argument for monism by filling in the relevant propositions or axiom (e.g., P5 for Proposition 5). Note that this is only one way to reconstruct the argument.

Proposition 3: No substance can act on or create a substance with a different attribute.

Argument: Substances with different attributes ‘have nothing in common with each other’ and so cannot be understood through each other; but (by Axiom __) they cannot then be causally connected.

Proposition 5: No two substances can share an attribute.

For any given attribute, there is only one instance. If there are multiple substances, then, they must each have a different attribute.

Argument: If there were more than one instance of a given attribute, there would have to be an explanation for why there are exactly that number of beings sharing the attribute and no more (by Axiom 3, the Principle of Sufficient Reason).

Suppose there were 20 minds. There would have to be an explanation for why there are 20 and not 21 or 19 or 666.

Dilemma: does this explanation (a) come from the attribute itself, or (b) from outside the substance altogether?

Not (a), since it’s no part of the attribute of thought that there be 20 instances of it.

Not (b), by ____. So our supposition is false: there is only one mind, and only one instance for any given attribute.

Proposition 6: One substance cannot be created (or destroyed) by another.

Argument: suppose one substance creates another. They will either (a) share an attribute or (b) not. Not (a), by _____. Not (b), by ____.

Proposition 7: Each substance exists necessarily.

Proposition 8: Each substance is infinite.

Argument: suppose a given substance is finite. This means it is limited by something else (e.g., my hand is finite in space, since it has spatial boundaries, beyond which there are other objects.)

They will either (a) share an attribute or (b) not.
Not (a), by ____.

Not (b), since it does not make sense for a substance to be limited by something ___________________.

How could thought be limited by extension, or vice versa?

Proposition 9: The more attributes something has, the more reality it has.

Spinoza denies the Cartesian claim that distinct attributes entail distinct substances. He might mean ‘reality’ here in an almost quantitative sense: something that is both thought and extension is more real than a substance whose only attribute is thought.

Proposition 11: God (by definition a substance possessing infinite attributes) exists.

God is by definition a being who is absolutely infinite; he is not merely infinite after his kind (as the series of positive integers is, or as mental substance might be). He is infinite in every possible way, which means he is a single substance that contains all attributes. (There are an infinity of these, but we only know two, thought and extension.)

Argument: Suppose God didn’t exist. The explanation for this would have to come either from (a) within God or (b) outside him.

Not (a), because that would hold only if he were logically self-contradictory.

Not (b), by ____.

Proposition 14: Only God exists.

If there were a substance other than God, it would either (a) share an attribute or (b) not.

Not (a), by ____.

Not (b): if it doesn’t share an attribute, if it’s a different kind of thing, then God would not be absolutely infinite (i.e., possessing an infinity of attributes).

3. Objection: Spinoza’s God is material (among other things). But matter is divisible; to be divided is to be imperfect,subject to destruction.

Reply: Matter isn’t divisible, although it is presented to our imagination as if it were. This means that no substance is divisible; if it were, it would be divided into ____________________, which is impossible (given ____).

  1. 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 Definition 6), 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 1—Hence it follows, that God is the efficient cause of all that can fall within the sphere of an infinite intellect.
    Corollary 2—It also follows that God is a cause in himself, and not through an accident of his nature.
    Corollary 3—It follows, thirdly, that God is the absolutely first cause.
  2. God acts solely by the laws of his own nature, and is not constrained by anyone.
    Proof—We have just shown (in Proposition 16), 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 Proposition 15), that without God nothing can be nor be conceived but that all things are in God. Wherefore nothing can exist; outside himself, whereby he can be conditioned or constrained to act. Wherefore God acts solely by the laws of his own nature, and is not constrained by anyone. Q.E.D.
    Corollary 1—It follows, first, that there can be no cause which, either extrinsically or intrinsically, besides the perfection of his own nature, moves God to act.
    Corollary 2—It follows, second, that God is the sole free cause. For God alone exists by the sole necessity of his nature (by Proposition 11 and Corollary 1 of Proposition 14), and acts by the sole necessity of his own nature, wherefore God is (by Definition 7) the sole free cause. Q.E.D.

    Note—Others think that God is a free cause, because he can, as they think, bring it about, that those things which we have said follow from his nature—that is, which are in his power, should not come to pass, or should not be produced by him. But this is the same as if they said, that God could bring it about, that it should follow from the nature of a triangle that its three interior angles should not be equal to two right angles; or that from a given cause no effect should follow, which is absurd.
    Moreover, I will show below, without the aid of this proposition, that neither intellect nor will appertain to God’s nature. I know that there are many who think that they can show, that supreme intellect and free will do appertain to God’s nature; for they say they know of nothing more perfect, which they can attribute to God, than that which is the highest perfection in ourselves. Further, although they conceive God as actually supremely intelligent, they yet do not believe that he can bring into existence everything which he actually understands, for they think that they would thus destroy God’s power. If, they contend, God had created everything which is in his intellect, he would not be able to create anything more, and this, they think, would clash with God’s omnipotence; therefore, they prefer to asset that God is indifferent to all things, and that he creates nothing except that which he has decided, by some absolute exercise of will, to create. However, I think I have shown sufficiently clearly (by Proposition 16), that from God’s supreme power, or infinite nature, an infinite number of things—that is, all things have necessarily flowed forth in an infinite number of ways, or always flow from the same necessity; in the same way as from the nature of a triangle it follows from eternity and for eternity, that its three interior angles are equal to two right angles. Wherefore the omnipotence of God has been displayed from all eternity, and will for all eternity remain in the same state of activity. This manner of treating the question attributes to God an omnipotence, in my opinion, far more perfect. For, otherwise, we are compelled to confess that God understands an infinite number of creatable things, which he will never be able to create, for, if he created all that he understands, he would, according to this showing, exhaust his omnipotence, and render himself imperfect. Wherefore, in order to establish that God is perfect, we should be reduced to establishing at the same time, that he cannot bring to pass everything over which his power extends; this seems to be a hypothesis most absurd, and most repugnant to God’s omnipotence.
    Further (to say a word here concerning the intellect and the will which we attribute to God), if intellect and will appertain to the eternal essence of God, we must take these words in some significance quite different from those they usually bear. For intellect and will, which should constitute the essence of God, would perforce be as far apart as the poles from the human intellect and will, in fact, would have nothing in common with them but the name; there would be about as much correspondence between the two as there is between the Dog, the heavenly constellation, and a dog, an animal that barks. This I will prove as follows. If intellect belongs to the divine nature, it cannot be in nature, as ours is generally thought to be, posterior to, or simultaneous with the things understood, inasmuch as God is prior to all things by reason of his causality (Corollary 1 of Proposition 16). On the contrary, the truth and formal essence of things is as it is, because it exists by representation as such in the intellect of God. Wherefore the intellect of God, in so far as it is conceived to constitute God’s essence, is, in reality, the cause of things, both of their essence and of their existence. This seems to have been recognized by those who have asserted, that God’s intellect, God’s will, and God’s power, are one and the same. As, therefore, God’s intellect is the sole cause of things, namely, both of their essence and existence, it must necessarily differ from them in respect to its essence, and in respect to its existence. For a cause differs from a thing it causes, precisely in the quality which the latter gains from the former.
    For example, a man is the cause of another man’s existence, but not of his essence (for the latter is an eternal truth), and, therefore, the two men may be entirely similar in essence, but must be different in existence; and hence if the existence of one of them cease, the existence of the other will not necessarily cease also; but if the essence of one could be destroyed, and be made false, the essence of the other would be destroyed also. Wherefore, a thing which is the cause both of the essence and of the existence of a given effect, must differ from such effect both in respect to its essence, and also in respect to its existence. Now the intellect of God is the cause both of the essence and the existence of our intellect; therefore, the intellect of God in so far as it is conceived to constitute the divine essence, differs from our intellect both in respect to essence and in respect to existence, nor can it in anywise agree there with save in name, as we said before. The reasoning would be identical in the case of the will, as anyone can easily see.
  1. Will cannot be called a free cause, but only a necessary cause.

Proof—Will is only a particular mode of thinking, like intellect; therefore (by Proposition 28) no volition can exist, nor be conditioned to act, unless it be conditioned by some cause other than itself, which cause is conditioned by a third cause, and so on to infinity. But if will be supposed infinite, it must also be conditioned to exist and act by God, not by virtue of his being substance absolutely infinite, but by virtue of his possessing an attribute which expresses the infinite and eternal essence of thought (by Proposition 23). Thus, however it be conceived, whether as finite or infinite, it requires a cause by which it should be conditioned to exist and act. Thus (Definition 7) it cannot be called a free cause, but only a necessary or constrained cause. Q.E.D.

Corollary 1—Hence it follows, first, that God does not act according to freedom of the will.

Corollary 2—It follows, second, that will and intellect stand in the same relation to the nature of God as do motion, and rest, and absolutely all natural phenomena, which must be conditioned by God (Proposition 29) to exist and act in a particular manner. For will, like the rest, stands in need of a cause, by which it is conditioned to exist and act in a particular manner. And although, when will or intellect be granted, an infinite number of results may follow, yet God cannot on that account be said to act from freedom of the will, anymore than the infinite number of results from motion and rest would justify us in saying that motion and rest act by free will. Wherefore will no more appertains to God than does anything else in nature, but stands in the same relation to him as motion, rest, and the like, which we have shown to follow from the necessity of the divine nature, and to be conditioned by it to exist and act in a particular manner.

  1. Things could not have been brought into being by God in any manner or in any order different from that which has in fact obtained.

Proof—All things necessarily follow from the nature of God (Proposition 16), and by the nature of God are conditioned to exist and act in a particular way (Proposition 29). If things, therefore, could have been of a different nature, or have been conditioned to act in a different way, so that the order of nature would have been different, God’s nature would also have been able to be different from what it now is; and therefore (by Proposition 11) that different nature also would have perforce existed, and consequently there would have been able to be two or more Gods. This (by Corollary 1 of Proposition 14) is absurd. Therefore things could not have been brought into being by God in any other manner, &c. Q.E.D.

Note 1—As I have thus shown, more clearly than the sun at noonday, that there is nothing to justify us in calling things contingent, I wish to explain briefly what meaning we shall attach to the word contingent; but I will first explain the words necessary and impossible.

A thing is called necessary either in respect to its essence or in respect to its cause; for the existence of a thing necessarily follows, either from its essence and definition, or from a given efficient cause. For similar reasons a thing is said to be impossible; namely, inasmuch as its essence or definition involves a contradiction, or because no external cause is granted, which is conditioned to produce such an effect; but a thing can in no respect be called contingent, save in relation to the imperfection of our knowledge.

A thing of which we do not know whether the essence does or does not involve a contradiction, or of which, knowing that it does not involve a contradiction, we are still in doubt concerning the existence, because the order of causes escapes us—such a thing, I say, cannot appear to us either necessary or impossible.

Wherefore we call it contingent or possible.

Note 2—It clearly follows from what we have said, that things have been brought into being by God in the highest perfection, inasmuch as they have necessarily followed from a most perfect nature. Nor does this prove any imperfection in God, for it has compelled us to affirm his perfection. From its contrary proposition, we should clearly gather (as I have just shown), that God is not supremely perfect, for if things had been brought into being in any other way, we should have to assign to God a nature different from that, which we are bound to attribute to him from the consideration of an absolutely perfect being.

I do not doubt, that many will see this claim as absurd, and will refuse to give their minds up to contemplating it, simply because they are accustomed to assign to God a freedom very different from that which we (Definition 7) have deduced. They assign to him, in short, absolute free will. However, I am also convinced that if such persons reflect on the matter, and duly weigh in their minds our series of propositions, they will reject such freedom as they now attribute to God, not only as nugatory, but also as a great impediment to organized knowledge. There is no need for me to repeat what I have said in the note to Proposition 17). But, for the sake of my opponents, I will show further, that although it be granted that will pertains to the essence of God, it nevertheless follows from his perfection, that things could not have been by him created other than they are, or in a different order; this is easily proved, if we reflect on what our opponents themselves concede, namely, that it depends solely on the decree and will of God, that each thing is what it is. If it were otherwise, God would not be the cause of all things. Further, that all the decrees of God have been ratified from all eternity by God himself. If it were otherwise, God would be convicted of imperfection or change. But in eternity there is no such thing as when, before, or after; hence it follows solely from the perfection of God, that God never can decree, or never could have decreed anything but what is; that God did not exist before his decrees, and would not exist without them. But, it is said, supposing that God had made a different universe, or had ordained other decrees from all eternity concerning nature and her order, we could not therefore conclude any imperfection in God. But persons who say this must admit that God can change his decrees. For if God had ordained any decrees concerning nature and her order, different from those which he has ordained—in other words, if he had willed and conceived something different concerning nature—he would perforce have had a different intellect from that which he has, and also a different will. But if it were allowable to assign to God a different intellect and a different will, without any change in his essence or his perfection, what would there be to prevent him changing the decrees which he has made concerning created things, and nevertheless remaining perfect? For his intellect and will concerning things created and their order are the same, in respect to his essence and perfection, however they be conceived.

Further, all the philosophers whom I have read admit that God’s intellect is entirely actual, and not at all potential; as they also admit that God’s intellect, and God’s will, and God’s essence are identical, it follows that, if God had had a different actual intellect and a different will, his essence would also have been different; and thus, as I concluded at first, if things had been brought into being by God in a different way from that which has obtained, God’s intellect and will, that is (as is admitted) his essence would perforce have been different, which is absurd.

As these things could not have been brought into being by God in any but the actual way and order which has obtained; and as the truth of this proposition follows from the supreme perfection of God; we can have no sound reason for persuading ourselves to believe that God did not wish to create all the things which were in his intellect, and to create them in the same perfection as he had understood them.

But, it will be said, there is in things no perfection nor imperfection; that which is in them, and which causes them to be called perfect or imperfect, good or bad, depends solely on the will of God. If God had so willed, he might have brought it about that what is now perfection should be extreme imperfection, and vice versa. What is such an assertion, but an open declaration that God, who necessarily understands that which he wishes, might bring it about by his will, that he should understand things differently from the way in which he does understand them? This (as we have just shown) is the height of absurdity. Wherefore, I may turn the argument against its employers, as follows: All things depend on the power of God.

In order that things should be different from what they are, God’s will would necessarily have to be different. But God’s will cannot be different (as we have just most clearly demonstrated) from God’s perfection. Therefore neither can things be different. I confess, that the theory which subjects all things to the will of an indifferent deity, and asserts that they are all dependent on his fiat, is less far from the truth than the theory of those, who maintain that God acts in all things with a view of promoting what is good. For these latter persons seem to set up something beyond God, which does not depend on God, but which God in acting looks to as an exemplar, or which he aims at as a definite goal. This is only another name for subjecting God to the dominion of destiny, an utter absurdity in respect to God, whom we have shown to be the first and only free cause of the essence of all things and also of their existence. I need, therefore, spend no time in refuting such wild theories.

3. God’s power is identical with his essence.

Proof—From the sole necessity of the essence of God it follows that God is the cause of himself (Proposition 11) and of all things (Proposition 16 and the Corollary). Wherefore the power of God, by which he and all things are and act, is identical with his essence. Q.E.D.

4. Whatsoever we conceive to be in the power of God, necessarily exists.

Proof—Whatsoever is in God’s power, must (by the last Proposition) be comprehended in his essence in such a manner, that it necessarily follows therefrom, and therefore necessarily exists. Q.E.D.

5. There is no cause from whose nature some effect does not follow.

Proof—Whatsoever exists expresses God’s nature or essence in a given conditioned manner (by the Corollary to Proposition 25); that is, (by Proposition 34.), whatsoever exists, expresses in a given conditioned manner God’s power, which is the cause of all things, therefore an effect must (by Proposition 16) necessarily follow.Q.E.D.