The Mind: Its Nature and Origin

I now pass on to explaining the results, which must necessarily follow from the essence of God, or of the eternal and infinite being; not, indeed, all of them (for we proved in Part i., Prop. xvi., that an infinite number must follow in an infinite number of ways), but only those which are able to lead us, as it were by the hand, to the knowledge of the human mind and its highest blessedness.

I now turn to explaining the results that must necessarily follow from the essence of God, the eternal and infinite being. I will not explain all of these results. For we proved in Part i., Prop. xvi., that infinitely many results must follow in infinitely many ways. Instead, I will explain only those results that can lead us, as if by the hand, to understanding the human mind and its highest blessedness.

DEFINITION I. By body I mean a mode which expresses in a certain determinate manner the essence of God, in so far as he is considered as an extended thing. (See Pt. i., Prop. xxv., Coroll.)

DEFINITION I. By body I mean a mode that expresses God's essence in a specific, definite way. Here, God is considered as an extended thing. (See Part I, Proposition 25, Corollary.)

DEFINITION II. I consider as belonging to the essence of a thing that, which being given, the thing is necessarily given also, and, which being removed, the thing is necessarily removed also; in other words, that without which the thing, and which itself without the thing, can neither be nor be conceived.

DEFINITION II. I consider something part of a thing’s essence if the thing necessarily exists whenever that element exists. If that element is removed, the thing is necessarily removed too. In other words, the thing cannot exist or be conceived without that element. Nor can that element exist or be conceived without the thing.

DEFINITION III. By idea, I mean the mental conception which is formed by the mind as a thinking thing.

DEFINITION III. By idea, I mean a mental concept formed by the mind as a thinking thing.

Explanation.—I say conception rather than perception, because the word perception seems to imply that the mind is passive in respect to the object; whereas conception seems to express an activity of the mind.

Explanation: I say conception rather than perception because perception seems to imply that the mind is passive toward the object. By contrast, conception seems to express an activity of the mind.

DEFINITION IV. By an adequate idea, I mean an idea which, in so far as it is considered in itself, without relation to the object, has all the properties or intrinsic marks of a true idea.

DEFINITION IV. By an adequate idea, I mean an idea considered in itself, without reference to its object. Considered this way, the idea has all the properties or internal marks of a true idea.

Explanation.—I say intrinsic, in order to exclude that mark which is extrinsic, namely, the agreement between the idea and its object (ideatum).

Explanation: I say intrinsic to exclude the external feature, namely, the agreement between an idea and its object (ideatum).

DEFINITION V. Duration is the indefinite continuance of existing.

DEFINITION V. Duration is the continuation of existence for an indefinite length of time.

Explanation.—I say indefinite, because it cannot be determined through the existence itself of the existing thing, or by its efficient cause, which necessarily gives the existence of the thing, but does not take it away.

Explanation. I say indefinite because it cannot be determined by the existing thing’s own existence or by its efficient cause. That cause necessarily brings the thing into existence, but does not end its existence.

DEFINITION VI. Reality and perfection I use as synonymous terms.

DEFINITION VI. I use reality and perfection to mean the same thing.

DEFINITION VII. By particular things, I mean things which are finite and have a conditioned existence; but if several individual things concur in one action, so as to be all simultaneously the effect of one cause, I consider them all, so far, as one particular thing.

DEFINITION VII. By particular things, I mean things that are finite and whose existence depends on certain conditions. But if several individual things act together, so that all are simultaneously the effect of one cause, I consider them all, in that respect, as one particular thing.

I. The essence of man does not involve necessary existence, that is, it may, in the order of nature, come to pass that this or that man does or does not exist.

I. Human essence does not require necessary existence. That is, in the order of nature, any particular person may or may not exist.

II. Man thinks.

II. Humans think.

III. Modes of thinking, such as love, desire, or any other of the passions, do not take place, unless there be in the same individual an idea of the thing loved, desired, &c. But the idea can exist without the presence of any other mode of thinking.

III. Modes of thinking, such as love, desire, or any other passion, occur only under one condition. The same individual must have an idea of the thing loved, desired, and so on. But the idea can exist without any other mode of thinking.

IV. We perceive that a certain body is affected in many ways.

IV. We perceive that a particular body is affected in many ways.

V. We feel and perceive no particular things, save bodies and modes of thought.

V. We feel and perceive no individual things except bodies and modes of thought.

N.B. The Postulates are given after the conclusion of Prop. xiii.

Note: The Postulates appear after the conclusion of Proposition 13.

PROP. I. Thought is an attribute of God, or God is a thinking thing.

PROPOSITION I. Thought is an attribute of God. In other words, God is a thinking being.

Proof.—Particular thoughts, or this and that thought, are modes which, in a certain conditioned manner, express the nature of God (Pt. i., Prop. xxv., Coroll.). God therefore possesses the attribute (Pt. i., Def. v.) of which the concept is involved in all particular thoughts, which latter are conceived thereby. Thought, therefore, is one of the infinite attributes of God, which express God's eternal and infinite essence (Pt. i., Def. vi.). In other words, God is a thinking thing. Q.E.D.

Proof. Particular thoughts, or individual instances of thought, are modes that express God's nature in a specific, conditioned way (Pt. i., Prop. xxv., Coroll.). God therefore has an attribute whose concept is involved in all particular thoughts (Pt. i., Def. v.). These thoughts are understood through that attribute. Thought, therefore, is one of God's infinite attributes, which express God's eternal and infinite essence (Pt. i., Def. vi.). In other words, God is a thinking thing. Q.E.D.

Note.—This proposition is also evident from the fact, that we are able to conceive an infinite thinking being. For, in proportion as a thinking being is conceived as thinking more thoughts, so is it conceived as containing more reality or perfection. Therefore a being, which can think an infinite number of things in an infinite number of ways, is, necessarily, in respect of thinking, infinite. As, therefore, from the consideration of thought alone, we conceive an infinite being, thought is necessarily (Pt. i., Deff. iv. and vi.) one of the infinite attributes of God, as we were desirous of showing.

Note. This proposition is also clear from the fact that we can conceive of an infinite thinking being. The more thoughts we conceive a thinking being as thinking, the more reality or perfection we conceive it as having. Therefore, a being that can think infinitely many things in infinitely many ways is necessarily infinite in its thinking. Thus, by considering thought alone, we conceive of an infinite being. Thought is therefore necessarily one of God's infinite attributes (Part I, Definitions IV and VI). This is what we wanted to show.

PROP. II. Extension is an attribute of God, or God is an extended thing.

PROPOSITION II. Extension is an attribute of God. In other words, God is an extended thing.

Proof.—The proof of this proposition is similar to that of the last.

Proof. The proof of this proposition is similar to the proof of the previous proposition.

PROP. III. In God there is necessarily the idea not only of his essence, but also of all things which necessarily follow from his essence.

PROP. III. In God, there is necessarily an idea of his essence. This idea also includes all things that necessarily follow from his essence.

Proof.—God (by the first Prop. of this Part) can think an infinite number of things in infinite ways, or (what is the same thing, by Prop. xvi., Part i.) can form the idea of his essence, and of all things which necessarily follow therefrom. Now all that is in the power of God necessarily is (Pt. i., Prop. xxxv.). Therefore, such an idea as we are considering necessarily is, and in God alone. Q.E.D. (Part i., Prop. xv.)

Proof. God can think an infinite number of things in infinite ways (by Proposition 1 of this Part). In other words, God can form the idea of his essence and of all things that necessarily follow from it. These statements mean the same thing by Proposition 16 of Part 1. Now everything within God’s power necessarily exists (Part 1, Proposition 35). Therefore, the idea we are considering necessarily exists, and exists in God alone. Q.E.D. (Part 1, Proposition 15.)

Note.—The multitude understand by the power of God the free will of God, and the right over all things that exist, which latter are accordingly generally considered as contingent. For it is said that God has the power to destroy all things, and to reduce them to nothing. Further, the power of God is very often likened to the power of kings. But this doctrine we have refuted (Pt. i., Prop. xxxii., Corolls. i. and ii.), and we have shown (Part i., Prop. xvi.) that God acts by the same necessity, as that by which he understands himself; in other words, as it follows from the necessity of the divine nature (as all admit), that God understands himself, so also does it follow by the same necessity, that God performs infinite acts in infinite ways. We further showed (Part i., Prop. xxxiv.), that God's power is identical with God's essence in action; therefore it is as impossible for us to conceive God as not acting, as to conceive him as non—existent. If we might pursue the subject further, I could point out, that the power which is commonly attributed to God is not only human (as showing that God is conceived by the multitude as a man, or in the likeness of a man), but involves a negation of power. However, I am unwilling to go over the same ground so often. I would only beg the reader again and again, to turn over frequently in his mind what I have said in Part I from Prop. xvi. to the end. No one will be able to follow my meaning, unless he is scrupulously careful not to confound the power of God with the human power and right of kings.

Note. Most people understand God's power as his free will and his authority over everything that exists. They therefore generally regard everything that exists as contingent, rather than necessary. For people say that God has the power to destroy everything and reduce it to nothing. God's power is also very often compared to the power of kings. But we have refuted this view (Part I, Proposition 32, Corollaries 1 and 2). We have also shown that God acts by the same necessity by which he understands himself (Part I, Proposition 16). In other words, everyone agrees that God's understanding of himself follows necessarily from his divine nature. By that same necessity, God also performs infinitely many acts in infinitely many ways. We further showed that God's power is identical with his essence in action (Part I, Proposition 34). So conceiving of God as not acting is as impossible as conceiving of him as nonexistent. If I were to pursue this subject further, I could show that the power commonly attributed to God is human. It shows that most people conceive of God as a man, or in the likeness of a man. But I could also show that this supposed power actually involves a denial of power. However, I do not wish to cover the same ground so often. I would only urge the reader, again and again, to reflect often on what I have said in Part I, from Proposition 16 to the end. No one will understand my meaning without taking the greatest care not to confuse God's power with the human power and authority of kings.

PROP. IV. The idea of God, from which an infinite number of things follow in infinite ways, can only be one.

PROP. IV. Infinitely many things follow from the idea of God in infinitely many ways. There can be only one such idea.

Proof.—Infinite intellect comprehends nothing save the attributes of God and his modifications (Part i., Prop. xxx.). Now God is one (Part i., Prop. xiv., Coroll.). Therefore the idea of God, wherefrom an infinite number of things follow in infinite ways, can only be one. Q.E.D.

Proof. The infinite intellect understands only God's attributes and his modifications (Part i., Prop. xxx.). Now God is one (Part i., Prop. xiv., Coroll.). Therefore, there can be only one idea of God, from which infinitely many things follow in infinitely many ways. Q.E.D.

PROP. V. The actual being of ideas owns God as its cause, only in so far as he is considered as a thinking thing, not in so far as he is unfolded in any other attribute; that is, the ideas both of the attributes of God and of particular things do not own as their efficient cause their objects (ideata) or the things perceived, but God himself in so far as he is a thinking thing.

PROP. V. The actual existence of ideas has God as its cause only when God is considered as a thinking thing. It does not have God as its cause when he is considered through any other attribute. That is, ideas of both God's attributes and particular things do not have their objects (ideata) as their efficient cause. These objects are the things perceived. Rather, the efficient cause of these ideas is God himself, considered as a thinking thing.

Proof.—This proposition is evident from Prop. iii. of this Part. We there drew the conclusion, that God can form the idea of his essence, and of all things which follow necessarily therefrom, solely because he is a thinking thing, and not because he is the object of his own idea. Wherefore the actual being of ideas owns for cause God, in so far as he is a thinking thing. It may be differently proved as follows: the actual being of ideas is (obviously) a mode of thought, that is (Part i., Prop. xxv., Coroll.) a mode which expresses in a certain manner the nature of God, in so far as he is a thinking thing, and therefore (Part i., Prop. x.) involves the conception of no other attribute of God, and consequently (by Part i., Ax. iv.) is not the effect of any attribute save thought. Therefore the actual being of ideas owns God as its cause, in so far as he is considered as a thinking thing, &c. Q.E.D.

Proof. This proposition follows clearly from Proposition 3 of this Part. There we concluded that God can form an idea of his essence and of everything that necessarily follows from it. God can do so solely because he is a thinking thing, not because he is the object of his own idea. Therefore, God causes the actual existence of ideas insofar as he is a thinking thing. The same point can be proved another way. The actual existence of ideas is obviously a mode of thought. That is, it is a mode that expresses God's nature in a particular way, insofar as he is a thinking thing (Part 1, Proposition 25, Corollary). Therefore, this mode involves no conception of any other attribute of God (Part 1, Proposition 10). Consequently, it cannot be the effect of any attribute except thought (Part 1, Axiom 4). Therefore, God causes the actual existence of ideas insofar as he is considered a thinking thing, and so on. Q.E.D.

PROP. VI. The modes of any given attribute are caused by God, in so far as he is considered through the attribute of which they are modes, and not in so far as he is considered through any other attribute.

PROP. VI. God causes the modes of any given attribute insofar as he is considered through that attribute. He does not cause those modes insofar as he is considered through any other attribute.

Proof.—Each attribute is conceived through itself, without any other (Part i., Prop. x.); wherefore the modes of each attribute involve the conception of that attribute, but not of any other. Thus (Part i., Ax. iv.) they are caused by God, only in so far as he is considered through the attribute whose modes they are, and not in so far as he is considered through any other. Q.E.D.

Proof. Each attribute is understood through itself, without reference to any other attribute (Part i., Prop. x.). So understanding the modes of each attribute involves understanding that attribute, but no other. Thus (Part i., Ax. iv.), God causes these modes only insofar as he is considered through the attribute they belong to. He does not cause them insofar as he is considered through any other attribute. Q.E.D.

Corollary.—Hence the actual being of things, which are not modes of thought, does not follow from the divine nature, because that nature has prior knowledge of the things. Things represented in ideas follow, and are derived from their particular attribute, in the same manner, and with the same necessity as ideas follow (according to what we have shown) from the attribute of thought.

Corollary: Things that are not modes of thought do not exist because the divine nature knows them in advance. Rather, things represented in ideas follow from their particular attribute. They follow in the same way and with the same necessity as ideas follow from the attribute of thought. As we have shown, ideas follow from that attribute.

PROP. VII. The order and connection of ideas is the same as the order and connection of things.

PROPOSITION VII. Ideas follow the same order and connections as things.

Proof.—This proposition is evident from Part i., Ax. iv. For the idea of everything that is caused depends on a knowledge of the cause, whereof it is an effect.

Proof. This proposition follows directly from Part I, Axiom IV. For the idea of anything caused depends on knowing the cause that produced it.

Corollary.—Hence God's power of thinking is equal to his realized power of action—that is, whatsoever follows from the infinite nature of God in the world of extension (formaliter), follows without exception in the same order and connection from the idea of God in the world of thought (objective).

Corollary. Thus, God's power of thinking equals his actual power of action. Everything that follows from God's infinite nature in the world of extension (formaliter) also follows from the idea of God in the world of thought (objective). All of it follows in the same order and connection, without exception.

Note.—Before going any further, I wish to recall to mind what has been pointed out above—namely, that whatsoever can be perceived by the infinite intellect as constituting the essence of substance, belongs altogether only to one substance: consequently, substance thinking and substance extended are one and the same substance, comprehended now through one attribute, now through the other. So, also, a mode of extension and the idea of that mode are one and the same thing, though expressed in two ways. This truth seems to have been dimly recognized by those Jews who maintained that God, God's intellect, and the things understood by God are identical. For instance, a circle existing in nature, and the idea of a circle existing, which is also in God, are one and the same thing displayed through different attributes. Thus, whether we conceive nature under the attribute of extension, or under the attribute of thought, or under any other attribute, we shall find the same order, or one and the same chain of causes—that is, the same things following in either case.

Note. Before going further, I want to recall a point made above. Everything the infinite intellect can perceive as constituting the essence of substance belongs entirely to one substance alone. Consequently, thinking substance and extended substance are one and the same substance, understood through one attribute or the other. Likewise, a mode of extension and the idea of that mode are one and the same thing, expressed in two ways. This truth seems to have been dimly recognized by those Jews who held the following view: God, God's intellect, and the things God understands are identical. For example, consider a circle existing in nature and the idea of that existing circle, which is also in God. The circle and its idea are one and the same thing, expressed through different attributes. So we may understand nature through the attribute of extension, through the attribute of thought, or through any other attribute. Whichever attribute we use, we find the same order, or the very same chain of causes. In other words, the same things follow in each case.

I said that God is the cause of an idea—for instance, of the idea of a circle,—in so far as he is a thinking thing; and of a circle, in so far as he is an extended thing, simply because the actual being of the idea of a circle can only be perceived as a proximate cause through another mode of thinking, and that again through another, and so on to infinity; so that, so long as we consider things as modes of thinking, we must explain the order of the whole of nature, or the whole chain of causes, through the attribute of thought only. And, in so far as we consider things as modes of extension, we must explain the order of the whole of nature through the attributes of extension only; and so on, in the case of the other attributes. Wherefore of things as they are in themselves God is really the cause, inasmuch as he consists of infinite attributes. I cannot for the present explain my meaning more clearly.

I said that God causes an idea, for example, the idea of a circle, insofar as he is a thinking thing. He causes a circle insofar as he is an extended thing. The reason is simply this: the actual existence of the idea of a circle can be understood only through another mode of thinking as its immediate cause. That mode must be understood through another, and so on to infinity. So, as long as we consider things as modes of thinking, we must explain nature’s entire order through thought alone. In other words, we must explain the whole chain of causes through the attribute of thought alone. And insofar as we consider things as modes of extension, we must explain nature’s entire order through extension alone. The same applies to the other attributes. Therefore, God is truly the cause of things as they are in themselves, insofar as he consists of infinite attributes. I cannot explain my meaning more clearly for now.

PROP. VIII. The ideas of particular things, or of modes, that do not exist, must be comprehended in the infinite idea of God, in the same way as the formal essences of particular things or modes are contained in the attributes of God.

PROP. VIII. Ideas of particular things or modes that do not exist must be included in the infinite idea of God. This is just as the formal essences of particular things or modes are contained in God’s attributes.

Proof.—This proposition is evident from the last; it is understood more clearly from the preceding note.

Proof: This proposition follows clearly from the previous one. The preceding note makes this proposition clearer.

Corollary.—Hence, so long as particular things do not exist, except in so far as they are comprehended in the attributes of God, their representations in thought or ideas do not exist, except in so far as the infinite idea of God exists; and when particular things are said to exist, not only in so far as they are involved in the attributes of God, but also in so far as they are said to continue, their ideas will also involve existence, through which they are said to continue.

Corollary. Therefore, as long as particular things exist only as contained in God's attributes, their ideas have a corresponding existence. These ideas, or representations in thought, exist only insofar as God's infinite idea exists. But when particular things are said to exist through duration, their existence is not limited to being contained in God's attributes. In that case, their ideas also include the existence through which those particular things are said to endure.

Note.—If anyone desires an example to throw more light on this question, I shall, I fear, not be able to give him any, which adequately explains the thing of which I here speak, inasmuch as it is unique; however, I will endeavour to illustrate it as far as possible. The nature of a circle is such that if any number of straight lines intersect within it, the rectangles formed by their segments will be equal to one another; thus, infinite equal rectangles are contained in a circle. Yet none of these rectangles can be said to exist, except in so far as the circle exists; nor can the idea of any of these rectangles be said to exist, except in so far as they are comprehended in the idea of the circle. Let us grant that, from this infinite number of rectangles, two only exist. The ideas of these two not only exist, in so far as they are contained in the idea of the circle, but also as they involve the existence of those rectangles; wherefore they are distinguished from the remaining ideas of the remaining rectangles.

Note. If anyone wants an example to make this question clearer, I fear I cannot provide one that explains it adequately. The subject I am discussing is unique. Still, I will try to illustrate it as clearly as possible. A circle has this property: if any number of straight lines intersect inside it, their segments form equal rectangles. Thus, a circle contains infinitely many equal rectangles. Yet none of these rectangles can be said to exist except insofar as the circle exists. Nor can an idea of any rectangle be said to exist except insofar as the circle’s idea contains that idea. Let us suppose that only two rectangles out of this infinite number exist. The ideas of these two exist not only insofar as the circle’s idea contains them. They also exist insofar as they involve the existence of those two rectangles. Therefore, these two ideas are distinct from the ideas of all the remaining rectangles.

PROP. IX. The idea of an individual thing actually existing is caused by God, not in so far as he is infinite, but in so far as he is considered as affected by another idea of a thing actually existing, of which he is the cause, in so far as he is affected by a third idea, and so on to infinity.

PROP. IX. God causes the idea of an individual thing that actually exists, but not insofar as he is infinite. Rather, he causes this idea insofar as he is considered affected by another idea of an actually existing thing. God causes that second idea insofar as he is affected by a third idea, and so on to infinity.

Proof.—The idea of an individual thing actually existing is an individual mode of thinking, and is distinct from other modes (by the Corollary and note to Prop. viii. of this part); thus (by Prop. vi. of this part) it is caused by God, in so far only as he is a thinking thing. But not (by Prop. xxviii. of Part i.) in so far as he is a thing thinking absolutely, only in so far as he is considered as affected by another mode of thinking; and he is the cause of this latter, as being affected by a third, and so on to infinity. Now, the order and connection of ideas is (by Prop. vii. of this book) the same as the order and connection of causes. Therefore of a given individual idea another individual idea, or God, in so far as he is considered as modified by that idea, is the cause; and of this second idea God is the cause, in so far as he is affected by another idea, and so on to infinity. Q.E.D.

Proof. The idea of an individual thing that actually exists is an individual mode of thinking, distinct from other modes. This follows from the Corollary and note to Proposition viii of this part. Thus, by Proposition vi of this part, God causes this idea only insofar as he is a thinking thing. But he does not cause it insofar as he thinks absolutely (by Proposition xxviii of Part i). He causes it only insofar as he is affected by another mode of thinking. And he causes that other mode insofar as he is affected by a third, and so on to infinity. Now, the order and connection of ideas is the same as the order and connection of causes. This follows from Proposition vii of this book. Therefore, another individual idea causes any given individual idea. Or, God causes the given idea insofar as he is considered to be modified by that other idea. And God causes this second idea insofar as he is affected by another idea, and so on to infinity. Q.E.D.

Corollary.—Whatsoever takes place in the individual object of any idea, the knowledge thereof is in God, in so far only as he has the idea of the object.

Corollary: Whatever happens in the individual object of any idea is known by God. God has this knowledge only insofar as he has the idea of that object.

Proof.—Whatsoever takes place in the object of any idea, its idea is in God (by Prop. iii. of this part), not in so far as he is infinite, but in so far as he is considered as affected by another idea of an individual thing (by the last Prop.); but (by Prop. vii. of this part) the order and connection of ideas is the same as the order and connection of things. The knowledge, therefore, of that which takes place in any individual object will be in God, in so far only as he has the idea of that object. Q.E.D.

Proof. Whatever happens in the object of any idea, the idea of that event is in God (Proposition iii of this part). This is not insofar as God is infinite. Rather, it is insofar as he is considered to be affected by another idea of an individual thing (the previous proposition). But the order and connection of ideas is the same as the order and connection of things (Proposition vii of this part). Therefore, knowledge of what happens in any individual object is in God only insofar as he has the idea of that object. Q.E.D.

PROP. X. The being of substance does not appertain to the essence of man—in other words, substance does not constitute the actual being² of man.

PROP. X. The being of substance is not part of human essence. In other words, substance does not constitute the actual being² of a human being.

Proof.—The being of substance involves necessary existence (Part i., Prop. vii.). If, therefore, the being of substance appertains to the essence of man, substance being granted, man would necessarily be granted also (II. Def. ii.), and, consequently, man would necessarily exist, which is absurd (II. Ax. i.). Therefore, &c. Q.E.D.

Proof. The being of substance involves necessary existence (Part i., Prop. vii.). If, therefore, the being of substance belongs to human essence, accepting substance would necessarily mean accepting human existence (II. Def. ii.). Consequently, humans would necessarily exist, which is absurd (II. Ax. i.). Therefore, etc. Q.E.D.

Note.—This proposition may also be proved from I.v., in which it is shown that there cannot be two substances of the same nature; for as there may be many men, the being of substance is not that which constitutes the actual being of man. Again, the proposition is evident from the other properties of substance—namely, that substance is in its nature infinite, immutable, indivisible, &c., as anyone may see for himself.

Note. This proposition can also be proved from I.v., which shows that two substances cannot have the same nature. Since there may be many men, the being of substance does not constitute the actual being of man. The proposition is also clear from the other properties of substance. Substance is by nature infinite, unchanging, indivisible, and so on, as anyone can see for themselves.

Corollary.—Hence it follows, that the essence of man is constituted by certain modifications of the attributes of God. For (by the last Prop.) the being of substance does not belong to the essence of man. That essence therefore (by i. 15) is something which is in God, and which without God can neither be nor be conceived, whether it be a modification (i. 25. Coroll.), or a mode which expresses God's nature in a certain conditioned manner.

Corollary. It follows that human essence consists of certain modifications of God's attributes. For, by the previous proposition, the being of substance does not belong to human essence. Therefore, by i. 15, human essence is something that exists in God. Without God, human essence can neither exist nor be conceived. This essence is a modification (i. 25. Coroll.), or a mode expressing God's nature in a certain conditioned way.

Note.—Everyone must surely admit, that nothing can be or be conceived without God. All men agree that God is the one and only cause of all things, both of their essence and of their existence; that is, God is not only the cause of things in respect to their being made (secundum fieri), but also in respect to their being (secundum esse).

Note. Everyone must surely admit that nothing can exist or be conceived without God. All people agree that God is the one and only cause of all things, both their essence and their existence. That is, God causes not only things to come into being (secundum fieri), but also their continued being (secundum esse).

At the same time many assert, that that, without which a thing cannot be nor be conceived, belongs to the essence of that thing; wherefore they believe that either the nature of God appertains to the essence of created things, or else that created things can be or be conceived without God; or else, as is more probably the case, they hold inconsistent doctrines. I think the cause for such confusion is mainly, that they do not keep to the proper order of philosophic thinking. The nature of God, which should be reflected on first, inasmuch as it is prior both in the order of knowledge and the order of nature, they have taken to be last in the order of knowledge, and have put into the first place what they call the objects of sensation; hence, while they are considering natural phenomena, they give no attention at all to the divine nature, and, when afterwards they apply their mind to the study of the divine nature, they are quite unable to bear in mind the first hypotheses, with which they have overlaid the knowledge of natural phenomena, inasmuch as such hypotheses are no help towards understanding the divine nature. So that it is hardly to be wondered at, that these persons contradict themselves freely.

At the same time, many claim that a thing’s essence includes whatever it cannot exist or be understood without. So they believe that God’s nature belongs to the essence of created things. Or they believe that created things can exist or be understood without God. Or, more probably, they hold inconsistent views. I think this confusion arises mainly because they do not follow the proper order of philosophical thinking. God’s nature should be considered first, because it comes first both in knowledge and in nature. Instead, they have put God’s nature last in the order of knowledge. They have put what they call the objects of sensation first. As a result, when considering natural phenomena, they pay no attention at all to God’s nature. Later, when they turn to studying God’s nature, they cannot keep their initial assumptions in mind. These are the assumptions they have imposed on their knowledge of natural phenomena. They cannot keep these assumptions in mind because the assumptions do nothing to help them understand God’s nature. So it is hardly surprising that these people freely contradict themselves.

However, I pass over this point. My intention her was only to give a reason for not saying, that that, without which a thing cannot be or be conceived, belongs to the essence of that thing: individual things cannot be or be conceived without God, yet God does not appertain to their essence. I said that "I considered as belonging to the essence of a thing that, which being given, the thing is necessarily given also, and which being removed, the thing is necessarily removed also; or that without which the thing, and which itself without the thing can neither be nor be conceived." (II. Def. ii.)

However, I will leave this point aside. My only aim here was to explain why I did not define a thing’s essence simply as something necessary for its existence or conception. Individual things cannot exist or be conceived without God, yet God does not belong to their essence. I said, "I consider something to belong to a thing’s essence if its presence necessarily implies the thing’s presence. Its removal must also necessarily imply the thing’s removal. In other words, neither the thing nor what belongs to its essence can exist or be conceived without the other." (II. Def. ii.)

PROP. XI. The first element, which constitutes the actual being of the human mind, is the idea of some particular thing actually existing.

PROP. XI. The first element that makes up the human mind’s actual being is the idea of some particular thing that actually exists.

Proof.—The essence of man (by the Coroll. of the last Prop.) is constituted by certain modes of the attributes of God, namely (by II. Ax. ii.), by the modes of thinking, of all which (by II. Ax. iii.) the idea is prior in nature, and, when the idea is given, the other modes (namely, those of which the idea is prior in nature) must be in the same individual (by the same Axiom). Therefore an idea is the first element constituting the human mind. But not the idea of a non—existent thing, for then (II. viii. Coroll.) the idea itself cannot be said to exist; it must therefore be the idea of something actually existing. But not of an infinite thing. For an infinite thing (I. xxi., xxii.), must always necessarily exist; this would (by II. Ax. i.) involve an absurdity. Therefore the first element, which constitutes the actual being of the human mind, is the idea of something actually existing. Q.E.D.

Proof. Human essence consists of certain modes of God's attributes (by the Coroll. of the last Prop.). These are modes of thinking (by II. Ax. ii.). An idea is prior in nature to all these modes (by II. Ax. iii.). When the idea is given, the other modes must be present in the same individual (by the same Axiom). These other modes are those to which the idea is prior in nature. Therefore, an idea is the first element that constitutes the human mind. But this cannot be the idea of a nonexistent thing. For then the idea itself could not be said to exist (II. viii. Coroll.). The idea must therefore be of something that actually exists. But it cannot be the idea of an infinite thing. For an infinite thing must necessarily exist always (I. xxi., xxii.). This necessary, eternal existence would imply an absurdity (by II. Ax. i.). Therefore, the first element constituting the actual being of the human mind is the idea of something that actually exists. Q.E.D.

Corollary.—Hence it follows, that the human mind is part of the infinite intellect of God; thus when we say, that the human mind perceives this or that, we make the assertion, that God has this or that idea, not in so far as he is infinite, but in so far as he is displayed through the nature of the human mind, or in so far as he constitutes the essence of the human mind; and when we say that God has this or that idea, not only in so far as he constitutes the essence of the human mind, but also in so far as he, simultaneously with the human mind, has the further idea of another thing, we assert that the human mind perceives a thing in part or inadequately.

Corollary: It follows that the human mind is part of God’s infinite intellect. So when we say the human mind perceives something, we are saying that God has that idea. We do not mean God insofar as he is infinite. We mean God insofar as he is expressed through the nature of the human mind, or constitutes its essence. Now suppose we say that God has an idea, not only insofar as he constitutes the human mind’s essence. Suppose we also mean God insofar as he has, along with the human mind, a further idea of another thing. In that case, we are saying that the human mind perceives something only partly or inadequately.

Note.—Here, I doubt not, readers will come to a stand, and will call to mind many things which will cause them to hesitate; I therefore beg them to accompany me slowly, step by step, and not to pronounce on my statements, till they have read to the end.

Note: I have no doubt that readers will pause here and recall many things that will make them hesitate. So I ask them to follow me slowly, step by step. I also ask them not to judge my statements until they have read to the end.

PROP. XII. Whatsoever comes to pass in the object of the idea, which constitutes the human mind, must be perceived by the human mind, or there will necessarily be an idea in the human mind of the said occurrence. That is, if the object of the idea constituting the human mind be a body, nothing can take place in that body without being perceived by the mind.

PROP. XII. The human mind must perceive everything that happens in the object of the idea constituting the human mind. In other words, the human mind must contain an idea of whatever happens in that object. Thus, if the object of the idea constituting the human mind is a body, the mind must perceive everything that happens in that body.

Proof.—Whatsoever comes to pass in the object of any idea, the knowledge thereof is necessarily in God (II. ix. Coroll.), in so far as he is considered as affected by the idea of the said object, that is (II. xi.), in so far as he constitutes the mind of anything. Therefore, whatsoever takes place in the object constituting the idea of the human mind, the knowledge thereof is necessarily in God, in so far as he constitutes the essence of the human mind; that is (by II. xi. Coroll.) the knowledge of the said thing will necessarily be in the mind, in other words the mind perceives it.

Proof. Whatever happens in the object of any idea is necessarily known by God (II. ix. Coroll.). God has this knowledge insofar as he is considered to be affected by the idea of that object. That is, he has this knowledge insofar as he constitutes the mind of anything (II. xi.). Therefore, whatever happens in the object of the idea constituting the human mind is necessarily known by God. God has this knowledge insofar as he constitutes the essence of the human mind. This means that knowledge of whatever happens in that object must be in the human mind (II. xi. Coroll.). In other words, the mind perceives whatever happens in that object.

Note.—This proposition is also evident, and is more clearly to be understood from II. vii., which see.

Note: This proposition is also clear. For a clearer understanding, see Part II, Proposition 7.

PROP. XIII. The object of the idea constituting the human mind is the body, in other words a certain mode of extension which actually exists, and nothing else.

PROP. XIII. The object of the idea that makes up the human mind is the body. In other words, it is a particular mode of extension that actually exists, and nothing else.

Proof.—If indeed the body were not the object of the human mind, the ideas of the modifications of the body would not be in God (II. ix. Coroll.) in virtue of his constituting our mind, but in virtue of his constituting the mind of something else; that is (II. xi. Coroll.) the ideas of the modifications of the body would not be in our mind: now (by II. Ax. iv.) we do possess the idea of the modifications of the body. Therefore the object of the idea constituting the human mind is the body, and the body as it actually exists (II. xi.). Further, if there were any other object of the idea constituting the mind besides body, then, as nothing can exist from which some effect does not follow (I. xxxvi.) there would necessarily have to be in our mind an idea, which would be the effect of that other object (II. xi.); but (I. Ax. v.) there is no such idea. Wherefore the object of our mind is the body as it exists, and nothing else. Q.E.D.

Proof. Suppose the body were not the object of the human mind. Then the ideas of the body’s changes would not be in God because he constitutes our mind (II. ix. Coroll.). Instead, those ideas would be in God because he constitutes the mind of something else. That is, the ideas of the body’s changes would not be in our mind (II. xi. Coroll.). But we do have the idea of the body’s changes (II. Ax. iv.). Therefore, the object of the idea constituting the human mind is the body, as the body actually exists (II. xi.). Further, suppose the idea constituting the mind had some object besides the body. Nothing can exist without producing some effect (I. xxxvi.). So our mind would necessarily contain an idea produced by that other object (II. xi.). But there is no such idea (I. Ax. v.). Therefore, the object of our mind is the body as the body exists, and nothing else. Q.E.D.

Note.—We thus comprehend, not only that the human mind is united to the body, but also the nature of the union between mind and body. However, no one will be able to grasp this adequately or distinctly, unless he first has adequate knowledge of the nature of our body. The propositions we have advanced hitherto have been entirely general, applying not more to men than to other individual things, all of which, though in different degrees, are animated.³ For of everything there is necessarily an idea in God, of which God is the cause, in the same way as there is an idea of the human body; thus whatever we have asserted of the idea of the human body must necessarily also be asserted of the idea of everything else. Still, on the other hand, we cannot deny that ideas, like objects, differ one from the other, one being more excellent than another and containing more reality, just as the object of one idea is more excellent than the object of another idea, and contains more reality.

Note. We thus understand not only that the human mind is united with the body, but also how they are united. However, no one can understand this union adequately or clearly without first having adequate knowledge of our body's nature. The propositions we have presented so far have been entirely general. They apply no more to humans than to other individual things, all of which are animated, though to different degrees.³ For there is necessarily an idea of everything in God, and God is the cause of each idea. This is true of every idea in the same way as it is true of the idea of the human body. Thus, everything we have said about the idea of the human body must necessarily apply to the idea of everything else. Yet we cannot deny that ideas, like objects, differ from one another. One idea is more excellent than another and contains more reality. This difference corresponds to the difference between their objects, one being more excellent than another and containing more reality.

Wherefore, in order to determine, wherein the human mind differs from other things, and wherein it surpasses them, it is necessary for us to know the nature of its object, that is, of the human body. What this nature is, I am not able here to explain, nor is it necessary for the proof of what I advance, that I should do so. I will only say generally, that in proportion as any given body is more fitted than others for doing many actions or receiving many impressions at once, so also is the mind, of which it is the object, more fitted than others for forming many simultaneous perceptions; and the more the actions of the body depend on itself alone, and the fewer other bodies concur with it in action, the more fitted is the mind of which it is the object for distinct comprehension. We may thus recognize the superiority of one mind over others, and may further see the cause, why we have only a very confused knowledge of our body, and also many kindred questions, which I will, in the following propositions, deduce from what has been advanced. Wherefore I have thought it worth while to explain and prove more strictly my present statements. In order to do so, I must premise a few propositions concerning the nature of bodies.

To understand how the human mind differs from other things and surpasses them, we must know the nature of its object. That object is the human body. I cannot explain the body’s nature here, nor is such an explanation necessary to prove what I am arguing. I will only make a general point. The better a body can perform many actions or receive many impressions at once, compared with other bodies, the better its mind can form many perceptions at once. And the more the body’s actions depend on the body alone, with fewer other bodies acting alongside it, the better its mind can understand things distinctly. We can thus recognize how one mind surpasses others. We can also see why our knowledge of our own body is so confused. These points also shed light on many related questions. In the following propositions, I will derive the answers from what has already been established. I have therefore thought it worthwhile to explain my present statements and prove them more rigorously. To do so, I must first present a few propositions about the nature of bodies.

AXIOM I. All bodies are either in motion or at rest.

AXIOM I. All bodies are either moving or at rest.

AXIOM II. Every body is moved sometimes more slowly, sometimes more quickly.

AXIOM II. Every body moves more slowly at some times and more quickly at others.

LEMMA I. Bodies are distinguished from one another in respect of motion and rest, quickness and slowness, and not in respect of substance.

LEMMA I. Bodies differ from one another in motion and rest, speed and slowness, but not in substance.

Proof.—The first part of this proposition is, I take it, self—evident. That bodies are not distinguished in respect of substance, is plain both from I. v. and I. viii. It is brought out still more clearly from I. xv, note.

Proof. The first part of this proposition is, I think, self-evident. Both I. v. and I. viii. make clear that bodies do not differ in substance. The note to I. xv. makes this lack of difference in substance even clearer.

LEMMA II. All bodies agree in certain respects.

LEMMA II. All bodies have certain features in common.

Proof.—All bodies agree in the fact, that they involve the conception of one and the same attribute (II., Def. i.). Further, in the fact that they may be moved less or more quickly, and may be absolutely in motion or at rest.

Proof. All bodies share this feature: they involve the concept of one and the same attribute (II., Def. i.). All bodies also share the capacity to move more slowly or quickly, and to be in motion or at rest.

LEMMA III. A body in motion or at rest must be determined to motion or rest by another body, which other body has been determined to motion or rest by a third body, and that third again by a fourth, and so on to infinity.

LEMMA III. A body in motion or at rest must be caused to move or remain at rest by another body. That second body must have been caused to move or remain at rest by a third body. The third body, in turn, must have been caused to move or remain at rest by a fourth body. This chain continues to infinity.

Proof.—Bodies are individual things (II., Def. i.), which (Lemma I.) are distinguished one from the other in respect to motion and rest; thus (I. xxviii.) each must necessarily be determined to motion or rest by another individual thing, namely (II. vi.), by another body, which other body is also (Ax. i.) in motion or at rest. And this body again can only have been set in motion or caused to rest by being determined by a third body to motion or rest. This third body again by a fourth, and so on to infinity. Q.E.D.

Proof. Bodies are individual things (II., Def. i.). They differ from one another in their motion and rest (Lemma I.). Thus, each body must necessarily be caused to move or rest by another individual thing (I. xxviii.). That other thing must be another body (II. vi.), itself either moving or at rest (Ax. i.). This second body, in turn, can only have been made to move or rest by a third body. The third body must likewise have been made to move or rest by a fourth, and so on to infinity. Q.E.D.

Corollary.—Hence it follows, that a body in motion keeps in motion, until it is determined to a state of rest by some other body; and a body at rest remains so, until it is determined to a state of motion by some other body. This is indeed self—evident. For when I suppose, for instance, that a given body, A, is at rest, and do not take into consideration other bodies in motion, I cannot affirm anything concerning the body A, except that it is at rest. If it afterwards comes to pass that A is in motion, this cannot have resulted from its having been at rest, for no other consequence could have been involved than its remaining at rest. If, on the other hand, A be given in motion, we shall, so long as we only consider A, be unable to affirm anything concerning it, except that it is in motion. If A is subsequently found to be at rest, this rest cannot be the result of A's previous motion, for such motion can only have led to continued motion; the state of rest therefore must have resulted from something, which was not in A, namely, from an external cause determining A to a state of rest.

Corollary. It follows that a body in motion stays in motion until another body causes it to stop. A body at rest stays at rest until another body causes it to move. This is self-evident. For example, suppose I consider a body, A, at rest, without considering other bodies in motion. I can say nothing about A except that A is at rest. If A later moves, that motion cannot have resulted from A’s being at rest. Being at rest could only have led to A’s remaining at rest. On the other hand, suppose A is in motion. As long as we consider only A, we can say nothing about A except that A is in motion. If A is later found at rest, that rest cannot have resulted from A’s previous motion. For that motion could only have led to continued motion. A’s rest must therefore have resulted from something outside A, namely, an external cause that made A stop.

Axiom I.—All modes, wherein one body is affected by another body, follow simultaneously from the nature of the body affected and the body affecting; so that one and the same body may be moved in different modes, according to the difference in the nature of the bodies moving it; on the other hand, different bodies may be moved in different modes by one and the same body.

Axiom I. All the ways one body is affected by another follow from the nature of both bodies together. So the same body may be moved in different ways, depending on the nature of the bodies moving it. On the other hand, different bodies may be moved in different ways by the same body.

Axiom II.—When a body in motion impinges on another body at rest, which it is unable to move, it recoils, in order to continue its motion, and the angle made by the line of motion in the recoil and the plane of the body at rest, whereon the moving body has impinged, will be equal to the angle formed by the line of motion of incidence and the same plane.

Axiom II. When a moving body strikes a body at rest but cannot move it, the moving body rebounds to continue moving. The path of the rebound forms an angle with the plane of the stationary body's surface where the impact occurred. This angle equals the angle formed by the incoming path and the same plane.

So far we have been speaking only of the most simple bodies, which are only distinguished one from the other by motion and rest, quickness and slowness. We now pass on to compound bodies.

So far, we have discussed only the simplest bodies. These bodies differ from one another only in motion and rest, speed and slowness. We now turn to compound bodies.

Definition.—When any given bodies of the same or different magnitude are compelled by other bodies to remain in contact, or if they be moved at the same or different rates of speed, so that their mutual movements should preserve among themselves a certain fixed relation, we say that such bodies are in union, and that together they compose one body or individual, which is distinguished from other bodies by the fact of this union.

Definition: Suppose bodies of the same or different sizes are forced by other bodies to stay in contact. Or suppose bodies move at the same or different speeds, so that their movements maintain a fixed relation to one another. We say that such bodies are united and together form one body or individual. This union distinguishes that body or individual from other bodies.

Axiom III.—In proportion as the parts of an individual, or a compound body, are in contact over a greater or less superficies, they will with greater or less difficulty admit of being moved from their position; consequently the individual will, with greater or less difficulty, be brought to assume another form. Those bodies, whose parts are in contact over large superficies, are called hard; those, whose parts are in contact over small superficies, are called soft; those, whose parts are in motion among one another, are called fluid.

Axiom III. The larger the area of contact between the parts of an individual, or compound body, the harder those parts are to move out of position. The smaller the area of contact, the easier those parts are to move. Consequently, the individual is harder or easier to reshape in the same proportion. Bodies whose parts touch over large areas are called hard. Bodies whose parts touch over small areas are called soft. Bodies whose parts move among one another are called fluid.

LEMMA IV. If from a body or individual, compounded of several bodies, certain bodies be separated, and if, at the same time, an equal number of other bodies of the same nature take their place, the individual will preserve its nature as before, without any change in its actuality (forma).

LEMMA IV. Suppose some bodies are removed from a body or individual made up of several bodies. If an equal number of other bodies of the same nature replace them at the same time, the individual will retain its nature as before. Its actuality (forma) will remain unchanged.

Proof.—Bodies (Lemma i.) are not distinguished in respect of substance: that which constitutes the actuality (formam) of an individual consists (by the last Def.) in a union of bodies; but this union, although there is a continual change of bodies, will (by our hypothesis) be maintained; the individual, therefore, will retain its nature as before, both in respect of substance and in respect of mode. Q.E.D.

Proof. Bodies do not differ in substance (Lemma i.). An individual’s actuality (formam) consists in a union of bodies, according to the last definition. But although the bodies continually change, their union will remain intact, according to our hypothesis. Therefore, the individual will retain its nature as before, both in substance and in mode. Q.E.D.

LEMMA V. If the parts composing an individual become greater or less, but in such proportion, that they all preserve the same mutual relations of motion and rest, the individual will still preserve its original nature, and its actuality will not be changed.

LEMMA V. If the parts making up an individual grow or shrink, but all keep the same relative proportions of motion and rest, the individual will keep its original nature. Its actuality will also remain unchanged.

Proof.—The same as for the last Lemma.

Proof: The same as for the previous lemma.

LEMMA VI. If certain bodies composing an individual be compelled to change the motion, which they have in one direction, for motion in another direction, but in such a manner, that they be able to continue their motions and their mutual communication in the same relations as before, the individual will retain its own nature without any change of its actuality.

LEMMA VI. Suppose some bodies making up an individual are forced to change their direction of motion. But suppose these bodies can continue moving and exchanging motion in the same relations as before. Then the individual will retain its own nature, with no change in its actuality.

Proof.—This proposition is self—evident, for the individual is supposed to retain all that, which, in its definition, we spoke of as its actual being.

Proof: This proposition is self-evident because the individual is assumed to retain all that its definition calls its actual being.

LEMMA VII. Furthermore, the individual thus composed preserves its nature, whether it be, as a whole, in motion or at rest, whether it be moved in this or that direction; so long as each part retains its motion, and preserves its communication with other parts as before.

LEMMA VII. Furthermore, the individual composed in this way preserves its nature, whether the whole is moving or at rest. The direction of movement does not matter either. This holds as long as each part maintains its motion and exchanges motion with the other parts as before.

Proof.—This proposition is evident from the definition of an individual prefixed to Lemma iv.

Proof. This proposition follows clearly from the definition of an individual given before Lemma iv.

Note.—We thus see, how a composite individual may be affected in many different ways, and preserve its nature notwithstanding. Thus far we have conceived an individual as composed of bodies only distinguished one from the other in respect of motion and rest, speed and slowness; that is, of bodies of the most simple character. If, however, we now conceive another individual composed of several individuals of diverse natures, we shall find that the number of ways in which it can be affected, without losing its nature, will be greatly multiplied. Each of its parts would consist of several bodies, and therefore (by Lemma vi.) each part would admit, without change to its nature, of quicker or slower motion, and would consequently be able to transmit its motions more quickly or more slowly to the remaining parts. If we further conceive a third kind of individuals composed of individuals of this second kind, we shall find that they may be affected in a still greater number of ways without changing their actuality. We may easily proceed thus to infinity, and conceive the whole of nature as one individual, whose parts, that is, all bodies, vary in infinite ways, without any change in the individual as a whole. I should feel bound to explain and demonstrate this point at more length, if I were writing a special treatise on body. But I have already said that such is not my object; I have only touched on the question, because it enables me to prove easily that which I have in view.

Note. We can now see how a composite individual may be affected in many different ways while still preserving its nature. So far, we have considered an individual composed of bodies distinguished only by motion and rest, speed and slowness. These are bodies of the simplest kind. Now suppose we consider another individual composed of several individuals of different natures. We will find far more ways in which this composite individual can be affected without losing its nature. Each part would consist of several bodies. Therefore, by Lemma vi., each part could move faster or slower without changing its nature. Each part could consequently transmit its motions to the other parts more quickly or more slowly. Suppose we then consider a third kind of individual, composed of individuals of this second kind. We will find that these individuals may be affected in still more ways without changing their actual being. We may easily continue this process to infinity and conceive of the whole of nature as one individual. The parts of this individual, that is, all bodies, vary in infinite ways, without changing the individual as a whole. I would feel obliged to explain and prove this point more fully if I were writing a separate treatise on body. But I have already said that this is not my aim. I have only touched on the subject because it lets me easily prove what I set out to establish.

I. The human body is composed of a number of individual parts, of diverse nature, each one of which is in itself extremely complex.

I. The human body is made up of a number of individual parts of different kinds. Each part is itself extremely complex.

II. Of the individual parts composing the human body some are fluid, some soft, some hard.

II. Some parts of the human body are fluid, some are soft, and some are hard.

III. The individual parts composing the human body, and consequently the human body itself, are affected in a variety of ways by external bodies.

III. External bodies affect the individual parts of the human body in various ways. As a result, they also affect the human body as a whole.

IV. The human body stands in need for its preservation of a number of other bodies, by which it is continually, so to speak, regenerated.

IV. The human body needs a number of other bodies to maintain itself. These other bodies continually renew the human body, so to speak.

V. When the fluid part of the human body is determined by an external body to impinge often on another soft part, it changes the surface of the latter, and, as it were, leaves the impression thereupon of the external body which impels it.

V. When an external body causes the fluid part of the human body to strike another soft part repeatedly, the fluid changes that soft part’s surface. In doing so, the fluid leaves, as it were, an impression of the external body that drives the fluid.

VI. The human body can move external bodies, and arrange them in a variety of ways.

VI. The human body can move bodies outside itself and arrange them in many ways.

PROP. XIV. The human mind is capable of perceiving a great number of things, and is so in proportion as its body is capable of receiving a great number of impressions.

PROP. XIV. The human mind can perceive a great many things. The more impressions its body can receive, the more things the mind can perceive.

Proof.—The human body (by Post. iii. and vi.) is affected in very many ways by external bodies, and is capable in very many ways of affecting external bodies. But (II. xii.) the human mind must perceive all that takes place in the human body; the human mind is, therefore, capable of perceiving a great number of things, and is so in proportion, &c. Q.E.D.

Proof. External bodies affect the human body in very many ways (by Post. iii. and vi.). The human body can also affect external bodies in very many ways. But the human mind must perceive everything that happens in the human body (II. xii.). Therefore, the human mind can perceive a great number of things, and this ability is proportional, etc. Q.E.D.

PROP. XV. The idea, which constitutes the actual being of the human mind, is not simple, but compounded of a great number of ideas.

PROP. XV. The idea that makes up the actual being of the human mind is not simple. Instead, it consists of a great many ideas.

Proof.—The idea constituting the actual being of the human mind is the idea of the body (II. xiii.), which (Post. i.) is composed of a great number of complex individual parts. But there is necessarily in God the idea of each individual part whereof the body is composed (II. viii. Coroll.); therefore (II. vii.), the idea of the human body is composed of these numerous ideas of its component parts. Q.E.D.

Proof. The idea that constitutes the actual being of the human mind is the idea of the body (II. xiii.). The body consists of many complex individual parts (Post. i.). But God necessarily has an idea of each individual part that makes up the body (II. viii. Coroll.). Therefore, the idea of the human body consists of these many ideas of its component parts (II. vii.). Q.E.D.

PROP. XVI. The idea of every mode, in which the human body is affected by external bodies, must involve the nature of the human body, and also the nature of the external body.

PROP. XVI. The idea of every way external bodies affect the human body must involve the human body's nature. The idea must also involve the external body's nature.

Proof.—All the modes, in which any given body is affected, follow from the nature of the body affected, and also from the nature of the affecting body (by Ax. i., after the Coroll. of Lemma iii.), wherefore their idea also necessarily (by I. Ax. iv.) involves the nature of both bodies; therefore, the idea of every mode, in which the human body is affected by external bodies, involves the nature of the human body and of the external body. Q.E.D.

Proof. All the ways a body is affected follow from both its own nature and the nature of the body affecting it. This follows from Axiom i., after the Corollary to Lemma iii. So the idea of these effects necessarily involves the nature of both bodies (by I. Axiom iv.). Therefore, the idea of every way external bodies affect the human body involves the nature of the human body. It also involves the nature of the external body. Q.E.D.

Corollary I.—Hence it follows, first, that the human mind perceives the nature of a variety of bodies, together with the nature of its own.

Corollary I. First, it follows that the human mind perceives the nature of various bodies, including its own body.

Corollary II.—It follows, secondly, that the ideas, which we have of external bodies, indicate rather the constitution of our own body than the nature of external bodies. I have amply illustrated this in the Appendix to Part I.

Corollary II. It follows, secondly, that our ideas of external bodies reveal more about our own body's condition than about those bodies' nature. I have illustrated this point in detail in the Appendix to Part I.

PROP. XVII. If the human body is affected in a manner which involves the nature of any external body, the human mind will regard the said external body as actually existing, or as present to itself, until the human body be affected in such a way, as to exclude the existence or the presence of the said external body.

PROP. XVII. If the human body is affected in a way involving an external body's nature, the mind will regard that external body as actually existing or present to the mind. The mind will keep this view until the human body is affected in a way that rules out the external body's existence or presence.

Proof.—This proposition is self—evident, for so long as the human body continues to be thus affected, so long will the human mind (II. xii.) regard this modification of the body—that is (by the last Prop.), it will have the idea of the mode as actually existing, and this idea involves the nature of the external body. In other words, it will have the idea which does not exclude, but postulates the existence or presence of the nature of the external body; therefore the mind (by II. xvi., Coroll. i.) will regard the external body as actually existing, until it is affected, &c. Q.E.D.

Proof. This proposition is self-evident. As long as the human body remains affected in this way, the human mind will perceive this bodily modification (II. xii.). That is, by the previous proposition, the mind will have an idea of the mode as actually existing. This idea involves the nature of the external body. In other words, the idea does not exclude, but presupposes, the existence or presence of the external body's nature. Therefore, the mind will regard the external body as actually existing (II. xvi., Coroll. i.). It will do so until it is affected, etc. Q.E.D.

Corollary.—The mind is able to regard as present external bodies, by which the human body has once been affected, even though they be no longer in existence or present.

Corollary: The mind can regard external bodies that once affected the human body as present. This is possible even though those external bodies no longer exist or are no longer present.

Proof.—When external bodies determine the fluid parts of the human body, so that they often impinge on the softer parts, they change the surface of the last named (Post. v.); hence (Ax. ii., after the Coroll. of Lemma iii.) they are refracted therefrom in a different manner from that which they followed before such change; and, further, when afterwards they impinge on the new surfaces by their own spontaneous movement, they will be refracted in the same manner, as though they had been impelled towards those surfaces by external bodies; consequently, they will, while they continue to be thus refracted, affect the human body in the same manner, whereof the mind (II. xii.) will again take cognizance—that is (II. xvii.), the mind will again regard the external body as present, and will do so, as often as the fluid parts of the human body impinge on the aforesaid surfaces by their own spontaneous motion. Wherefore, although the external bodies, by which the human body has once been affected, be no longer in existence, the mind will nevertheless regard them as present, as often as this action of the body is repeated. Q.E.D.

Proof. When external bodies direct the human body's fluid parts to strike its softer parts repeatedly, the softer parts' surfaces change (Post. v.). As a result, the fluid parts are deflected from those surfaces differently than before the change (Ax. ii., after the Coroll. of Lemma iii.). Later, when the fluid parts strike the changed surfaces through their own spontaneous motion, they will be deflected in the same way. The deflection will be just as if external bodies had driven the fluid parts toward those surfaces. Consequently, as long as the fluid parts continue to be deflected this way, they will affect the human body in the same way. The mind will again become aware of this effect (II. xii.). That is, the mind will again regard the external body as present (II. xvii.). The mind will do so whenever the fluid parts strike those surfaces through their own spontaneous motion. Therefore, although the external bodies that once affected the human body may no longer exist, the mind will nevertheless regard them as present whenever this bodily action is repeated. Q.E.D.

Note.—We thus see how it comes about, as is often the case, that we regard as present many things which are not. It is possible that the same result may be brought about by other causes; but I think it suffices for me here to have indicated one possible explanation, just as well as if I had pointed out the true cause. Indeed, I do not think I am very far from the truth, for all my assumptions are based on postulates, which rest, almost without exception, on experience, that cannot be controverted by those who have shown, as we have, that the human body, as we feel it, exists (Coroll. after II. xiii.). Furthermore (II. vii. Coroll., II. xvi. Coroll. ii.), we clearly understand what is the difference between the idea, say, of Peter, which constitutes the essence of Peter's mind, and the idea of the said Peter, which is in another man, say, Paul. The former directly answers to the essence of Peter's own body, and only implies existence so long as Peter exists; the latter indicates rather the disposition of Paul's body than the nature of Peter, and, therefore, while this disposition of Paul's body lasts, Paul's mind will regard Peter as present to itself, even though he no longer exists. Further, to retain the usual phraseology, the modifications of the human body, of which the ideas represent external bodies as present to us, we will call the images of things, though they do not recall the figure of things. When the mind regards bodies in this fashion, we say that it imagines. I will here draw attention to the fact, in order to indicate where error lies, that the imaginations of the mind, looked at in themselves, do not contain error. The mind does not err in the mere act of imagining, but only in so far as it is regarded as being without the idea, which excludes the existence of such things as it imagines to be present to it. If the mind, while imagining non—existent things as present to it, is at the same time conscious that they do not really exist, this power of imagination must be set down to the efficacy of its nature, and not to a fault, especially if this faculty of imagination depend solely on its own nature—that is (I. Def. vii.), if this faculty of imagination be free.

Note. We can now see why we often regard things as present even when they are not. Other causes may produce the same result. But here I think giving one possible explanation is enough, just as if I had identified the true cause. Indeed, I do not think I am far from the truth. All my assumptions are based on postulates that rest, almost without exception, on experience. Those who have shown, as we have, that the human body exists as we feel it cannot dispute that experience (Coroll. after II. xiii.). Furthermore, we clearly understand the difference between two ideas of Peter (II. vii. Coroll., II. xvi. Coroll. ii.). One constitutes the essence of Peter's mind. The other exists in another man, say, Paul. The first corresponds directly to the essence of Peter's own body and implies existence only as long as Peter exists. The second tells us more about the state of Paul's body than about Peter's nature. Therefore, as long as this state of Paul's body lasts, Paul's mind will regard Peter as present. This remains so even if Peter no longer exists. Further, to keep the usual terminology, we will call certain modifications of the human body the images of things. These are modifications whose ideas represent external bodies as present to us, though the modifications do not reproduce those bodies' shapes. When the mind regards bodies in this way, we say that it imagines. To show where error lies, I want to emphasize that the mind's imaginings, considered in themselves, contain no error. The mind does not make an error simply by imagining. Error arises only insofar as the mind lacks an idea that rules out the existence of things it imagines as present. Suppose the mind imagines nonexistent things as present while also knowing that those things do not really exist. In that case, we must attribute this power of imagination to the strength of the mind's nature, not to a defect. This is especially true if the power of imagination depends solely on the mind's own nature. That is, if this power of imagination is free (I. Def. vii.).

PROP. XVIII. If the human body has once been affected by two or more bodies at the same time, when the mind afterwards imagines any of them, it will straightway remember the others also.

PROP. XVIII. Suppose two or more bodies have once affected the human body at the same time. If the mind later imagines any one of those bodies, the mind will immediately remember the others too.

Proof.—The mind (II. xvii. Coroll.) imagines any given body, because the human body is affected and disposed by the impressions from an external body, in the same manner as it is affected when certain of its parts are acted on by the said external body; but (by our hypothesis) the body was then so disposed, that the mind imagined two bodies at once; therefore, it will also in the second case imagine two bodies at once, and the mind, when it imagines one, will straightway remember the other. Q.E.D.

Proof. The mind (II. xvii. Coroll.) imagines a given body because impressions from an external body affect and shape the human body. These impressions put the human body in the same state as when the external body acts on certain parts of it. But, by our hypothesis, the human body was then in a state that made the mind imagine two bodies at once. Therefore, in the second case too, the mind will imagine two bodies at once. So, when the mind imagines one, the mind will immediately remember the other. Q.E.D.

Note.—We now clearly see what Memory is. It is simply a certain association of ideas involving the nature of things outside the human body, which association arises in the mind according to the order and association of the modifications (affectiones) of the human body. I say, first, it is an association of those ideas only, which involve the nature of things outside the human body: not of ideas which answer to the nature of the said things: ideas of the modifications of the human body are, strictly speaking (II. xvi.), those which involve the nature both of the human body and of external bodies. I say, secondly, that this association arises according to the order and association of the modifications of the human body, in order to distinguish it from that association of ideas, which arises from the order of the intellect, whereby the mind perceives things through their primary causes, and which is in all men the same. And hence we can further clearly understand, why the mind from the thought of one thing, should straightway arrive at the thought of another thing, which has no similarity with the first; for instance, from the thought of the word pomum (an apple), a Roman would straightway arrive at the thought of the fruit apple, which has no similitude with the articulate sound in question, nor anything in common with it, except that the body of the man has often been affected by these two things; that is, that the man has often heard the word pomum, while he was looking at the fruit; similarly every man will go on from one thought to another, according as his habit has ordered the images of things in his body. For a soldier, for instance, when he sees the tracks of a horse in sand, will at once pass from the thought of a horse to the thought of a horseman, and thence to the thought of war, &c.; while a countryman will proceed from the thought of a horse to the thought of a plough, a field, &c. Thus every man will follow this or that train of thought, according as he has been in the habit of conjoining and associating the mental images of things in this or that manner.

Note. We now clearly see what memory is. Memory is simply a certain association of ideas that involve the nature of things outside the human body. This association arises in the mind following the order and association of changes (affectiones) in the human body. First, I mean only ideas that involve the nature of things outside the human body. I do not mean ideas that correspond to the nature of those things. Strictly speaking, ideas of changes in the human body involve the nature of both the human body and external bodies (II. xvi.). Second, this association follows the order and association of changes in the human body. I specify this to distinguish memory from the association of ideas that follows the order of the intellect. Through this intellectual association, the mind perceives things through their primary causes. This association is the same in all people. We can therefore also clearly understand why one thought immediately leads the mind to another, entirely dissimilar thought. For example, thinking of the word pomum (an apple) would immediately lead a Roman to think of the fruit. The apple bears no resemblance to the spoken sound. Nor do the two have anything in common, except that both have often affected the person's body together. That is, the person has often heard the word pomum while looking at the fruit. Similarly, everyone moves from one thought to another according to how habit has arranged images of things in their body. For example, a soldier who sees horse tracks in sand will immediately pass from thinking of a horse to a horseman. From there, he will think of war, and so on. A farmer, however, will pass from thinking of a horse to a plough, a field, and so on. Thus everyone follows one train of thought or another according to their habitual way of connecting and associating mental images.

PROP. XIX. The human mind has no knowledge of the body, and does not know it to exist, save through the ideas of the modifications whereby the body is affected.

PROP. XIX. The human mind knows the body only through ideas of the changes the body undergoes. Only through these ideas does the mind know that the body exists.

Proof.—The human mind is the very idea or knowledge of the human body (II. xiii.), which (II. ix.) is in God, in so far as he is regarded as affected by another idea of a particular thing actually existing: or, inasmuch as (Post. iv.) the human body stands in need of very many bodies whereby it is, as it were, continually regenerated; and the order and connection of ideas is the same as the order and connection of causes (II. vii.); this idea will therefore be in God, in so far as he is regarded as affected by the ideas of very many particular things. Thus God has the idea of the human body, or knows the human body, in so far as he is affected by very many other ideas, and not in so far as he constitutes the nature of the human mind; that is (by II. xi. Coroll.), the human mind does not know the human body. But the ideas of the modifications of body are in God, in so far as he constitutes the nature of the human mind, or the human mind perceives those modifications (II. xii.), and consequently (II. xvi.) the human body itself, and as actually existing; therefore the mind perceives thus far only the human body. Q.E.D.

Proof. The human mind is the very idea or knowledge of the human body (II. xiii.). This idea is in God insofar as he is affected by another idea of a particular thing that actually exists (II. ix.). Or consider that the human body needs very many bodies through which it is, as it were, continually renewed (Post. iv.). The order and connection of ideas is the same as the order and connection of causes (II. vii.). Therefore, the idea of the human body is in God insofar as he is affected by ideas of very many particular things. Thus God has the idea of the human body, or knows the human body, insofar as very many other ideas affect him. He does not know the body insofar as he constitutes the nature of the human mind. That is, the human mind does not know the human body (II. xi. Coroll.). But the ideas of the body's modifications are in God insofar as he constitutes the nature of the human mind. In other words, the human mind perceives those modifications (II. xii.). Consequently, the mind perceives the human body itself as actually existing (II. xvi.). Therefore, the mind perceives the human body only to this extent. Q.E.D.

PROP. XX. The idea or knowledge of the human mind is also in God, following in God in the same manner, and being referred to God in the same manner, as the idea or knowledge of the human body.

PROP. XX. The idea or knowledge of the human mind is also in God. This knowledge arises in God just as the idea or knowledge of the human body does. Both are related to God in the same way.

Proof.—Thought is an attribute of God (II. i.); therefore (II. iii.) there must necessarily be in God the idea both of thought itself and of all its modifications, consequently also of the human mind (II. xi.). Further, this idea or knowledge of the mind does not follow from God, in so far as he is infinite, but in so far as he is affected by another idea of an individual thing (II. ix.). But (II. vii.) the order and connection of ideas is the same as the order and connection of causes; therefore this idea or knowledge of the mind is in God and is referred to God, in the same manner as the idea or knowledge of the body. Q.E.D.

Proof. Thought is an attribute of God (II. i.). Therefore (II. iii.), God must necessarily contain the idea of thought itself and of all its modifications. Consequently, God must also contain the idea of the human mind (II. xi.). Further, this idea or knowledge of the mind does not follow from God insofar as he is infinite. Rather, it follows from God insofar as he is affected by another idea of an individual thing (II. ix.). But (II. vii.) the order and connection of ideas is the same as the order and connection of causes. Therefore, this idea or knowledge of the mind is in God and relates to God in the same way as the idea or knowledge of the body. Q.E.D.

PROP. XXI. This idea of the mind is united to the mind in the same way as the mind is united to the body.

PROP. XXI. This idea of the mind is united with the mind just as the mind is united with the body.

Proof.—That the mind is united to the body we have shown from the fact, that the body is the object of the mind (II. xii. and xiii.); and so for the same reason the idea of the mind must be united with its object, that is, with the mind in the same manner as the mind is united to the body. Q.E.D.

Proof. We have shown that the mind is united to the body because the body is the mind’s object (II. xii. and xiii.). So, for the same reason, the idea of the mind must be united to its object, the mind. This union must be just like the union of the mind and body. Q.E.D.

Note.—This proposition is comprehended much more clearly from what we have said in the note to II. vii. We there showed that the idea of body and body, that is, mind and body (II. xiii.), are one and the same individual conceived now under the attribute of thought, now under the attribute of extension; wherefore the idea of the mind and the mind itself are one and the same thing, which is conceived under one and the same attribute, namely, thought. The idea of the mind, I repeat, and the mind itself are in God by the same necessity and follow from him from the same power of thinking. Strictly speaking, the idea of the mind, that is, the idea of an idea, is nothing but the distinctive quality (forma) of the idea in so far as it is conceived as a mode of thought without reference to the object; if a man knows anything, he, by that very fact, knows that he knows it, and at the same time knows that he knows that he knows it, and so on to infinity. But I will treat of this hereafter.

Note. This proposition is much clearer in light of what we said in the note to II. vii. There we showed that the idea of the body and the body are one and the same individual. In other words, the mind and body are one and the same individual (II. xiii.). This individual is 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. Both are conceived under the same attribute, namely, thought. I repeat, the idea of the mind and the mind itself exist in God by the same necessity. Both follow from him through the same power of thinking. Strictly speaking, the idea of the mind is the idea of an idea. It is nothing but the idea’s distinctive quality (forma), considered as a mode of thought without reference to its object. If someone knows anything, then by that very fact they know that they know it. At the same time, they know that they know that they know it, and so on to infinity. But I will discuss this further later.

PROP. XXII. The human mind perceives not only the modifications of the body, but also the ideas of such modifications.

PROPOSITION XXII. The human mind perceives changes in the body. It also perceives the ideas of those changes.

Proof.—The ideas of the ideas of modifications follow in God in the same manner, and are referred to God in the same manner, as the ideas of the said modifications. This is proved in the same way as II. xx. But the ideas of the modifications of the body are in the human mind (II. xii.), that is, in God, in so far as he constitutes the essence of the human mind; therefore the ideas of these ideas will be in God, in so far as he has the knowledge or idea of the human mind, that is (II. xxi.), they will be in the human mind itself, which therefore perceives not only the modifications of the body, but also the ideas of such modifications. Q.E.D.

Proof. Ideas of ideas of modifications follow in God in the same way as ideas of the modifications themselves. They also relate to God in the same way. The proof is the same as for II. xx. But ideas of the body’s modifications are in the human mind (II. xii.). That is, they are in God insofar as he constitutes the essence of the human mind. Therefore, ideas of these ideas will be in God insofar as he has knowledge or an idea of the human mind. That is (II. xxi.), these further ideas will be in the human mind itself. The human mind therefore perceives not only the body’s modifications but also the ideas of those modifications. Q.E.D.

PROP. XXIII. The mind does not know itself, except in so far as it perceives the ideas of the modifications of the body.

PROPOSITION XXIII. The mind knows itself only to the extent that it perceives ideas of changes in the body.

Proof.—The idea or knowledge of the mind (II. xx.) follows in God in the same manner, and is referred to God in the same manner, as the idea or knowledge of the body. But since (II. xix.) the human mind does not know the human body itself, that is (II. xi. Coroll.), since the knowledge of the human body is not referred to God, in so far as he constitutes the nature of the human mind; therefore, neither is the knowledge of the mind referred to God, in so far as he constitutes the essence of the human mind; therefore (by the same Coroll. II. xi.), the human mind thus far has no knowledge of itself. Further the ideas of the modifications, whereby the body is affected, involve the nature of the human body itself (II. xvi.), that is (II. xiii.), they agree with the nature of the mind; wherefore the knowledge of these ideas necessarily involves knowledge of the mind; but (by the last Prop.) the knowledge of these ideas is in the human mind itself; wherefore the human mind thus far only has knowledge of itself. Q.E.D.

Proof. The idea or knowledge of the mind follows in God just as the idea or knowledge of the body does (II. xx.). It also relates to God in the same way. But the human mind does not know the human body itself (II. xix.). That is, knowledge of the human body does not relate to God insofar as he constitutes the human mind’s nature (II. xi. Coroll.). Therefore, knowledge of the mind likewise does not relate to God insofar as he constitutes the human mind’s essence. Therefore, to this extent, the human mind has no knowledge of itself (by the same Coroll. II. xi.). Furthermore, the ideas of the changes affecting the body involve the nature of the human body itself (II. xvi.). That is, these ideas agree with the nature of the mind (II. xiii.). Therefore, knowledge of these ideas necessarily involves knowledge of the mind. But knowledge of these ideas is in the human mind itself (by the preceding proposition). Therefore, the human mind knows itself only to this extent. Q.E.D.

PROP. XXIV. The human mind does not involve an adequate knowledge of the parts composing the human body.

PROP. XXIV. The human mind does not include adequate knowledge of the parts that make up the human body.

Proof.—The parts composing the human body do not belong to the essence of that body, except in so far as they communicate their motions to one another in a certain fixed relation (Def. after Lemma iii.), not in so far as they can be regarded as individuals without relation to the human body. The parts of the human body are highly complex individuals (Post. i.), whose parts (Lemma iv.) can be separated from the human body without in any way destroying the nature and distinctive quality of the latter, and they can communicate their motions (Ax. i., after Lemma iii.) to other bodies in another relation; therefore (II. iii.) the idea or knowledge of each part will be in God, inasmuch (II. ix.) as he is regarded as affected by another idea of a particular thing, which particular thing is prior in the order of nature to the aforesaid part (II. vii.). We may affirm the same thing of each part of each individual composing the human body; therefore, the knowledge of each part composing the human body is in God, in so far as he is affected by very many ideas of things, and not in so far as he has the idea of the human body only, in other words, the idea which constitutes the nature of the human mind (II. xiii); therefore (II. xi. Coroll.), the human mind does not involve an adequate knowledge of the human body. Q.E.D.

Proof. The parts composing the human body belong to its essence only under a specific condition. They must communicate their motions to one another in a certain fixed relation (Def. after Lemma iii.). They do not belong to its essence when considered as individuals apart from the human body. The parts of the human body are highly complex individuals (Post. i.). The parts of these individuals can be separated from the human body without destroying its nature or distinctive character (Lemma iv.). These parts can also communicate their motions to other bodies in a different relation (Ax. i., after Lemma iii.). Therefore, the idea or knowledge of each part is in God (II. iii.). This is so insofar as God is considered as affected by another idea of a particular thing (II. ix.). That particular thing comes before the part in the order of nature (II. vii.). We may say the same of each part of each individual composing the human body. Therefore, knowledge of each part composing the human body is in God insofar as he is affected by very many ideas of things. It is not in God insofar as he has only the idea of the human body. That is, it is not in God insofar as he has only the idea constituting the human mind’s nature (II. xiii). Therefore, the human mind does not contain adequate knowledge of the human body (II. xi. Coroll.). Q.E.D.

PROP. XXV. The idea of each modification of the human body does not involve an adequate knowledge of the external body.

PROP. XXV. The idea of each change in the human body does not provide adequate knowledge of the external body.

Proof.—We have shown that the idea of a modification of the human body involves the nature of an external body, in so far as that external body conditions the human body in a given manner. But, in so far as the external body is an individual, which has no reference to the human body, the knowledge or idea thereof is in God (II. ix.), in so far as God is regarded as affected by the idea of a further thing, which (II. vii.) is naturally prior to the said external body. Wherefore an adequate knowledge of the external body is not in God, in so far as he has the idea of the modification of the human body; in other words, the idea of the modification of the human body does not involve an adequate knowledge of the external body. Q.E.D.

Proof. We have shown that the idea of a modification of the human body involves the nature of an external body. This holds insofar as the external body affects the human body in a particular way. But consider the external body as an individual, apart from its relation to the human body. Knowledge, or the idea, of the external body is in God (II. ix.). This holds insofar as God is understood as affected by the idea of another thing. That other thing is prior in nature to the external body (II. vii.). Therefore, adequate knowledge of the external body is not in God insofar as he has the idea of the human body's modification. In other words, the idea of the human body's modification does not involve adequate knowledge of the external body. Q.E.D.

PROP. XXVI. The human mind does not perceive any external body as actually existing, except through the ideas of the modifications of its own body.

PROP. XXVI. The human mind perceives an external body as actually existing only through ideas of changes in its own body.

Proof.—If the human body is in no way affected by a given external body, then (II. vii.) neither is the idea of the human body, in other words, the human mind, affected in any way by the idea of the existence of the said external body, nor does it in any manner perceive its existence. But, in so far as the human body is affected in any way by a given external body, thus far (II. xvi. and Coroll.) it perceives that external body. Q.E.D.

Proof. Suppose the human body is not affected in any way by a given external body. Then (II. vii.) the idea of the human body, in other words, the human mind, is also unaffected. The idea of that external body's existence does not affect the mind in any way. Nor does the mind perceive that body's existence in any way. But insofar as a given external body affects the human body, the mind perceives that external body (II. xvi. and Coroll.). Q.E.D.

Corollary.—In so far as the human mind imagines an external body, it has not an adequate knowledge thereof.

Corollary: To the extent that the human mind imagines an external body, the mind lacks adequate knowledge of that body.

Proof.—When the human mind regards external bodies through the ideas of the modifications of its own body, we say that it imagines (see II. xvii. note); now the mind can only imagine external bodies as actually existing. Therefore (by II. xxv.), in so far as the mind imagines external bodies, it has not an adequate knowledge of them. Q.E.D.

Proof. When the human mind perceives external bodies through ideas of changes in its own body, we say the mind imagines (see II. xvii. note). Now, the mind can only imagine external bodies as actually existing. Therefore, insofar as the mind imagines external bodies, the mind does not have adequate knowledge of them (by II. xxv.). Q.E.D.

PROP. XXVII. The idea of each modification of the human body does not involve an adequate knowledge of the human body itself.

PROP. XXVII. The idea of each change in the human body does not include adequate knowledge of the body itself.

Proof.—Every idea of a modification of the human body involves the nature of the human body, in so far as the human body is regarded as affected in a given manner (II. xvi.). But, inasmuch as the human body is an individual which may be affected in many other ways, the idea of the said modification, &c. Q.E.D.

Proof. Every idea of a change in the human body involves the body's nature. It involves that nature insofar as the body is considered to be affected in a particular way (II. xvi.). But because the human body is an individual that may be affected in many other ways, the idea of that change, etc. Q.E.D.

PROP. XXVIII. The ideas of the modifications of the human body, in so far as they have reference only to the human mind, are not clear and distinct, but confused.

PROP. XXVIII. Ideas of changes in the human body, insofar as these ideas relate only to the human mind, are not clear and distinct but confused.

Proof.—The ideas of the modifications of the human body involve the nature both of the human body and of external bodies (II. xvi.); they must involve the nature not only of the human body but also of its parts; for the modifications are modes (Post. iii.), whereby the parts of the human body, and, consequently, the human body as a whole are affected. But (by II. xxiv., xxv.) the adequate knowledge of external bodies, as also of the parts composing the human body, is not in God, in so far as he is regarded as affected by the human mind, but in so far as he is regarded as affected by other ideas. These ideas of modifications, in so far as they are referred to the human mind alone, are as consequences without premisses, in other words, confused ideas. Q.E.D.

Proof. Ideas of changes in the human body involve the nature of both the human body and external bodies (II. xvi.). These ideas must involve not only the nature of the human body but also the nature of its parts. For these changes are modes (Post. iii.) through which the body's parts, and consequently the whole body, are affected. But adequate knowledge of external bodies and the parts composing the human body is not in God insofar as he is considered to be affected by the human mind (II. xxiv., xxv.). Rather, this knowledge is in God insofar as he is considered to be affected by other ideas. Thus, considered in relation to the human mind alone, these ideas of bodily changes are like conclusions without premises. In other words, they are confused ideas. Q.E.D.

Note.—The idea which constitutes the nature of the human mind is, in the same manner, proved not to be, when considered in itself alone, clear and distinct; as also is the case with the idea of the human mind, and the ideas of the ideas of the modifications of the human body, in so far as they are referred to the mind only, as everyone may easily see.

Note. The same reasoning applies to the idea that makes up the nature of the human mind. When considered on its own, this idea is proved not to be clear and distinct. The same is true of the idea of the human mind, when referred to the mind alone. It is also true of the ideas of the ideas of changes in the human body, under the same condition. Everyone can easily see this.

PROP. XXIX. The idea of the idea of each modification of the human body does not involve an adequate knowledge of the human mind.

PROP. XXIX. The idea of the idea of each change in the human body does not provide adequate knowledge of the human mind.

Proof.—The idea of a modification of the human body (II. xxvii.) does not involve an adequate knowledge of the said body, in other words, does not adequately express its nature; that is (II. xiii.) it does not agree with the nature of the mind adequately; therefore (I. Ax. vi) the idea of this idea does not adequately express the nature of the human mind, or does not involve an adequate knowledge thereof.

Proof. The idea of a modification of the human body (II. xxvii.) does not provide adequate knowledge of that body. In other words, the idea does not adequately express the body’s nature. That is (II. xiii.), the idea does not adequately agree with the mind’s nature. Therefore (I. Ax. vi), the idea of this idea does not adequately express the nature of the human mind. In other words, this further idea does not provide adequate knowledge of the human mind.

Corollary.—Hence it follows that the human mind, when it perceives things after the common order of nature, has not an adequate but only a confused and fragmentary knowledge of itself, of its own body, and of external bodies. For the mind does not know itself, except in so far as it perceives the ideas of the modifications of body (II. xxiii.). It only perceives its own body (II. xix.) through the ideas of the modifications, and only perceives external bodies through the same means; thus, in so far as it has such ideas of modification, it has not an adequate knowledge of itself (II. xxix.), nor of its own body (II. xxvii.), nor of external bodies (II. xxv.), but only a fragmentary and confused knowledge thereof (II. xxviii. and note). Q.E.D.

Corollary. It follows that when the human mind perceives things in the ordinary order of nature, its knowledge is inadequate. The mind has only confused and fragmentary knowledge of itself, its own body, and external bodies. For the mind knows itself only insofar as it perceives ideas of changes in the body (II. xxiii.). The mind perceives its own body only through ideas of these changes (II. xix.). The mind also perceives external bodies only through these same ideas. Thus, insofar as the mind has such ideas of bodily changes, its knowledge of itself is inadequate (II. xxix.). Its knowledge of its own body (II. xxvii.) and of external bodies (II. xxv.) is also inadequate. Instead, the mind has only fragmentary and confused knowledge of itself and these bodies (II. xxviii. and note). Q.E.D.

Note.—I say expressly, that the mind has not an adequate but only a confused knowledge of itself, its own body, and of external bodies, whenever it perceives things after the common order of nature; that is, whenever it is determined from without, namely, by the fortuitous play of circumstance, to regard this or that; not at such times as it is determined from within, that is, by the fact of regarding several things at once, to understand their points of agreement, difference, and contrast. Whenever it is determined in anywise from within, it regards things clearly and distinctly, as I will show below.

Note. I expressly say that the mind has only confused, not adequate, knowledge of itself, its body, and external bodies. This is so whenever the mind perceives things in the ordinary course of nature. That is, whenever outside forces, through chance circumstances, direct the mind to consider one thing or another. But this does not apply when the mind is directed from within. In that case, the mind considers several things at once to understand their similarities, differences, and contrasts. Whenever the mind is directed from within in any way, it sees things clearly and distinctly, as I will show below.

PROP. XXX. We can only have a very inadequate knowledge of the duration of our body.

PROP. XXX. We can have only a very limited understanding of how long our body lasts.

Proof.—The duration of our body does not depend on its essence (II. Ax. i.), nor on the absolute nature of God (I. xxi.). But (I. xxviii.) it is conditioned to exist and operate by causes, which in their turn are conditioned to exist and operate in a fixed and definite relation by other causes, these last again being conditioned by others, and so on to infinity. The duration of our body therefore depends on the common order of nature, or the constitution of things. Now, however a thing may be constituted, the adequate knowledge of that thing is in God, in so far as he has the ideas of all things, and not in so far as he has the idea of the human body only. (II. ix. Coroll.) Wherefore the knowledge of the duration of our body is in God very inadequate, in so far as he is only regarded as constituting the nature of the human mind; that is (II. xi. Coroll.), this knowledge is very inadequate to our mind. Q.E.D.

Proof. The duration of our body does not depend on its essence (II. Ax. i.). Nor does it depend on the absolute nature of God (I. xxi.). Instead, causes determine our body to exist and act (I. xxviii.). Other causes, in turn, determine those causes to exist and act in a fixed and definite relation. Still other causes determine these later causes, and so on to infinity. The duration of our body therefore depends on the general order of nature, or the arrangement of things. Now, however a thing is arranged, adequate knowledge of that thing exists in God insofar as he has the ideas of all things. Such knowledge does not exist in God insofar as he has only the idea of the human body (II. ix. Coroll.). Therefore, knowledge of our body's duration is very inadequate in God insofar as he constitutes only the human mind's nature. That is, our mind's knowledge of our body's duration is very inadequate (II. xi. Coroll.). Q.E.D.

PROP. XXXI. We can only have a very inadequate knowledge of the duration of particular things external to ourselves.

PROP. XXXI. Our knowledge of how long particular things outside ourselves last can only be very inadequate.

Proof.—Every particular thing, like the human body, must be conditioned by another particular thing to exist and operate in a fixed and definite relation; this other particular thing must likewise be conditioned by a third, and so on to infinity. (I. xxviii.) As we have shown in the foregoing proposition, from this common property of particular things, we have only a very inadequate knowledge of the duration of our body; we must draw a similar conclusion with regard to the duration of particular things, namely, that we can only have a very inadequate knowledge of the duration thereof. Q.E.D.

Proof. Every particular thing, like the human body, must depend on another particular thing to exist and act in a fixed, definite way. That other thing must likewise depend on a third, and so on to infinity. (I. xxviii.) As we showed in the preceding proposition, this shared property gives us only a very inadequate knowledge of our body's duration. We must draw the same conclusion about the duration of particular things. We can have only a very inadequate knowledge of how long they last. Q.E.D.

Corollary.—Hence it follows that all particular things are contingent and perishable. For we can have no adequate idea of their duration (by the last Prop.), and this is what we must understand by the contingency and perishableness of things. (I. xxxiii., Note i.) For (I. xxix.), except in this sense, nothing is contingent.

Corollary. It follows that all particular things are contingent and perishable. For we can have no adequate idea of how long they last (by the previous proposition). This lack of an adequate idea is what we must understand by the contingency and perishability of things. (I. xxxiii., Note i.) For outside this sense, nothing is contingent (I. xxix.).

PROP. XXXII. All ideas, in so far as they are referred to God, are true.

PROPOSITION XXXII. All ideas are true insofar as they are considered in relation to God.

Proof.—All ideas which are in God agree in every respect with their objects (II. vii. Coroll.), therefore (I. Ax. vi.) they are all true. Q.E.D.

Proof. All ideas in God agree in every respect with their objects (II. vii. Coroll.). Therefore, all these ideas are true (I. Ax. vi.). Q.E.D.

PROP. XXXIII. There is nothing positive in ideas, which causes them to be called false.

PROP. XXXIII. No actual feature of an idea makes that idea false.

Proof.—If this be denied, conceive, if possible, a positive mode of thinking, which should constitute the distinctive quality of falsehood. Such a mode of thinking cannot be in God (II. xxxii.); external to God it cannot be or be conceived (I. xv.). Therefore there is nothing positive in ideas which causes them to be called false. Q.E.D.

Proof. If you deny this, imagine, if possible, a positive mode of thought that defines what makes an idea false. Such a mode of thought cannot be in God (II. xxxii.). Nor can it exist or be conceived outside God (I. xv.). Therefore, nothing positive in ideas causes them to be called false. Q.E.D.

PROP. XXXIV. Every idea, which in us is absolute or adequate and perfect, is true.

PROPOSITION XXXIV. Every idea in us that is absolute or adequate and perfect is true.

Proof.—When we say that an idea in us is adequate and perfect, we say, in other words (II. xi. Coroll.), that the idea is adequate and perfect in God, in so far as he constitutes the essence of our mind; consequently (II. xxxii.), we say that such an idea is true. Q.E.D.

Proof. When we say an idea in us is adequate and perfect, we mean the following (II. xi. Coroll.). The idea is adequate and perfect in God, insofar as he constitutes the essence of our mind. Consequently (II. xxxii.), we are saying that such an idea is true. Q.E.D.

PROP. XXXV. Falsity consists in the privation of knowledge, which inadequate, fragmentary, or confused ideas involve.

PROP. XXXV. Falsity is the lack of knowledge involved in inadequate, fragmentary, or confused ideas.

Proof.—There is nothing positive in ideas, which causes them to be called false (II. xxxiii.); but falsity cannot consist in simple privation (for minds, not bodies, are said to err and to be mistaken), neither can it consist in absolute ignorance, for ignorance and error are not identical; wherefore it consists in the privation of knowledge, which inadequate, fragmentary, or confused ideas involve. Q.E.D.

Proof. Nothing positive in ideas causes them to be called false (II. xxxiii.). But falsity cannot consist simply in an absence (for minds, not bodies, are said to err and be mistaken). Nor can falsity consist in complete ignorance, because ignorance and error are not the same. Therefore, falsity consists in the lack of knowledge involved in inadequate, fragmentary, or confused ideas. Q.E.D.

Note.—In the note to II. xvii. I explained how error consists in the privation of knowledge, but in order to throw more light on the subject I will give an example. For instance, men are mistaken in thinking themselves free; their opinion is made up of consciousness of their own actions, and ignorance of the causes by which they are conditioned. Their idea of freedom, therefore, is simply their ignorance of any cause for their actions. As for their saying that human actions depend on the will, this is a mere phrase without any idea to correspond thereto. What the will is, and how it moves the body, they none of them know; those who boast of such knowledge, and feign dwellings and habitations for the soul, are wont to provoke either laughter or disgust. So, again, when we look at the sun, we imagine that it is distant from us about two hundred feet; this error does not lie solely in this fancy, but in the fact that, while we thus imagine, we do not know the sun's true distance or the cause of the fancy. For although we afterwards learn, that the sun is distant from us more than six hundred of the earth's diameters, we none the less shall fancy it to be near; for we do not imagine the sun as near us, because we are ignorant of its true distance, but because the modification of our body involves the essence of the sun, in so far as our said body is affected thereby.

Note. In the note to II. xvii., I explained how error consists in a lack of knowledge. But to make this clearer, I will give an example. People are mistaken, for instance, in thinking themselves free. Their belief comes from awareness of their own actions and ignorance of the causes that determine those actions. Their idea of freedom, then, is simply their ignorance of any cause for their actions. As for their claim that human actions depend on the will, these are merely words with no corresponding idea. None of them knows what the will is or how it moves the body. Those who boast of such knowledge and invent homes and dwelling places for the soul tend to provoke laughter or disgust. Similarly, when we look at the sun, we imagine it to be about two hundred feet away. The error does not lie solely in this impression. It also lies in our ignorance, while having this impression, of the sun's true distance and what causes the impression. For even after learning that the sun is more than six hundred Earth diameters away, we still imagine it nearby. We do not imagine the sun nearby because we are ignorant of its true distance. Rather, we imagine it nearby because the change in our body involves the sun's essence insofar as the sun affects our body.

PROP. XXXVI. Inadequate and confused ideas follow by the same necessity, as adequate or clear and distinct ideas.

PROP. XXXVI. Inadequate and confused ideas arise just as necessarily as adequate, or clear and distinct, ideas.

Proof.—All ideas are in God (I. xv.), and in so far as they are referred to God are true (II. xxxii.) and (II. vii. Coroll.) adequate; therefore there are no ideas confused or inadequate, except in respect to a particular mind (cf. II. xxiv. and xxviii.); therefore all ideas, whether adequate or inadequate, follow by the same necessity (II. vi.). Q.E.D.

Proof. All ideas are in God (I. xv.). Insofar as ideas are considered in relation to God, they are true (II. xxxii.) and adequate (II. vii. Coroll.). Therefore, ideas are confused or inadequate only in relation to a particular mind (cf. II. xxiv. and xxviii.). Therefore, all ideas, whether adequate or inadequate, follow with the same necessity (II. vi.). Q.E.D.

PROP. XXXVII. That which is common to all (cf. Lemma II., above), and which is equally in a part and in the whole, does not constitute the essence of any particular thing.

PROP. XXXVII. A property common to all things and equally present in a part and the whole does not constitute the essence of any particular thing. (See Lemma II above.)

Proof.—If this be denied, conceive, if possible, that it constitutes the essence of some particular thing; for instance, the essence of B. Then (II. Def. ii.) it cannot without B either exist or be conceived; but this is against our hypothesis. Therefore it does not appertain to B's essence, nor does it constitute the essence of any particular thing. Q.E.D.

Proof. If you deny this, suppose, if possible, that it constitutes the essence of some particular thing. For example, suppose it constitutes the essence of B. Then (II. Def. ii.) it can neither exist nor be conceived without B. But this contradicts our hypothesis. Therefore, it does not belong to B’s essence, nor does it constitute the essence of any particular thing. Q.E.D.

PROP. XXXVIII. Those things, which are common to all, and which are equally in a part and in the whole, cannot be conceived except adequately.

PROP. XXXVIII. Things common to all and equally present in a part and the whole can only be understood adequately.

Proof.—Let A be something, which is common to all bodies, and which is equally present in the part of any given body and in the whole. I say A cannot be conceived except adequately. For the idea thereof in God will necessarily be adequate (II. vii. Coroll.), both in so far as God has the idea of the human body, and also in so far as he has the idea of the modifications of the human body, which (II. xvi., xxv., xxvii.) involve in part the nature of the human body and the nature of external bodies; that is (II. xii., xiii.), the idea in God will necessarily be adequate, both in so far as he constitutes the human mind, and in so far as he has the ideas, which are in the human mind. Therefore the mind (II. xi. Coroll.) necessarily perceives A adequately, and has this adequate perception, both in so far as it perceives itself, and in so far as it perceives its own or any external body, nor can A be conceived in any other manner. Q.E.D.

Proof. Let A be something common to all bodies and equally present in any body's parts and whole. I claim that A can only be conceived adequately. For God's idea of A must be adequate (II. vii. Coroll.). This holds both insofar as God has the idea of the human body and insofar as he has the idea of its modifications. These modifications partly involve the nature of the human body and the nature of external bodies (II. xvi., xxv., xxvii.). That is (II. xii., xiii.), God's idea of A must be adequate insofar as he constitutes the human mind. It must also be adequate insofar as he has the ideas present in the human mind. Therefore, the mind necessarily perceives A adequately (II. xi. Coroll.). The mind has this adequate perception both when perceiving itself and when perceiving its own body or any external body. A cannot be conceived in any other way. Q.E.D.

Corollary—Hence it follows that there are certain ideas or notions common to all men; for (by Lemma ii.) all bodies agree in certain respects, which (by the foregoing Prop.) must be adequately or clearly and distinctly perceived by all.

Corollary: It follows that certain ideas or notions are common to all people. For, by Lemma ii., all bodies share certain features. By the preceding Proposition, these shared features must be perceived adequately, or clearly and distinctly, by everyone.

PROP. XXXIX. That, which is common to and a property of the human body and such other bodies as are wont to affect the human body, and which is present equally in each part of either, or in the whole, will be represented by an adequate idea in the mind.

PROP. XXXIX. Suppose a property is shared by the human body and other bodies that commonly affect the human body. Suppose this property is equally present in every part of each body or in each body as a whole. The mind will then represent this property through an adequate idea.

Proof.—If A be that, which is common to and a property of the human body and external bodies, and equally present in the human body and in the said external bodies, in each part of each external body and in the whole, there will be an adequate idea of A in God (II. vii. Coroll.), both in so far as he has the idea of the human body, and in so far as he has the ideas of the given external bodies. Let it now be granted, that the human body is affected by an external body through that, which it has in common therewith, namely, A; the idea of this modification will involve the property A (II. xvi.), and therefore (II. vii. Coroll.) the idea of this modification, in so far as it involves the property A, will be adequate in God, in so far as God is affected by the idea of the human body; that is (II. xiii.), in so far as he constitutes the nature of the human mind; therefore (II. xi. Coroll.) this idea is also adequate in the human mind. Q.E.D.

Proof. Suppose A is a property shared by the human body and external bodies. Suppose A is equally present in the human body, in every part of each external body, and in the whole. Then God will have an adequate idea of A (II. vii. Coroll.). This holds both insofar as he has the idea of the human body and insofar as he has ideas of those external bodies. Now suppose an external body affects the human body through their shared property, A. The idea of this modification will include the property A (II. xvi.). Therefore, insofar as the idea of this modification includes A, that idea will be adequate in God (II. vii. Coroll.). It will be adequate insofar as God is affected by the idea of the human body. That is, it will be adequate insofar as he constitutes the nature of the human mind (II. xiii.). Therefore, this idea is also adequate in the human mind (II. xi. Coroll.). Q.E.D.

Corollary.—Hence it follows that the mind is fitted to perceive adequately more things, in proportion as its body has more in common with other bodies.

Corollary: It follows that the mind can adequately perceive more things as its body has more in common with other bodies.

PROP. XL. Whatsoever ideas in the mind follow from ideas which are therein adequate, are also themselves adequate.

PROP. XL. All ideas in the mind that follow from adequate ideas in that mind are also adequate.

Proof.—This proposition is self—evident. For when we say that an idea in the human mind follows from ideas which are therein adequate, we say, in other words (II. xi. Coroll.), that an idea is in the divine intellect, whereof God is the cause, not in so far as he is infinite, nor in so far as he is affected by the ideas of very many particular things, but only in so far as he constitutes the essence of the human mind.

Proof. This proposition is self-evident. For when we say that an idea in the human mind follows from adequate ideas in that mind, we mean the following (II. xi. Coroll.). The idea exists in the divine intellect, and God is its cause. But God causes the idea not insofar as he is infinite, nor insofar as he is affected by ideas of very many particular things. He causes the idea only insofar as he constitutes the essence of the human mind.

Note I.—I have thus set forth the cause of those notions, which are common to all men, and which form the basis of our ratiocination. But there are other causes of certain axioms or notions, which it would be to the purpose to set forth by this method of ours; for it would thus appear what notions are more useful than others, and what notions have scarcely any use at all. Furthermore, we should see what notions are common to all men, and what notions are only clear and distinct to those who are unshackled by prejudice, and we should detect those which are ill—founded. Again we should discern whence the notions called secondary derived their origin, and consequently the axioms on which they are founded, and other points of interest connected with these questions. But I have decided to pass over the subject here, partly because I have set it aside for another treatise, partly because I am afraid of wearying the reader by too great prolixity. Nevertheless, in order not to omit anything necessary to be known, I will briefly set down the causes, whence are derived the terms styled transcendental, such as Being, Thing, Something. These terms arose from the fact, that the human body, being limited, is only capable of distinctly forming a certain number of images (what an image is I explained in the II. xvii. note) within itself at the same time; if this number be exceeded, the images will begin to be confused; if this number of images, of which the body is capable of forming distinctly within itself, be largely exceeded, all will become entirely confused one with another. This being so, it is evident (from II. Prop. xvii. Coroll., and xviii.) that the human mind can distinctly imagine as many things simultaneously, as its body can form images simultaneously. When the images become quite confused in the body, the mind also imagines all bodies confusedly without any distinction, and will comprehend them, as it were, under one attribute, namely, under the attribute of Being, Thing, &c. The same conclusion can be drawn from the fact that images are not always equally vivid, and from other analogous causes, which there is no need to explain here; for the purpose which we have in view it is sufficient for us to consider one only. All may be reduced to this, that these terms represent ideas in the highest degree confused. From similar causes arise those notions, which we call general, such as man, horse, dog, &c. They arise, to wit, from the fact that so many images, for instance, of men, are formed simultaneously in the human mind, that the powers of imagination break down, not indeed utterly, but to the extent of the mind losing count of small differences between individuals (e.g. colour, size, &c.) and their definite number, and only distinctly imagining that, in which all the individuals, in so far as the body is affected by them, agree; for that is the point, in which each of the said individuals chiefly affected the body; this the mind expresses by the name man, and this it predicates of an infinite number of particular individuals. For, as we have said, it is unable to imagine the definite number of individuals. We must, however, bear in mind, that these general notions are not formed by all men in the same way, but vary in each individual according as the point varies, whereby the body has been most often affected and which the mind most easily imagines or remembers. For instance, those who have most often regarded with admiration the stature of man, will by the name of man understand an animal of erect stature; those who have been accustomed to regard some other attribute, will form a different general image of man, for instance, that man is a laughing animal, a two—footed animal without feathers, a rational animal, and thus, in other cases, everyone will form general images of things according to the habit of his body.

Note I. I have now explained the cause of the notions shared by all people, which form the basis of our reasoning. But certain axioms or notions have other causes that would be worth explaining through our method. Such an explanation would show which notions are more useful than others, and which have hardly any use. We would also see which notions everyone shares. We would see which notions are clear and distinct only to people free from prejudice, and identify those without sound foundations. We would also discover the origin of the notions called secondary, and consequently the axioms on which they are based. Other interesting points connected with these questions would also become clear. But I have decided to leave this subject aside here. Partly, I have reserved it for another work. Partly, I fear that discussing it at too great a length would tire the reader. Nevertheless, to leave out nothing necessary to know, I will briefly explain the origins of the terms called transcendental. Examples include Being, Thing, and Something. These terms arose because the human body has limits. At any one time, the body can form only a certain number of distinct images within itself. I explained what an image is in the note to II. xvii. If this number is exceeded, the images begin to blur together. If the number is greatly exceeded, all the images become completely confused with one another. It therefore follows from II. Prop. xvii. Coroll., and xviii. that the mind has a corresponding limit. The mind can distinctly imagine only as many things at once as the body can form images at once. When the body's images become completely confused, the mind also imagines all bodies confusedly, without distinguishing them. The mind then groups these bodies, as it were, under one attribute, namely Being, Thing, and so on. The same conclusion follows from the fact that images are not always equally vivid, and from other similar causes. There is no need to explain these other causes here. For our purpose, considering just one cause is enough. All these explanations come down to this: these terms represent ideas that are confused to the highest degree. Similar causes produce the notions we call general, such as man, horse, and dog. For example, so many images of individual people form in the mind at once that the imagination's powers break down. The breakdown is not complete. Rather, the mind loses track of small differences between individuals, such as colour and size, and of their exact number. The mind distinctly imagines only what all these individuals share, insofar as they affect the body. For this shared feature is how each individual chiefly affected the body. The mind expresses this shared feature by the word man, and attributes it to infinitely many particular individuals. For, as we have said, the mind cannot imagine the exact number of individuals. We must remember, however, that not everyone forms these general notions in the same way. General notions vary from person to person. They depend on the feature that has most often affected the body, and that the mind most easily imagines or remembers. For example, some people have most often admired the upright posture of human beings. By man, these people will understand an animal with an upright posture. People accustomed to noticing another attribute will form a different general image of man. They may understand man as a laughing animal, a two-footed animal without feathers, or a rational animal. Likewise, in other cases, everyone forms general images of things according to the habits of their body.

It is thus not to be wondered at, that among philosophers, who seek to explain things in nature merely by the images formed of them, so many controversies should have arisen.

So the many disputes among philosophers who try to explain nature solely through mental images should come as no surprise.

Note II.—From all that has been said above it is clear, that we, in many cases, perceive and form our general notions:—(1.) From particular things represented to our intellect fragmentarily, confusedly, and without order through our senses (II. xxix. Coroll.); I have settled to call such perceptions by the name of knowledge from the mere suggestions of experience.⁴

Note II. All that has been said above makes clear that, in many cases, we perceive and form general ideas as follows: (1.) From particular things presented to our minds through our senses in fragments, confusedly, and without order (II. xxix. Coroll.). I have chosen to call such perceptions knowledge based on the mere suggestions of experience.⁴

(2.) From symbols, e.g., from the fact of having read or heard certain words we remember things and form certain ideas concerning them, similar to those through which we imagine things (II. xviii. note). I shall call both these ways of regarding things knowledge of the first kind, opinion, or imagination. (3.) From the fact that we have notions common to all men, and adequate ideas of the properties of things (II. xxxviii. Coroll., xxxix. and Coroll. and xl.); this I call reason and knowledge of the second kind. Besides these two kinds of knowledge, there is, as I will hereafter show, a third kind of knowledge, which we will call intuition. This kind of knowledge proceeds from an adequate idea of the absolute essence of certain attributes of God to the adequate knowledge of the essence of things. I will illustrate all three kinds of knowledge by a single example. Three numbers are given for finding a fourth, which shall be to the third as the second is to the first. Tradesmen without hesitation multiply the second by the third, and divide the product by the first; either because they have not forgotten the rule which they received from a master without any proof, or because they have often made trial of it with simple numbers, or by virtue of the proof of the nineteenth proposition of the seventh book of Euclid, namely, in virtue of the general property of proportionals.

(2.) From symbols. For example, reading or hearing certain words makes us remember things and form certain ideas about them. These ideas resemble those through which we imagine things (II. xviii. note). I call both these ways of viewing things knowledge of the first kind, opinion, or imagination. (3.) From notions common to all people and adequate ideas of the properties of things (II. xxxviii. Coroll., xxxix. and Coroll. and xl.). I call this reason and knowledge of the second kind. Besides these two kinds of knowledge, there is a third kind, as I will show later. We will call this third kind intuition. Intuition begins with an adequate idea of the absolute essence of certain attributes of God. From this idea, intuition proceeds to adequate knowledge of the essence of things. I will illustrate all three kinds of knowledge with a single example. Three numbers are given, and we must find a fourth. The fourth must have the same ratio to the third as the second has to the first. Merchants immediately multiply the second by the third and divide the result by the first. They do so for one of three reasons. They may remember the rule taught to them without proof by a teacher. Or they may have tested the rule often with simple numbers. Or they may rely on the proof of proposition nineteen in book seven of Euclid. That proof rests on the general property of proportional numbers.

But with very simple numbers there is no need of this. For instance, one, two, three, being given, everyone can see that the fourth proportional is six; and this is much clearer, because we infer the fourth number from an intuitive grasping of the ratio, which the first bears to the second.

But with very simple numbers, there is no need for this. For example, given one, two, and three, everyone can see that the fourth proportional is six. This conclusion is much clearer because we infer the fourth number by intuitively grasping the ratio of the first to the second.

PROP. XLI. Knowledge of the first kind is the only source of falsity, knowledge of the second and third kinds is necessarily true.

PROPOSITION XLI. Knowledge of the first kind is the only source of falsehood. Knowledge of the second and third kinds is necessarily true.

Proof.—To knowledge of the first kind we have (in the foregoing note) assigned all those ideas, which are inadequate and confused; therefore this kind of knowledge is the only source of falsity (II. xxxv.). Furthermore, we assigned to the second and third kinds of knowledge those ideas which are adequate; therefore these kinds are necessarily true (II. xxxiv.). Q.E.D.

Proof. In the preceding note, we classified all inadequate and confused ideas as knowledge of the first kind. Therefore, knowledge of the first kind is the only source of falsity (II. xxxv.). We also classified adequate ideas as knowledge of the second and third kinds. Therefore, these two kinds of knowledge are necessarily true (II. xxxiv.). Q.E.D.

PROP. XLII. Knowledge of the second and third kinds, not knowledge of the first kind, teaches us to distinguish the true from the false.

PROPOSITION XLII. Knowledge of the second and third kinds teaches us to tell truth from falsehood. Knowledge of the first kind does not.

Proof.—This proposition is self—evident. He, who knows how to distinguish between true and false, must have an adequate idea of true and false. That is (II. xl., note ii.), he must know the true and the false by the second or third kind of knowledge.

Proof. This proposition is self-evident. Anyone who can distinguish between true and false must have an adequate idea of true and false. In other words (II. xl., note ii.), they must know true and false through the second or third kind of knowledge.

PROP. XLIII. He, who has a true idea, simultaneously knows that he has a true idea, and cannot doubt of the truth of the thing perceived.

PROP. XLIII. Anyone who has a true idea knows at the same time that the idea is true. They cannot doubt the truth of what they perceive.

Proof.—A true idea in us is an idea which is adequate in God, in so far as he is displayed through the nature of the human mind (II. xi. Coroll.). Let us suppose that there is in God, in so far as he is displayed through the human mind, an adequate idea, A. The idea of this idea must also necessarily be in God, and be referred to him in the same way as the idea A (by II. xx., whereof the proof is of universal application). But the idea A is supposed to be referred to God, in so far as he is displayed through the human mind; therefore, the idea of the idea A must be referred to God in the same manner; that is (by II. xi. Coroll.), the adequate idea of the idea A will be in the mind, which has the adequate idea A; therefore he, who has an adequate idea or knows a thing truly (II. xxxiv.), must at the same time have an adequate idea or true knowledge of his knowledge; that is, obviously, he must be assured. Q.E.D.

Proof: A true idea in us is an idea adequate in God, insofar as he is expressed through the human mind (II. xi. Coroll.). Suppose there is an adequate idea, A, in God, insofar as he is expressed through the human mind. The idea of A must also necessarily exist in God and relate to him in the same way as A. This follows from II. xx., whose proof applies universally. But A is assumed to relate to God insofar as he is expressed through the human mind. Therefore, the idea of A must relate to God in the same way. Thus, the adequate idea of A will exist in the mind that has the adequate idea A (II. xi. Coroll.). Therefore, anyone who has an adequate idea, or knows something truly (II. xxxiv.), must also have adequate knowledge of that knowledge. In other words, such a person must clearly be certain. Q.E.D.

Note.—I explained in the note to II. xxi. what is meant by the idea of an idea; but we may remark that the foregoing proposition is in itself sufficiently plain. No one, who has a true idea, is ignorant that a true idea involves the highest certainty. For to have a true idea is only another expression for knowing a thing perfectly, or as well as possible. No one, indeed, can doubt of this, unless he thinks that an idea is something lifeless, 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 anything, unless he do first understand it? In other words, who can know that he is sure of a thing, unless he be first sure of that thing? Further, what can there be more clear, and more certain, than a true idea as a standard of truth? Even as light displays both itself and darkness, so is truth a standard both of itself and of falsity.

Note. I explained what an idea of an idea means in the note to II. xxi. But we may observe that the preceding proposition is clear enough on its own. Anyone who has a true idea knows that a true idea involves the highest certainty. Having a true idea simply means knowing something perfectly, or as well as possible. Indeed, no one can doubt this unless they think an idea is something lifeless, like a picture on a panel. But an idea is a mode of thinking, the very act of understanding. And who, I ask, can know that they understand something unless they first understand it? In other words, who can know that they are certain of something unless they are first certain of it? Further, what could be clearer or more certain than a true idea as a standard of truth? Just as light reveals both itself and darkness, truth is the standard both of itself and of falsity.

I think I have thus sufficiently answered these questions—namely, if a true idea is distinguished from a false idea, only in so far as it is said to agree with its object, a true idea has no more reality or perfection than a false idea (since the two are only distinguished by an extrinsic mark); consequently, neither will a man who has a true idea have any advantage over him who has only false ideas. Further, how comes it that men have false ideas? Lastly, how can anyone be sure, that he has ideas which agree with their objects? These questions, I repeat, I have, in my opinion, sufficiently answered. The difference between a true idea and a false idea is plain: from what was said in II. xxxv., the former is related to the latter as being is to not—being. The causes of falsity I have set forth very clearly in II. xix. and II. xxxv. with the note. From what is there stated, the difference between a man who has true ideas, and a man who has only false ideas, is made apparent. As for the last question—as to how a man can be sure that he has ideas that agree with their objects, I have just pointed out, with abundant clearness, that his knowledge arises from the simple fact, that he has an idea which corresponds with its object—in other words, that truth is its own standard. We may add that our mind, in so far as it perceives things truly, is part of the infinite intellect of God (II. xi. Coroll.); therefore, the clear and distinct ideas of the mind are as necessarily true as the ideas of God.

I think I have now answered the following questions adequately. If a true idea differs from a false idea only by agreeing with its object, the difference is merely external. A true idea would therefore have no more reality or perfection than a false idea. Consequently, someone with a true idea would have no advantage over someone with only false ideas. Further, how do people come to have false ideas? Finally, how can anyone be sure that their ideas agree with their objects? These questions, I repeat, have in my opinion been adequately answered. The difference between a true idea and a false idea is clear. As explained in II. xxxv., a true idea relates to a false idea as being relates to nonbeing. I explained the causes of falsity very clearly in II. xix. and II. xxxv., including the note. Those explanations also make clear the difference between someone with true ideas and someone with only false ideas. The last question asks how someone can be sure that their ideas agree with their objects. I have just shown very clearly that this certainty comes simply from having an idea that corresponds to its object. In other words, truth is its own standard. We may add that our mind, insofar as it perceives things truly, is part of God's infinite intellect (II. xi. Coroll.). Therefore, the mind's clear and distinct ideas are as necessarily true as God's ideas.

PROP. XLIV. It is not in the nature of reason to regard things as contingent, but as necessary.

PROP. XLIV. Reason by its nature sees things not as things that could be otherwise, but as necessary.

Proof.—It is in the nature of reason to perceive things truly (II. xli.), namely (I. Ax. vi.), as they are in themselves—that is (I. xxix.), not as contingent, but as necessary. Q.E.D.

Proof. Reason by its nature perceives things truly (II. xli.), meaning (I. Ax. vi.), as they are in themselves. That is, reason perceives things (I. xxix.) not as contingent, but as necessary. Q.E.D.

Corollary I.—Hence it follows, that it is only through our imagination that we consider things, whether in respect to the future or the past, as contingent.

Corollary I. It follows that only through our imagination do we consider things, whether past or future, to be contingent.

Note.—How this way of looking at things arises, I will briefly explain. We have shown above (II. xvii. and Coroll.) that the mind always regards things as present to itself, even though they be not in existence, until some causes arise which exclude their existence and presence. Further (II. xviii.), we showed that, if the human body has once been affected by two external bodies simultaneously, the mind, when it afterwards imagines one of the said external bodies, will straightway remember the other—that is, it will regard both as present to itself, unless there arise causes which exclude their existence and presence. Further, no one doubts that we imagine time, from the fact that we imagine bodies to be moved some more slowly than others, some more quickly, some at equal speed. Thus, let us suppose that a child yesterday saw Peter for the first time in the morning, Paul at noon, and Simon in the evening; then, that today he again sees Peter in the morning. It is evident, from II. Prop. xviii., that, as soon as he sees the morning light, he will imagine that the sun will traverse the same parts of the sky, as it did when he saw it on the preceding day; in other words, he will imagine a complete day, and, together with his imagination of the morning, he will imagine Peter; with noon, he will imagine Paul; and with evening, he will imagine Simon—that is, he will imagine the existence of Paul and Simon in relation to a future time; on the other hand, if he sees Simon in the evening, he will refer Peter and Paul to a past time, by imagining them simultaneously with the imagination of a past time. If it should at any time happen, that on some other evening the child should see James instead of Simon, he will, on the following morning, associate with his imagination of evening sometimes Simon, sometimes James, not both together: for the child is supposed to have seen, at evening, one or other of them, not both together. His imagination will therefore waver; and, with the imagination of future evenings, he will associate first one, then the other—that is, he will imagine them in the future, neither of them as certain, but both as contingent. This wavering of the imagination will be the same, if the imagination be concerned with things which we thus contemplate, standing in relation to time past or time present: consequently, we may imagine things as contingent, whether they be referred to time present, past, or future.

Note. I will briefly explain how this way of seeing things arises. We showed above (II. xvii. and Coroll.) that the mind always regards things as present, even when they do not exist. The mind continues to do so until causes arise that rule out those things’ existence and presence. We also showed (II. xviii.) that the human body may once have been affected by two external bodies at the same time. If so, whenever the mind later imagines one of those bodies, it will immediately remember the other. In other words, the mind will regard both bodies as present, unless causes arise that rule out their existence and presence. Further, no one doubts that we imagine time because we imagine bodies moving at different speeds. Some move more slowly than others, some more quickly, and some at the same speed. Suppose, then, that yesterday a child saw Peter for the first time in the morning, Paul at noon, and Simon in the evening. Suppose that today the child again sees Peter in the morning. As II. Prop. xviii. makes clear, the child will imagine the sun’s course as soon as he sees the morning light. He will imagine the sun crossing the same parts of the sky as on the previous day. In other words, he will imagine a complete day. Along with imagining the morning, he will imagine Peter. With noon, he will imagine Paul, and with evening, Simon. In other words, he will imagine Paul and Simon as existing at a future time. On the other hand, if he sees Simon in the evening, he will place Peter and Paul in the past. He will do so by imagining them together with a past time. Now suppose that, on some other evening, the child sees James instead of Simon. The following morning, he will associate his image of evening sometimes with Simon and sometimes with James, but not with both together. For we have supposed that the child saw one or the other in the evening, not both together. His imagination will therefore waver. With his image of future evenings, he will associate first one, then the other. In other words, he will imagine both as existing in the future, neither as certain, but both as contingent. The imagination will waver in the same way when we consider things in relation to past or present time. Consequently, we may imagine things as contingent whether we place them in the present, past, or future.

Corollary II.—It is in the nature of reason to perceive things under a certain form of eternity (sub quâdam æternitatis specie).

Corollary II. Reason by its nature perceives things from a certain perspective of eternity (sub quâdam æternitatis specie).

Proof.—It is in the nature of reason to regard things, not as contingent, but as necessary (II. xliv.). Reason perceives this necessity of things (II. xli.) truly—that is (I. Ax. vi.), as it is in itself. But (I. xvi.) this necessity of things is the very necessity of the eternal nature of God; therefore, it is in the nature of reason to regard things under this form of eternity. We may add that the bases of reason are the notions (II. xxxviii.), which answer to things common to all, and which (II. xxxvii.) do not answer to the essence of any particular thing: which must therefore be conceived without any relation to time, under a certain form of eternity.

Proof. Reason naturally regards things as necessary, not contingent (II. xliv.). Reason perceives this necessity truly (II. xli.), that is, as the necessity exists in itself (I. Ax. vi.). But this necessity of things is the very necessity of God’s eternal nature (I. xvi.). Therefore, reason naturally regards things in this form of eternity. We may add that reason rests on notions corresponding to what all things have in common (II. xxxviii.). These notions do not correspond to the essence of any particular thing (II. xxxvii.). They must therefore be conceived without any relation to time, in a certain form of eternity.

PROP. XLV. Every idea of every body, or of every particular thing actually existing, necessarily involves the eternal and infinite essence of God.

PROP. XLV. Every idea of a body or particular thing that actually exists necessarily involves God's eternal and infinite essence.

Proof.—The idea of a particular thing actually existing necessarily involves both the existence and the essence of the said thing (II. viii.). Now particular things cannot be conceived without God (I. xv.); but, inasmuch as (II. vi.) they have God for their cause, in so far as he is regarded under the attribute of which the things in question are modes, their ideas must necessarily involve (I. Ax. iv.) the conception of the attributes of those ideas—that is (I. vi.), the eternal and infinite essence of God. Q.E.D.

Proof. The idea of a particular thing that actually exists necessarily involves both its existence and its essence (II. viii.). Now particular things cannot be conceived without God (I. xv.). But God causes these things insofar as he is understood through the attribute of which these things are modes (II. vi.). Their ideas must therefore necessarily involve the concept of the attributes of those ideas (I. Ax. iv.). That is, their ideas must involve the eternal and infinite essence of God (I. vi.). Q.E.D.

Note.—By existence I do not here mean duration—that is, existence in so far as it is conceived abstractedly, and as a certain form of quantity. I am speaking of the very nature of existence, which is assigned to particular things, because they follow in infinite numbers and in infinite ways from the eternal necessity of God's nature (I. xvi.). I am speaking, I repeat, of the very existence of particular things, in so far as they are in God. For although each particular thing be conditioned by another particular thing to exist in a given way, yet the force whereby each particular thing perseveres in existing follows from the eternal necessity of God's nature (cf. I. xxiv. Coroll.).

Note. By existence I do not mean duration, or existence considered abstractly as a certain kind of quantity. I am speaking of the very nature of existence attributed to particular things. These things have existence because they follow in infinite numbers and infinite ways from the eternal necessity of God's nature (I. xvi.). I repeat, I am speaking of the very existence of particular things insofar as they are in God. Although another particular thing determines how each particular thing exists, the power to continue existing has a different source. That power follows from the eternal necessity of God's nature (see I. xxiv. Coroll.).

PROP. XLVI. The knowledge of the eternal and infinite essence of God which every idea involves is adequate and perfect.

PROP. XLVI. Every idea includes knowledge of God's eternal and infinite essence. This knowledge is adequate and perfect.

Proof.—The proof of the last proposition is universal; and whether a thing be considered as a part or a whole, the idea thereof, whether of the whole or of a part (by the last Prop.), will involve God's eternal and infinite essence. Wherefore, that, which gives knowledge of the eternal and infinite essence of God, is common to all, and is equally in the part and in the whole; therefore (II. xxxviii.) this knowledge will be adequate. Q.E.D.

Proof. The proof of the previous proposition applies universally. Whether a thing is considered as a part or a whole, the idea of it involves God's eternal and infinite essence. This holds for the idea of either the whole or a part (by the previous proposition). Therefore, what gives knowledge of God's eternal and infinite essence is common to all, equally present in part and whole. Therefore (II. xxxviii.), this knowledge is adequate. Q.E.D.

PROP. XLVII. The human mind has an adequate knowledge of the eternal and infinite essence of God.

PROPOSITION XLVII. The human mind has adequate knowledge of God’s eternal and infinite essence.

Proof.—The human mind has ideas (II. xxii.), from which (II. xxiii.) it perceives itself and its own body (II. xix.) and external bodies (II. xvi. Coroll. i. and II. xvii.) as actually existing; therefore (II. xlv. and xlvi.) it has an adequate knowledge of the eternal and infinite essence of God. Q.E.D.

Proof. The human mind has ideas (II. xxii.). Through these ideas, the mind perceives itself (II. xxiii.) and its own body (II. xix.) as actually existing. It also perceives external bodies as actually existing (II. xvi. Coroll. i. and II. xvii.). Therefore, the mind has adequate knowledge of God’s eternal and infinite essence (II. xlv. and xlvi.). Q.E.D.

Note.—Hence we see, that the infinite essence and the eternity of God are known to all. Now as all things are in God, and are conceived through God, we can from this knowledge infer many things, which we may adequately know, and we may form that third kind of knowledge of which we spoke in the note to II. xl., and of the excellence and use of which we shall have occasion to speak in Part V. Men have not so clear a knowledge of God as they have of general notions, because they are unable to imagine God as they do bodies, and also because they have associated the name God with images of things that they are in the habit of seeing, as indeed they can hardly avoid doing, being, as they are, men, and continually affected by external bodies. Many errors, in truth, can be traced to this head, namely, that we do not apply names to things rightly. For instance, when a man says that the lines drawn from the centre of a circle to its circumference are not equal, he then, at all events, assuredly attaches a meaning to the word circle different from that assigned by mathematicians. So again, when men make mistakes in calculation, they have one set of figures in their mind, and another on the paper. If we could see into their minds, they do not make a mistake; they seem to do so, because we think, that they have the same numbers in their mind as they have on the paper. If this were not so, we should not believe them to be in error, any more than I thought that a man was in error, whom I lately heard exclaiming that his entrance hall had flown into a neighbour's hen, for his meaning seemed to me sufficiently clear. Very many controversies have arisen from the fact, that men do not rightly explain their meaning, or do not rightly interpret the meaning of others. For, as a matter of fact, as they flatly contradict themselves, they assume now one side, now another, of the argument, so as to oppose the opinions, which they consider mistaken and absurd in their opponents.

Note. From this we see that God’s infinite essence and eternity are known to everyone. Now, all things are in God and are understood through God. So from this knowledge we can infer many things that we may know adequately. We may also develop the third kind of knowledge discussed in the note to II. xl. We will have occasion to discuss the excellence and use of this knowledge in Part V. People do not know God as clearly as they know general notions. This is because they cannot picture God as they picture bodies. It is also because they associate the name God with images of things they habitually see. Indeed, they can hardly avoid these associations, since they are human and constantly affected by external bodies. Many errors can, in fact, be traced to our failure to apply names to things correctly. Suppose someone says that the lines drawn from a circle’s center to its circumference are not equal. That person certainly means something different by the word circle than mathematicians do. Similarly, when people make mistakes in calculation, they have one set of numbers in mind and another on paper. If we could see into their minds, we would see that they are not making a mistake. They seem mistaken because we assume that the numbers in their minds match those on paper. Without that assumption, we would not believe they were mistaken. Recently, I heard someone exclaim that his entrance hall had flown into a neighbor’s hen. I did not think he was mistaken either, because his meaning seemed clear enough to me. Very many disputes arise because people do not explain their meaning correctly or do not correctly interpret what others mean. In fact, while flatly contradicting themselves, they take first one side of an argument, then the other. They do so to oppose their opponents’ opinions, which they consider mistaken and absurd.

PROP. XLVIII. In the mind there is no absolute or free will; but the mind is determined to wish this or that by a cause, which has also been determined by another cause, and this last by another cause, and so on to infinity.

PROP. XLVIII. The mind has no absolute or free will. Instead, a cause determines the mind to want one thing or another. That cause is itself determined by another cause, and that cause by yet another, and so on without end.

Proof.—The mind is a fixed and definite mode of thought (II. xi.), therefore it cannot be the free cause of its actions (I. xvii. Coroll. ii.); in other words, it cannot have an absolute faculty of positive or negative volition; but (by I. xxviii.) it must be determined by a cause, which has also been determined by another cause, and this last by another, &c. Q.E.D.

Proof. The mind is a fixed and definite mode of thought (II. xi.). Therefore, the mind cannot be the free cause of its actions (I. xvii. Coroll. ii.). In other words, the mind cannot have an absolute ability to will or refuse. Instead, the mind must be determined by a cause (I. xxviii.). That cause has also been determined by another cause, and that cause by yet another, and so on. Q.E.D.

Note.—In the same way it is proved, that there is in the mind no absolute faculty of understanding, desiring, loving, &c. Whence it follows, that these and similar faculties are either entirely fictitious, or are merely abstract and general terms, such as we are accustomed to put together from particular things. Thus the intellect and the will stand in the same relation to this or that idea, or this or that volition, as "lapidity" to this or that stone, or as "man" to Peter and Paul. The cause which leads men to consider themselves free has been set forth in the Appendix to Part I. But, before I proceed further, I would here remark that, by the will to affirm and decide, I mean the faculty, not the desire. I mean, I repeat, the faculty, whereby the mind affirms or denies what is true or false, not the desire, wherewith the mind wishes for or turns away from any given thing. After we have proved, that these faculties of ours are general notions, which cannot be distinguished from the particular instances on which they are based, we must inquire whether volitions themselves are anything besides the ideas of things. We must inquire, I say, whether there is in the mind any affirmation or negation beyond that, which the idea, in so far as it is an idea, involves. On which subject see the following proposition, and II. Def. iii., lest the idea of pictures should suggest itself. For by ideas I do not mean images such as are formed at the back of the eye, or in the midst of the brain, but the conceptions of thought.

Note. The same reasoning proves that the mind has no absolute faculty of understanding, desiring, loving, and so on. So these and similar faculties are either entirely imaginary or merely abstract, general terms drawn from particular things. Thus intellect relates to a particular idea, and will to a particular act of willing, in the same way that "lapidity" relates to a particular stone, or "man" to Peter and Paul. The reason people consider themselves free has been explained in the Appendix to Part I. But before going further, I want to clarify what I mean by the will to affirm and decide. I mean a faculty, not a desire. Again, I mean the faculty by which the mind affirms or denies what is true or false. I do not mean the desire by which the mind seeks or turns away from any particular thing. Once we have proved that our faculties are general concepts, we must examine individual acts of willing. These general concepts cannot be distinguished from the particular instances on which they are based. We must ask whether acts of willing themselves are anything beyond ideas of things. In other words, does the mind contain any affirmation or denial beyond what an idea, simply as an idea, involves? On this question, see the following proposition and Part II, Definition iii, to avoid confusing ideas with pictures. By ideas I do not mean images formed at the back of the eye or within the brain. I mean concepts formed in thought.

PROP. XLIX. There is in the mind no volition or affirmation and negation, save that which an idea, inasmuch as it is an idea, involves.

PROP. XLIX. The mind has no act of will, affirmation, or denial beyond what an idea involves simply as an idea.

Proof.—There is in the mind no absolute faculty of positive or negative volition, but only particular volitions, namely, this or that affirmation, and this or that negation. Now let us conceive a particular volition, namely, the mode of thinking whereby the mind affirms, that the three interior angles of a triangle are equal to two right angles. This affirmation involves the conception or idea of a triangle, that is, without the idea of a triangle it cannot be conceived. It is the same thing to say, that the concept A must involve the concept B, as it is to say, that A cannot be conceived without B. Further, this affirmation cannot be made (II. Ax. iii.) without the idea of a triangle. Therefore, this affirmation can neither be nor be conceived, without the idea of a triangle. Again, this idea of a triangle must involve this same affirmation, namely, that its three interior angles are equal to two right angles. Wherefore, and vice versâ, this idea of a triangle can neither be nor be conceived without this affirmation, therefore, this affirmation belongs to the essence of the idea of a triangle, and is nothing besides. What we have said of this volition (inasmuch as we have selected it at random) may be said of any other volition, namely, that it is nothing but an idea. Q.E.D.

Proof. The mind has no absolute faculty for willing either affirmation or denial. It has only particular acts of willing, namely, this or that affirmation, and this or that denial. Now consider a particular act of willing. Take the form of thought in which the mind affirms that a triangle’s three interior angles equal two right angles. This affirmation involves the concept or idea of a triangle. In other words, the affirmation cannot be conceived without the idea of a triangle. Saying that concept A must involve concept B means the same as saying that A cannot be conceived without B. Furthermore, this affirmation cannot be made (II. Ax. iii.) without the idea of a triangle. Therefore, this affirmation can neither exist nor be conceived without the idea of a triangle. In turn, the idea of a triangle must involve this same affirmation: its three interior angles equal two right angles. Conversely, then, the idea of a triangle can neither exist nor be conceived without this affirmation. Therefore, this affirmation belongs to the essence of the idea of a triangle and is nothing beyond that idea. We selected this particular act of willing at random. So what we have said about it applies to any other act of willing: it is nothing but an idea. Q.E.D.

Corollary.—Will and understanding are one and the same.

Corollary: Will and understanding are the same thing.

Proof.—Will and understanding are nothing beyond the individual volitions and ideas (II. xlviii. and note). But a particular volition and a particular idea are one and the same (by the foregoing Prop.); therefore, will and understanding are one and the same. Q.E.D.

Proof: Will and understanding are nothing more than individual acts of will and ideas (II. xlviii. and note). But a particular act of will and a particular idea are one and the same (by the previous proposition). Therefore, will and understanding are one and the same. Q.E.D.

Note.—We have thus removed the cause which is commonly assigned for error. For we have shown above, that falsity consists solely in the privation of knowledge involved in ideas which are fragmentary and confused. Wherefore, a false idea, inasmuch as it is false, does not involve certainty. When we say, then, that a man acquiesces in what is false, and that he has no doubts on the subject, we do not say that he is certain, but only that he does not doubt, or that he acquiesces in what is false, inasmuch as there are no reasons, which should cause his imagination to waver (see II. xliv. note). Thus, although the man be assumed to acquiesce in what is false, we shall never say that he is certain. For by certainty we mean something positive (II. xliii. and note), not merely the absence of doubt.

Note. We have thus ruled out the commonly proposed cause of error. For we have shown above that falsity consists only in the lack of knowledge involved in fragmentary and confused ideas. So a false idea, insofar as it is false, does not involve certainty. When we say that someone accepts something false and has no doubts about it, we do not mean he is certain. We mean only that he does not doubt, or that he accepts something false because nothing makes his imagination waver (see II. xliv. note). Thus, although we assume that someone accepts something false, we will never say that he is certain. For by certainty we mean something positive (II. xliii. and note), not merely the absence of doubt.

However, in order that the foregoing proposition may be fully explained, I will draw attention to a few additional points, and I will furthermore answer the objections which may be advanced against our doctrine. Lastly, in order to remove every scruple, I have thought it worth while to point out some of the advantages, which follow therefrom. I say "some," for they will be better appreciated from what we shall set forth in the fifth part.

However, to explain the previous proposition fully, I will draw attention to a few additional points. I will also answer objections that may be raised against our doctrine. Finally, to remove every doubt, I have thought it worthwhile to point out some advantages that follow from our doctrine. I say "some," because these advantages will be better appreciated in light of what we explain in the fifth part.

I begin, then, with the first point, and warn my readers to make an accurate distinction between an idea, or conception of the mind, and the images of things which we imagine. It is further necessary that they should distinguish between idea and words, whereby we signify things. These three—namely, images, words, and ideas—are by many persons either entirely confused together, or not distinguished with sufficient accuracy or care, and hence people are generally in ignorance, how absolutely necessary is a knowledge of this doctrine of the will, both for philosophic purposes and for the wise ordering of life. Those who think that ideas consist in images which are formed in us by contact with external bodies, persuade themselves that the ideas of those things, whereof we can form no mental picture, are not ideas, but only figments, which we invent by the free decree of our will; they thus regard ideas as though they were inanimate pictures on a panel, and, filled with this misconception, do not see that an idea, inasmuch as it is an idea, involves an affirmation or negation. Again, those who confuse words with ideas, or with the affirmation which an idea involves, think that they can wish something contrary to what they feel, affirm, or deny. This misconception will easily be laid aside by one, who reflects on the nature of knowledge, and seeing that it in no wise involves the conception of extension, will therefore clearly understand, that an idea (being a mode of thinking) does not consist in the image of anything, nor in words. The essence of words and images is put together by bodily motions, which in no wise involve the conception of thought.

I begin, then, with the first point. I urge readers to distinguish carefully between an idea, or conception of the mind, and the images of things we imagine. They must also distinguish ideas from the words we use to represent things. Many people either completely confuse images, words, and ideas, or fail to distinguish them carefully and precisely enough. As a result, people generally do not understand how essential knowledge of this doctrine of the will is. Such knowledge is necessary both for philosophy and for guiding life wisely. Some people think ideas consist of images formed in us through contact with external bodies. They convince themselves that things we cannot picture in our minds cannot be objects of ideas. Instead, they regard such ideas as mere inventions that we freely choose to create through our will. They therefore treat ideas as though they were lifeless pictures on a panel. Because of this misunderstanding, they fail to see that an idea, simply by being an idea, involves affirmation or denial. Others confuse words with ideas, or with the affirmation an idea involves. They think they can wish for something contrary to what they feel, affirm, or deny. Anyone who reflects on the nature of knowledge will easily abandon this misunderstanding. They will see that knowledge in no way involves the concept of extension. They will therefore clearly understand that an idea, as a mode of thought, consists neither of an image nor of words. Words and images are constituted by bodily movements, and these movements in no way involve the concept of thought.

These few words on this subject will suffice: I will therefore pass on to consider the objections, which may be raised against our doctrine. Of these, the first is advanced by those, who think that the will has a wider scope than the understanding, and that therefore it is different therefrom. The reason for their holding the belief, that the will has wider scope than the understanding, is that they assert, that they have no need of an increase in their faculty of assent, that is of affirmation or negation, in order to assent to an infinity of things which we do not perceive, but that they have need of an increase in their faculty of understanding. The will is thus distinguished from the intellect, the latter being finite and the former infinite. Secondly, it may be objected that experience seems to teach us especially clearly, that we are able to suspend our judgment before assenting to things which we perceive; this is confirmed by the fact that no one is said to be deceived, in so far as he perceives anything, but only in so far as he assents or dissents.

These few words on the subject will be enough. I will therefore turn to the objections that may be raised against our doctrine. The first comes from those who think the will has a wider scope than the understanding. They therefore think the will is different from the understanding. Their reason is that, they say, their capacity to assent needs no increase to cover infinitely many things we do not perceive. By assent, they mean affirmation or denial. But they say their capacity to understand would need to increase to grasp those things. They thus distinguish the will from the intellect, treating the intellect as finite and the will as infinite. Second, someone may object that experience seems to teach us especially clearly that we can suspend our judgment. We can do so before assenting to things we perceive. This seems confirmed by the fact that no one is said to be mistaken simply by perceiving something. A person is said to be mistaken only by agreeing or disagreeing.

For instance, he who feigns a winged horse, does not therefore admit that a winged horse exists; that is, he is not deceived, unless he admits in addition that a winged horse does exist. Nothing therefore seems to be taught more clearly by experience, than that the will or faculty of assent is free and different from the faculty of understanding. Thirdly, it may be objected that one affirmation does not apparently contain more reality than another; in other words, that we do not seem to need for affirming, that what is true is true, any greater power than for affirming, that what is false is true. We have, however, seen that one idea has more reality or perfection than another, for as objects are some more excellent than others, so also are the ideas of them some more excellent than others; this also seems to point to a difference between the understanding and the will. Fourthly, it may be objected, if man does not act from free will, what will happen if the incentives to action are equally balanced, as in the case of Buridan's ass? Will he perish of hunger and thirst? If I say that he would, I shall seem to have in my thoughts an ass or the statue of a man rather than an actual man. If I say that he would not, he would then determine his own action, and would consequently possess the faculty of going and doing whatever he liked. Other objections might also be raised, but, as I am not bound to put in evidence everything that anyone may dream, I will only set myself to the task of refuting those I have mentioned, and that as briefly as possible.

For example, someone who imagines a winged horse does not thereby accept that a winged horse exists. In other words, he is not mistaken unless he also accepts that a winged horse actually exists. Experience therefore seems to teach nothing more clearly than this: the will, or ability to assent, is free and distinct from the understanding. Third, someone may object that one affirmation apparently contains no more reality than another. In other words, affirming that something true is true seems to require no greater power than affirming that something false is true. Yet we have seen that one idea has more reality or perfection than another. Just as some objects are more excellent than others, so some ideas of those objects are more excellent than others. This difference between ideas also seems to suggest a difference between the understanding and the will. Fourth, someone may object: if people do not act from free will, what happens when their motives are equally balanced? Consider the case of Buridan's ass. Will a person in that situation die of hunger and thirst? If I say yes, I will seem to be thinking of an ass or a human statue, not an actual person. If I say no, the person would then determine his own action. He would therefore have the ability to go and do whatever he liked. Other objections might also be raised. But I am not obliged to present every objection anyone might dream up. I will therefore limit myself to refuting the objections I have mentioned, as briefly as possible.

To the first objection I answer, that I admit that the will has a wider scope than the understanding, if by the understanding be meant only clear and distinct ideas; but I deny that the will has a wider scope than the perceptions, and the faculty of forming conceptions; nor do I see why the faculty of volition should be called infinite, any more than the faculty of feeling: for, as we are able by the same faculty of volition to affirm an infinite number of things (one after the other, for we cannot affirm an infinite number simultaneously), so also can we, by the same faculty of feeling, feel or perceive (in succession) an infinite number of bodies. If it be said that there is an infinite number of things which we cannot perceive, I answer, that we cannot attain to such things by any thinking, nor, consequently, by any faculty of volition. But, it may still be urged, if God wished to bring it about that we should perceive them, he would be obliged to endow us with a greater faculty of perception, but not a greater faculty of volition than we have already. This is the same as to say that, if God wished to bring it about that we should understand an infinite number of other entities, it would be necessary for him to give us a greater understanding, but not a more universal idea of entity than that which we have already, in order to grasp such infinite entities. We have shown that will is a universal entity or idea, whereby we explain all particular volitions—in other words, that which is common to all such volitions.

To the first objection, I answer that I agree the will has a wider scope than the understanding. But I agree only if “understanding” means clear and distinct ideas alone. I deny that the will has a wider scope than our perceptions and our ability to form concepts. Nor do I see why our ability to will should be called infinite any more than our ability to feel. For with the same ability to will, we can affirm an infinite number of things, one after another. We cannot affirm an infinite number at once. Likewise, with the same ability to feel, we can feel or perceive an infinite number of bodies in succession. Someone may say that there are infinitely many things we cannot perceive. I answer that no thinking can reach such things, and consequently neither can any ability to will. But someone may still object: if God wanted us to perceive those things, he would have to increase our ability to perceive. Yet he would not have to increase our ability to will. Making this objection is the same as making the following claim. If God wanted us to understand infinitely many other entities, he would have to give us greater understanding. But to grasp those infinitely many entities, we would not need a more universal idea of entity than we already have. We have shown that will is a universal entity or idea through which we explain all particular acts of willing. In other words, will is what all such acts have in common.

As, then, our opponents maintain that this idea, common or universal to all volitions, is a faculty, it is little to be wondered at that they assert, that such a faculty extends itself into the infinite, beyond the limits of the understanding: for what is universal is predicated alike of one, of many, and of an infinite number of individuals.

Our opponents, then, maintain that the idea common to all acts of will is a faculty. So it is hardly surprising that they claim this faculty extends infinitely beyond the limits of understanding. For a universal idea applies equally to one individual, to many individuals, and to an infinite number of individuals.

To the second objection I reply by denying, that we have a free power of suspending our judgment: for, when we say that anyone suspends his judgment, we merely mean that he sees, that he does not perceive the matter in question adequately. Suspension of judgment is, therefore, strictly speaking, a perception, and not free will. In order to illustrate the point, let us suppose a boy imagining a horse, and perceive nothing else. Inasmuch as this imagination involves the existence of the horse (II. xvii. Coroll.), and the boy does not perceive anything which would exclude the existence of the horse, he will necessarily regard the horse as present: he will not be able to doubt of its existence, although he be not certain thereof. We have daily experience of such a state of things in dreams; and I do not suppose that there is anyone, who would maintain that, while he is dreaming, he has the free power of suspending his judgment concerning the things in his dream, and bringing it about that he should not dream those things, which he dreams that he sees; yet it happens, notwithstanding, that even in dreams we suspend our judgment, namely, when we dream that we are dreaming.

To the second objection, I reply by denying that we can freely choose to suspend judgment. When we say someone suspends judgment, we mean only that they recognize their understanding of the matter is inadequate. Strictly speaking, then, suspending judgment is a perception, not an act of free will. To illustrate this point, suppose a boy imagines a horse and perceives nothing else. This imagined image involves the horse’s existence (II. xvii. Coroll.). Since the boy perceives nothing that would rule out the horse’s existence, he will necessarily regard the horse as present. He will be unable to doubt its existence, although he is not certain of it. We experience this state of affairs daily in dreams. I do not suppose anyone would claim that, while dreaming, they can freely choose to suspend judgment about their dreams. Nor would anyone claim they can thereby stop dreaming the things they dream they see. Nevertheless, even in dreams we sometimes suspend judgment, namely, when we dream that we are dreaming.

Further, I grant that no one can be deceived, so far as actual perception extends—that is, I grant that the mind's imaginations, regarded in themselves, do not involve error (II. xvii. note); but I deny, that a man does not, in the act of perception, make any affirmation. For what is the perception of a winged horse, save affirming that a horse has wings? If the mind could perceive nothing else but the winged horse, it would regard the same as present to itself: it would have no reasons for doubting its existence, nor any faculty of dissent, unless the imagination of a winged horse be joined to an idea which precludes the existence of the said horse, or unless the mind perceives that the idea which it possess of a winged horse is inadequate, in which case it will either necessarily deny the existence of such a horse, or will necessarily be in doubt on the subject.

Further, I grant that no one can be mistaken as far as perception itself goes. That is, the mind's imaginings, considered in themselves, do not involve error (II. xvii. note). But I deny that a person makes no affirmation in the act of perception. For what is perceiving a winged horse but affirming that a horse has wings? If the mind could perceive nothing but the winged horse, the mind would regard the horse as present. The mind would have no reason to doubt the horse's existence and no ability to reject it, except under two conditions. Either the image of a winged horse is joined to an idea that rules out the horse's existence. Or the mind perceives that its idea of a winged horse is inadequate. In that case, the mind will necessarily either deny that such a horse exists or doubt whether such a horse exists.

I think that I have anticipated my answer to the third objection, namely, that the will is something universal which is predicated of all ideas, and that it only signifies that which is common to all ideas, namely, an affirmation, whose adequate essence must, therefore, in so far as it is thus conceived in the abstract, be in every idea, and be, in this respect alone, the same in all, not in so far as it is considered as constituting the idea's essence: for, in this respect, particular affirmations differ one from the other, as much as do ideas. For instance, the affirmation which involves the idea of a circle, differs from that which involves the idea of a triangle, as much as the idea of a circle differs from the idea of a triangle.

I think I have already anticipated my answer to the third objection. The will is a universal concept that applies to all ideas. It means only what all ideas have in common, namely, an affirmation. Therefore, the adequate essence of affirmation, when understood in this abstract way, must be present in every idea. Only in this respect is affirmation the same in all ideas. It is not the same when considered as forming the essence of each idea. For in that respect, particular affirmations differ from one another as much as ideas do. For example, the affirmation involving the idea of a circle differs from the affirmation involving the idea of a triangle. The difference is as great as the difference between the idea of a circle and the idea of a triangle.

Further, I absolutely deny, that we are in need of an equal power of thinking, to affirm that that which is true is true, and to affirm that that which is false is true. These two affirmations, if we regard the mind, are in the same relation to one another as being and not—being; for there is nothing positive in ideas, which constitutes the actual reality of falsehood (II. xxxv. note, and xlvii. note).

Further, I absolutely deny that affirming a truth requires the same power of thought as affirming a falsehood as true. If we consider the mind, these two affirmations relate to each other as being relates to nonbeing. For nothing positive in ideas gives falsehood any actual reality (II. xxxv. note, and xlvii. note).

We must therefore conclude, that we are easily deceived, when we confuse universals with singulars, and the entities of reason and abstractions with realities. As for the fourth objection, I am quite ready to admit, that a man placed in the equilibrium described (namely, as perceiving nothing but hunger and thirst, a certain food and a certain drink, each equally distant from him) would die of hunger and thirst. If I am asked, whether such an one should not rather be considered an ass than a man; I answer, that I do not know, neither do I know how a man should be considered, who hangs himself, or how we should consider children, fools, madmen, &c.

We must therefore conclude that we are easily deceived when we confuse universals with particular things. We are also easily deceived when we confuse mental constructs and abstractions with realities. As for the fourth objection, I readily admit that a man in the balanced state described would die of hunger and thirst. Such a man perceives only hunger and thirst, some food, and some drink, each equally distant from him. If asked whether such a person should be considered a donkey rather than a man, I answer that I do not know. Nor do I know how to regard a man who hangs himself, or children, fools, madmen, and so on.

It remains to point out the advantages of a knowledge of this doctrine as bearing on conduct, and this may be easily gathered from what has been said. The doctrine is good,

What remains is to show how knowing this doctrine can help guide our conduct. These advantages can easily be gathered from what has already been said. The doctrine is good,

1. Inasmuch as it teaches us to act solely according to the decree of God, and to be partakers in the Divine nature, and so much the more, as we perform more perfect actions and more and more understand God. Such a doctrine not only completely tranquilizes our spirit, but also shows us where our highest happiness or blessedness is, namely, solely in the knowledge of God, whereby we are led to act only as love and piety shall bid us. We may thus clearly understand, how far astray from a true estimate of virtue are those who expect to be decorated by God with high rewards for their virtue, and their best actions, as for having endured the direst slavery; as if virtue and the service of God were not in itself happiness and perfect freedom.

1. This doctrine teaches us to act only according to God’s decree and to share in the Divine nature. We share more in that nature as our actions become more perfect and our understanding of God grows. This doctrine not only brings complete peace to our spirit, but also shows us where our greatest happiness or blessedness lies. That happiness lies solely in knowing God, and this knowledge leads us to act only as love and piety direct. We can therefore clearly see how badly some people misunderstand virtue. They expect God to grant them great rewards for their virtue and their best actions. They expect these rewards as though they had endured the harshest slavery. They act as if virtue and serving God were not themselves happiness and perfect freedom.

2. Inasmuch as it teaches us, how we ought to conduct ourselves with respect to the gifts of fortune, or matters which are not in our power, and do not follow from our nature. For it shows us, that we should await and endure fortune's smiles or frowns with an equal mind, seeing that all things follow from the eternal decree of God by the same necessity, as it follows from the essence of a triangle, that the three angles are equal to two right angles.

2. It teaches us how to deal with fortune's gifts, or things beyond our control that do not follow from our nature. It shows us that we should await and endure good or bad fortune with an even mind. For all things follow from God's eternal decree with the same necessity as a triangle's properties follow from its essence. Just as necessarily, a triangle's three angles add up to two right angles.

3. This doctrine raises social life, inasmuch as it teaches us to hate no man, neither to despise, to deride, to envy, or to be angry with any. Further, as it tells us that each should be content with his own, and helpful to his neighbour, not from any womanish pity, favour, or superstition, but solely by the guidance of reason, according as the time and occasion demand, as I will show in Part III.

3. This doctrine improves social life by teaching us not to hate, despise, ridicule, envy, or be angry with anyone. It also teaches that everyone should be content with what they have and help their neighbors. Such help should come not from feminine pity, favoritism, or superstition, but solely from reason’s guidance, as circumstances require. I will explain this in Part III.

4. Lastly, this doctrine confers no small advantage on the commonwealth; for it teaches how citizens should be governed and led, not so as to become slaves, but so that they may freely do whatsoever things are best.

4. Finally, this doctrine offers a considerable benefit to the state, because it teaches how citizens should be governed and guided. The aim is not to make citizens slaves, but to allow them to freely do whatever is best.

I have thus fulfilled the promise made at the beginning of this note, and I thus bring the second part of my treatise to a close. I think I have therein explained the nature and properties of the human mind at sufficient length, and, considering the difficulty of the subject, with sufficient clearness. I have laid a foundation, whereon may be raised many excellent conclusions of the highest utility and most necessary to be known, as will, in what follows, be partly made plain.

I have now fulfilled the promise I made at the beginning of this note. With that, I bring the second part of my treatise to a close. I believe I have explained the nature and properties of the human mind in enough detail. Given the difficulty of the subject, I also believe my explanation is clear enough. I have laid a foundation from which many valuable conclusions may be drawn. These conclusions are extremely useful and essential to know, as the following pages will partly show.