|E2: PROP. 1. Thought is an attribute of God, or God is a thinking thing.|
|Proof.--Particular thoughts, or this or that thought, are modes which, in a certain conditioned manner, express the nature of God (E1P25C). God therefore possesses the attribute (E1D5) 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 (E1D6). In other words, God is a thinking thing. Q.E.D.|
|Referenced in: E2P2,- E2P3,- E2P20|
|E2: PROP. 1, 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 (E1D4 and E1D6) one of the infinite attributes of God, as we were desirous of showing.|
|E2: PROP. 2. 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 (E2P1).|
|E2: PROP. 3. 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 E2P1) can think an infinite number of things in infinite ways, or (what is the same thing, by E1P16) 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. (E1P35) Therefore, such an idea as we are considering necessarily is, and in God alone. Q.E.D. (E1P15)|
|Referenced in: E2P5,- E2P9C,- E2P20,- E2P24,- E5P22,- E5P35|
| E2: PROP. 3, 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 (E1P32C1 and E1P32C2), and we have shown (E1P16) 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 (E1P34), 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 1. from E1P16 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.
|E2: PROP. 4. 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 (E1P30). Now God is one (E1P14C1). Therefore the idea of God, wherefrom an infinite number of things follow in infinite ways, can only be one. Q.E.D.|
|E2: PROP. 5. 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 E2P3 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
It may be differently proved as follows: the actual being of ideas is (obviously) a mode of thought, that is (E1P25C) a mode which expresses in a certain manner the nature of God, in so far as he is a thinking thing, and therefore (E1P10) involves the conception of no other attribute of God, and consequently (by E1A4) 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, etc. Q.E.D.
|Referenced in: Let68b-P01|
|E2: PROP. 6. 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 (E1P10); wherefore the modes of each attribute involve the conception of that attribute, but not of any other. Thus (E1A4) 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.|
|Referenced in: E2P9,- E2P13L3,- E2P36,- E2P45,- E3P2,- E3P11N,- E4P7,- E4P29,- Let66-P02|
|E2: PROP. 6, 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.|
|Referenced in: E2P36,- E5P1|
|E2: PROP. 7. The order and connection of ideas is the same as the order and connection of things.|
|Proof.--This proposition is evident from E1A4. For the idea of everything that is caused depends on a knowledge of the cause, whereof it is an effect.|
|Referenced in: E2P8,- E2P9,- E2P9C,- E2P12N,- E2P15,- E2P19,- E2P20,- E2P24,- E2P25,- E2P26,- E3P11,- E3P12,- E5P1|
|E2: PROP. 7, 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).|
|Referenced in: E2P32,- E2P36,- E2P38,- E2P39,- E3P28,- E5P1|
| E2: PROP. 7 Corollary, 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
as constituting the essence of
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
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 [Or, perhaps more clearly; "can only be perceived through another mode of thinking as a proximate cause" --TNeff], 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 attribute of extension only; and so on, in the case of 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.
|Referenced in: E2P8,- E2P12N,- E2P21N,- E3P2N,- Let66-P02,- Let68-P01|
|E2: PROP. 8. 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 E2P7; it is understood more clearly from the preceding note E2P7CN.|
|Referenced in: E3P11N|
|E2: PROP. 8, 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.|
|Referenced in: E2P9,- E2P11,- E2P15,- E2P45,- E3P11N,- E5P21,- E5P23|
|E2: PROP. 8 Corollary, 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.|
|Referenced in: E2P9,- E3P11N|
|E2: PROP. 9. 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 E2P8C and E2P8CN of this part); thus (by E2P6 of this part) it is caused by God, in so far only as he is a thinking thing. But not (by E1P28 of Part 1.) 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 E2P7 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.|
|Referenced in: E2P9C,- E2P19,- E2P20,- E2P24,- E2P25,- E3P1|
|E2: PROP. 9, 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 E2P3 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. E2P9); but (by E2P7 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.|
|Referenced in: E2P12,- E2P13,- E2P30,- E3P10|
|E2: PROP. 10. The being of substance does not appertain to the essence of man--in other words, substance does not constitute the actual being ["Forma"] of man.|
|Proof.--The being of substance involves necessary existence (E1P7). If, therefore, the being of substance appertains to the essence of man, substance being granted, man would necessarily be granted also (E2D2), and, consequently, man would necessarily exist, which is absurd (E2A1). Therefore, etc. Q.E.D.|
|Referenced in: E2P10C|
|E2: PROP. 10, Note. --This proposition may also be proved from E1P5, 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, etc., as anyone may see for himself.|
|E2: PROP. 10, Corollary.--Hence it follows, that the essence of man is constituted by certain modifications of the attributes of God.|
|For (by the last Prop.E2P10) the being of substance does not belong to the essence of man. That essence therefore (by E1P15) is something which is in God, and which without God can neither be nor be conceived, whether it be a modification (E1P25C), or a mode which expresses God's nature in a certain conditioned manner.|
|Referenced in: E2P11, - E4P29|
| E2: PROP. 10 Corollary, 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
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 here 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." (E2D2)
|E2: PROP. 11. 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. E2P10C) is constituted by certain modes of the attributes of God, namely (by E2A2), by the modes of thinking, of all which (by E2A3) 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 (E2P8C) 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 (E1P21, E1P22), must always necessarily exist; this would (by E2A1) 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.|
|Referenced in: E2P12,- E2P13,- E2P20,- E2P48,- E3P2,- E3P3,- E3P10,- E3DOE,- E4P37,- E5P9,- E5P38|
|E2: PROP. 11, 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.|
|Referenced in: E2P12,- E2P13,- E2P19,- E2P22,- E2P23,- E2P24,- E2P30,- E2P34,- E2P38,- E2P39,- E2P40,- E2P43,- E2P43N,- E3P1,- E3P28, - E5P36|
|E2: PROP. 11 Corollary, 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.|
|E2: PROP. 12. 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 (E2P9C), in so far as he is considered as affected by the idea of the said object, that is (E2P11), 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 nature of the human mind; that is (by E2P11C) the knowledge of the said thing will necessarily be in the mind, in other words the mind perceives it.|
|Referenced in: E2P13,- E2P14,- E2P17,- E2P17C,- E2P19,- E2P21,- E2P22,- E2P38,- E3P2N,- E4P7,- E5P4|
|E2: PROP. 12, Note. --This proposition is also evident, and is more clearly to be understood from E2P7 [E2P7CN], which see.|