PROP. I. Thought is an attribute of God, or God is a thinking thing.
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.
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.
PROP. II. Extension is an attribute of God, or God is an extended thing.
Proof. — The proof of this proposition is similar to that of the last.
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.
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.)
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.
PROP. IV. The idea of God, from which an infinite number of things follow in infinite ways, can only be one.
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.
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.
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.
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.
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.
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.
PROP. VII. The order and connection of ideas is the same as the order and connection of 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.
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).
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.
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.
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.
Proof. — This proposition is evident from the last; it is understood more clearly from the preceding note.
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.
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.
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.
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.
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.
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.
PROP. X. The being of substance does not appertain to the essence of man—in other words, substance does not constitute the actual being of man.
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.
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.
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.
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).
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.
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.)
PROP. XI. The first element, which constitutes the actual being of the human mind, is the idea of some particular thing actually existing.
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.
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.
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.
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.
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.
Note. — This proposition is also evident, and is more clearly to be understood from II. vii., which see.
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.
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.
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. 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.
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.
AXIOM I. All bodies are either in motion or at rest.
AXIOM II. Every body is moved sometimes more slowly, sometimes more quickly.
LEMMA I. Bodies are distinguished from one another in respect of motion and rest, quickness and slowness, and not in respect of 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.
LEMMA II. All bodies agree in certain respects.
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.
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.
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.
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.
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 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.
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.
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.
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.
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).
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.
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.
Proof. — The same as for the last 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.
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.
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.
Proof. — This proposition is evident from the definition of an individual prefixed to 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.