Ethics

Definition 1. By cause of itself I understand that whose essence involves existence, or that whose nature cannot be conceived except as existing.

Definition 2. A thing is said to be finite in its own kind when it can be limited by another thing of the same nature. For example, a body is called finite because we always conceive another that is greater. In the same way, a thought is limited by another thought. But a body is not limited by a thought, nor a thought by a body.

Definition 3. By substance I understand that which is in itself and is conceived through itself: that is, that whose concept does not require the concept of another thing from which it must be formed.

Definition 4. By attribute I understand that which the intellect perceives of a substance as constituting its essence.

Definition 5. By mode I understand the affections of a substance, or that which is in another, through which it is also conceived.note

Definition 6. By God I understand a being absolutely infinite, that is, a substance consisting of infinite attributes, each of which expresses an eternal and infinite essence.

Explanation. I say absolutely infinite, not infinite in its own kind. For of whatever is infinite only in its own kind, we can deny infinite attributes; but to the essence of what is absolutely infinite belongs whatever expresses essence and involves no negation.

Definition 7. That thing will be called free which exists from the necessity of its own nature alone and is determined to act by itself alone. That thing, on the other hand, will be called necessary, or rather compelled, which is determined by another to exist and to produce effects in a fixed and determinate way.

Definition 8. By eternity I understand existence itself, insofar as it is conceived to follow necessarily from the definition alone of an eternal thing.

Explanation. For such existence is conceived as an eternal truth, like the essence of the thing, and therefore cannot be explained by duration or time, even if duration is conceived as lacking a beginning and an end.

Axiom 1. Everything that is, is either in itself or in another.

Axiom 2. What cannot be conceived through another must be conceived through itself.

Axiom 3. From a given determinate cause an effect necessarily follows; and conversely, if no determinate cause is given, it is impossible for an effect to follow.

Axiom 4. Knowledge of an effect depends on knowledge of its cause, and involves it.

Axiom 5. Things that have nothing in common with each other also cannot be understood through each other; that is, the concept of the one does not involve the concept of the other.

Axiom 6. A true idea must agree with its object.note

Axiom 7. If a thing can be conceived as not existing, its essence does not involve existence.

Proposition 1. Substance is by nature prior to its affections.

Demonstration. This is evident from Definitions 3 and 5.

Proposition 2. Two substances having different attributes have nothing in common with each other.

Demonstration. This too is evident from Definition 3. For each must be in itself and must be conceived through itself; that is, the concept of the one does not involve the concept of the other.

Proposition 3. When things have nothing in common with each other, one of them cannot be the cause of the other.

Demonstration. If they have nothing in common with each other, then (by Axiom 5) they cannot be understood through each other either; and so (by Axiom 4) one cannot be the cause of the other. QED

Proposition 4. Two or more distinct things are distinguished from one another either by a difference in the attributes of the substances or by a difference in their affections.

Demonstration. Everything that is, is either in itself or in another (by Axiom 1); that is (by Definitions 3 and 5), outside the intellect there is nothing except substances and their affections. There is nothing, then, outside the intellect through which several things can be distinguished from one another except substances—or, what is the same thing (by Definition 4), their attributes—and their affections. QED

Proposition 5. In the nature of things there cannot be two or more substances of the same nature or attribute.

Demonstration. If there were several distinct substances, they would have to be distinguished from one another either by a difference of attributes or by a difference of affections (by the preceding proposition). If only by a difference of attributes, then it will be granted that there is only one of the same attribute. But if by a difference of affections, then, since a substance is by nature prior to its affections (by Proposition 1), let the affections be set aside and the substance be considered in itself—that is (by Definition 3 and Axiom 6), considered truly—and it cannot be conceived as distinguished from another. That is (by the preceding proposition), there cannot be several substances, but only one. QED

Proposition 6. One substance cannot be produced by another substance.

Demonstration. In the nature of things there cannot be two substances of the same attribute (by the preceding proposition), that is (by Proposition 2), two substances that have something in common with each other. And so (by Proposition 3) one cannot be the cause of the other; that is, one cannot be produced by the other. QED

Corollary. From this it follows that a substance cannot be produced by anything else. For in the nature of things there is nothing except substances and their affections, as is evident from Axiom 1 and Definitions 3 and 5. But it cannot be produced by a substance (by the preceding proposition). Therefore a substance cannot be produced by anything else at all. QED

Alternatively. This is demonstrated even more easily from the absurdity of the contradictory. For if a substance could be produced by something else, knowledge of it would have to depend on knowledge of its cause (by Axiom 4); and so (by Definition 3) it would not be a substance.

Proposition 7. It pertains to the nature of substance to exist.

Demonstration. A substance cannot be produced by anything else (by the Corollary to the preceding proposition); it will therefore be the cause of itself; that is (by Definition 1), its essence necessarily involves existence, or it pertains to its nature to exist. QED

Proposition 8. Every substance is necessarily infinite.

Demonstration. A substance of one attribute exists only as a single, unique substance (by Proposition 5), and it pertains to its nature to exist (by Proposition 7). It will therefore be of its nature to exist either as finite or as infinite. But not as finite. For then (by Definition 2) it would have to be limited by another substance of the same nature, which would also have to exist necessarily (by Proposition 7); and so there would be two substances of the same attribute, which is absurd (by Proposition 5). It exists, therefore, as infinite. QED

Scholium 1. Since being finite is in truth partly a negation, and being infinite is the absolute affirmation of the existence of some nature, it follows from Proposition 7 alone that every substance must be infinite.

Scholium 2. I do not doubt that all who judge things confusedly, and are not accustomed to know things through their first causes, find it difficult to grasp the demonstration of Proposition 7. This is, of course, because they do not distinguish between the modifications of substances and substances themselves, nor do they know how things are produced. So it happens that they ascribe to substances the beginning they see natural things have. For those who do not know the true causes of things confuse everything. Without any resistance of mind they picture trees speaking just as readily as people, and imagine that people are formed from stones as readily as from seed, and that any forms whatever change into any others. So too those who confuse the divine nature with human nature easily attribute human affects to God, especially as long as they are also ignorant of how affects are produced in the mind. But if people paid attention to the nature of substance, they would not doubt the truth of Proposition 7 in the least. Indeed, this propositionnote

Proposition 9. The more reality or being each thing has, the more attributes belong to it.

Demonstration. This is evident from Definition 4.

Proposition 10. Each attribute of a single substance must be conceived through itself.

Demonstration. For an attribute is that which the intellect perceives of a substance as constituting its essence (by Definition 4); and so (by Definition 3) it must be conceived through itself. QED

Scholium. From this it is clear that although two attributes may be conceived as really distinct—that is, one without the help of the other—we still cannot conclude from this that they constitute two beings, or two different substances. For it is of the nature of substance that each of its attributes is conceived through itself, since all the attributes it has have always been in it together, and one could not be produced by another; rather, each expresses the reality or being of substance.

Demonstration. If you deny this, conceive, if you can, that God does not exist. Then (by Axiom 7) his essence does not involve existence. But this (by Proposition 7) is absurd. Therefore God necessarily exists. QED

Alternatively. For each thing a cause or reason must be assigned, both for why it exists and for why it does not exist. For example, if a triangle exists, there must be a reason or cause why it exists; and if it does not exist, there must also be a reason or cause that prevents it from existing, or that takes its existence away. This reason or cause must be contained either in the nature of the thing or outside it. For example, the very nature of a square circle shows the reason why it does not exist: namely, that it involves a contradiction. Why a substance, by contrast, does exist likewise follows from its nature alone, since that nature involves existence (see Proposition 7).

Alternatively. To be able not to exist is lack of power; and conversely, to be able to exist is power (as is self-evident). So if what now necessarily exists is nothing but finite beings, then finite beings are more powerful than a being absolutely infinite; and this (as is self-evident) is absurd. Therefore either nothing exists, or a being absolutely infinite also necessarily exists. But we exist, either in ourselves or in something else that necessarily exists (see Axiom 1 and Proposition 7). Therefore a being absolutely infinite—that is (by Definition 6), God—necessarily exists. QED

Scholium. In this last demonstration I chose to show God’s existence a posteriori, so that the demonstration would be grasped more easily—not because God’s existence does not follow a priori from this same foundation. For since being able to exist is power, it follows that the more reality belongs to the nature of a thing, the more strength it has of itself to exist; and so a being absolutely infinite, or God, has of itself an absolutely infinite power of existing, and for that reason exists absolutely. Yet perhaps many will not easily be able to see the force of this demonstration, because they are used to contemplating only things that come about from external causes. Among these, they see that things which come about quickly—that is, which exist easily—also perish easily; and conversely they judge that things are harder to bring about—that is, less easy to bring into existence—the more they conceive to belong to them.note

Proposition 12. No attribute of substance can be truly conceived from which it would follow that substance can be divided.

Demonstration. For the parts into which a substance so conceived would be divided will either retain the nature of substance or not. If the first, then (by Proposition 8) each part will have to be infinite and (by Proposition 6) the cause of itself, and (by Proposition 5) will have to consist of a different attribute; and so several substances could be formed from one, which (by Proposition 6) is absurd. Besides, the parts (by Proposition 2) would have nothing in common with their whole, and the whole (by Definition 4 and Proposition 10) could both be and be conceived without its parts, which no one can doubt is absurd. But if the second is supposed—namely, that the parts will not retain the nature of substance—then, when the whole substance had been divided into equal parts, it would lose the nature of substance and cease to be, which (by Proposition 7) is absurd.

Proposition 13. A substance absolutely infinite is indivisible.

Demonstration. For if it were divisible, the parts into which it would be divided will either retain the nature of a substance absolutely infinite or not. If the first, there will be several substances of the same nature, which (by Proposition 5) is absurd. If the second is supposed, then (as above) a substance absolutely infinite could cease to be, which (by Proposition 11) is also absurd.

Corollary. From these it follows that no substance—and consequently no corporeal substance, insofar as it is substance—is divisible.

Scholium. That substance is indivisible is understood more simply from this alone: that the nature of substance cannot be conceived except as infinite, and that by a part of substance nothing can be understood except a finite substance, which (by Proposition 8) implies an obvious contradiction.

Proposition 14. Except God, no substance can be or be conceived.

Demonstration. 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). So if there were any substance besides God, it would have to be explained through some attribute of God, and thus two substances of the same attribute would exist, which (by Proposition 5) is absurd. And so no substance outside God can be, and consequently none can be conceived either. For if it could be conceived, it would necessarily have to be conceived as existing; but this (by the first part of this demonstration) is absurd. Therefore outside God no substance can be or be conceived. QED

Corollary 1. From this it follows very clearly, first, that God is unique: that is (by Definition 6), in the nature of things there is only one substance, and it is absolutely infinite, as we already hinted in the Scholium to Proposition 10.

Corollary 2. It follows, second, that the extended thing and the thinking thing are either attributes of God or (by Axiom 1) affections of God’s attributes.note

Demonstration. Except God, no substance is or can be conceived (by Proposition 14), that is (by Definition 3), no thing that is in itself and is conceived through itself. But modes (by Definition 5) can neither be nor be conceived without substance; so they can be in the divine nature alone, and can be conceived through it alone. But there is nothing except substances and modes (by Axiom 1). Therefore nothing can be or be conceived without God. QED

Scholium. There are those who imagine that God, like a human being, consists of a body and a mind and is subject to passions. But how far such people stray from the true knowledge of God is clear enough from what has already been demonstrated. I leave them aside, however; for all who have in any way contemplated the divine nature deny that God is corporeal. They prove this very well, too, from the fact that by body we understand any quantity having length, breadth and depth, bounded by some definite shape—and nothing more absurd than this could be said of God, that is, of a being absolutely infinite. Yet at the same time, by the other arguments with which they try to demonstrate this same point, they clearly show that they remove corporeal or extended substance itself entirely from the divine nature, and they hold that it was created by God. But by what divine power it could have been created they have no idea at all—which clearly shows that they do not understand what they themselves are saying.

Proposition 16. From the necessity of the divine nature there must follow infinitely many things in infinitely many ways (that is, everything that can fall under an infinite intellect).

Demonstration. This proposition should be plain to everyone, provided he attends to the fact that from the given definition of any thing the intellect infers several properties that really do follow necessarily from it (that is, from the very essence of the thing); and it infers more properties the more reality the definition of the thing expresses, that is, the more reality the essence of the thing defined involves. But since the divine nature has absolutely infinite attributes (by Definition 6), each of which also expresses an essence infinite in its own kind, from its necessity, therefore, there must necessarily follow infinitely many things in infinitely many ways (that is, everything that can fall under an infinite intellect). QED

Corollary 1. From this it follows, first, that God is the efficient cause of all things that can fall under an infinite intellect.

Corollary 2. It follows, secondly, that God is a cause through himself, and not by accident.

Corollary 3. It follows, thirdly, that God is absolutely the first cause.

Proposition 17. God acts from the laws of his own nature alone, and is compelled by no one.

Demonstration. We have just shown, in Proposition 16, that from the necessity of the divine nature alone—or (what is the same thing) from the laws of that nature alone—infinitely many things absolutely follow. And in Proposition 15 we demonstrated that nothing can be or be conceived without God, but that all things are in God. Therefore there can be nothing outside him by which he is determined or compelled to act. And so God acts from the laws of his own nature alone, and is compelled by no one. QED

Corollary 1. From this it follows, first, that there is no cause, either from without or from within, that moves God to act, except the perfection of his own nature.

Corollary 2. It follows, secondly, that God alone is a free cause. For God alone exists from the necessity of his own nature alone (by Proposition 11 and Corollary 1 of Proposition 14), and acts from the necessity of his own nature alone (by the preceding proposition). Therefore (by Definition 7) he alone is a free cause. QED

Scholium. Others think that God is a free cause because—so they think—he can bring it about that the things we have said follow from his nature (that is, the things that are in his power) should not happen, or should not be produced by him. But this is the same as saying that God can bring it about that it should not follow from the nature of a triangle that its three angles are equal to two right angles; or that from a given cause the effect should not follow—which is absurd. Further on I shall show, without the help of this proposition, that neither intellect nor will belongs to God’s nature. I know, of course, that there are many who think they can demonstrate that the highest intellect and a free will belong to God’s nature. For they say they know nothing more perfect that they could attribute to God than what is the highest perfection in us.

Proposition 18. God is the immanent, not the transitive, cause of all things.note

Demonstration. All things that are, are in God and must be conceived through God (by Proposition 15); and so (by Corollary 1 of Proposition 16 of this part) God is the cause of the things that are in him. That is the first point. Next, outside God there can be no substance (by Proposition 14), that is (by Definition 3), no thing that is in itself outside God. That was the second point. God, therefore, is the immanent, not the transitive, cause of all things. QED

Proposition 19. God, or all the attributes of God, are eternal.

Demonstration. For God (by Definition 6) is substance, which (by Proposition 11) necessarily exists; that is (by Proposition 7), a substance to whose nature it belongs to exist, or (what is the same thing) from whose definition it follows that it exists; and so (by Definition 8) he is eternal. Next, by the attributes of God we must understand that which (by Definition 4) expresses the essence of the divine substance, that is, that which belongs to substance: that very thing, I say, the attributes themselves must involve. But eternity belongs to the nature of substance (as I have already demonstrated from Proposition 7). Therefore each of the attributes must involve eternity, and so all are eternal. QED

Scholium. This Proposition is also perfectly clear from the way in which I demonstrated God’s existence (Proposition 11). From that demonstration, I say, it is established that God’s existence, like his essence, is an eternal truth. I have also demonstrated God’s eternity in another way (Proposition 19 of my Principles of Descartes’s Philosophy), and there is no need to repeat that here.note

Proposition 20. God’s existence and his essence are one and the same.

Demonstration. God and all his attributes are eternal (by the preceding proposition); that is (by Definition 8), each of his attributes expresses existence. Therefore the same attributes of God that (by Definition 4) explain God’s eternal essence at the same time explain his eternal existence. That is, the very thing that constitutes God’s essence at the same time constitutes his existence; and so his existence and his essence are one and the same. QED

Corollary 1. From this it follows, first, that God’s existence, like his essence, is an eternal truth.

Corollary 2. It follows, secondly, that God, or all of God’s attributes, are unchangeable. For if they changed with respect to existence, they would also (by the preceding proposition) have to change with respect to essence; that is (as is self-evident), from true they would become false—which is absurd.

Proposition 21. All things that follow from the absolute nature of any attribute of God must always have existed and be infinite; in other words, through that same attribute they are eternal and infinite.

Demonstration. Conceive, if you can (supposing you deny this), that in some attribute of God something follows from its absolute nature that is finite and has a determinate existence or duration—for example, the idea of God in thought. Now thought, since it is supposed to be an attribute of God, is necessarily (by Proposition 11) infinite by its nature. But insofar as it has the idea of God, it is supposed finite. Yet (by Definition 2) it cannot be conceived as finite unless it is limited by thought itself. But not by thought itself insofar as it constitutes the idea of God, for to that extent it is supposed to be finite. Therefore by thought insofar as it does not constitute the idea of God—thought which nevertheless (by Proposition 11) must necessarily exist. There is, then, thought that does not constitute the idea of God, and so the idea of God does not necessarily follow from its nature insofar as it is absolute thought.

Next, what follows in this way from the necessity of the nature of some attribute cannot have a determinate existence or duration. For if you deny this, suppose that a thing following from the necessity of the nature of some attribute is given in some attribute of God—for example, the idea of God in thought—and suppose that at some time it did not exist, or will not exist. Now since thought is supposed to be an attribute of God, it must exist both necessarily and unchangeably (by Proposition 11 and Corollary 2 of Proposition 20). So beyond the limits of the duration of the idea of God (for it is supposed at some time not to have existed, or not to be going to exist), thought will have to exist without the idea of God. But this is contrary to the hypothesis, for it is supposed that the idea of God necessarily follows from the given thought.

Proposition 22. Whatever follows from some attribute of God insofar as it is modified by a modification that, through that attribute, exists both necessarily and as infinite, must also exist both necessarily and as infinite.

Demonstration. The demonstration of this proposition proceeds in the same way as the demonstration of the preceding one.

Proposition 23. Every mode that exists both necessarily and as infinite must necessarily have followed either from the absolute nature of some attribute of God, or from some attribute modified by a modification that exists both necessarily and as infinite.

Demonstration. For a mode is in another, through which it must be conceived (by Definition 5); that is (by Proposition 15), it is in God alone, and can be conceived through God alone. If, then, a mode is conceived to exist necessarily and to be infinite, each of these must necessarily be inferred or perceived through some attribute of God, insofar as that attribute is conceived to express infinity and necessity of existence, or (what by Definition 8 is the same thing) eternity; that is (by Definition 6 and Proposition 19), insofar as it is considered absolutely. A mode, therefore, that exists both necessarily and as infinite must have followed from the absolute nature of some attribute of God—either immediately (on which see Proposition 21), or through the mediation of some modification that follows from its absolute nature, that is (by the preceding proposition), that exists both necessarily and as infinite. QED

Proposition 24. The essence of things produced by God does not involve existence.

Demonstration. This is evident from Definition 1. For that whose nature (considered in itself, that is) involves existence is cause of itself, and exists from the necessity of its own nature alone.

Corollary. From this it follows that God is the cause not only of things’ beginning to exist, but also of their persevering in existence—or (to use a Scholastic term) that God is the cause of the being of things, their causa essendi. For whether things exist or do not exist, whenever we attend to their essence we find that it involves neither existence nor duration. So their essence cannot be the cause either of their existence or of their duration; only God can, to whose nature alone it belongs to exist (by Corollary 1 of Proposition 14).

Proposition 25. God is the efficient cause not only of the existence of things, but also of their essence.

Demonstration. If you deny this, then God is not the cause of the essence of things; and so (by Axiom 4) the essence of things can be conceived without God. But this (by Proposition 15) is absurd. Therefore God is the cause of the essence of things too. QED

Scholium. This Proposition follows more clearly from Proposition 16. For it follows from that proposition that, given the divine nature, both the essence and the existence of things must necessarily be inferred. In a word, in the same sense in which God is called cause of himself, he must also be called the cause of all things. This will become still clearer from the following corollary.

Corollary. Particular things are nothing but affections of God’s attributes, or modes by which God’s attributes are expressed in a certain and determinate way. The demonstration is evident from Proposition 15 and Definition 5.

Proposition 26. A thing that has been determined to do something was necessarily so determined by God; and a thing that has not been determined by God cannot determine itself to do anything.

Demonstration. That through which things are said to be determined to do something is necessarily something positive (as is self-evident). And so God, from the necessity of his nature, is the efficient cause both of its essence and of its existence (by Propositions 25 and 16). That was the first point. The second claim also follows very clearly from this. For if a thing not determined by God could determine itself, the first part of this proposition would be false—which is absurd, as we have shown.

Proposition 27. A thing that has been determined by God to do something cannot render itself undetermined.

Demonstration. This Proposition is evident from Axiom 3.

Proposition 28. No singular thing—no thing, that is, which is finite and has a determinate existence—can exist or be determined to act unless it is determined to exist and to act by another cause, which is also finite and has a determinate existence; and again, this cause too cannot exist or be determined to act unless it is determined to exist and to act by another, which is also finite and has a determinate existence; and so on to infinity.

Demonstration. Whatever is determined to exist and to act has been so determined by God (by Proposition 26 and the Corollary to Proposition 24). But what is finite and has a determinate existence could not have been produced by the absolute nature of any attribute of God; for whatever follows from the absolute nature of any attribute of God is infinite and eternal (by Proposition 21). It must, therefore, have followed from God, or from some attribute of his, insofar as that is considered to be affected by some mode. For apart from substance and modes nothing is given (by Axiom 1 and Definitions 3 and 5), and modes (by the Corollary to Proposition 25) are nothing but affections of God’s attributes. But neither could it have followed from God, or from some attribute of his, insofar as that is affected by a modification that is eternal and infinite (by Proposition 22).

Scholium. Some things had to be produced by God immediately—namely, those that follow necessarily from his absolute nature—and others through the mediation of these first ones, though the others can neither be nor be conceived without God. From this it follows, first, that God is absolutely the proximate cause of the things immediately produced by him, and not merely proximate “in his own kind,” as they say. For God’s effects can neither be nor be conceived without their cause (by Proposition 15 and the Corollary to Proposition 24). It follows, secondly, that God cannot properly be called the remote cause of singular things—except perhaps in order to distinguish these from the things he has produced immediately, or rather from those that follow from his absolute nature. For by a remote cause we understand one that is in no way conjoined with its effect.

Proposition 29. In nature there is nothing contingent; all things have been determined from the necessity of the divine nature to exist and to act in a certain way.

Demonstration. Whatever is, is in God (by Proposition 15). But God cannot be called a contingent thing, for (by Proposition 11) he exists necessarily, not contingently. Next, the modes of the divine nature have also followed from it necessarily, not contingently (by Proposition 16)—either insofar as the divine nature is considered absolutely (by Proposition 21), or insofar as it is considered as determined to act in a certain way (by Proposition 27). Further, God is the cause of these modes not only insofar as they simply exist (by the Corollary to Proposition 24), but also (by Proposition 26) insofar as they are considered as determined to do something. If they have not been determined by God (by the same

Scholium. Before going further, I want to explain here—or rather to point out—what we must understand by Natura naturans and what by Natura naturata. For I think it is already established from what precedes that by Natura naturans we must understand what is in itself and is conceived through itself, or those attributes of substance that express eternal and infinite essence; that is (by Corollary 1 of Proposition 14 and Corollary 2 of Proposition 17), God insofar as he is considered as a free cause. By Natura naturata, on the other hand, I understand everything that follows from the necessity of God’s nature, or of each of God’s attributes; that is, all the modes of God’s attributes, insofar as they are considered as things that are in God and can neither be nor be conceived without God.note

Proposition 30. An intellect, whether actually finite or actually infinite, must comprehend God’s attributes and God’s affections, and nothing else.

Demonstration. A true idea must agree with its object (by Axiom 6); that is (as is self-evident), what is contained objectively in the intellect must necessarily be given in Nature. But in Nature (by Corollary 1 of Proposition 14) there is only one substance, namely God; and there are no affections (by Proposition 15) other than those that are in God and that (by the same Proposition) can neither be nor be conceived without God. Therefore an intellect, whether actually finite or actually infinite, must comprehend God’s attributes and God’s affections, and nothing else. QED

Proposition 31. Actual intellect, whether finite or infinite, like will, desire, love, etc., must be referred to Natura naturata, not to Natura naturans.

Demonstration. By intellect (as is self-evident) we do not understand absolute thought, but only a certain mode of thinking, which differs from other modes, such as desire, love, etc.; and so (by Definition 5) it must be conceived through absolute thought. That is (by Proposition 15 and Definition 6), it must be conceived through some attribute of God that expresses the eternal and infinite essence of thought, in such a way that without that attribute it can neither be nor be conceived. And therefore (by the Scholium to Proposition 29) it must be referred to Natura naturata, not to Natura naturans, as must the other modes of thinking. QED

Scholium. The reason I speak here of actual intellect is not that I grant there is any potential intellect. Rather, because I want to avoid all confusion, I have chosen to speak only of what we perceive most clearly—namely, the very act of understanding, than which we perceive nothing more clearly. For we can understand nothing that does not lead to a more perfect knowledge of understanding.

Proposition 32. The will cannot be called a free cause, but only a necessary one.

Demonstration. The will is only a certain mode of thinking, like the intellect. And so (by Proposition 28) each volition can neither exist nor be determined to act unless it is determined by another cause, and this in turn by another, and so on to infinity. And if the will is supposed to be infinite, it too must be determined to exist and to act by God—not insofar as he is absolutely infinite substance, but insofar as he has an attribute that expresses the infinite and eternal essence of thought (by Proposition 23). In whatever way the will is conceived, then, whether as finite or as infinite, it requires a cause by which it is determined to exist and to act; and so (by Definition 7) it cannot be called a free cause, but only a necessary or compelled one. QED

Corollary 1. From this it follows, first, that God does not act from freedom of the will.

Corollary 2. It follows, secondly, that will and intellect are related to God’s nature as motion and rest are, and, absolutely, as are all natural things, which (by Proposition 29) must be determined by God to exist and to act in a certain way. For the will, like everything else, needs a cause by which it is determined to exist and to act in a certain way. And although infinitely many things follow from a given will or intellect, God cannot on that account be said to act from freedom of the will, any more than he can be said to act from freedom of motion and rest because of what follows from motion and rest (for infinitely many things follow from these too).

Proposition 33. Things could not have been produced by God in any other way or in any other order than they have been produced.

Demonstration. For all things have followed necessarily from God’s given nature (by Proposition 16), and have been determined from the necessity of God’s nature to exist and to act in a certain way (by Proposition 29). So if things could have been of another nature, or could have been determined to act in another way, so that the order of nature would be different, then God’s nature too could be other than it now is; and hence (by Proposition 11) that other nature would also have to exist, and consequently there could be two or more Gods—which (by Corollary 1 of Proposition 14) is absurd. Therefore things could not have been produced in any other way or in any other order, etc. QED

Scholium 1. Since I have shown here, more clearly than the noonday sun, that there is absolutely nothing in things on account of which they could be called contingent, I now want to explain briefly what we should understand by contingent—but first, what we should understand by necessary and impossible. A thing is called necessary either by reason of its essence or by reason of its cause. For a thing’s existence follows necessarily either from its essence and definition, or from a given efficient cause. A thing is also called impossible for these same reasons: namely, either because its essence or definition involves a contradiction, or because there is no external cause determined to produce such a thing. But a thing is called contingent for no other reason than a defect in our knowledge.

Scholium 2. From what has been said it clearly follows that things have been produced by God with the highest perfection, since they have followed necessarily from a given, most perfect nature. Nor does this convict God of any imperfection; for it is his very perfection that has compelled us to affirm it. Indeed, from the contrary it would clearly follow (as I have just shown) that God is not supremely perfect: for if things had been produced in another way, we would have to attribute to God another nature, different from the one we have been compelled to attribute to him from considering a most perfect Being. I do not doubt, however, that many will hoot this view down as absurd, and will not be willing to set their minds to weighing it—and for no other reason than that they are used to attributing to God another kind of freedom, very different from the one we have set out (Definition 7): namely, an absolute will.

Since, therefore, things could not have been produced by God in any other way or order, and since the truth of this follows from God’s supreme perfection, no sound reason can persuade us to believe that God did not will to create all the things that are in his intellect, with the very same perfection with which he understands them. But they will say that there is no perfection or imperfection in things; that what is in them, on account of which they are called perfect or imperfect, good or bad, depends on God’s will alone; and so, had God so willed, he could have brought it about that what is now perfection would be the greatest imperfection, and the reverse.

Proposition 34. God’s power is his very essence.

Demonstration. For from the necessity of God’s essence alone it follows that God is the cause of himself (by Proposition 11) and (by Proposition 16 and its Corollary) of all things. Therefore God’s power, by which he and all things are and act, is his very essence. QED

Proposition 35. Whatever we conceive to be in God’s power necessarily is.

Demonstration. For whatever is in God’s power must (by the preceding proposition) be so contained in his essence that it necessarily follows from it; and so it necessarily is. QED

Proposition 36. Nothing exists from whose nature some effect does not follow.

Demonstration. Whatever exists expresses the nature, or essence, of God in a certain and determinate way (by the Corollary to Proposition 25); that is (by Proposition 34), whatever exists expresses in a certain and determinate way the power of God, which is the cause of all things; and so (by Proposition 16) some effect must follow from it. QED

With this I have sufficiently explained what I promised in the first place. Now, to show that Nature has no end set before it, and that all final causes are nothing but human fictions, does not take much. For I believe this is already clear enough, both from the foundations and causes from which I have shown this prejudice took its origin, and from Proposition 16 and the Corollaries of Proposition 32, and besides from all the passages in which I have shown that all things in nature proceed by a certain eternal necessity and with the highest perfection. I shall, however, add this further point: this doctrine about ends turns Nature completely upside down. For it regards as an effect what is in fact a cause, and vice versa. Next, it makes what is prior by nature posterior. And finally, it renders what is supreme and most perfect the most imperfect.

Once people had persuaded themselves that everything that happens happens for their sake, they had to judge that what is most important in each thing is what is most useful to them, and to value most highly all the things by which they were most agreeably affected. Hence they had to form these notions by which to explain the natures of things: Good, Bad, Order, Confusion, Hot, Cold, Beauty and Ugliness. And because they think themselves free, these further notions arose: Praise and Blame, Wrongdoing and Merit. These latter I shall explain below, after I have dealt with human nature; the former I shall briefly explain here. Everything that promotes health and the worship of God they called Good; what is contrary to these, Bad.

We see, therefore, that all the notions by which the common people usually explain Nature are only ways of imagining, and indicate the nature of nothing, but only the constitution of the imagination. And because they have names as if they were beings existing outside the imagination, I call them beings not of reason but of imagination. So all the arguments drawn against us from such notions can easily be repelled. For many people argue like this: if all things have followed from the necessity of God’s most perfect nature, where then have so many imperfections in Nature come from—the corruption of things to the point of stench, the ugliness of things that provokes nausea, confusion, evil, wrongdoing, and so on? But, as I have just said, these are easily refuted.note

These are the prejudices I undertook to point out here. If any others of this sort still remain, anyone can correct them with a little reflection.

I now pass on to explaining those things that must necessarily have followed from the essence of God, or the eternal and infinite Being. Not all of them, indeed—for we have demonstrated in Proposition 16 of Part 1 that infinitely many things must follow from it in infinitely many ways—but only those that can lead us, as if by the hand, to the knowledge of the human mind and its highest blessedness.

Definition 1. By body I understand a mode that expresses, in a certain and determinate way, God’s essence insofar as it is considered as an extended thing (see the Corollary to Proposition 25 of Part 1).

Definition 2. I say that there belongs to the essence of a thing that which, if it is given, the thing is necessarily posited, and if it is taken away, the thing is necessarily taken away; or that without which the thing can neither be nor be conceived, and which, conversely, can neither be nor be conceived without the thing.

Definition 3. By idea I understand a concept of the mind, which the mind forms because it is a thinking thing.

Explanation. I say concept rather than perception because the word perception seems to indicate that the mind is passive in relation to its object, whereas concept seems to express an action of the mind.

Definition 4. By adequate idea I understand an idea which, insofar as it is considered in itself, without relation to its object, has all the properties, or intrinsic marks, of a true idea.

Explanation. I say intrinsic in order to exclude what is extrinsic, namely the agreement of the idea with its object.

Definition 5. Duration is the indefinite continuation of existing.

Explanation. I say indefinite because it can in no way be determined by the very nature of the existing thing, nor yet by the efficient cause, which necessarily posits the thing’s existence but does not take it away.

Definition 6. By reality and perfection I understand the same thing.

Definition 7. By singular things I understand things that are finite and have a determinate existence. And if several individuals so concur in one action that all of them together are the cause of one effect, I consider them all, to that extent, as one singular thing.

Axiom 1. The essence of man does not involve necessary existence; that is, in the order of Nature it can equally happen that this or that man exists and that he does not exist.

Axiom 2. Man thinks.

Axiom 3. Modes of thinking, such as love, desire, or whatever else is called by the name of an affect of the mind, do not exist unless there is in the same individual an idea of the thing loved, desired, and so on. But an idea can exist even though no other mode of thinking exists.

Axiom 4. We feel that a certain body is affected in many ways.

Axiom 5. We neither feel nor perceive any singular things except bodies and modes of thinking.

For the Postulates, see after Proposition 13.

Proposition 1. Thought is an attribute of God, or God is a thinking thing.

Demonstration. Singular thoughts, or this and that thought, are modes that express God’s nature in a certain and determinate way (by the Corollary to Proposition 25 of Part 1). Therefore there belongs to God (by Definition 5 of Part 1) an attribute whose concept all singular thoughts involve, and through which they are also conceived. Thought, therefore, is one of God’s infinite attributes, which expresses God’s eternal and infinite essence (see Definition 6 of Part 1); or, God is a thinking thing. QED

Scholium. This Proposition is also evident from the fact that we can conceive an infinite thinking being. For the more things a thinking being can think, the more reality, or perfection, we conceive it to contain. Therefore a being that can think infinitely many things in infinitely many ways is necessarily infinite in its power of thinking. Since, then, by attending to thought alone we conceive an infinite Being, thought is necessarily (by Definitions 4 and 6 of Part 1) one of God’s infinite attributes, as we wished to show.

Proposition 2. Extension is an attribute of God, or God is an extended thing.

Demonstration. The demonstration of this proceeds in the same way as that of the preceding proposition.

Proposition 3. In God there is necessarily an idea both of his essence and of everything that necessarily follows from his essence.

Demonstration. For God (by Proposition 1 of this part) can think infinitely many things in infinitely many ways, or (what is the same, by Proposition 16 of Part 1) can form the idea of his essence and of everything that necessarily follows from it. But everything that is in God’s power necessarily is (by Proposition 35 of Part 1). Therefore such an idea necessarily exists, and (by Proposition 15 of Part 1) exists nowhere but in God. QED

Scholium. By God’s power the common people understand God’s free will and his right over all things that exist, which are therefore commonly regarded as contingent. For they say that God has the power to destroy everything and reduce it to nothing. Further, they very often compare God’s power with the power of kings. But we have refuted this in Corollaries 1 and 2 to Proposition 32 of Part 1, and in Proposition 16 of Part 1 we showed that God acts with the same necessity by which he understands himself. That is, just as it follows from the necessity of the divine nature (as everyone unanimously maintains) that God understands himself, so it follows with the same necessity that God does infinitely many things in infinitely many ways. Next, in Proposition 34 of Part 1 we showed that God’s power is nothing but God’s active essence; and so it is as impossible for us to conceive that God does not act as that God does not exist.

Proposition 4. The idea of God, from which infinitely many things follow in infinitely many ways, can only be one.

Demonstration. The infinite intellect comprehends nothing except God’s attributes and his affections (by Proposition 30 of Part 1). But God is unique (by Corollary 1 to Proposition 14 of Part 1). Therefore the idea of God, from which infinitely many things follow in infinitely many ways, can only be one. QED

Proposition 5. The formal being of ideas recognizes God as its cause only insofar as he is considered as a thinking thing, and not insofar as he is explained through another attribute. That is, the ideas both of God’s attributes and of singular things recognize as their efficient cause not the objects of the ideas themselves, that is, the things perceived, but God himself, insofar as he is a thinking thing.

Demonstration. This is indeed evident from Proposition 3 of this part. For there we concluded that God can form the idea of his essence, and of everything that necessarily follows from it, solely from the fact that God is a thinking thing, and not from the fact that he is the object of his idea. Therefore the formal being of ideas recognizes God as its cause insofar as he is a thinking thing. But it can be demonstrated differently, in this way. The formal being of ideas is a mode of thinking (as is self-evident), that is (by the Corollary to Proposition 25 of Part 1), a mode that expresses in a certain way God’s nature insofar as he is a thinking thing; and so (by Proposition 10 of Part 1) it involves the concept of no other attribute of God, and consequently (by Axiom 4 of Part 1) is the effect of no other attribute but thought. And so the formal being of ideas recognizes God as its cause only insofar as he is considered as a thinking thing, etc.

Proposition 6. The modes of any attribute have God as their cause only insofar as he is considered under the attribute of which they are modes, and not insofar as he is considered under any other.

Demonstration. For each attribute is conceived through itself, without any other (by Proposition 10 of Part 1). So the modes of each attribute involve the concept of their own attribute, but not of another; and so (by Axiom 4 of Part 1) they have God as their cause only insofar as he is considered under the attribute of which they are modes, and not insofar as he is considered under any other. QED

Corollary. From this it follows that the formal being of things that are not modes of thinking does not follow from the divine nature because God first knew those things. Rather, the objects of ideas follow and are derived from their own attributes in the same way and with the same necessity as we have shown ideas to follow from the attribute of thought.

Demonstration. This is evident from Axiom 4 of Part 1. For the idea of anything caused depends on knowledge of the cause of which it is the effect.

Corollary. From this it follows that God’s power of thinking is equal to his actual power of acting. That is, whatever follows formally from God’s infinite nature all follows objectively in God from the idea of God, in the same order and with the same connection.

Scholium. Here, before we go any further, we must recall what we showed above: namely, that whatever can be perceived by an infinite intellect as constituting the essence of a substance belongs to one substance only, and consequently that thinking substance and extended substance are one and the same substance, which is comprehended now under this attribute, now under that. So also a mode of extension and the idea of that mode are one and the same thing, but expressed in two ways. Some of the Hebrews seem to have seen this as if through a mist—those, namely, who maintain that God, God’s intellect, and the things understood by him are one and the same. For example,note

Proposition 8. The ideas of singular things, or modes, that do not exist must be comprehended in God’s infinite idea in the same way as the formal essences of singular things, or modes, are contained in God’s attributes.

Demonstration. This Proposition is evident from the preceding one, but it is understood more clearly from the preceding scholium.

Corollary. From this it follows that, as long as singular things do not exist except insofar as they are comprehended in God’s attributes, their objective being, or their ideas, do not exist except insofar as God’s infinite idea exists. And when singular things are said to exist not only insofar as they are comprehended in God’s attributes, but also insofar as they are said to endure, their ideas too will involve the existence through which they are said to endure.

Scholium. If anyone wants an example to explain this matter more fully, I certainly cannot give one that adequately explains the thing I am speaking of here, since it is unique. Still, I shall try to illustrate it as far as possible. The circle is of such a nature that, for all straight lines intersecting one another within it, the rectangles formed from their segments are equal to one another. So a circle contains infinitely many rectangles equal to one another. Yet none of them can be said to exist except insofar as the circle exists; nor can the idea of any of these rectangles be said to exist except insofar as it is comprehended in the idea of the circle. Now let us conceive that, of those infinitely many rectangles, only two exist, namely E and D.note

Proposition 9. The idea of a singular thing that actually exists has God as its cause not insofar as he is infinite, but insofar as he is considered as affected by another idea of a singular thing that actually exists; and of this idea, too, God is the cause insofar as he is affected by a third, and so on to infinity.

Demonstration. The idea of a singular thing that actually exists is a singular mode of thinking, distinct from the others (by the Corollary and Scholium to Proposition 8 of this part); and so (by Proposition 6 of this part) it has God as its cause only insofar as he is a thinking thing. Yet not (by Proposition 28 of Part 1) insofar as he is a thinking thing absolutely, but insofar as he is considered as affected by another mode of thinking; and of this mode, too, God is the cause insofar as he is affected by another mode of thinking, and so on to infinity. But the order and connection of ideas (by Proposition 7 of this part) is the same as the order and connection of causes. Therefore the cause of one singular idea is another idea, or God insofar as he is considered as affected by another idea; and of this one, too, he is the cause insofar as he is affected by another, and so on to infinity. QED

Corollary. Of whatever happens in the singular object of any idea, there is knowledge in God only insofar as he has the idea of that same object.

Demonstration. Of whatever happens in the object of any idea, there is an idea in God (by Proposition 3 of this part), not insofar as he is infinite, but insofar as he is considered as affected by another idea of a singular thing (by the preceding proposition). But (by Proposition 7 of this part) the order and connection of ideas is the same as the order and connection of things. Therefore knowledge of what happens in any singular object will be in God only insofar as he has the idea of that same object. QED

Proposition 10. The being of substance does not pertain to the essence of man; that is, substance does not constitute the form of man.

Demonstration. For the being of substance involves necessary existence (by Proposition 7 of Part 1). If, then, the being of substance pertained to the essence of man, it would follow that, given substance, man would necessarily be given (by Definition 2 of this part), and consequently man would necessarily exist—which (by Axiom 1 of this part) is absurd. Therefore, etc. QED

Scholium. This proposition is also demonstrated from Proposition 5 of Part 1, namely that there are not two substances of the same nature. Since many men can exist, what constitutes the form of man is not the being of substance. The proposition is evident, moreover, from the other properties of substance—namely, that substance is by its nature infinite, immutable, indivisible, and so on—as anyone can easily see.

Corollary. From this it follows that the essence of man is constituted by certain modifications of God’s attributes.

Demonstration. For the being of substance does not pertain to the essence of man (by the preceding proposition). It is therefore (by Proposition 15 of Part 1) something that is in God, and that can neither be nor be conceived without God; that is (by the Corollary to Proposition 25 of Part 1), an affection, or mode, which expresses God’s nature in a certain and determinate way.

Scholium. Everyone must surely grant that nothing can be or be conceived without God. For all agree that God is the sole cause of all things, of their essence as well as of their existence; that is, God is the cause of things not only with respect to their coming to be, as they say, but also with respect to their being. Yet at the same time most people say that whatever a thing can neither be nor be conceived without pertains to that thing’s essence. And so they believe either that the nature of God pertains to the essence of created things, or that created things can be or be conceived without God—or, what is more certain, they are not consistent with themselves. The cause of this, I believe, was that they did not keep to the proper order of philosophizing.note

Proposition 11. The first thing that constitutes the actual being of the human mind is nothing other than the idea of some singular thing actually existing.

Demonstration. The essence of man (by the Corollary to the preceding proposition) is constituted by certain modes of God’s attributes, namely (by Axiom 2 of this part) by modes of thinking. Of all these (by Axiom 3 of this part) the idea is prior in nature, and when it is given, the other modes (those, that is, to which the idea is prior in nature) must be in the same individual (by the same axiom). And so an idea is the first thing that constitutes the being of the human mind. But not the idea of a thing that does not exist. For then (by the Corollary to Proposition 8 of this part) the idea itself could not be said to exist. It will therefore be the idea of a thing actually existing. But not of an infinite thing. For an infinite thing (by Propositions 21 and 22 of Part 1) must always necessarily exist, and this (by Axiom 1 of this part) is absurd. Therefore the first thing that constitutes the actual being of the human mind is the idea of a singular thing actually existing.

Corollary. From this it follows that the human mind is a part of the infinite intellect of God. Hence, when we say that the human mind perceives this or that, we are saying nothing other than that God—not insofar as he is infinite, but insofar as he is explained through the nature of the human mind, that is, insofar as he constitutes the essence of the human mind—has this or that idea. And when we say that God has this or that idea not only insofar as he constitutes the nature of the human mind, but insofar as he also has the idea of another thing together with the human mind, then we say that the human mind perceives the thing only in part, that is, inadequately.

Scholium. Here, no doubt, readers will get stuck and will think up many objections to hold things up. For this reason I ask them to proceed slowly with me, step by step, and not to pass judgment on these matters until they have read everything through.

Proposition 12. Whatever happens in the object of the idea constituting the human mind must be perceived by the human mind; that is, there will necessarily be an idea of that thing in the mind. In other words, if the object of the idea constituting the human mind is a body, nothing can happen in that body that is not perceived by the mind.

Demonstration. For whatever happens in the object of any idea, knowledge of it is necessarily in God (by the Corollary to Proposition 9 of this part) insofar as he is considered as affected by the idea of that same object; that is (by Proposition 11 of this part), insofar as he constitutes the mind of some thing. Therefore, whatever happens in the object of the idea constituting the human mind, knowledge of it is necessarily in God insofar as he constitutes the nature of the human mind; that is (by the Corollary to Proposition 11 of this part), knowledge of that thing will necessarily be in the mind, or the mind perceives it. QED

Scholium. This proposition is also evident, and is more clearly understood, from the Scholium to Proposition 7 of this part; see there.

Proposition 13. The object of the idea constituting the human mind is the body—that is, a certain mode of extension actually existing—and nothing else.

Demonstration. For if the body were not the object of the human mind, the ideas of the affections of the body would not be in God (by the Corollary to Proposition 9 of this part) insofar as he constitutes our mind, but insofar as he constitutes the mind of another thing; that is (by the Corollary to Proposition 11 of this part), the ideas of the affections of the body would not be in our mind. But (by Axiom 4 of this part) we do have ideas of the affections of the body. Therefore the object of the idea constituting the human mind is the body, and the body (by Proposition 11 of this part) as actually existing. Next, if besides the body there were also another object of the mind, then, since nothing exists from which some effect does not follow (by Proposition 36 of Part 1), there would necessarily have to be in our mind the idea of some effect of it (by Proposition 11 of this part). But (by Axiom 5 of this part) there is no idea of it. Therefore the object of our mind is the existing body and nothing else.

Corollary. From this it follows that man consists of a mind and a body, and that the human body exists as we sense it.

Scholium. From this we understand not only that the human mind is united to the body, but also what is to be understood by the union of mind and body. But no one will be able to understand this union adequately, or distinctly, unless he first knows adequately the nature of our body. For what we have shown so far is entirely general, and does not pertain more to men than to other individuals, all of which, though in different degrees, are nevertheless animate. For of each thing there is necessarily an idea in God, of which God is the cause, in the same way as there is of the human body. And so whatever we have said of the idea of the human body must necessarily be said of the idea of any thing.

Axiom 1. All bodies are either in motion or at rest.

Axiom 2. Each body moves now more slowly, now more quickly.

Lemma 1. Bodies are distinguished from one another by reason of motion and rest, speed and slowness, and not by reason of substance.

Demonstration. The first part of this I take to be self-evident. That bodies are not distinguished by reason of substance is evident both from Proposition 5 and from Proposition 8 of Part 1, but more clearly from what was said in the Scholium to Proposition 15 of Part 1.

Lemma 2. All bodies agree in certain things.

Demonstration. For all bodies agree in this: that they involve the concept of one and the same attribute (by Definition 1 of this part). Next, in that they can move now more slowly, now more quickly, and, without qualification, can now be in motion, now at rest.

Lemma 3. A body in motion or at rest must have been determined to motion or rest by another body, which was also determined to motion or rest by another, and that one in turn by another, and so on to infinity.

Demonstration. Bodies (by Definition 1 of this part) are singular things which (by Lemma 1) are distinguished from one another by reason of motion and rest. And so (by Proposition 28 of Part 1) each must necessarily have been determined to motion or rest by another singular thing, namely (by Proposition 6 of this part) by another body, which (by Axiom 1) is also either in motion or at rest. But this body too (by the same reasoning) could not have been in motion or at rest unless it had been determined to motion or rest by another, and this one in turn (by the same reasoning) by another, and so on to infinity. QED

Corollary. From this it follows that a body in motion continues to move until it is determined to rest by another body, and that a body at rest likewise continues at rest until it is determined to motion by another. This is also self-evident. For when I suppose that a body, say A, is at rest, and pay no attention to other bodies in motion, I can say nothing about body A except that it is at rest. If it then happens that body A moves, this surely could not have come about from its being at rest; for from that nothing else could follow than that body A remain at rest. If, on the other hand, A is supposed to be moving, then as long as we attend only to A, we can affirm nothing about it except that it is moving.

Axiom 1. All the ways in which a body is affected by another body follow from the nature of the body affected and at the same time from the nature of the body affecting it. So one and the same body is moved in different ways according to the differing natures of the bodies moving it, and, conversely, different bodies are moved in different ways by one and the same body.

Axiom 2. When a body in motion strikes another at rest which it cannot move, it is reflected so as to continue moving; and the angle that the line of the reflected motion makes with the surface of the body at rest which it struck will be equal to the angle that the line of the incident motion makes with that same surface.

So much for the simplest bodies, those that are distinguished from one another only by motion and rest, speed and slowness. Now let us move up to composite bodies.

Definition. When a number of bodies, of the same or of different size, are so constrained by other bodies that they lie upon one another, or, if they are moving at the same or at different degrees of speed, that they communicate their motions to one another in a certain fixed ratio, we shall say that those bodies are united with one another, and that together they all compose one body, or individual, which is distinguished from others by this union of bodies.

Axiom 3. The larger or smaller the surfaces over which the parts of an individual, or composite body, lie upon one another, the harder or easier it is to force them to change their position, and consequently the harder or easier it is to bring it about that the individual itself takes on another shape. From this I shall call bodies whose parts lie upon one another over large surfaces hard; those whose parts do so over small surfaces, soft; and finally those whose parts move among one another, fluid.

Lemma 4. If from a body, or individual, composed of many bodies, some bodies are removed, and at the same time as many others of the same nature take their place, the individual will retain its nature as before, without any change of its form.

Demonstration. For bodies are not distinguished by reason of substance (by Lemma 1), and what constitutes the form of an individual consists in a union of bodies (by the preceding definition). But this union (by hypothesis) is retained, even though there is a continual change of bodies. Therefore the individual will retain its nature as before, with respect both to substance and to mode. QED

Lemma 5. If the parts composing an individual become larger or smaller, but in such proportion that all keep the same ratio of motion and rest to one another as before, the individual will likewise retain its nature as before, without any change of form.

Demonstration. The demonstration of this is the same as that of the preceding lemma.

Lemma 6. If certain bodies composing an individual are compelled to turn the motion they have toward one direction toward another, but in such a way that they can continue their motions and communicate them to one another in the same ratio as before, the individual will likewise retain its nature, without any change of form.

Demonstration. This is self-evident. For the individual is supposed to retain everything that, in its definition, we said constitutes its form.

Lemma 7. Further, an individual so composed retains its nature whether it moves as a whole or is at rest, and whether it moves in this direction or that, provided each part retains its motion and communicates it to the others as before.

Demonstration. This is evident from its definition, which see before Lemma 4.

Scholium. From this, then, we see how a composite individual can be affected in many ways and still preserve its nature. So far we have conceived an individual composed only of bodies that are distinguished from one another only by motion and rest, speed and slowness, that is, one composed of the simplest bodies. If we now conceive another, composed of many individuals of different natures, we shall find that it can be affected in many other ways and still preserve its nature. For since each of its parts is composed of many bodies, each part will be able (by the preceding lemma), without any change in its nature, to move now more slowly, now more quickly, and consequently to communicate its motions to the others more quickly or more slowly. And if we further conceive a third kind of individual, composed of individuals of this second kind, we shall find that it can be affected in many other ways, without any change of its form.

Postulate 1. The human body is composed of a great many individuals (of different natures), each of which is highly composite.

Postulate 2. Of the individuals of which the human body is composed, some are fluid, some soft, and some, finally, hard.

Postulate 3. The individuals composing the human body, and consequently the human body itself, are affected by external bodies in a great many ways.

Postulate 4. To be preserved, the human body needs a great many other bodies, by which it is continually, as it were, regenerated.

Postulate 5. When a fluid part of the human body is determined by an external body to strike frequently against another, soft part, it changes the surface of that part and, as it were, imprints on it certain traces of the external body that is driving it.

Postulate 6. The human body can move external bodies in a great many ways, and arrange them in a great many ways.

Proposition 14. The human mind is capable of perceiving a great many things, and is the more capable, the more ways its body can be disposed.

Demonstration. For the human body (by Postulates 3 and 6) is affected in a great many ways by external bodies, and is disposed to affect external bodies in a great many ways. But the human mind must perceive everything that happens in the human body (by Proposition 12 of this part). The human mind is therefore capable of perceiving a great many things, and is the more capable, etc. QED

Proposition 15. The idea that constitutes the formal being of the human mind is not simple, but composed of a great many ideas.

Demonstration. The idea that constitutes the formal being of the human mind is the idea of the body (by Proposition 13 of this part), which (by Postulate 1) is composed of a great many highly composite individuals. But of each individual composing the body there is necessarily an idea in God (by the Corollary to Proposition 8 of this part). Therefore (by Proposition 7 of this part) the idea of the human body is composed of these many ideas of its component parts. QED

Proposition 16. The idea of any way in which the human body is affected by external bodies must involve the nature of the human body and at the same time the nature of the external body.

Demonstration. For all the ways in which a body is affected follow from the nature of the body affected and at the same time from the nature of the affecting body (by Axiom 1 after the Corollary to Lemma 3). So the idea of them (by Axiom 4 of Part 1) will necessarily involve the nature of each body. And so the idea of any way in which the human body is affected by an external body involves the nature of the human body and of the external body. QED

Corollary 1. From this it follows, first, that the human mind perceives the nature of a great many bodies together with the nature of its own body.

Corollary 2. It follows, second, that the ideas we have of external bodies indicate the constitution of our own body more than the nature of the external bodies. I have explained this with many examples in the Appendix to Part 1.

Proposition 17. If the human body is affected in a way that involves the nature of some external body, the human mind will regard that external body as actually existing, or as present to it, until the body is affected by an affect that excludes the existence or presence of that body.

Demonstration. This is evident. For as long as the human body is affected in this way, the human mind (by Proposition 12 of this part) will regard this affection of the body; that is (by the preceding proposition), it will have the idea of a mode actually existing which involves the nature of the external body—an idea that does not exclude but posits the existence or presence of the nature of the external body. And so the mind (by Corollary 1 of the preceding proposition) will regard the external body as actually existing, or as present, until it is affected, etc. QED

Corollary. The mind will be able to regard external bodies by which the human body has once been affected as if they were present, even though they do not exist and are not present.

Demonstration. When external bodies so determine the fluid parts of the human body that they frequently strike against the softer parts, they change the surfaces of these (by Postulate 5). As a result (see Axiom 2 after the Corollary to Lemma 3) the fluid parts are reflected from them in a different way than they used to be before; and afterwards too, when by their own spontaneous motion they meet these new surfaces, they are reflected in the same way as when they were driven toward those surfaces by the external bodies. Consequently, while they continue to move after being reflected in this way, they affect the human body in the same way, and the mind (by Proposition 12 of this part) will think of this again; that is (by Proposition 17 of this part), the mind will again regard the external body as present. And this will happen as often as the fluid parts of the human body meet those same surfaces by their own spontaneous motion.

Scholium. We see, then, how it can happen that we regard things that do not exist as if they were present, as often happens. And it is possible that this comes about from other causes; but it is enough for me here to have shown one through which I can explain the matter just as if I had shown it through its true cause. Nor do I believe that I stray far from the true cause, since all the postulates I have assumed contain hardly anything that is not established by experience—which we are not permitted to doubt, now that we have shown that the human body exists as we sense it (see the Corollary after Proposition 13 of this part). Further (from the preceding corollary and Corollary 2 of Proposition 16 of this part), we clearly understand the difference between, for example, the idea of Peter which constitutes the essence of Peter’s own mind, and the idea of Peter which is in another man, say in Paul.

Proposition 18. If the human body has once been affected by two or more bodies at the same time, then when the mind afterwards imagines one of them, it will immediately recollect the others as well.

Demonstration. The mind (by the preceding corollary) imagines a body because the human body is affected and disposed by the traces of the external body in the same way as it was affected when some of its parts were driven by that external body. But (by hypothesis) the body was at that time so disposed that the mind imagined two bodies at once. Therefore it will now also imagine two at once, and when the mind imagines either of them, it will immediately recollect the other as well. QED

Scholium. From this we clearly understand what memory is. For it is nothing other than a certain linking of ideas involving the nature of things outside the human body—a linking that occurs in the mind according to the order and linking of the affections of the human body. I say, first, that it is a linking only of those ideas that involve the nature of things outside the human body, not of ideas that explain the nature of those things. For these are in fact (by Proposition 16 of this part) ideas of affections of the human body, which involve the nature both of the human body and of external bodies. I say, second, that this linking occurs according to the order and linking of the affections of the human body, to distinguish it from the linking of ideas that occurs according to the order of the intellect—the order by which the mind perceives things through their first causes, and which is the same in all men.

Proposition 19. The human mind does not know the human body itself, nor does it know that the body exists, except through ideas of the affections by which the body is affected.

Demonstration. For the human mind is the very idea, or knowledge, of the human body (by Proposition 13 of this part), which (by Proposition 9 of this part) is indeed in God insofar as he is considered as affected by another idea of a singular thing. Or rather, since (by Postulate 4) the human body needs a great many bodies by which it is continually, as it were, regenerated, and since the order and connection of ideas is the same (by Proposition 7 of this part) as the order and connection of causes, this idea will be in God insofar as he is considered as affected by the ideas of a great many singular things. God, therefore, has the idea of the human body, or knows the human body, insofar as he is affected by a great many other ideas, and not insofar as he constitutes the nature of the human mind; that is (by the Corollary to Proposition 11 of this part), the human mind does not know the human body.

Proposition 20. There is also in God an idea, or knowledge, of the human mind, which follows in God and is related to God in the same way as the idea, or knowledge, of the human body.

Demonstration. Thought is an attribute of God (by Proposition 1 of this part). And so (by Proposition 3 of this part) there must necessarily be in God an idea both of thought and of all its affections, and consequently (by Proposition 11 of this part) of the human mind as well. Next, this idea, or knowledge, of the mind does not follow as being in God insofar as he is infinite, but insofar as he is affected by another idea of a singular thing (by Proposition 9 of this part). But the order and connection of ideas is the same as the order and connection of causes (by Proposition 7 of this part). Therefore this idea, or knowledge, of the mind follows in God and is related to God in the same way as the idea, or knowledge, of the body. QED

Proposition 21. This idea of the mind is united to the mind in the same way as the mind itself is united to the body.

Demonstration. We have shown that the mind is united to the body from the fact that the body is the object of the mind (see Propositions 12 and 13 of this part). And so, by that same reasoning, the idea of the mind must be united with its object, that is, with the mind itself, in the same way as the mind itself is united to the body. QED

Scholium. This proposition is understood far more clearly from what was said in the Scholium to Proposition 7 of this part. For there we showed that the idea of the body and the body—that is (by Proposition 13 of this part), the mind and the body—are one and the same individual, conceived now under the attribute of Thought, now under the attribute of Extension. So the idea of the mind and the mind itself are one and the same thing, conceived under one and the same attribute, namely Thought. The idea of the mind, I say, and the mind itself follow in God with the same necessity from the same power of thinking. For in truth the idea of the mind, that is, the idea of an idea, is nothing other than the form of the idea insofar as this is considered as a mode of thinking without relation to its object. For as soon as someone knows something, by that very fact he knows that he knows it, and at the same time he knows that he knows that he knows it, and so on to infinity.

Proposition 22. The human mind perceives not only the affections of the body but also the ideas of these affections.

Demonstration. The ideas of the ideas of affections follow in God and are related to God in the same way as the ideas of affections themselves; this is demonstrated in the same way as Proposition 20 of this part. But the ideas of the affections of the body are in the human mind (by Proposition 12 of this part), that is (by the Corollary to Proposition 11 of this part), in God insofar as he constitutes the essence of the human mind. Therefore the ideas of these ideas will be in God insofar as he has the knowledge, or idea, of the human mind, that is (by Proposition 21 of this part), in the human mind itself, which therefore perceives not only the affections of the body but also their ideas. QED

Proposition 23. The mind does not know itself except insofar as it perceives the ideas of the affections of the body.

Demonstration. The idea or knowledge of the mind follows in God in the same way, and is related to God in the same way, as the idea or knowledge of the body (by Proposition 20 of this part). But since the human mind does not know the human body itself (by Proposition 19 of this part)—that is (by the Corollary to Proposition 11 of this part), since knowledge of the human body is not related to God insofar as he constitutes the nature of the human mind—neither is knowledge of the mind related to God insofar as he constitutes the essence of the human mind; and so (by the same Corollary to Proposition 11 of this part) the human mind, to that extent, does not know itself. Next, the ideas of the affections by which the body is affected involve the nature of the human body itself (by Proposition 16 of this part), that is (by Proposition 13 of this part), they agree with the nature of the mind; so knowledge of these ideas will necessarily involve knowledge of the mind.

Proposition 24. The human mind does not involve adequate knowledge of the parts that compose the human body.

Demonstration. The parts that compose the human body pertain to the essence of the body itself only insofar as they communicate their motions to one another in a certain fixed ratio (see the Definition after the Corollary to Lemma 3), and not insofar as they can be considered as individuals, without relation to the human body. For the parts of the human body are highly composite individuals (by Postulate 1), whose parts (by Lemma 4) can be separated from the human body while its nature and form are wholly preserved, and can communicate their motions to other bodies in another ratio (see Axiom 1 after Lemma 3). And so (by Proposition 3 of this part) the idea or knowledge of any part will be in God—and indeed (by Proposition 9 of this part) insofar as he is considered as affected by another idea of a singular thing, a singular thing that is prior to the part itself in the order of Nature (by Proposition 7 of this part).

Proposition 25. The idea of any affection of the human body does not involve adequate knowledge of an external body.

Demonstration. We have shown that the idea of an affection of the human body involves the nature of an external body to the extent that the external body determines the human body itself in some definite way (see Proposition 16 of this part). But insofar as the external body is an individual that is not related to the human body, its idea or knowledge is in God (by Proposition 9 of this part) insofar as God is considered as affected by the idea of another thing, which (by Proposition 7 of this part) is prior in nature to the external body itself. So adequate knowledge of the external body is not in God insofar as he has the idea of the affection of the human body; in other words, the idea of an affection of the human body does not involve adequate knowledge of the external body. QED

Proposition 26. The human mind perceives no external body as actually existing except through the ideas of the affections of its own body.

Demonstration. If the human body is in no way affected by some external body, then (by Proposition 7 of this part) neither is the idea of the human body—that is (by Proposition 13 of this part), the human mind—affected in any way by the idea of that body’s existence; in other words, it does not perceive the existence of that external body in any way. But insofar as the human body is affected in some way by some external body, to that extent (by Proposition 16 of this part, with its Corollary) it perceives the external body. QED

Corollary. Insofar as the human mind imagines an external body, it does not have adequate knowledge of it.

Demonstration. When the human mind regards external bodies through the ideas of the affections of its own body, we say that it imagines (see the Scholium to Proposition 17 of this part); nor can the mind imagine external bodies as actually existing in any other way (by the preceding proposition). And so (by Proposition 25 of this part), insofar as the mind imagines external bodies, it does not have adequate knowledge of them. QED

Proposition 27. The idea of any affection of the human body does not involve adequate knowledge of the human body itself.

Demonstration. Any idea of any affection of the human body involves the nature of the human body to the extent that the human body itself is considered to be affected in some definite way (see Proposition 16 of this part). But insofar as the human body is an individual that can be affected in many other ways, its idea, etc. (See the Demonstration of Proposition 25 of this part.)

Proposition 28. The ideas of the affections of the human body, insofar as they are related only to the human mind, are not clear and distinct, but confused.

Demonstration. For the ideas of the affections of the human body involve the nature both of external bodies and of the human body itself (by Proposition 16 of this part); and they must involve the nature not only of the human body but also of its parts, since affections are modes (by Postulate 3) by which the parts of the human body, and consequently the whole body, are affected. But (by Propositions 24 and 25 of this part) adequate knowledge of external bodies, as also of the parts that compose the human body, is in God not insofar as he is considered as affected by the human mind, but insofar as he is considered as affected by other ideas. These ideas of affections, then, insofar as they are related to the human mind alone, are like conclusions without premises—that is (as is self-evident), confused ideas. QED

Scholium. It can be demonstrated in the same way that the idea which constitutes the nature of the human mind is not, considered in itself alone, clear and distinct; and the same holds for the idea of the human mind, and for the ideas of the ideas of the affections of the human body, insofar as they are related to the mind alone—as anyone can easily see.

Proposition 29. The idea of the idea of any affection of the human body does not involve adequate knowledge of the human mind.

Demonstration. For the idea of an affection of the human body (by Proposition 27 of this part) does not involve adequate knowledge of the body itself—in other words, it does not adequately express its nature; that is (by Proposition 13 of this part), it does not agree adequately with the nature of the mind. And so (by Axiom 6 of Part 1) the idea of this idea does not adequately express the nature of the human mind; in other words, it does not involve adequate knowledge of it. QED

Corollary. From this it follows that whenever the human mind perceives things in the common order of Nature, it has adequate knowledge neither of itself, nor of its own body, nor of external bodies, but only confused and fragmentary knowledge. For the mind does not know itself except insofar as it perceives the ideas of the affections of the body (by Proposition 23 of this part). And it does not perceive its own body (by Proposition 19 of this part) except through those very ideas of affections, and it is also only through them (by Proposition 26 of this part) that it perceives external bodies. And so, insofar as it has these ideas, it has adequate knowledge neither of itself (by Proposition 29 of this part), nor of its own body (by Proposition 27 of this part), nor of external bodies (by Proposition 25 of this part), but only (by Proposition 28 of this part, with its Scholium) fragmentary and confused knowledge. QED

Scholium. I say expressly that the mind has adequate knowledge neither of itself, nor of its own body, nor of external bodies, but only confused and fragmentary knowledge, whenever it perceives things in the common order of Nature—that is, whenever it is determined externally, by the chance encounters of things, to regard this or that; and not whenever it is determined internally, namely by regarding many things at once, to understand their agreements, differences and oppositions. For whenever it is disposed internally, in this or some other way, it then regards things clearly and distinctly, as I shall show below.

Proposition 30. We can have only a quite inadequate knowledge of the duration of our body.

Demonstration. The duration of our body does not depend on its essence (by Axiom 1 of this part), nor even on the absolute nature of God (by Proposition 21 of Part 1). Rather (by Proposition 28 of Part 1), it is determined to exist and to act by causes of such a kind that they too are determined by others to exist and to act in a certain and determinate way, and these again by others, and so on to infinity. The duration of our body, therefore, depends on the common order of Nature and on the way things are constituted. But adequate knowledge of how things are constituted is in God insofar as he has the ideas of all of them, and not insofar as he has only the idea of the human body (by the Corollary to Proposition 9 of this part). So knowledge of the duration of our body is quite inadequate in God insofar as he is considered only to constitute the nature of the human mind;

Proposition 31. We can have only a quite inadequate knowledge of the duration of the singular things outside us.

Demonstration. For each singular thing, like the human body, must be determined to exist and to act in a certain and determinate way by another singular thing; and this again by another, and so on to infinity (by Proposition 28 of Part 1). Now since we demonstrated in the preceding proposition, from this common property of singular things, that we have only a quite inadequate knowledge of the duration of our body, the same must be concluded about the duration of singular things: namely, that we can have only a quite inadequate knowledge of it. QED

Corollary. From this it follows that all particular things are contingent and corruptible. For we can have no adequate knowledge of their duration (by the preceding proposition), and this is what we must understand by the contingency of things and the possibility of their corruption (see Scholium 1 to Proposition 33 of Part 1). For (by Proposition 29 of Part 1) apart from this there is nothing contingent.

Proposition 32. All ideas, insofar as they are related to God, are true.

Demonstration. For all the ideas that are in God agree entirely with their objects (by the Corollary to Proposition 7 of this part), and so (by Axiom 6 of Part 1) they are all true. QED

Proposition 33. There is nothing positive in ideas on account of which they are called false.

Demonstration. If you deny this, conceive, if you can, a positive mode of thinking that constitutes the form of error, or falsity. This mode of thinking cannot be in God (by the preceding proposition); but outside God it can neither be nor be conceived (by Proposition 15 of Part 1). And so there can be nothing positive in ideas on account of which they are called false. QED

Proposition 34. Every idea that in us is absolute, that is, adequate and perfect, is true.

Demonstration. When we say that there is in us an adequate and perfect idea, we are saying nothing other (by the Corollary to Proposition 11 of this part) than that there is an adequate and perfect idea in God insofar as he constitutes the essence of our mind; and consequently (by Proposition 32 of this part) we are saying nothing other than that such an idea is true. QED

Proposition 35. Falsity consists in the privation of knowledge that inadequate—that is, fragmentary and confused—ideas involve.

Demonstration. There is nothing positive in ideas that constitutes the form of falsity (by Proposition 33 of this part). But falsity cannot consist in absolute privation (for it is minds, not bodies, that are said to err or be deceived), nor yet in absolute ignorance, for to be ignorant and to err are different things. It consists, therefore, in the privation of knowledge that inadequate knowledge of things—that is, inadequate and confused ideas—involves. QED

Proposition 36. Inadequate and confused ideas follow with the same necessity as adequate, or clear and distinct, ideas.

Demonstration. All ideas are in God (by Proposition 15 of Part 1), and, insofar as they are related to God, they are true (by Proposition 32 of this part) and (by the Corollary to Proposition 7 of this part) adequate. And so none are inadequate or confused except insofar as they are related to the singular mind of some individual (on this see Propositions 24 and 28 of this part). And so all of them, adequate and inadequate alike, follow with the same necessity (by the Corollary to Proposition 6 of this part). QED

Proposition 37. What is common to all things (on these, see Lemma 2 above), and is equally in the part and in the whole, does not constitute the essence of any singular thing.

Demonstration. If you deny this, conceive, if you can, that it constitutes the essence of some singular thing—say, the essence of B. Then (by Definition 2 of this part) it will be unable either to be or to be conceived without B. But this is contrary to the hypothesis. Therefore it does not pertain to the essence of B, nor does it constitute the essence of any other singular thing. QED

Proposition 38. Those things that are common to all, and are equally in the part and in the whole, can only be conceived adequately.

Demonstration. Let A be something that is common to all bodies, and is equally in the part of any body and in the whole. I say that A can only be conceived adequately. For its idea (by the Corollary to Proposition 7 of this part) will necessarily be adequate in God, both insofar as he has the idea of the human body and insofar as he has the ideas of its affections, which (by Propositions 16, 25 and 27 of this part) partly involve the nature both of the human body and of external bodies. That is (by Propositions 12 and 13 of this part), this idea will necessarily be adequate in God insofar as he constitutes the human mind, or insofar as he has the ideas that are in the human mind. The mind, therefore (by the Corollary to Proposition 11 of this part), necessarily perceives A adequately—and does so both insofar as it perceives itself and insofar as it perceives its own body or any external body whatever—nor can A be conceived in any other way. QED

Corollary. From this it follows that there are certain ideas, or notions, common to all human beings. For (by Lemma 2) all bodies agree in certain things, which (by the preceding proposition) must be perceived by all adequately, that is, clearly and distinctly.

Proposition 39. If something is common to, and proper to, the human body and certain external bodies by which the human body is usually affected, and is equally in the part of each of these and in the whole, its idea too will be adequate in the mind.

Demonstration. Let A be what is common and proper to the human body and certain external bodies, what is equally in the human body and in those external bodies, and what, finally, is equally in the part of each external body and in the whole. There will be an adequate idea of A itself in God (by the Corollary to Proposition 7 of this part), both insofar as he has the idea of the human body and insofar as he has the ideas of the external bodies posited. Now suppose that the human body is affected by an external body through what it has in common with it, that is, by A. The idea of this affection will involve the property A (by Proposition 16 of this part), and so

Corollary. From this it follows that the mind is the more capable of perceiving many things adequately, the more things its body has in common with other bodies.

Proposition 40. Whatever ideas follow in the mind from ideas that are adequate in it are also adequate.

Demonstration. This is evident. For when we say that an idea follows in the human mind from ideas that are adequate in it, we are saying nothing other (by the Corollary to Proposition 11 of this part) than that there is in the divine intellect itself an idea of which God is the cause, not insofar as he is infinite, nor insofar as he is affected by the ideas of a great many singular things, but insofar as he constitutes only the essence of the human mind.

Scholium 1. With this I have explained the cause of the notions that are called common, and that are the foundations of our reasoning. But there are other causes of certain axioms or notions which it would be worthwhile to explain by this method of ours; for from them it would become clear which notions are more useful than the rest, and which are of scarcely any use; then, which are common, which are clear and distinct only to those who are free of prejudices, and finally which are ill-founded. It would also become clear where those notions they call second notions, and consequently the axioms founded on them, took their origin, along with other things I have at times thought about in connection with these matters. But since I have reserved these for another treatise, and also so as not to cause weariness by excessive length on this subject, I have decided to pass over the matter here.note

Proposition 41. Knowledge of the first kind is the only cause of falsity; knowledge of the second and third kinds is necessarily true.

Demonstration. We said in the preceding scholium that to knowledge of the first kind belong all those ideas that are inadequate and confused; and so (by Proposition 35 of this part) this knowledge is the only cause of falsity. Next, we said that to knowledge of the second and third kinds belong those ideas that are adequate; and so (by Proposition 34 of this part) it is necessarily true. QED

Proposition 42. Knowledge of the second and third kinds, and not of the first, teaches us to distinguish the true from the false.

Demonstration. This Proposition is self-evident. For whoever knows how to distinguish between the true and the false must have an adequate idea of the true and the false; that is (by Scholium 2 to Proposition 40 of this part), must know the true and the false by the second or third kind of knowledge.

Proposition 43. Whoever has a true idea knows at the same time that he has a true idea, and cannot doubt the truth of the thing.

Demonstration. A true idea in us is one that is adequate in God insofar as he is explained through the nature of the human mind (by the Corollary to Proposition 11 of this part). Let us suppose, then, that there is in God, insofar as he is explained through the nature of the human mind, an adequate idea, A. Of this idea there must necessarily also be in God an idea that is related to God in the same way as the idea A (by Proposition 20 of this part, whose demonstration is universal). But the idea A is supposed to be related to God insofar as he is explained through the nature of the human mind; therefore the idea of the idea A must also be related to God in the same way;

Scholium. In the Scholium to Proposition 21 of this part I explained what the idea of an idea is. But it should be noted that the preceding proposition is sufficiently evident by itself. For no one who has a true idea is unaware that a true idea involves the highest certainty; for to have a true idea means nothing other than to know a thing perfectly, or in the best way. And surely no one can doubt this unless he thinks that an idea is something mute, like a picture on a panel, and not a mode of thinking—namely, the very act of understanding. And who, I ask, can know that he understands some thing unless he first understands the thing? That is, who can know that he is certain about some thing unless he is first certain about that thing? Again, what can there be that is clearer and more certain than a true idea, to serve as the standard of truth?

Proposition 44. It is of the nature of reason to regard things not as contingent but as necessary.

Demonstration. It is of the nature of reason to perceive things truly (by Proposition 41 of this part), namely (by Axiom 6 of Part 1) as they are in themselves, that is (by Proposition 29 of Part 1), not as contingent but as necessary. QED

Corollary 1. From this it follows that it depends on the imagination alone that we regard things, with respect to both the past and the future, as contingent.

Scholium. How this comes about I shall explain briefly. We showed above (Proposition 17 of this part, with its Corollary) that the mind, even if things do not exist, nevertheless always imagines them as present to itself, unless causes occur that exclude their present existence. Next, we showed (Proposition 18 of this part) that if the human body has once been affected by two external bodies at the same time, then when the mind later imagines either of them, it will immediately recollect the other as well—that is, it will regard both as present to itself, unless causes occur that exclude their present existence. Moreover, no one doubts that we also imagine time—namely, from the fact that we imagine some bodies to move more slowly than others, or more quickly, or equally quickly. Let us suppose, then, a boy who yesterday, for the first time, saw Peter in the morning, Paul at noon and Simeon in the evening, and who today again sees Peter in the morning.

Corollary 2. It is of the nature of reason to perceive things from a certain standpoint of eternity.note

Demonstration. For it is of the nature of reason to regard things as necessary and not as contingent (by the preceding proposition). And it perceives this necessity of things truly (by Proposition 41 of this part), that is (by Axiom 6 of Part 1), as it is in itself. But (by Proposition 16 of Part 1) this necessity of things is the very necessity of God’s eternal nature. Therefore it is of the nature of reason to regard things from this standpoint of eternity. Add that the foundations of reason are notions (by Proposition 38 of this part) that explain what is common to all things, and that (by Proposition 37 of this part) explain the essence of no singular thing; they must therefore be conceived without any relation to time, from a certain standpoint of eternity. QED

Proposition 45. Each idea of any body, or of any singular thing that actually exists, necessarily involves the eternal and infinite essence of God.

Demonstration. The idea of a singular thing that actually exists necessarily involves both the essence and the existence of that thing (by the Corollary to Proposition 8 of this part). But singular things (by Proposition 15 of Part 1) cannot be conceived without God. Rather, since they have God for their cause (by Proposition 6 of this part) insofar as he is considered under the attribute of which the things themselves are modes, their ideas must necessarily involve (by Axiom 4 of Part 1) the concept of their attribute, that is (by Definition 6 of Part 1), the eternal and infinite essence of God. QED

Scholium. By existence here I do not mean duration—that is, existence insofar as it is conceived abstractly, as a kind of quantity. I am speaking of the very nature of existence, which is attributed to singular things because infinitely many things follow in infinitely many ways from the eternal necessity of God’s nature (see Proposition 16 of Part 1). I am speaking, I say, of the very existence of singular things insofar as they are in God. For although each one is determined by another singular thing to exist in a certain way, the force by which each perseveres in existing nonetheless follows from the eternal necessity of God’s nature. On this, see the Corollary to Proposition 24 of Part 1.

Proposition 46. The knowledge of God’s eternal and infinite essence that each idea involves is adequate and perfect.

Demonstration. The demonstration of the preceding proposition is universal: whether a thing is considered as a part or as a whole, its idea, whether of the whole or of a part, will involve God’s eternal and infinite essence (by the preceding proposition). So what gives knowledge of God’s eternal and infinite essence is common to all things, and is equally in the part and in the whole; and therefore (by Proposition 38 of this part) this knowledge will be adequate. QED

Proposition 47. The human mind has adequate knowledge of God’s eternal and infinite essence.

Demonstration. The human mind has ideas (by Proposition 22 of this part) from which (by Proposition 23 of this part) it perceives itself, its body (by Proposition 19 of this part), and external bodies (by Corollary 1 to Proposition 16 and by Proposition 17 of this part) as actually existing. Therefore (by Propositions 45 and 46 of this part) it has adequate knowledge of God’s eternal and infinite essence. QED

Scholium. From this we see that God’s infinite essence and his eternity are known to all. And since all things are in God and are conceived through God, it follows that from this knowledge we can deduce a great many things that we know adequately, and so form that third kind of knowledge of which we spoke in Scholium 2 to Proposition 40 of this part, and of whose excellence and usefulness we shall have occasion to speak in Part 5. That people do not have as clear a knowledge of God as they have of the common notions comes from this: they cannot imagine God as they imagine bodies, and they have joined the name God to the images of things they are used to seeing—something people can hardly avoid, since they are continually affected by external bodies. And indeed most errors consist in this alone: that we do not apply names to things correctly.

Proposition 48. In the mind there is no absolute, or free, will; rather, the mind is determined to will this or that by a cause, which is also determined by another, and this again by another, and so on to infinity.

Demonstration. The mind is a certain and determinate mode of thinking (by Proposition 11 of this part), and therefore (by Corollary 2 to Proposition 17 of Part 1) it cannot be a free cause of its actions; that is, it cannot have an absolute faculty of willing and not willing. Rather, it must be determined to will this or that (by Proposition 28 of Part 1) by a cause, which is also determined by another, and this again by another, and so on. QED

Scholium. In the same way it is demonstrated that there is in the mind no absolute faculty of understanding, desiring, loving, and so on. It follows that these and similar faculties are either wholly fictitious or nothing but metaphysical beings, that is, universals, which we are accustomed to form from particulars. So intellect and will are related to this or that idea, or to this or that volition, in the same way as stoniness is related to this or that stone, or man to Peter and Paul. The cause of people’s thinking themselves free we explained in the Appendix to Part 1. But before I go further, I should note here that by will I understand the faculty of affirming and denying, not desire. I mean, I say, the faculty by which the mind affirms or denies what is true or what is false—not the desire by which the mind seeks things or turns away from them.

Proposition 49. There is in the mind no volition—that is, no affirmation or negation—besides the one that an idea, insofar as it is an idea, involves.

Demonstration. There is in the mind (by the preceding proposition) no absolute faculty of willing and not willing, but only singular volitions, namely this or that affirmation and this or that negation. Let us conceive, then, some singular volition—say, the mode of thinking by which the mind affirms that the three angles of a triangle are equal to two right angles. This affirmation involves the concept, or idea, of a triangle; that is, it cannot be conceived without the idea of a triangle. For it is the same whether I say that A must involve the concept of B or that A cannot be conceived without B. Next, this affirmation (by Axiom 3 of this part) also cannot be without the idea of a triangle. So this affirmation can neither be nor be conceived without the idea of a triangle. Further, this idea of a triangle must involve this same affirmation, namely that its three angles are equal to two right angles.

Corollary. Will and intellect are one and the same.

Demonstration. Will and intellect are nothing besides the singular volitions and ideas themselves (by Proposition 48 of this part and its Scholium). But a singular volition and a singular idea are one and the same (by the preceding proposition). Therefore will and intellect are one and the same. QED

Scholium. With this we have removed what is commonly held to be the cause of error. We showed above that falsity consists only in the privation that fragmentary and confused ideas involve. So a false idea, insofar as it is false, does not involve certainty. When we say, then, that someone rests content with false things and does not doubt them, we are not saying that he is certain, only that he does not doubt—or that he rests content with false things because there are no causes that make his imagination waver. On this, see the Scholium to Proposition 44 of this part. However firmly a person is supposed to cling to false things, then, we shall never say that he is certain. For by certainty we understand something positive (see Proposition 43 of this part with its Scholium), not the privation of doubt; whereas by the privation of certainty we understand falsity. But to explain the preceding proposition more fully, some points remain to be made.

I begin, then, with the first, and I urge my readers to distinguish carefully between an idea, or concept of the mind, and the images of the things we imagine. Next, they must distinguish between ideas and the words by which we signify things. For because many people either confuse these three—images, words, and ideas—entirely, or distinguish them not accurately enough, or not cautiously enough, they have been wholly ignorant of this doctrine of the will, which it is absolutely necessary to know, both for speculation and for ordering one’s life wisely.

Let these few warnings on the subject suffice. I pass, then, to the objections mentioned above.

The first of these is that people think it established that the will extends more widely than the intellect, and is therefore different from it. The reason they think the will extends more widely than the intellect is that, as they say, they know by experience that they need no greater faculty of assenting—that is, of affirming and denying—than the one they already have in order to assent to infinitely many other things that we do not perceive; whereas they would need a greater faculty of understanding. The will, then, is distinguished from the intellect in that the intellect is finite and the will infinite.

Second, it can be objected to us that experience seems to teach nothing more clearly than that we can suspend our judgment so as not to assent to the things we perceive. This is also confirmed by the fact that no one is said to be deceived insofar as he perceives something, but only insofar as he assents or dissents. For example, someone who invents a winged horse does not thereby grant that a winged horse exists; that is, he is not thereby deceived, unless at the same time he grants that a winged horse exists. Experience seems to teach nothing more clearly, then, than that the will, or the faculty of assenting, is free and different from the faculty of understanding.

Third, it can be objected that one affirmation does not seem to contain more reality than another; that is, we do not seem to need greater power to affirm that what is true is true than to affirm that something false is true. But we do perceive that one idea has more reality, or perfection, than another: for as some objects are more excellent than others, so too some of their ideas are more perfect than others. From this, too, the difference between will and intellect seems to be established.

Fourth, it can be objected: if a person does not act from freedom of the will, what will happen if he is in a state of equilibrium, like Buridan’s ass? Will he perish of hunger and thirst? If I grant that he will, I would seem to be conceiving an ass, or a statue of a man, not a man. If I deny it, then he will determine himself, and consequently has the faculty of going and of doing whatever he wants. Other objections could perhaps be raised besides these; but since I am not obliged to dwell on whatever anyone may dream up, I shall take care to answer only these, and as briefly as I can.note

To the first, I say that I grant that the will extends more widely than the intellect, if by intellect they mean only clear and distinct ideas. But I deny that the will extends more widely than perceptions, or the faculty of conceiving. Nor do I see why the faculty of willing should be called infinite any more than the faculty of sensing. For just as we can affirm infinitely many things with the same faculty of willing (one after another, though, since we cannot affirm infinitely many at once), so too we can sense, or perceive, infinitely many bodies with the same faculty of sensing (one after another, that is). And if they say that there are infinitely many things we cannot perceive, I reply that we cannot reach them by any thought, and consequently not by any faculty of willing either.

To the second objection I reply by denying that we have a free power of suspending judgment. For when we say that someone suspends judgment, we are saying nothing but that he sees that he does not perceive the thing adequately. Suspension of judgment, then, is really a perception, not free will. To understand this clearly, let us conceive a child who imagines a [winged] horse and perceives nothing else. Since this imagining of the horse involves the horse’s existence (by the Corollary to Proposition 17 of this part), and the child perceives nothing that cancels the horse’s existence, he will necessarily regard the horse as present; nor will he be able to doubt its existence, though he will not be certain of it.

With this I think I have also answered the third objection. The will is something universal, predicated of all ideas, which signifies only what is common to all ideas, namely affirmation. Its adequate essence, therefore, insofar as it is conceived abstractly in this way, must be in each idea, and only in this respect is it the same in all; but not insofar as it is considered to constitute the essence of the idea, for in that respect singular affirmations differ from one another as much as the ideas themselves do. For example, the affirmation that the idea of a circle involves differs from the one that the idea of a triangle involves as much as the idea of a circle differs from the idea of a triangle. Next, I flatly deny that we need an equal power of thinking to affirm that what is true is true as to affirm that what is false is true.

Finally, as regards the fourth objection, I say that I fully grant that a person placed in such an equilibrium (one, that is, who perceives nothing but thirst and hunger, and such-and-such food and such-and-such drink, equally distant from him) will perish of hunger and thirst. If they ask me whether such a person should not be reckoned an ass rather than a man, I say that I do not know—just as I also do not know how to reckon someone who hangs himself, or how to reckon children, fools, those who have lost their minds, and so on.

It remains, finally, to show how much knowledge of this doctrine contributes to the conduct of life. We shall easily see this from the following points.

1. It teaches that we act by God’s bidding alone, and that we share in the divine nature—the more so, the more perfect the actions we perform and the more and more we understand God. This doctrine, then, besides bringing complete peace of mind, has this further merit: it teaches us in what our highest happiness, or blessedness, consists—namely, in the knowledge of God alone, by which we are led to do only what love and piety urge. From this we understand clearly how far from a true estimate of virtue those people stray who, for their virtue and their best actions, expect to be decorated by God with the highest rewards, as if for the hardest servitude—as though virtue itself, and the service of God, were not happiness itself and the highest freedom.note

2. It teaches how we ought to conduct ourselves regarding matters of fortune, that is, things not in our power—things that do not follow from our nature: namely, to expect and bear both faces of fortune with an even mind. For all things follow from God’s eternal decree with the same necessity as it follows from the essence of a triangle that its three angles are equal to two right angles.

3. This doctrine contributes to social life, in that it teaches us to hate no one, disdain no one, mock no one, be angry with no one, envy no one. Further, it teaches that each person should be content with what is his own, and should help his neighbor—not from sentimental pity, partiality, or superstition, but from the guidance of reason alone, as time and circumstance require, as I shall show in Part 4.

4. Finally, this doctrine also contributes no little to society as a whole, in that it teaches how citizens are to be governed and led: not so that they may be slaves, but so that they may freely do what is best. With this I have completed what I had resolved to treat in this scholium, and so I bring this Second Part of ours to a close. In it I think I have explained the nature of the human mind and its properties at sufficient length, and as clearly as the difficulty of the subject allows, and have set out things from which many excellent conclusions can be drawn—highly useful and necessary to know—as will partly become clear from what follows.

Definition 1. I call a cause adequate when its effect can be clearly and distinctly perceived through it; I call it inadequate, or partial, when its effect cannot be understood through it alone.

Definition 2. I say that we act when something happens, in us or outside us, of which we are the adequate cause; that is (by the preceding Definition), when from our nature something follows, in us or outside us, that can be clearly and distinctly understood through our nature alone. On the other hand, I say that we are acted on when something happens in us, or follows from our nature, of which we are only a partial cause.

Definition 3. By affect I understand the affections of the body by which the body’s power of acting is increased or diminished, aided or restrained, and at the same time the ideas of these affections.

So if we can be the adequate cause of one of these affections, then by affect I understand an action; otherwise, a passion.

Postulate 1. The human body can be affected in many ways by which its power of acting is increased or diminished, and also in other ways that make its power of acting neither greater nor less.

This Postulate, or Axiom, rests on Postulate 1 and Lemmas 5 and 7, for which see after Proposition 13 of Part 2.

Postulate 2. The human body can undergo many changes and nonetheless retain the impressions, or traces, of objects (on which see Postulate 5 of Part 2), and consequently the same images of things (for their definition, see the Scholium to Proposition 17 of Part 2).

Proposition 1. Our mind acts in some things and is acted on in others: namely, insofar as it has adequate ideas, it necessarily acts in some things, and insofar as it has inadequate ideas, it is necessarily acted on in some things.

Demonstration. In every human mind some ideas are adequate, and others fragmentary and confused (by Scholium 2 to Proposition 40 of Part 2). Now the ideas that are adequate in someone’s mind are adequate in God insofar as he constitutes the essence of that mind (by the Corollary to Proposition 11 of Part 2); and those that are inadequate in the mind are also adequate in God (by the same Corollary), not insofar as he contains in himself only the essence of that mind, but insofar as he also contains in himself the minds of other things at the same time. Next, from any given idea some effect must necessarily follow (by Proposition 36 of Part 1), of which God is the adequate cause (see Definition 1 of this part)—not insofar as he is infinite, but insofar as he is considered as affected by that given idea (see Proposition 9 of Part 2).

Corollary. From this it follows that the mind is subject to more passions the more inadequate ideas it has, and, conversely, acts more the more adequate ideas it has.

Proposition 2. The body cannot determine the mind to think, nor can the mind determine the body to motion or to rest, or to anything else (if there is anything else).

Demonstration. All modes of thinking have God for their cause insofar as he is a thinking thing, and not insofar as he is explained by another attribute (by Proposition 6 of Part 2). So what determines the mind to think is a mode of Thought, not of Extension; that is (by Definition 1 of Part 2), it is not a body. That was the first point. Next, the motion and rest of a body must arise from another body, which was also determined to motion or rest by another; and, without qualification, whatever arises in a body must have arisen from God insofar as he is considered as affected by some mode of Extension, and not insofar as he is considered as affected by some mode of Thought (by the same Proposition 6 of Part 2); that is, it cannot arise from the mind, which (by Proposition 11 of Part 2) is a mode of thinking. That was the second point. Therefore neither can the body determine the mind, etc. QED

Scholium. This is understood more clearly from what was said in the Scholium to Proposition 7 of Part 2: namely, that the mind and the body are one and the same thing, conceived now under the attribute of Thought, now under the attribute of Extension. Hence the order, or connection, of things is one, whether Nature is conceived under this attribute or under that; and consequently the order of the actions and passions of our body is by nature simultaneous with the order of the actions and passions of the mind. This is also evident from the way we demonstrated Proposition 12 of Part 2.

Proposition 3. The actions of the mind arise from adequate ideas alone; the passions depend on inadequate ideas alone.

Demonstration. The first thing that constitutes the essence of the mind is nothing but the idea of an actually existing body (by Propositions 11 and 13 of Part 2). This idea (by Proposition 15 of Part 2) is composed of many others, of which some (by the Corollary to Proposition 38 of Part 2) are adequate, and some inadequate (by the Corollary to Proposition 29 of Part 2). Whatever follows from the nature of the mind, then, and has the mind as its proximate cause, through which it must be understood, must necessarily follow from either an adequate or an inadequate idea. But insofar as the mind has inadequate ideas (by Proposition 1 of this part), to that extent it is necessarily acted on. Therefore the actions of the mind follow from adequate ideas alone, and the mind is acted on only because it has inadequate ideas. QED

Scholium. We see, then, that passions are related to the mind only insofar as it has something that involves negation—that is, insofar as it is considered as a part of Nature that cannot be clearly and distinctly perceived through itself, without the other parts. In this way I could show that passions are related to singular things in the same way as to the mind, and cannot be perceived in any other way; but my purpose is to treat the human mind alone.

Proposition 4. No thing can be destroyed except by an external cause.

Demonstration. This Proposition is evident through itself. For the definition of any thing affirms the thing’s essence and does not deny it; that is, it posits the thing’s essence and does not take it away. So as long as we attend only to the thing itself, and not to external causes, we shall be able to find nothing in it that can destroy it. QED

Proposition 5. Things are of a contrary nature—that is, cannot be in the same subject—to the extent that one can destroy the other.

Demonstration. For if they could agree with each other, or be in the same subject at the same time, then there could be something in the same subject that could destroy it, which (by the preceding Proposition) is absurd. Therefore things, etc. QED

Demonstration. For singular things are modes by which God’s attributes are expressed in a certain and determinate way (by the Corollary to Proposition 25 of Part 1); that is (by Proposition 34 of Part 1), they are things that express, in a certain and determinate way, the power of God by which God is and acts. And no thing has in itself anything by which it can be destroyed, or that takes its existence away (by Proposition 4 of this part); on the contrary, it is opposed to everything that can take its existence away (by the preceding Proposition). And so, as far as it can by its own power, it strives to persevere in its being. QED

Proposition 7. The striving by which each thing strives to persevere in its being is nothing but the actual essence of the thing itself.

Demonstration. From the given essence of any thing certain things necessarily follow (by Proposition 36 of Part 1), and things can do nothing other than what necessarily follows from their determinate nature (by Proposition 29 of Part 1). So the power or striving of any thing, by which it does or strives to do anything, either alone or with others—that is (by Proposition 6 of this part), the power or striving by which it strives to persevere in its being—is nothing but the given, or actual, essence of the thing itself. QED

Proposition 8. The striving by which each thing strives to persevere in its being involves no finite time, but an indefinite time.

Demonstration. For if it involved a limited time, which determined the thing’s duration, then it would follow from the very power by which the thing exists, taken alone, that after that limited time the thing could not exist, but would have to be destroyed. But this (by Proposition 4 of this part) is absurd. Therefore the striving by which a thing exists involves no definite time. On the contrary, since (by the same Proposition 4 of this part) if the thing is destroyed by no external cause, it will always go on existing by the same power by which it now exists, this striving involves an indefinite time. QED

Proposition 9. The mind, both insofar as it has clear and distinct ideas and insofar as it has confused ones, strives to persevere in its being for an indefinite duration, and is conscious of this striving of its own.

Demonstration. The essence of the mind is constituted by adequate and inadequate ideas (as we showed in Proposition 3 of this part); and so (by Proposition 7 of this part) it strives to persevere in its being both insofar as it has the latter and insofar as it has the former—and this (by Proposition 8 of this part) for an indefinite duration. But since the mind (by Proposition 23 of Part 2) is necessarily conscious of itself through the ideas of the affections of the body, the mind is therefore (by Proposition 7 of this part) conscious of its striving. QED

Proposition 10. An idea that excludes the existence of our body cannot be in our mind, but is contrary to it.

Demonstration. Whatever can destroy our body cannot be in it (by Proposition 5 of this part). And so the idea of that thing cannot be in God insofar as he has the idea of our body (by the Corollary to Proposition 9 of Part 1); that is (by Propositions 11 and 13 of Part 2), the idea of that thing cannot be in our mind. On the contrary, since (by Propositions 11 and 13 of Part 2) the first thing that constitutes the essence of the mind is the idea of an actually existing body, the first and principal striving of our mind is (by Proposition 7 of this part) to affirm the existence of our body. And so an idea that denies the existence of our body is contrary to our mind. QED

Proposition 11. Whatever increases or diminishes, aids or restrains, our body’s power of acting, the idea of that same thing increases or diminishes, aids or restrains, our mind’s power of thinking.

Demonstration. This Proposition is evident from Proposition 7 of Part 2, or also from Proposition 14 of Part 2.

Scholium. We see, then, that the mind can undergo great changes, passing now to a greater, now to a lesser perfection; and these passions explain to us the affects of joy and sadness. In what follows, therefore, by joy I shall understand the passion by which the mind passes to a greater perfection; and by sadness, the passion by which it passes to a lesser perfection. Further, the affect of joy, when it is related to the mind and body together, I call localized pleasure or cheerfulness; that of sadness, pain or melancholy. But it should be noted that localized pleasure and pain are related to a person when one part of him is affected more than the rest, whereas cheerfulness and melancholy are related to him when all parts are equally affected. What desire is, I explained in the Scholium to Proposition 9 of this part; and besides these three I recognize no other primary affect. For I shall show in what follows that the rest arise from these three.note

In the Scholium to Proposition 17 of Part 2 we showed that the idea that constitutes the essence of the mind involves the existence of the body for as long as the body itself exists. Next, from what we showed in the Corollary to Proposition 8 of Part 2 and in its Scholium, it follows that the present existence of our mind depends on this alone: that the mind involves the actual existence of the body. Finally, we showed that the power of the mind by which it imagines things and remembers them also depends on this (see Propositions 17 and 18 of Part 2, with its Scholium): that it involves the actual existence of the body. From this it follows that the present existence of the mind and its power of imagining are taken away as soon as the mind ceases to affirm the present existence of the body. But the cause of the mind’s ceasing to affirm this existence of the body cannot be the mind itself (by Proposition 4 of this part), nor again the body’s ceasing to be.

Proposition 12. The mind, as far as it can, strives to imagine those things that increase or aid the body’s power of acting.

Demonstration. As long as the human body is affected in a way that involves the nature of some external body, the human mind will regard that body as present (by Proposition 17 of Part 2); and consequently (by Proposition 7 of Part 2), as long as the human mind regards some external body as present—that is (by the Scholium to the same Proposition 17), imagines it—the human body is affected in a way that involves the nature of that external body. And so, as long as the mind imagines things that increase or aid our body’s power of acting, the body is affected in ways that increase or aid its power of acting (see Postulate 1 of this part); and consequently (by Proposition 11 of this part), for that long the mind’s power of thinking is increased or aided. Hence (by Proposition 6 or 9 of this part) the mind, as far as it can, strives to imagine those things. QED

Proposition 13. When the mind imagines things that diminish or restrain the body’s power of acting, it strives, as far as it can, to recall things that exclude their existence.

Demonstration. As long as the mind imagines anything of this kind, the power of both mind and body is diminished or restrained (as we demonstrated in the preceding Proposition). Nevertheless the mind will go on imagining it until it imagines something else that excludes its present existence (by Proposition 17 of Part 2). That is (as we have just shown), the power of mind and body is diminished or restrained until the mind imagines something else that excludes the existence of this thing—something which the mind (by Proposition 9 of this part) will therefore strive, as far as it can, to imagine or recall. QED

Corollary. From this it follows that the mind is averse to imagining things that diminish or restrain its own power and the body’s.

Scholium. From this we understand clearly what love and hatred are. Love is nothing but joy accompanied by the idea of an external cause, and hatred nothing but sadness accompanied by the idea of an external cause. We see, further, that one who loves necessarily strives to have present and to preserve the thing he loves; and, on the other hand, one who hates strives to remove and destroy the thing he hates. But of all this more fully in what follows.

Proposition 14. If the mind has once been affected by two affects at the same time, then when it is later affected by one of them, it will also be affected by the other.

Demonstration. If the human body has once been affected by two bodies at the same time, then when the mind later imagines one of them, it will immediately recall the other as well (by Proposition 18 of Part 2). But the mind’s imaginings indicate the affects of our body more than the nature of external bodies (by Corollary 2 to Proposition 16 of Part 2). Therefore if the body, and consequently the mind (see Definition 3 of this part), has once been affected by two affects, then when it is later affected by one of them, it will also be affected by the other. QED

Proposition 15. Anything whatever can be, accidentally, the cause of joy, sadness, or desire.

Demonstration. Suppose the mind is affected by two affects at the same time: one that neither increases nor diminishes its power of acting, and another that either increases or diminishes it (see Postulate 1 of this part). From the preceding Proposition it is evident that when the mind is later affected by the first through its true cause—which (by hypothesis) of itself neither increases nor diminishes the mind’s power of thinking—it will immediately be affected also by the second, which does increase or diminish its power of thinking; that is (by the Scholium to Proposition 11 of this part), it will be affected by joy or sadness. And so that thing will be the cause of joy or sadness not through itself but accidentally. In this same way it can easily be shown that the thing can be, accidentally, the cause of desire. QED

Corollary. Merely from having regarded a thing with an affect of joy or sadness of which it is not itself the efficient cause, we can love it or hate it.

Demonstration. For from this alone it comes about (by Proposition 14 of this part) that the mind, when it later imagines this thing, is affected by an affect of joy or sadness—that is (by the Scholium to Proposition 11 of this part), that the power of mind and body is increased or diminished, etc. And consequently (by Proposition 12 of this part) it comes about that the mind desires to imagine the thing, or (by the Corollary to Proposition 13 of this part) is averse to it; that is (by the Scholium to Proposition 13 of this part), that it loves or hates it. QED

Scholium. From this we understand how it can happen that we love or hate some things without any cause known to us, but only from sympathy (as they say) and antipathy. To this we must also refer those objects that affect us with joy or sadness merely because they have something similar to objects that usually affect us with those same affects, as I shall show in the next Proposition. I know, of course, that the authors who first introduced these names “sympathy” and “antipathy” meant them to signify certain occult qualities of things; but nonetheless I believe we may also understand by them qualities that are known, or manifest.

Proposition 16. Merely from imagining that a thing has something similar to an object that usually affects the mind with joy or sadness, we shall love it or hate it, even though that in which the thing is similar to the object is not the efficient cause of these affects.

Demonstration. That which is similar to the object we have (by hypothesis) regarded in the object itself with an affect of joy or sadness. And so (by Proposition 14 of this part), when the mind is affected by its image, it will immediately also be affected by the one affect or the other; and consequently the thing that we perceive to have this same feature will be (by Proposition 15 of this part) accidentally a cause of joy or sadness. And so (by the preceding Corollary), even though that in which it is similar to the object is not the efficient cause of these affects, we shall still love it or hate it. QED

Proposition 17. If we imagine that a thing which usually affects us with an affect of sadness has something similar to another thing which usually affects us with an equally great affect of joy, we shall hate it and at the same time love it.

Demonstration. For (by hypothesis) this thing is through itself a cause of sadness, and (by the Scholium to Proposition 13 of this part) insofar as we imagine it with this affect, we hate it. And insofar as we imagine, besides, that it has something similar to another thing that usually affects us with an equally great affect of joy, we shall love it with an equally great striving of joy (by the preceding Proposition). And so we shall hate it and at the same time love it. QED

Scholium. This constitution of the mind, which arises from two contrary affects, is called vacillation of mind. It stands to affect as doubt stands to imagination (see the Scholium to Proposition 44 of Part 2); and vacillation of mind and doubt differ from each other only in degree. But it should be noted that in the preceding Proposition I deduced these vacillations of mind from causes that are the cause of one affect through themselves and of the other accidentally. I did this because in that way they could more easily be deduced from what went before—not because I deny that vacillations of mind usually arise from an object that is the efficient cause of both affects. For the human body (by Postulate 1 of Part 2) is composed of a great many individuals of different natures, and so

Proposition 18. A person is affected by the image of a past or future thing with the same affect of joy and sadness as by the image of a present thing.

Demonstration. As long as a person is affected by the image of a thing, he will regard the thing as present even if it does not exist (by Proposition 17 of Part 2 with its Corollary); and he does not imagine it as past or future except insofar as its image is joined to the image of past or future time (see the Scholium to Proposition 44 of Part 2). So the image of a thing, considered in itself alone, is the same whether it is related to future or past time or to the present; that is (by Corollary 2 to Proposition 16 of Part 2), the constitution, or affect, of the body is the same whether the image is of a past or future thing or of a present one. And so the affect of joy and sadness is the same whether the image is of a past or future thing or of a present one. QED

Scholium 1. I call a thing past or future here insofar as we have been or shall be affected by it: for example, insofar as we have seen it or shall see it, it has refreshed us or will refresh us, it has harmed us or will harm us, and so on. For insofar as we imagine it in this way, we affirm its existence; that is, the body is affected by no affect that excludes the thing’s existence, and so (by Proposition 17 of Part 2) the body is affected by the image of the thing in the same way as if the thing itself were present. But since it generally happens that those who have had much experience vacillate as long as they regard a thing as future or past, and very often doubt its outcome

Scholium 2. From what has just been said we understand what hope, fear, confidence, despair, gladness, and remorse are. Hope is nothing but an inconstant joy arising from the image of a future or past thing whose outcome we doubt. Fear, on the other hand, is an inconstant sadness, also arising from the image of a doubtful thing. Further, if the doubt is removed from these affects, hope becomes confidence and fear becomes despair—namely, joy or sadness arising from the image of a thing we feared or hoped for. Gladness, next, is joy arising from the image of a past thing whose outcome we doubted. Finally, remorse is sadness opposite to gladness.note

Proposition 19. One who imagines that what he loves is being destroyed will be saddened; if, on the other hand, he imagines that it is being preserved, he will rejoice.

Demonstration. The mind, as far as it can, strives to imagine those things that increase or aid the body’s power of acting (by Proposition 12 of this part), that is (by the Scholium to Proposition 13 of this part), the things it loves. But the imagination is aided by whatever posits the existence of a thing, and, on the other hand, is restrained by whatever excludes a thing’s existence (by Proposition 17 of Part 2). Therefore images of things that posit the existence of the loved thing aid the striving by which the mind strives to imagine the loved thing—that is (by the Scholium to Proposition 11 of this part), they affect the mind with joy. And those that, on the contrary, exclude the existence of the loved thing restrain that same striving of the mind—that is (by the same Scholium), they affect the mind with sadness. So one who imagines that what he loves is being destroyed will be saddened, etc. QED

Proposition 20. One who imagines that what he hates is being destroyed will rejoice.

Demonstration. The mind (by Proposition 13 of this part) strives to imagine things that exclude the existence of the things by which the body’s power of acting is diminished or restrained; that is (by the Scholium to the same Proposition), it strives to imagine things that exclude the existence of the things it hates. And so the image of a thing that excludes the existence of what the mind hates aids this striving of the mind—that is (by the Scholium to Proposition 11 of this part), it affects the mind with joy. So one who imagines that what he hates is being destroyed will rejoice. QED

Proposition 21. One who imagines what he loves to be affected with joy or sadness will also be affected with joy or sadness; and each of these affects will be greater or lesser in the lover as it is greater or lesser in the thing loved.

Demonstration. Images of things that posit the existence of the loved thing aid the striving by which the mind strives to imagine the loved thing itself (as we demonstrated in Proposition 19 of this part). But joy posits the existence of the joyful thing, and does so the more, the greater the affect of joy is; for it is (by the Scholium to Proposition 11 of this part) a transition to a greater perfection. Therefore the image, in the lover, of the loved thing’s joy aids the striving of his mind—that is (by the Scholium to Proposition 11 of this part), it affects the lover with joy, and with a greater joy the greater this affect was in the loved thing. This was the first point. Next, insofar as a thing is affected with sadness, to that extent it is destroyed, and the more so the greater the sadness with which it is affected

Proposition 22. If we imagine someone affecting with joy a thing we love, we shall be affected with love toward him. If, on the other hand, we imagine him affecting it with sadness, we shall also be affected with hatred toward him.

Demonstration. Whoever affects a thing we love with joy or sadness also affects us with joy or sadness—provided, that is, that we imagine the loved thing affected with that joy or sadness (by the preceding Proposition). But this joy or sadness is supposed to be in us accompanied by the idea of an external cause. Therefore (by the Scholium to Proposition 13 of this part), if we imagine someone affecting a thing we love with joy or sadness, we shall be affected with love or hatred toward him. QED

Scholium. Proposition 21 explains to us what pity is, which we can define as sadness arising from another’s harm. But by what name we should call the joy that arises from another’s good, I do not know. Further, love toward someone who has done good to another we shall call approval; and, on the other hand, hatred toward someone who has done harm to another we shall call indignation. Finally, it should be noted that we pity not only a thing we have loved (as we showed in Proposition 21) but also one toward which we previously had no affect, provided we judge it to be like ourselves (as I shall show below). And so we also approve of one who has done good to someone like us, and, on the other hand, are indignant at one who has harmed someone like us.

Proposition 23. One who imagines what he hates to be affected with sadness will rejoice; if, on the other hand, he imagines it to be affected with joy, he will be saddened. And each of these affects will be greater or lesser as its contrary is greater or lesser in what he hates.

Demonstration. Insofar as a hated thing is affected with sadness, to that extent it is destroyed, and the more so the greater the sadness with which it is affected (by the Scholium to Proposition 11 of this part). So one who (by Proposition 20 of this part) imagines that the thing he hates is affected with sadness will, on the contrary, be affected with joy—and with a greater joy the greater the sadness with which he imagines the hated thing to be affected. This was the first point. Next, joy posits the existence of the joyful thing (by the same Scholium to Proposition 11 of this part), and does so the more, the greater the joy is conceived to be. If someone imagines one whom he hates affected with joy, this imagining (by Proposition 13 of this part) will restrain his striving; that is (by the Scholium to Proposition 11 of this part), the one who hates will be affected with sadness, etc. QED

Scholium. This joy can hardly be solid and free of all conflict of mind. For (as I shall show shortly, in Proposition 27 of this part) insofar as one imagines a thing like oneself affected with sadness, to that extent one must be saddened; and the reverse, if one imagines it affected with joy. But here we are attending to hatred alone.

Proposition 24. If we imagine that someone affects with joy a thing we hate, we will be affected with hatred toward him as well. If, on the other hand, we imagine that he affects that same thing with sadness, we will be affected with love toward him.

Demonstration. This Proposition is demonstrated in the same way as Proposition 22 of this part; see that Proposition.

Scholium. These and similar affects of hatred are related to envy, which is therefore nothing but hatred itself, insofar as it is considered to dispose a person so that he rejoices at another’s misfortune and, on the other hand, is saddened by that person’s good fortune.

Proposition 25. We strive to affirm, of ourselves and of a thing we love, everything that we imagine affects us, or the loved thing, with joy; and, on the other hand, to deny everything that we imagine affects us, or the loved thing, with sadness.

Demonstration. Whatever we imagine affects a loved thing with joy or sadness affects us with joy or sadness (by Proposition 21 of this part). But the mind (by Proposition 12 of this part) strives, as far as it can, to imagine the things that affect us with joy—that is (by Proposition 17 of Part 2 and its Corollary), to regard them as present—and, on the other hand (by Proposition 13 of this part), to exclude the existence of the things that affect us with sadness. Therefore we strive to affirm, of ourselves and of a thing we love, everything that we imagine affects us, or the loved thing, with joy; and conversely. QED

Proposition 26. We strive to affirm, of a thing we hate, everything that we imagine affects it with sadness, and, on the other hand, to deny whatever we imagine affects it with joy.

Demonstration. This Proposition follows from Proposition 23, as the preceding one follows from Proposition 21 of this part.

Scholium. From these we see that it easily happens that a person thinks more highly than is just of himself and of a thing he loves, and, on the other hand, less highly than is just of a thing he hates. When this imagining concerns the person himself who thinks more highly of himself than is just, it is called pride. It is a species of madness, because the person dreams with his eyes open that he can do all the things he attains by imagination alone; he therefore regards them as real and exults in them, as long as he cannot imagine the things that exclude their existence and limit his own power of acting. Pride, then, is joy born of the fact that a person thinks more highly of himself than is just. Next, the joy that arises from a person’s thinking more highly of another than is just is called overestimation; and finally, the joy that arises from thinking less highly of another than is just is called scorn.

Proposition 27. If we imagine that a thing like us, toward which we have had no affect, is affected with some affect, we are by that very fact affected with a similar affect.

Demonstration. The images of things are affections of the human body whose ideas represent external bodies as present to us (by the Scholium to Proposition 17 of Part 2); that is (by Proposition 16 of Part 2), affections whose ideas involve the nature of our body and, at the same time, the present nature of the external body. If, therefore, the nature of the external body is like the nature of our body, then the idea of the external body we imagine will involve an affection of our body like the affection of the external body. Consequently, if we imagine someone like us affected with some affect, this imagining will express an affection of our body like that affect. And so, from the fact that we imagine a thing like us to be affected with some affect, we are affected with an affect like its own. But if we hate a thing like us, then to that extent (by Proposition 23 of this part) we will be affected with an affect contrary to its own, not a similar one. QED

Scholium. This imitation of affects, when it concerns sadness, is called pity (on which see the Scholium to Proposition 22 of this part); but when it concerns desire it is called emulation, which therefore is nothing but the desire for a thing that is generated in us from the fact that we imagine others like us to have the same desire.

Corollary 1. If we imagine that someone toward whom we have had no affect affects a thing like us with joy, we will be affected with love toward him. If, on the other hand, we imagine that he affects it with sadness, we will be affected with hatred toward him.

Demonstration. This is demonstrated from the preceding Proposition in the same way as Proposition 22 of this part is demonstrated from Proposition 21.

Corollary 2. We cannot hate a thing we pity on account of the fact that its misery affects us with sadness.

Demonstration. For if we could hate it on that account, then (by Proposition 23 of this part) we would rejoice at its sadness, which is contrary to the hypothesis.

Corollary 3. We will strive, as far as we can, to free a thing we pity from its misery.

Demonstration. Whatever affects a thing we pity with sadness affects us too with a similar sadness (by the preceding Proposition). And so we will strive to think up whatever takes away that cause’s existence, or destroys it (by Proposition 13 of this part); that is (by the Scholium to Proposition 9 of this part), we will have an appetite to destroy it, or will be determined to destroy it. And so we will strive to free the thing we pity from its misery. QED

Scholium. This will, or appetite, to do good, which arises from our pitying the thing on which we want to confer a benefit, is called benevolence, which therefore is nothing but desire arising from pity. As for love and hatred toward someone who has done good or harm to a thing we imagine to be like us, see the Scholium to Proposition 22 of this part.

Proposition 28. We strive to further the occurrence of whatever we imagine leads to joy; but whatever we imagine is opposed to it, or leads to sadness, we strive to remove or destroy.

Demonstration. Whatever we imagine leads to joy we strive, as far as we can, to imagine (by Proposition 12 of this part); that is (by Proposition 17 of Part 2), we will strive, as far as we can, to regard it as present, or as actually existing. But the mind’s striving, or power, in thinking is equal to and by nature simultaneous with the body’s striving, or power, in acting (as clearly follows from the Corollary to Proposition 7 and the Corollary to Proposition 11 of Part 2). Therefore we strive without qualification for it to exist; that is (which, by the Scholium to Proposition 9 of this part, is the same thing), we have an appetite for it and aim at it. That was the first point. Next, if we imagine that what we believe to be the cause of sadness—that is

Proposition 29. We will also strive to do whatever we imagine people look upon with joy, and, on the other hand, we will be averse to doing what we imagine people∗ are averse to.

Demonstration. From the fact that we imagine people to love or hate something, we will love or hate the same thing (by Proposition 27 of this part); that is (by the Scholium to Proposition 13 of this part), we will by that very fact rejoice or be saddened at that thing’s presence. And so (by the preceding Proposition) we will strive to do whatever we imagine people love, or look upon with joy, etc. QED

Scholium. This striving to do something, and also to refrain from doing something, solely in order to please people, is called ambition, especially when we strive so eagerly to please the crowd that we do or omit certain things to our own harm or another’s; otherwise it is usually called courtesy. Next, the joy with which we imagine another’s action by which he has striven to please us I call praise; and the sadness with which, on the contrary, we are averse to his action I call blame.

Proposition 30. If someone has done something that he imagines affects others with joy, he will be affected with joy accompanied by the idea of himself as its cause; that is, he will regard himself with joy. If, on the other hand, he has done something that he imagines affects others with sadness, he will regard himself with sadness.

Demonstration. Whoever imagines that he affects others with joy or sadness will by that very fact (by Proposition 27 of this part) be affected with joy or sadness. But since a person (by Propositions 19 and 23 of Part 2) is conscious of himself through the affections by which he is determined to act, whoever has done something that he imagines affects others with joy will be affected with joy together with consciousness of himself as its cause; that is, he will regard himself with joy; and conversely. QED

Scholium. Since love (by the Scholium to Proposition 13 of this part) is joy accompanied by the idea of an external cause, and hatred is sadness accompanied likewise by the idea of an external cause, this joy and sadness will be species of love and hatred. But because love and hatred are related to external objects, we will signify these affects by other names. Joy accompanied by the idea of an internal cause we will call glory, and the sadness contrary to it shame—understand: when the joy or sadness arises from a person’s believing that he is praised or blamed. Otherwise, I will call joy accompanied by the idea of an internal cause self-contentment, and the sadness contrary to it repentance. Next, sincenote

Proposition 31. If we imagine that someone loves, desires, or hates something that we ourselves love, desire, or hate, we will by that very fact love it, etc., more steadfastly. But if we imagine that he is averse to what we love, or the reverse, then we will suffer vacillation of mind.

Demonstration. From the mere fact that we imagine someone loves something, we will by that very fact love it (by Proposition 27 of this part). But we are supposing that we love it already, apart from this. So a new cause is added to our love, by which it is fostered; and so by this very fact we will love what we love more steadfastly. Next, from the fact that we imagine someone is averse to something, we will be averse to it (by the same Proposition). But if we suppose that we love that very thing at the same time, then at the same time we will both love it and be averse to it; that is (see the Scholium to Proposition 17 of this part), we will suffer vacillation of mind. QED

Corollary. From this and from Proposition 28 of this part it follows that each person strives, as far as he can, to bring it about that everyone loves what he himself loves, and hates what he himself hates. Hence the Poet’s lines: As lovers, let us hope alike and fear alike; / he is made of iron who loves what another allows.note

Scholium. This striving to bring it about that everyone approves what one loves or hates is in truth ambition (see the Scholium to Proposition 29 of this part). And so we see that each person by nature has an appetite for the others to live according to his own temperament. Since all have this appetite equally, they equally get in one another’s way; and since all want to be praised, or loved, by all, they hate one another.

Proposition 32. If we imagine that someone enjoys a thing that only one person can possess, we will strive to bring it about that he does not possess it.

Demonstration. From the mere fact that we imagine someone enjoys a thing (by Proposition 27 of this part with its Corollary 1), we will love that thing and desire to enjoy it. But (by hypothesis) we imagine that his enjoying this same thing stands in the way of this joy of ours. Therefore (by Proposition 28 of this part) we will strive that he should not possess it. QED

Scholium. We see, then, that human nature is generally so constituted that people pity those who fare badly and envy those who fare well, and (by the preceding Proposition) with a hatred the greater, the more they love the thing they imagine another possesses. We see next that from the same property of human nature from which it follows that people are compassionate, it also follows that they are envious and ambitious. Finally, if we are willing to consult experience itself, we will find that it teaches all these things, especially if we attend to the first years of our life.

Proposition 33. When we love a thing like ourselves, we strive, as far as we can, to bring it about that it loves us in return.

Demonstration. A thing we love we strive, as far as we can, to imagine in preference to others (by Proposition 12 of this part). If, therefore, the thing is like us, we will strive to affect it with joy in preference to others (by Proposition 29 of this part); that is, we will strive, as far as we can, to bring it about that the loved thing is affected with joy accompanied by the idea of us—that is (by the Scholium to Proposition 13 of this part), that it loves us in return. QED

Proposition 34. The greater the affect with which we imagine a loved thing to be affected toward us, the more we will glory.

Demonstration. We strive (by the preceding Proposition), as far as we can, to bring it about that a loved thing loves us in return; that is (by the Scholium to Proposition 13 of this part), that the loved thing is affected with joy accompanied by the idea of us. So the greater the joy with which we imagine the loved thing is affected on our account, the more this striving is assisted; that is (by Proposition 11 of this part with its Scholium), the greater the joy with which we are affected. But when we rejoice because we have affected another like us with joy, we regard ourselves with joy (by Proposition 30 of this part). Therefore the greater the affect with which we imagine a loved thing to be affected toward us, the greater the joy with which we will regard ourselves; that is (by the Scholium to Proposition 30 of this part), the more we will glory. QED

Proposition 35. If someone imagines that a loved thing is joining another to itself by the same bond of friendship by which he alone used to possess it, or by a closer one, he will be affected with hatred toward the loved thing itself and will envy that other person.

Demonstration. The greater the love with which someone imagines a loved thing to be affected toward him, the more he will glory (by the preceding Proposition); that is (by the Scholium to Proposition 30 of this part), the more he will rejoice. And so (by Proposition 28 of this part) he will strive, as far as he can, to imagine the loved thing bound to him as closely as possible. This striving, or appetite, is encouraged if he imagines that another desires the same thing for himself (by Proposition 31 of this part). But this striving, or appetite, is supposed to be checked by the image of the loved thing itself, accompanied by the image of the one whom the loved thing is joining to itself. Therefore (by the Scholium to Proposition 11 of this part) he will by that very fact be affected with sadness, accompanied by the idea of the loved thing as its cause and at the same time by the image of the other; that is (by the Scholium to Proposition 13 of this part), he will be affected with hatred toward the loved thing, and at the same time toward that other person

Scholium. This hatred toward a loved thing, joined with envy, is called jealousy, which is therefore nothing but a vacillation of mind arising from love and hatred together, accompanied by the idea of another who is envied. Moreover, this hatred toward the loved thing will be greater in proportion to the joy with which the jealous person used to be affected by the loved thing’s reciprocal love, and also in proportion to the affect with which he was affected toward the one he imagines the loved thing is joining to itself. For if he hated that person, he will by that very fact hate the loved thing (by Proposition 24 of this part), because he imagines that it affects with joy what he himself hates; and also (by the Corollary to Proposition 15 of this part) because he is compelled to join the image of the loved thing to the image of the one he hates.

Proposition 36. One who recollects a thing in which he once took delight desires to possess it under the same circumstances as when he first took delight in it.

Demonstration. Whatever a person has seen together with a thing that delighted him will (by Proposition 15 of this part) be accidentally a cause of joy. And so (by Proposition 28 of this part) he will desire to possess all of it together with the thing that delighted him; that is, he will desire to possess the thing with all the same circumstances as when he first took delight in it. QED

Corollary. So if the lover finds that one of those circumstances is missing, he will be saddened.

Demonstration. For insofar as he finds some circumstance missing, he imagines something that excludes that thing’s existence. But since, out of love, he desires that thing, or circumstance (by the preceding Proposition), then (by Proposition 19 of this part), insofar as he imagines it missing, he will be saddened. QED

Scholium. This sadness, insofar as it concerns the absence of what we love, is called longing.

Proposition 37. The desire that arises from sadness or joy, and from hatred or love, is greater the greater the affect is.

Demonstration. Sadness diminishes or checks a person’s power of acting (by the Scholium to Proposition 11 of this part); that is (by Proposition 7 of this part), it diminishes or checks the striving by which a person strives to persevere in his being. And so (by Proposition 5 of this part) it is contrary to this striving, and whatever a person affected with sadness strives for is to remove the sadness. But (by the definition of sadness) the greater the sadness, the greater the part of the person’s power of acting to which it must be opposed. Therefore the greater the sadness, the greater the power of acting with which the person will strive, in turn, to remove it; that is (by the Scholium to Proposition 9 of this part), the greater the desire, or appetite, with which he will strive to remove the sadness. Next, since joy

Proposition 38. If someone has begun to hate a thing he loved, so that his love is completely destroyed, then, given an equal cause, he will hate it with a greater hatred than if he had never loved it—and the greater, the greater his love had been before.

Demonstration. For if someone begins to hate a thing he loves, more of his appetites are checked than if he had not loved it. For love is a joy (by the Scholium to Proposition 13 of this part) which a person strives, as far as he can, to preserve (by Proposition 28 of this part); and he does so (by the same Scholium) by regarding the loved thing as present and by affecting it with joy as far as he can (by Proposition 21 of this part). This striving (by the preceding Proposition) is the greater, the greater the love, as is the striving to bring it about that the loved thing loves him in return (see Proposition 33 of this part). But these strivings are checked by hatred toward the loved thing (by the Corollary to Proposition 13 and by Proposition 23 of this part). Therefore the lover

Proposition 39. One who hates someone will strive to do him evil, unless he fears that a greater evil to himself will arise from it; and, on the other hand, one who loves someone will strive, by the same law, to do him good.

Demonstration. To hate someone is (by the Scholium to Proposition 13 of this part) to imagine him as a cause of sadness. And so (by Proposition 28 of this part) one who hates someone will strive to remove or destroy him. But if he fears from this something sadder, or (what is the same thing) a greater evil to himself, and believes he can avoid it by not doing to the one he hates the evil he was planning, he will desire to refrain from doing evil (by the same Proposition 28 of this part). And he will do so (by Proposition 37 of this part) with a greater striving than the one that held him to doing evil, so that this striving will prevail, as we maintained. The demonstration of the second part proceeds in the same way. Therefore one who hates someone, etc. QED

Scholium. By good I here understand every kind of joy, and further whatever leads to it—especially whatever satisfies a longing, of whatever kind it may be. By evil I understand every kind of sadness, and especially whatever frustrates a longing. For we showed above (in the Scholium to Proposition 9 of this part) that we do not desire anything because we judge it to be good; on the contrary, we call good what we desire, and consequently we call evil what we are averse to. So each person judges, or evaluates, from his own affect what is good and what is evil, what is better and what worse, and finally what is best and what worst. Thus the greedy person judges an abundance of money to be best, and a lack of it worst. The ambitious person desires nothing so much as glory, and on the other hand dreads nothing so much as shame.

Proposition 40. One who imagines that he is hated by someone, and does not believe he has given that person any cause for hatred, will hate him in return.

Demonstration. One who imagines someone affected with hatred will by that very fact also be affected with hatred (by Proposition 27 of this part), that is (by the Scholium to Proposition 13 of this part), with sadness accompanied by the idea of an external cause. But (by hypothesis) he imagines no cause of this sadness except the one who hates him. Therefore, from the fact that he imagines he is hated by someone, he will be affected with sadness accompanied by the idea of the one who hates him; that is (by the same Scholium), he will hate him. QED

Scholium. But if he imagines that he has given just cause for the hatred, then (by Proposition 30 of this part and its Scholium) he will be affected with shame. But this (by Proposition 25 of this part) rarely happens. Moreover, this reciprocation of hatred can also arise from the fact that hatred is followed by a striving to do evil to the one who is hated (by Proposition 39 of this part). So one who imagines that he is hated by someone will imagine that person as the cause of some evil, or sadness; and so he will be affected with sadness, or fear, accompanied by the idea of the one who hates him as its cause—that is, he will be affected with hatred in return, as above.

Corollary 1. One who imagines that someone he loves is affected with hatred toward him will be torn by hatred and love at once. For insofar as he imagines that he is hated by that person, he is determined (by the preceding Proposition) to hate him in return. But (by hypothesis) he loves him nonetheless. Therefore he will be torn by hatred and love at once.

Corollary 2. If someone imagines that some evil has been done to him out of hatred by a person toward whom he previously had no affect, he will immediately strive to return the same evil to that person.

Demonstration. One who imagines someone affected with hatred toward him will hate him in return (by the preceding Proposition), and (by Proposition 26 of this part) will strive to think up everything that can affect that person with sadness, and will be eager to inflict it on him (by Proposition 39 of this part). But (by hypothesis) the first thing of this kind that he imagines is the evil done to himself. Therefore he will immediately strive to inflict the same evil on that person. QED

Scholium. The striving to do evil to one we hate is called anger; the striving to return an evil done to us is called vengeance.

Proposition 41. If someone imagines that he is loved by someone, and does not believe he has given any cause for this (which can happen by the Corollary to Proposition 15 and by Proposition 16 of this part), he will love that person in return.

Demonstration. This Proposition is demonstrated in the same way as the preceding one. See also its Scholium.

Scholium. But if he believes that he has given just cause for the love, he will glory (by Proposition 30 of this part with its Scholium). This happens rather often (by Proposition 25 of this part), and we have said that its opposite occurs when someone imagines he is hated by someone (see the Scholium to the preceding Proposition). Further, this reciprocal love, and consequently (by Proposition 39 of this part) the striving to do good to one who loves us and who (by the same Proposition 39 of this part) strives to do good to us, is called gratitude, or thankfulness. And so it is evident that people are far readier for vengeance than for repaying a kindness.

Corollary. One who imagines that he is loved by someone he hates will be torn by hatred and love at once. This is demonstrated in the same way as the first Corollary of the preceding Proposition.

Scholium. But if hatred prevails, he will strive to do evil to the one by whom he is loved. This affect is called cruelty, especially if the one who loves is believed to have given none of the usual causes for hatred.

Proposition 42. One who has conferred a benefit on someone, moved by love or by hope of glory, will be saddened if he sees that the benefit is received ungratefully.

Demonstration. One who loves a thing like himself strives, as far as he can, to bring it about that he is loved by it in return (by Proposition 33 of this part). So one who has conferred a benefit on someone out of love does so from the longing that possesses him to be loved in return—that is (by Proposition 34 of this part), from hope of glory, or (by the Scholium to Proposition 30 of this part) of joy. And so (by Proposition 12 of this part) he will strive, as far as he can, to imagine this cause of glory, or to regard it as actually existing. But (by hypothesis) he imagines something else that excludes that cause’s existence. Therefore (by Proposition 19 of this part) he will by that very fact be saddened. QED

Proposition 43. Hatred is increased by reciprocal hatred, and can, on the other hand, be destroyed by love.

Demonstration. If someone imagines that the one he hates is affected with hatred toward him in return, a new hatred arises by that very fact (by Proposition 40 of this part), while (by hypothesis) the first still endures. But if, on the contrary, he imagines that person to be affected with love toward him, then insofar as he imagines this, he regards himself with joy (by Proposition 30 of this part), and to that extent (by Proposition 29 of this part) will strive to please that person; that is (by Proposition 41 of this part), to that extent he strives not to hate him and not to affect him with any sadness. This striving (by Proposition 37 of this part) will be greater or less in proportion to the affect from which it arises. And so, if it is greater than the striving that arises from hatred, by which he strives to affect the thing he hates with sadness (by Proposition 26 of this part), it will prevail over it and wipe the hatred from his mind. QED

Proposition 44. Hatred that is completely conquered by love passes into love; and the love is therefore greater than if hatred had not preceded it.

Demonstration. This proceeds in the same way as the demonstration of Proposition 38 of this part. For one who begins to love a thing he hates, or used to regard with sadness, rejoices by the very fact that he loves. And to this joy, which love involves (see its definition in the Scholium to Proposition 13 of this part), is added the joy that arises from the fact that the striving to remove the sadness that hatred involves (as we showed in Proposition 37 of this part) is wholly assisted, accompanied by the idea of the one he hated as its cause.

Scholium. Although this is so, no one will strive to hate something, or to be affected with sadness, in order to enjoy this greater joy. That is, no one will desire to suffer a loss in the hope of recovering it, or long to be ill in the hope of getting well. For each person will always strive to preserve his being and to remove sadness as far as he can. If, on the contrary, it could be conceived that a person could desire to hate someone in order to love him all the more afterward, then he would always desire to hate him. For the greater the hatred had been, the greater the love will be, and so he will always desire that the hatred be increased more and more. For the same reason a person would strive to be more and more ill, in order afterward to enjoy a greater joy from the restoration of his health; and so he would always strive to be ill—which (by Proposition 6 of this part) is absurd.

Proposition 45. If someone imagines that someone like himself is affected with hatred toward a thing like himself that he loves, he will hate that person.

Demonstration. For the loved thing hates in return the one who hates it (by Proposition 40 of this part). And so the lover, who imagines that someone hates the loved thing, by that very fact imagines the loved thing to be affected with hatred, that is (by the Scholium to Proposition 13 of this part), with sadness; and consequently (by Proposition 21 of this part) he is saddened, and that accompanied by the idea of the one who hates the loved thing as its cause. That is (by the Scholium to Proposition 13 of this part), he will hate him. QED

Proposition 46. If someone has been affected with joy or sadness by someone of a class or nation different from his own, accompanied by the idea of that person, under the universal name of the class or nation, as its cause, he will love or hate not only that person but everyone of the same class or nation.

Demonstration. The demonstration of this is evident from Proposition 16 of this part.

Proposition 47. The joy that arises from our imagining that a thing we hate is destroyed, or affected with some other evil, does not arise without some sadness of mind.

Demonstration. This is evident from Proposition 27 of this part. For insofar as we imagine a thing like ourselves to be affected with sadness, to that extent we are saddened.

Scholium. This Proposition can also be demonstrated from the Corollary to Proposition 17 of Part 2. For whenever we recall a thing, even though it does not actually exist, we still regard it as present, and the body is affected in the same way. So insofar as the memory of the thing remains strong, a person is determined to regard it with sadness. While the image of the thing still remains, this determination is indeed restrained by the memory of those things that exclude its existence, but it is not removed. And so the person rejoices only insofar as this determination is restrained. Hence it comes about that this joy, which arises from the misfortune of the thing we hate, is repeated as often as we recall that thing. For, as we have said, when the image of the thing is aroused, since it involves the existence of the thing itself, it determines the person to regard the thing with the same sadness with which he used to regard it when it existed.

Proposition 48. Love and hatred toward, for example, Peter are destroyed if the sadness that the latter involves, and the joy that the former involves, are joined to the idea of another cause; and each is diminished to the extent that we imagine that Peter was not the sole cause of either.

Demonstration. This is evident from the mere definition of love and hatred, which see in the Scholium to Proposition 13 of this part. For joy is called love of Peter, and sadness hatred of Peter, solely because Peter is considered to be the cause of the one affect or the other. So when this is removed, wholly or in part, the affect toward Peter is also diminished, wholly or in part. QED

Proposition 49. Love and hatred toward a thing we imagine to be free must both be greater, from an equal cause, than toward a thing we imagine to be necessary.

Demonstration. A thing we imagine to be free must be perceived through itself, without others (by Definition 7 of Part 1). So if we imagine it to be the cause of joy or sadness, by that very fact (by the Scholium to Proposition 13 of this part) we shall love or hate it, and that (by the preceding Proposition) with the greatest love or hatred that can arise from the given affect. But if we imagine the thing that is the cause of that affect as necessary, then (by the same Definition 7 of Part 1) we shall imagine it to be the cause of that affect not alone but together with others, and so (by the preceding Proposition) our love or hatred toward it will be less. QED

Scholium. It follows from this that people, because they think themselves free, pursue one another with greater love or hatred than they do other things. To this is added the imitation of the affects, on which see Propositions 27, 34, 40 and 43 of this part.

Proposition 50. Anything whatever can be, accidentally, a cause of hope or fear.

Demonstration. This Proposition is demonstrated in the same way as Proposition 15 of this part, which see together with Scholium 2 to Proposition 18 of this part.

Scholium. Things that are accidentally causes of hope or fear are called good or bad omens. And insofar as these omens are causes of hope or fear, to that extent (by the definition of hope and fear, which see in Scholium 2 to Proposition 18 of this part) they are causes of joy or sadness. Consequently (by the Corollary to Proposition 15 of this part) to that extent we love or hate them, and (by Proposition 28 of this part) we strive either to employ them as means to what we hope for, or to remove them as obstacles or causes of fear. Further, it follows from Proposition 25 of this part that we are so constituted by nature that we readily believe what we hope for, but believe with difficulty what we fear, and that we think more or less of these things than is just. And from these have arisen the superstitions by which people everywhere are troubled.

Proposition 51. Different people can be affected in different ways by one and the same object, and one and the same person can be affected in different ways by one and the same object at different times.

Demonstration. The human body (by Postulate 3 of Part 2) is affected by external bodies in a great many ways. So two people can be affected in different ways at the same time; and therefore (by Axiom 1, which comes after Lemma 3, which see after Proposition 13 of Part 2) they can be affected in different ways by one and the same object. Again (by the same Postulate), the human body can be affected now in this way, now in another; and consequently (by the same Axiom) it can be affected in different ways by one and the same object at different times. QED

Scholium. We see, then, that it can happen that what one person loves another hates, and what one fears another does not; and that one and the same person may now love what he formerly hated, and now dare what he formerly feared, and so on. Again, since each person judges from his own affect what is good, what is bad, what is better and what is worse (see the Scholium to Proposition 39 of this part), it follows that people can vary as much in judgment as in affect.∗ Hence it comes about that when we compare some people with others, we distinguish them solely by the difference of their affects, and call some fearless, others timid, and others by some other name. For example,

Proposition 52. An object that we have previously seen together with others, or that we imagine to have nothing but what is common to many, we shall not regard for as long as one that we imagine to have something singular.

Demonstration. As soon as we imagine an object we have seen with others, we at once recall the others as well (by Proposition 18 of Part 2, and see also its Scholium), and so from regarding one we immediately pass to regarding another. And the same holds for an object that we imagine to have nothing but what is common to many. For by that very fact we suppose that we regard nothing in it that we have not previously seen with others. But when we suppose that we imagine in some object something singular, which we have never seen before, we are saying nothing other than that the mind, while it regards that object, has nothing else in itself to whose regard it can pass from regarding that one; and so it is determined to regard that object alone. Therefore an object, etc. QED

Scholium. This affection of the mind, or imagination of a singular thing, insofar as it occupies the mind alone, is called wonder. If it is aroused by an object we fear, it is called consternation, because wonder at an evil keeps a person so suspended in regarding it alone that he cannot think of other things by which he might avoid that evil. But if what we wonder at is some person’s prudence, diligence or something of the kind, then, because by that very fact we regard that person as far surpassing us, wonder is called veneration; otherwise it is called horror, if what we wonder at is a person’s anger, envy and the like. Again, if we wonder at the prudence, diligence and so on of a person we love, our love will by that very fact be greater (by Proposition 12 of this part), and this love joined to wonder, or veneration, we call devotion.

Opposed to wonder is disdain. Its cause, however, is usually this: from seeing someone wonder at, love or fear something, and so on, or from the fact that a thing at first sight appears like things we wonder at, love, fear and so on (by Proposition 15 of this part with its Corollary, and Proposition 27 of this part), we are determined to wonder at, love or fear that same thing. But if, from the thing’s presence or from a more accurate consideration of it, we are compelled to deny of it everything that can be a cause of wonder, love, fear and so on, then the mind, from the very presence of the thing, remains determined to think of what is not in the object rather than of what is in it—whereas, on the contrary, from an object’s presence it usually thinks chiefly of what is in the object.

Proposition 53. When the mind regards itself and its power of acting, it rejoices, and the more so the more distinctly it imagines itself and its power of acting.

Demonstration. A person does not know himself except through the affections of his body and their ideas (by Propositions 19 and 23 of Part 2). So when it happens that the mind can regard itself, it is by that very fact supposed to pass to a greater perfection, that is (by the Scholium to Proposition 11 of this part), to be affected with joy—and with a greater joy the more distinctly it can imagine itself and its power of acting. QED

Corollary. This joy is fostered more and more the more a person imagines himself to be praised by others. For the more he imagines himself praised by others, the greater the joy with which he imagines others to be affected by him, accompanied by the idea of himself (by the Scholium to Proposition 29 of this part); and so (by Proposition 27 of this part) he himself is affected with greater joy, accompanied by the idea of himself. QED

Proposition 54. The mind strives to imagine only those things that posit its power of acting.

Demonstration. The striving, or power, of the mind is the very essence of the mind (by Proposition 7 of this part). But the essence of the mind (as is self-evident) affirms only what the mind is and can do, not what it is not and cannot do. So it strives to imagine only what affirms, or posits, its power of acting. QED

Proposition 55. When the mind imagines its lack of power, it is by that very fact saddened.

Demonstration. The essence of the mind affirms only what the mind is and can do; in other words, it is of the nature of the mind to imagine only those things that posit its power of acting (by the preceding Proposition). So when we say that the mind, while it regards itself, imagines its lack of power, we are saying nothing other than that, while the mind strives to imagine something that posits its power of acting, this striving of it is restrained—that is (by the Scholium to Proposition 11 of this part), that it is saddened. QED

Corollary. This sadness is fostered more and more if the mind imagines itself to be blamed by others. This is demonstrated in the same way as the Corollary to Proposition 53 of this part.

Scholium. This sadness, accompanied by the idea of our own weakness, is called humility; but the joy that arises from regarding ourselves is called philautia [self-love] or self-contentment. And since this joy is repeated as often as a person regards his virtues, or his power of acting, it also comes about that everyone is eager to tell of his own deeds and to show off his strength of body and of mind alike, and that for this reason people are a nuisance to one another. From this it again follows that people are by nature envious (see the Scholium to Proposition 24 and the Scholium to Proposition 32 of this part); that is, they are glad at the weakness of their equals and, on the other hand, saddened by their virtue.

Corollary. No one envies anyone’s virtue except an equal’s.

Demonstration. Envy is hatred itself (see the Scholium to Proposition 24 of this part), or (by the Scholium to Proposition 13 of this part) sadness, that is (by the Scholium to Proposition 11 of this part), an affection by which a person’s power of acting, or striving, is restrained. But a person (by the Scholium to Proposition 9 of this part) strives to do, and desires, nothing except what can follow from his own given nature. So a person will not desire to have predicated of himself any power of acting, or (what is the same thing) virtue, that is proper to another’s nature and foreign to his own. Hence his desire cannot be restrained—that is (by the Scholium to Proposition 11 of this part), he himself cannot be saddened—by regarding some virtue in someone unlike himself, and consequently he will not be able to envy that person either. But he can envy his equal, who is supposed to be of the same nature as himself. QED

Scholium. So when we said above, in the Scholium to Proposition 52 of this part, that we venerate a person because we wonder at his prudence, strength of character and so on, this happens (as is evident from the Proposition itself) because we imagine these virtues to be in him singularly, and not as common to our nature. And so we shall no more envy him for them than we envy trees their height or lions their strength, and so on.

Proposition 56. There are as many species of joy, sadness and desire—and consequently of every affect composed of these, such as vacillation of mind, or derived from them, namely love, hatred, hope, fear and so on—as there are species of objects by which we are affected.

Demonstration. Joy and sadness, and consequently the affects composed of them or derived from them, are passions (by the Scholium to Proposition 11 of this part). But we are necessarily acted on (by Proposition 1 of this part) insofar as we have inadequate ideas; and only insofar as we have them (by Proposition 3 of this part) are we acted on—that is (see Scholium 1 to Proposition 40 of Part 2), we are necessarily acted on only insofar as we imagine, or (see Proposition 17 of Part 2 with its Scholium) insofar as we are affected by an affection that involves both the nature of our body and the nature of an external body. So the nature of each passion must necessarily be explained in such a way that the nature of the object by which we are affected is expressed. Thus the joy that arises from, say, object

Scholium. Among the species of affects, which (by the preceding Proposition) must be very many, the notable ones are gluttony, drunkenness, lust, greed and ambition. These are nothing but notions of love or desire that explain the nature of each of these two affects through the objects to which they are related. For by gluttony, drunkenness, lust, greed and ambition we understand nothing other than an immoderate love or desire for feasting, drinking, sexual union, wealth and glory. Moreover, these affects, insofar as we distinguish them from others only by the object to which they are related, have no contraries. For temperance, which we usually oppose to gluttony, sobriety, which we oppose to drunkenness, and finally chastity, which we oppose to lust, are not affects or passions; rather, they indicate a power of the mind that moderates these affects. For the rest, I cannot explain the remaining species of affects here (because there are as many as there are species of objects), nor, if I could, is it necessary.

Proposition 57. Each affect of each individual differs from the affect of another as much as the essence of the one differs from the essence of the other.

Demonstration. This Proposition is evident from Axiom 1, which see after Lemma 3 of the Scholium to Proposition 13 of Part 2. Nevertheless, we shall demonstrate it from the definitions of the three primary affects.

All affects are related to desire, joy or sadness, as the definitions we have given of them show. But desire is the very nature, or essence, of each person (see its definition in the Scholium to Proposition 9 of this part). Therefore the desire of each individual differs from the desire of another as much as the nature, or essence, of the one differs from the essence of the other. Next, joy and sadness are passions by which each person’s power, or striving to persevere in his being, is increased or diminished, aided or restrained (by Proposition 11 of this part and its Scholium). But by the striving to persevere in one’s being, insofar as it is related to the mind and body together, we understand appetite and desire

Scholium. From this it follows that the affects of the animals called irrational (for we can by no means doubt that brutes have feelings, now that we know the origin of the mind) differ from human affects as much as their nature differs from human nature. Both horse and human are indeed driven by the lust to procreate; but the one by an equine lust, the other by a human one. So too the lusts and appetites of insects, fish and birds must be different in each case. Therefore, although each individual lives content with the nature of which it consists, and rejoices in it, yet that life with which each is content, and that rejoicing, are nothing other than the idea, or soul, of that individual; and so the rejoicing of one differs in nature from the rejoicing of another as much as the essence of the one differs from the essence of the other. Finally, it follows from the preceding Proposition that there is no small difference between the rejoicing by which, say, a drunkard

Proposition 58. Besides the joy and desire that are passions, there are other affects of joy and desire that are related to us insofar as we act.

Demonstration. When the mind conceives itself and its power of acting, it rejoices (by Proposition 53 of this part). But the mind necessarily regards itself when it conceives a true, or adequate, idea (by Proposition 43 of Part 2). And the mind does conceive some adequate ideas (by Scholium 2 to Proposition 40 of Part 2). Therefore it also rejoices insofar as it conceives adequate ideas, that is (by Proposition 1 of this part), insofar as it acts. Next, the mind strives to persevere in its being both insofar as it has clear and distinct ideas and insofar as it has confused ones (by Proposition 9 of this part). But by striving we understand desire (by the Scholium to the same Proposition). Therefore desire is also related to us insofar as we understand, or (by Proposition 1 of this part) insofar as we act. QED

Proposition 59. Among all the affects that are related to the mind insofar as it acts, there are none except those that are related to joy or desire.

Demonstration. All affects are related to desire, joy or sadness, as the definitions we have given of them show. But by sadness we understand that by which the mind’s power of thinking is diminished or restrained (by Proposition 11 of this part and its Scholium). So insofar as the mind is saddened, to that extent its power of understanding—that is (by Proposition 1 of this part), its power of acting—is diminished or restrained. Hence no affects of sadness can be related to the mind insofar as it acts, but only affects of joy and desire, which (by the preceding Proposition) are to that extent also related to the mind. QED

Scholium. All the actions that follow from affects related to the mind insofar as it understands I refer to strength of character, which I divide into tenacity and nobility. For by tenacity I understand the desire by which each person strives to preserve his being from the dictate of reason alone.

By nobility, on the other hand, I understand the desire by which each person, from the dictate of reason alone, strives to aid other people and join them to himself in friendship. So those actions that aim only at the advantage of the agent I refer to tenacity, and those that aim at the advantage of another as well I refer to nobility. Thus temperance, sobriety, presence of mind in danger and so on are species of tenacity, whereas modesty, mercy and so on are species of nobility. And with this I think I have explained the principal affects and vacillations of mind that arise from the combination of the three primary affects—namely desire, joy and sadness—and have shown them through their first causes. From this it is clear that we are driven about in many ways by external causes, and that, like waves of the sea driven by contrary winds, we toss to and fro, unaware of our outcome and our fate. But I said that I have shown only the principal conflicts of mind, not all that there can be.

Explanation. We said above, in the Scholium to Proposition 9 of this part, that desire is appetite together with consciousness of it, and that appetite is the very essence of a human being insofar as it is determined to do the things that serve its preservation. But in the same Scholium I also pointed out that in reality I recognize no difference between human appetite and desire. For whether a person is conscious of his appetite or not, the appetite remains one and the same. So, lest I seem to commit a tautology, I did not want to explain desire through appetite, but took care to define it in such a way as to include together all the strivings of human nature that we signify by the names appetite, will, desire or impulse. For I could have said that desire is the very essence of a human being insofar as it is conceived as determined to do something. But from this definition

Definition 2. Joy is a person’s passage from a lesser to a greater perfection.

Definition 3. Sadness is a person’s passage from a greater to a lesser perfection.

Explanation. I say passage. For joy is not perfection itself. If a person were born with the perfection to which he passes, he would possess it without the affect of joy. This appears more clearly from the affect of sadness, which is its contrary. For no one can deny that sadness consists in the passage to a lesser perfection, not in the lesser perfection itself, since a person cannot be saddened insofar as he shares in some perfection. Nor can we say that sadness consists in the privation of a greater perfection. For privation is nothing, whereas the affect of sadness is an act, which therefore can be nothing other than the act of passing to a lesser perfection—that is, the act by which a person’s power of acting is diminished or restrained (see the Scholium to Proposition 11 of this part).

Definition 4. Wonder is an imagining of some thing in which the mind remains fixed, because this singular imagining has no connection with the others (see Proposition 52 of this part, with its Scholium).

Explanation. In the Scholium to Proposition 18 of Part 2 we showed the cause why the mind, from contemplating one thing, immediately falls to thinking of another: namely, because the images of those things are linked together and so ordered that one follows another. This cannot be conceived when the image of a thing is new; instead, the mind will be held in contemplating that thing until it is determined by other causes to think of other things. So the imagining of a new thing, considered in itself, is of the same nature as the others; and for this reason I do not count wonder among the affects. Nor do I see any reason why I should, since this distraction of the mind does not arise from any positive cause that distracts it from other things, but only from the absence of the cause by which the mind is determined, from contemplating one thing, to think of others.

Definition 5. Disdain is an imagining of some thing that touches the mind so little that the mind is moved by the thing’s presence to imagine what is not in the thing rather than what is in it (see the Scholium to Proposition 52 of this part).

I pass over here the definitions of veneration and disparagement, because no affects, as far as I know, take their names from them.

Definition 6. Love is joy accompanied by the idea of an external cause.

Explanation. This definition explains the essence of love clearly enough. The definition given by those authors who define love as the will of the lover to join himself to the thing loved expresses not the essence of love but a property of it. And because these authors did not see the essence of love clearly enough, they could not have any clear concept of its property either; hence everyone has judged their definition to be quite obscure.

Definition 7. Hatred is sadness accompanied by the idea of an external cause.

Explanation. What should be noted here is easily perceived from what was said in the Explanation of the preceding definition (see also the Scholium to Proposition 13 of this part).

Definition 8. Attraction is joy accompanied by the idea of some thing that is accidentally the cause of joy.

Definition 9. Aversion is sadness accompanied by the idea of some thing that is accidentally the cause of sadness (on these, see the Scholium to Proposition 15 of this part).

Definition 10. Devotion is love toward one whom we wonder at.

Explanation. We showed in Proposition 52 of this part that wonder arises from the novelty of a thing. So if it happens that we often imagine what we wonder at, we shall cease to wonder at it; and so we see that the affect of devotion easily degenerates into simple love.

Definition 11. Mockery is joy arising from our imagining that something we disdain is present in a thing we hate.

Explanation. Insofar as we disdain a thing we hate, we deny existence to it (see the Scholium to Proposition 52 of this part), and to that extent (by Proposition 20 of this part) we rejoice. But since we suppose that a person nevertheless hates what he mocks, it follows that this joy is not solid (see the Scholium to Proposition 47 of this part).

Definition 12. Hope is an inconstant joy, arising from the idea of a future or past thing about whose outcome we are to some extent in doubt.

Definition 13. Fear is an inconstant sadness, arising from the idea of a future or past thing about whose outcome we are to some extent in doubt (on these, see Scholium 2 to Proposition 18 of this part).

Explanation. From these definitions it follows that there is no hope without fear, and no fear without hope. For whoever hangs on hope and doubts a thing’s outcome is supposed to imagine something that excludes the existence of the future thing; and so to that extent he is saddened (by Proposition 19 of this part), and consequently, while he hangs on hope, he fears that the thing may not happen. Whoever, on the other hand, is in fear—that is, doubts the outcome of a thing he hates—also imagines something that excludes the existence of that thing; and so (by Proposition 20 of this part) he rejoices, and consequently to that extent he has hope that it will not happen.

Definition 14. Confidence is joy arising from the idea of a future or past thing concerning which the cause of doubt has been removed.

Definition 15. Despair is sadness arising from the idea of a future or past thing concerning which the cause of doubt has been removed.

Explanation. Confidence, then, arises from hope, and despair from fear, when the cause of doubt about a thing’s outcome is removed. This happens because a person imagines the past or future thing as being there and contemplates it as present, or because he imagines other things that exclude the existence of the things that cast doubt into his mind. For although we can never be certain about the outcome of singular things (by the Corollary to Proposition 31 of Part 2), it can still happen that we do not doubt their outcome. For we have shown (see the Scholium to Proposition 49 of Part 2) that not doubting a thing is one thing, and having certainty of it another. And so it can happen that we are affected by the image of a past or future thing with the same affect of joy or sadness as by the image of a present thing, as we demonstrated in Proposition 18 of this part; see it together with its Scholia.

Definition 16. Gladness is joy accompanied by the idea of a past thing that has turned out better than we had hoped.

Definition 17. Remorse is sadness accompanied by the idea of a past thing that has turned out worse than we had hoped.

Definition 18. Pity is sadness accompanied by the idea of an evil that has befallen another whom we imagine to be like us (see the Scholium to Proposition 22 and the Scholium to Proposition 27 of this part).

Explanation. There seems to be no difference between pity and compassion, except perhaps that pity concerns the affect as a single occurrence, while compassion concerns the settled disposition to it.

Definition 19. Approval is love toward someone who has done good to another.

Definition 20. Indignation is hatred toward someone who has done harm to another.

Explanation. I know that in common usage these words mean something else. But my purpose is to explain not the meaning of words but the nature of things, and to designate them by words whose customary meaning is not wholly at odds with the meaning in which I wish to use them. Let it suffice to have pointed this out once. As for the cause of these affects, see Corollary 1 to Proposition 27 and the Scholium to Proposition 22 of this part.

Definition 21. Overestimation is thinking more highly of someone than is right, out of love.

Definition 22. Scorn is thinking less highly of someone than is right, out of hatred.

Explanation. Overestimation, then, is an effect, or property, of love, and scorn of hatred. So overestimation can also be defined as love insofar as it so affects a person that he thinks more highly than is right of the thing loved; and, conversely, scorn as hatred insofar as it so affects a person that he thinks less highly than is right of the one he hates (on these, see the Scholium to Proposition 26 of this part).

Definition 23. Envy is hatred insofar as it so affects a person that he is saddened by another’s happiness and, conversely, rejoices at another’s misfortune.

Explanation. Envy is commonly opposed by compassion, which, therefore, in spite of the word’s usual meaning, can be defined as follows:

Definition 24. Compassion is love insofar as it so affects a person that he rejoices at another’s good and, conversely, is saddened by another’s misfortune.

Explanation. On envy, see further the Scholium to Proposition 24 and the Scholium to Proposition 32 of this part. These, then, are the affects of joy and sadness that are accompanied by the idea of an external thing as their cause, either directly or accidentally. From here I pass to the others, which are accompanied by the idea of an internal thing as their cause.

Definition 25. Self-contentment is joy arising from a person’s contemplating himself and his own power of acting.

Definition 26. Humility is sadness arising from a person’s contemplating his own lack of power, or weakness.

Explanation. Self-contentment is opposed to humility insofar as we understand by it the joy that arises from contemplating our power of acting. But insofar as we also understand by it joy accompanied by the idea of some deed that we believe we did by a free decree of the mind, it is opposed to repentance, which we define as follows:

Definition 27. Repentance is sadness accompanied by the idea of some deed that we believe we did by a free decree of the mind.

Explanation. We have shown the causes of these affects in the Scholium to Proposition 51 of this part, and in Propositions 53, 54 and 55 of this part and the Scholium to the last. On the free decree of the mind, see the Scholium to Proposition 35 of Part 2. But it should also be noted here that it is no wonder that sadness follows absolutely all the acts customarily called wrong, and joy those called right. For we easily understand from what was said above that this depends chiefly on upbringing. Parents, by condemning the former and often scolding their children for them, and by recommending and praising the latter, have brought it about that stirrings of sadness are joined to the one kind and stirrings of joy to the other. Experience itself confirms this. For custom and religion are not the same for everyone; on the contrary, what is sacred for some is profane for others, and what is honorable for some is shameful for others.

Definition 28. Pride is thinking more highly of oneself than is right, out of self-love.

Explanation. Pride, then, differs from overestimation in that the latter relates to an external object, whereas pride relates to the person himself, who thinks more highly of himself than is right. Moreover, as overestimation is an effect or property of love, so pride is an effect or property of philautia [self-love]. It can therefore also be defined as self-love, or self-contentment, insofar as it so affects a person that he thinks more highly of himself than is right (see the Scholium to Proposition 26 of this part). There is no affect contrary to this one. For no one thinks less highly of himself than is right out of hatred of himself; indeed, no one thinks less highly of himself than is right insofar as he imagines that he cannot do this or that. For whatever a person imagines he cannot do, he necessarily imagines; and by this imagining he is so disposed that he really cannot do what he imagines he cannot do.

Definition 29. Self-abasement is thinking less highly of oneself than is right, out of sadness.

Explanation. Yet we often oppose humility to pride; but then we attend more to the effects of the two than to their nature. For we usually call proud someone who boasts too much (see the Scholium to Proposition 30 of this part), who tells of nothing but his own virtues and nothing but others’ vices, who wants to be preferred to everyone, and who, finally, goes about with the dignity and finery usual among those placed far above him. On the other hand, we call humble someone who often blushes, who confesses his own vices and tells of others’ virtues, who gives way to everyone, and who, finally, walks with head bowed and neglects to adorn himself. These affects, however—humility and self-abasement—are very rare.

Definition 30. Glory is joy accompanied by the idea of some action of ours that we imagine others praise.

Definition 31. Shame is sadness accompanied by the idea of some action that we imagine others blame.

Explanation. On these, see the Scholium to Proposition 30 of this part. But here the difference between shame and modesty should be noted. Shame is the sadness that follows a deed one is ashamed of; modesty is the fear, or timidity, of shame, by which a person is restrained from committing something shameful. Shamelessness is usually opposed to modesty; but it is not really an affect, as I shall show in its place. The names of the affects, however (as I have already pointed out), concern their usage more than their nature. With this I have finished the affects of joy and sadness that I had set out to explain. I proceed, then, to those that I relate to desire.note

Definition 32. Longing is a desire, or appetite, to possess some thing, which is encouraged by the memory of that thing and at the same time restrained by the memory of other things that exclude the existence of the thing wanted.

Explanation. When we remember some thing, as we have often said already, we are by that very fact disposed to contemplate it with the same affect as if it were present. But while we are awake, this disposition, or striving, is usually checked by the images of things that exclude the existence of what we remember. So when we remember a thing that affected us with some kind of joy, by that very fact we strive to contemplate it as present with the same affect of joy—a striving that is immediately checked by the memory of things that exclude its existence. Longing, therefore, is really a sadness, opposed to the joy that arises from the absence of a thing we hate (on which see the Scholium to Proposition 47 of this part). But because the name longing seems to concern desire, I relate this affect to the affects of desire.

Definition 33. Emulation is the desire for some thing that is generated in us because we imagine that others have the same desire.

Explanation. Someone who flees because he sees others flee, or who is afraid because he sees others afraid; or again, someone who, seeing that another has burned his hand, draws back his own hand and moves his body as if his own hand were burning—such a person we shall say imitates another’s affect, but not that he emulates it. This is not because we know one cause for emulation and another for imitation, but because custom has brought it about that we call someone an emulator only when he imitates what we judge honorable, useful or pleasant. As for the cause of emulation, see Proposition 27 of this part with its Scholium. And on why envy is usually joined to this affect, see Proposition 32 of this part with its Scholium.

Definition 34. Gratitude, or thankfulness, is a desire, or eagerness of love, by which we strive to benefit one who has conferred a benefit on us from a like affect of love. See Proposition 39, with the Scholium to Proposition 41 of this part.

Definition 35. Benevolence is a desire to benefit one whom we pity. See the Scholium to Proposition 27 of this part.

Definition 36. Anger is a desire by which, out of hatred, we are driven to do evil to one we hate. See Proposition 39 of this part.

Definition 37. Vengeance is a desire by which, out of reciprocal hatred, we are roused to do evil to one who, from a like affect, has done us harm. See Corollary 2 to Proposition 40 of this part, with its Scholium.

Definition 38. Cruelty, or savagery, is a desire by which someone is roused to do evil to one whom we love or pity.

Explanation. Opposed to cruelty is mercy, which is not a passion but a power of the mind by which a person governs anger and vengeance.

Definition 39. Timidity is a desire to avoid a greater evil, which we fear, by a lesser one. See the Scholium to Proposition 39 of this part.

Definition 40. Daring is a desire by which someone is driven to do something at a risk that his equals are afraid to face.

Definition 41. Cowardice is said of someone whose desire is restrained by fear of a danger that his equals dare to face.

Explanation. Cowardice, then, is nothing but fear of some evil that most people do not usually fear; so I do not relate it to the affects of desire. Yet I wanted to explain it here, because, insofar as we attend to desire, it really is opposed to the affect of daring.

Definition 42. Consternation is said of someone whose desire to avoid an evil is restrained by wonder at the evil he fears.

Explanation. Consternation, then, is a species of cowardice. But because consternation arises from a double fear, it can more conveniently be defined as a fear that holds a person so stunned or wavering that he cannot ward off the evil. I say stunned insofar as we understand his desire to ward off the evil to be restrained by wonder. And I say wavering insofar as we conceive that same desire to be restrained by fear of another evil that torments him equally, so that he does not know which of the two to avert. On these, see the Scholium to Proposition 39 and the Scholium to Proposition 52 of this part. As for cowardice and daring, see the Scholium to Proposition 51 of this part.

Definition 43. Courtesy, or modesty, is a desire to do what pleases people and to refrain from what displeases them.

Definition 44. Ambition is an excessive desire for glory.

Explanation. Ambition is a desire by which all the affects are encouraged and strengthened (by Propositions 27 and 31 of this part); and so this affect can hardly be overcome. For as long as a person is held by any desire, he is necessarily held by this one as well. All the best people, says Cicero, are most led by glory. Even philosophers put their names on the books they write about despising glory, etc.note

Definition 45. Gluttony is an immoderate desire for, or even love of, feasting.

Definition 46. Drunkenness is an immoderate desire for and love of drinking.

Definition 47. Greed is an immoderate desire for and love of riches.

Definition 48. Lust is also a desire for and love of the joining of bodies.

Explanation. Whether this desire for intercourse is moderate or not, it is usually called lust. Further, these five affects (as I pointed out in the Scholium to Proposition 56 of this part) have no contraries. For modesty is a species of ambition (on which see the Scholium to Proposition 29 of this part). And I have also already pointed out that temperance, sobriety and chastity indicate a power of the mind, not a passion. And although it can happen that a greedy, ambitious or timid person abstains from too much food, drink and sex, still greed, ambition and timidity are not contrary to gluttony, drunkenness or lust. For the greedy person usually longs to gorge himself on other people’s food and drink. And the ambitious person, provided he hopes it will stay secret, will restrain himself in nothing; and if he lives among drunkards and the lustful, he will be all the more inclined to those same vices precisely because he is ambitious.

I pass over in silence the definitions of jealousy and the other vacillations of the mind, both because they arise from the combination of affects we have already defined and because most of them have no names—which shows that for the practice of life it is enough to know them only in general. For the rest, it is clear from the definitions of the affects we have explained that they all arise from desire, joy or sadness—or rather, that they are nothing but these three, each of which is usually called by various names on account of its various relations and extrinsic denominations. If we now wish to attend to these primitive affects, and to what we said above about the nature of the mind, we shall be able to define the affects, insofar as they are related to the mind alone, as follows.

General Definition of the Affects. An affect, which is called a pathema [passion] of the mind, is a confused idea by which the mind affirms of its body, or of some part of it, a greater or lesser force of existing than before, and by which, once it is given, the mind itself is determined to think of this rather than that.

Explanation. I say, first, that an affect, or passion of the mind, is a confused idea. For we have shown (see Proposition 3 of this part) that the mind is acted on only insofar as it has inadequate, or confused, ideas. I say next, by which the mind affirms of its body, or of some part of it, a greater or lesser force of existing than before. For all the ideas of bodies that we have indicate the actual constitution of our own body (by Corollary 2 to Proposition 16 of Part 2) more than the nature of the external body. But the idea that constitutes the form of an affect must indicate or express a constitution of the body, or of some part of it, which the body itself, or some part of it, has because its power of acting, or force of existing, is increased or diminished, aided or restrained.

Preface. Human lack of power in governing and restraining the affects I call bondage. For a person subject to the affects is not his own master but is under the control of fortune, in whose power he is to such an extent that he is often compelled, although he sees the better course for himself, still to follow the worse. In this Part I have set out to demonstrate the cause of this, and what good or bad the affects have besides. But before I begin, I should like to say a few words first about perfection and imperfection, and about good and evil.

When someone has resolved to make something and has finished it, he will say that his thing is perfect—and not only he, but everyone who rightly knows, or believes he knows, the mind and aim of the author of that work. For example, if someone sees some work (which I suppose is not yet completed) and knows that its author’s aim is to build a house, he will say that the house is imperfect; and, on the other hand, that it is perfect as soon as he sees the work brought to the end its author had resolved to give it. But if someone sees a work the like of which he had never seen, and does not know the maker’s intention, he certainly cannot know whether that work is perfect or imperfect. And this seems to have been the first meaning of these words. But after people began to form universal ideas, and to devise models of houses, buildings, towers, etc.,note

As for good and evil, they too indicate nothing positive in things, considered in themselves, and are nothing but modes of thinking, or notions, which we form because we compare things with one another. For one and the same thing can at the same time be good and bad, and also indifferent. For example, music is good for someone who is melancholy, bad for someone in mourning, and neither good nor bad for someone who is deaf. But although this is how things stand, we must still keep these words. For since we desire to form an idea of the human being as a model of human nature for us to look to, it will be useful for us to keep these same words in the sense I have described. In what follows, then, by good I shall understand what we know with certainty to be a means by which we may come ever closer to the model of human nature that we set before ourselves.

Definition 1. By good I shall understand what we certainly know to be useful to us.

Definition 2. By bad, on the other hand, I shall understand what we certainly know prevents us from possessing some good.

(On these, see the end of the preceding Preface.)

Definition 3. I call singular things contingent insofar as, when we attend only to their essence, we find nothing that necessarily posits their existence or that necessarily excludes it.

Definition 4. I call the same singular things possible insofar as, when we attend to the causes from which they must be produced, we do not know whether those causes are determined to produce them.

(In Scholium 1 to Proposition 33 of Part 1 I drew no distinction between the possible and the contingent, because there was no need to distinguish them precisely there.)

Definition 5. By contrary affects I shall understand, in what follows, those that pull a person in different directions even though they are of the same kind—such as gluttony and greed, which are species of love. They are contrary not by nature but by accident.

Definition 6. What I understand by an affect toward a future, present or past thing I have explained in Scholia 1 and 2 to Proposition 18 of Part 3; see there.

(But it should be noted here, in addition, that we can distinctly imagine distance in time, as in space, only up to a certain limit. That is, just as we usually imagine all objects that are more than two hundred feet away from us—that is, whose distance from where we are exceeds what we can distinctly imagine—to be equally far from us, as if they were all on the same plane, so too we imagine all objects whose time of existing we imagine to be separated from the present by a longer interval than we usually imagine distinctly as being equally far from the present, and we refer them, as it were, to a single moment of time.)

Definition 7. By the end for the sake of which we do something, I understand appetite.

Definition 8. By virtue and power I understand the same thing. That is (by Proposition 7 of Part 3), virtue, insofar as it is related to a human being, is the very essence or nature of that human being, insofar as he has the power of bringing about certain things that can be understood through the laws of his own nature alone.

Axiom. There is no singular thing in Nature than which there is not another more powerful and stronger. Given any thing whatever, there is another more powerful by which the given thing can be destroyed.

Proposition 1. Nothing positive that a false idea has is removed by the presence of the true, insofar as it is true.

Demonstration. Falsity consists only in the privation of knowledge that inadequate ideas involve (by Proposition 35 of Part 2), and these ideas have nothing positive on account of which they are called false (by Proposition 33 of Part 2). On the contrary, insofar as they are related to God, they are true (by Proposition 32 of Part 2). So if what a false idea has that is positive were removed by the presence of the true, insofar as it is true, then a true idea would be removed by itself, which (by Proposition 4 of Part 3) is absurd. Therefore nothing positive that a false idea has, etc. QED

Scholium. This Proposition is understood more clearly from Corollary 2 to Proposition 16 of Part 2. For an imagination is an idea that indicates the present constitution of the human body more than the nature of the external body—not distinctly, indeed, but confusedly; and this is why the mind is said to err. For example, when we look at the sun, we imagine it to be about two hundred feet away from us. In this we are deceived only as long as we do not know its true distance. When its distance is known, the error is removed, but not the imagination—that is, the idea of the sun, which explains its nature only insofar as the body is affected by it. And so, even though we know its true distance, we shall nonetheless imagine it as near to us.