EDITORIAL PREFACE

IN JULY 1675 Oldenburg wrote nervously to Spinoza to inquire about the prospect of publication of the Ethics:

From your reply of 5 July I understand that you intend to publish that five-part Treatise of yours. Permit me, I beg you, to advise you, out of your sincere regard for me, not to include in it anything which may seem in any way whatever, to overthrow the practice of religious virtue.… I shall not decline to receive copies of this Treatise; I would only ask that when the time comes, they be sent by way of a certain Dutch merchant, resident in London, who will see that they are soon forwarded. There will be no need to mention that such books have been sent to me.… (Letter 62, IV/273)

Oldenburg need not have worried. Some time later Spinoza sent him the following reply:

When I received your letter of 22 July, I was on the point of leaving for Amsterdam, to see to the printing of the book I wrote you about. While I was occupied with this, a rumor was spread everywhere that a book of mine about God was in the press, and that in it I strove to show that there is no God. Many people believed this rumor. So certain theologians—who had, perhaps, started the rumor themselves—seized this opportunity to complain about me to the Prince and the magistrates. Moreover, the stupid Cartesians, who are thought to favor me, would not stop trying to remove this suspicion from themselves by denouncing my opinions and writings everywhere.

When I learned this from certain trustworthy men, who also told me that the theologians were everywhere plotting against me, I decided to put off the publication I was planning until I saw how the matter would turn out.… But every day it gets worse, and I am uncertain what to do. (Letter 68, IV/299)

Thus was the world deprived, within Spinoza’s lifetime, of one of the great classics of modern philosophical thought, a work, ironically, that begins by arguing at length for God’s existence, and ends with the conclusion that the knowledge and love of God are man’s greatest good.

When Spinoza died, a year and a half later, his work could be published, and the slow process of recognition could begin. But not until he had been taken up by leading figures of the German enlightenment—by Lessing, Goethe, and Herder, among others—did his work receive much sympathetic attention.1 Since then the Ethics has always had a wide audience, particularly—and in view of its technical difficulty and forbidding form, surprisingly—among people not themselves professional philosophers, but poets, dramatists, and novelists.2

Much of this interest no doubt stems from the psychology and morality of the latter parts of the Ethics, from its serene, but remorseless dissection of human nature, and its (apparent) attempt to establish an acceptable ethic on the unpromising foundation of subjectivism, egoism, and determinism.3 But in part the interest must come also from fascination with the difficult question whether we can really regard as religious a thinker who has rejected so forcefully so much of what has usually been regarded as essential to religion in the West.

This is not the place to try to solve the perennial problems of Spinoza’s philosophy. But some attempt must be made here to disarm the resistance which the axiomatic form of his masterwork seems, inevitably, to arouse. The topic is one on which quite divergent views have been expressed.4

Sometimes, for example, it is suggested that Spinoza’s philosophy required axiomatic exposition, that conceiving the world as he did, as a tightly knit deterministic system, he could not properly have expressed this conception in any other way; or that conceiving knowledge as he did, he would have regarded deduction from self-evident premises as the only suitably scientific way of presenting his philosophy. At the opposite extreme, it is sometimes held that the axiomatic exposition is merely a literary device designed to conceal the author’s personality, to capitalize on the prestige of geometry, or even to avoid the temptation to quote Scripture—but having no further significance.

The truth, I suggest, is that Spinoza’s choice of the axiomatic method represents nothing more, and nothing less, than an awesome commitment to intellectual honesty and clarity. Spinoza wishes to use no important term without explaining the sense in which it is to be understood, to make no crucial assumption without identifying it as a proposition taken to require no argument, to draw no conclusion without being very explicit about why that conclusion is thought to follow from his assumptions. This can be very tedious, as he well realizes (cf. E IVP18 S). But the serious reader who is prepared to use those terms as Spinoza does, and who shares Spinoza’s assumptions, is forced to ask himself why he should not also accept Spinoza’s conclusions. And it is only fair to point out that many of Spinoza’s contemporaries did share those assumptions and did use those terms in a way very close to the way Spinoza used them.5

Again, it is a mistake to suppose that, when Spinoza designates something as an axiom, he really thinks that no one could question it, and is not willing to listen to argument about it. The history of his experiments with axiomatic exposition shows clearly enough that he is prepared to be flexible, and that what at one stage is treated as an axiom, may at a later stage be treated as a theorem, if experience shows that his readers resist the assumption.6 He does, of course, think that some propositions are more suited to be axioms than others. But he is not extravagantly optimistic about the ability of his readers to see what they should see, and this gives him a strong incentive to reduce his assumptions to a minimum (cf. II/49/26 ff.). And any serious attempt at argument must make some assumptions which, for the time being, at least, are not questioned.

But while this line of defense may be sound enough, as far as it goes, it does not go far enough. The difficulty for the modern reader of Spinoza’s Ethics is not so much that he finds flaws in the demonstrations (though he may, of course), nor even that he rejects the axioms (though, again, he may), but that much of the language in which the axioms and demonstrations are framed has by now fallen into disuse, so that its very meaning is quite obscure to him. The clarity the axiomatization seemed to promise is not easy to find. A glossary-index may provide a partial solution to this difficulty. But unless it is very argumentative it cannot deal with the really fundamental problem.

It must be recognized that some of the terms which are central to Spinoza’s philosophy are not merely out of fashion in twentieth-century philosophy, but would be rejected by many philosophers of our time as meaningless. The term ‘substance’ is a good example. For many people these days it is axiomatic that the empiricist critique of this concept demonstrated its bankruptcy. (By “axiomatic” I understand here something we learned when we were first introduced to philosophy.)

And yet it is arguable that this rejection has been too hasty: that the traditional use of the concept of substance was too complex to have been disposed of so simply; that there are two distinguishable strains in that use—the concept of an unknowable subject of predicates, and the concept of an independent being; that the empiricist critique touches only the first of these strains; and that only the second is of much importance for the understanding of Spinoza.7 If this is correct and if other contentious concepts can be similarly rehabilitated, Spinoza’s philosophy may once again be ripe for reevaluation.

These reflections may do something to diminish the resistance many readers have to the form of the Ethics. But there remains the practical problem of how even the reader of good will is to cope with a procedure that makes great demands on his patience.

On a first reading it is probably advisable to concentrate on the propositions, corollaries, scholia, prefaces, and appendices, leaving the demonstrations till later. This will make it easier to grasp the structure of the work, and give the reader some feeling for what is central and what is subsidiary. ‘Corollaries’ are often more important than the proposition they follow, and the scholia often offer more intuitive arguments for the propositions just demonstrated, or reply to what Spinoza regards as natural and important objections. The longer scholia, prefaces, and appendices tend to punctuate major divisions within the work and to sum up key contentions.

On a second reading, of course, it is essential to study the demonstrations carefully. Seeing how a proposition is argued for is often a useful way of clarifying its sense. It is also helpful to check the steps of a demonstration against the citations. For when Spinoza cites an axiom, definition, or proposition in a subsequent demonstration, he sometimes paraphrases it in a way that illuminates what has gone before. And in any case, it is instructive to see what Spinoza takes the implications and significance of a proposition to be. But the best advice is Spinoza’s own—to proceed slowly and to abstain from judgment until everything has been read through (IIP11CS). This is not easy. Spinoza’s philosophy is not easy. But as he also says, all things excellent are as difficult as they are rare (VP42S).

I close with a few observations on the probable date of composition of the Ethics and the status of our text. As we have seen, Spinoza took steps to publish this work in 1675, though it did not appear until 1677 and may have undergone some revision even after 1675. On that ground we might regard the Ethics as a late work, or at any rate, later than the Theological-Political Treatise, published in 1670. On the other hand, we can see from the early correspondence with Oldenburg that Spinoza was circulating drafts of the material for Part I as early as 1661. So we might conclude that Spinoza was occupied with writing this work, off and on, for most of his adult life.

Nevertheless, it now seems possible to be more precise than that about the composition of our text. We know from Letter 28 that toward the middle of 1665 Spinoza was near the end of a first draft of the Ethics (i.e., near the end of the third part of what was probably, at that stage, conceived as a three-part work). Recent research on the relation between the OP and NS versions of the Ethics also suggests certain conclusions about the extent of the revision the first two parts may have undergone after 1665.

Gebhardt had noted (II/315-317, 340-345) that divergences between the OP text and NS translation were much more common in the first two parts of the Ethics than they were in the last three, and that frequently the NS seemed to have more text than the OP had. He inferred from this that the NS translation of E I-II was done from a manuscript that represented an earlier draft of the Ethics and that in revising Spinoza had deliberately omitted certain passages, sometimes to avoid giving unnecessary offense.8 He therefore incorporated many passages from the NS translation into his text. Occasionally9 he translated his additions into Latin. One might question whether the editor of a critical edition should interfere with the text in this way, but Gebhardt believed that the practice of modern editors of Kant’s first Critique provided a precedent for indicating (as he thought) the differences between earlier and later drafts.

I believe that Akkerman (2, 77-176) has definitively refuted this theory and shown the correctness of an alternative account of the variations: that the NS translation of E I-II is essentially the work of Balling,10 while the NS translation of E III-V is by Glazemaker; and that the tendency of the NS version of E I-II to show more text than the NS version of E III-V stems from Balling’s different style of translating, in particular his willingness to take greater liberties with the text than Glazemaker would take. Akkerman makes his case for this via a meticulous examination of the translating styles of the two men in other works they are known to have translated, noting differences in prose style, in the kinds of license they allow themselves, in the kinds of mistakes they are apt to make, and in the way they treat key terms. One hesitates to speak of demonstration in any matter such as this, but Akkerman’s argument is very impressive.

The principal implication of his research, as far as the establishment of the text is concerned, is that where the NS seems to have more text than the OP, this is almost invariably because the translator has amplified the text to make it clearer, or used a pair of Dutch terms to render one Latin term, in the hope of better capturing the implications of the Latin, and not because the text he was translating varied from the OP text.

But Akkerman’s research also, it seems to me, has implications for the study of the development of Spinoza’s thought. If Balling was the author of the translation of E I-II used by the editors of the NS, and if no significant changes were made in that text after Balling translated it, then Balling’s death would provide a date after which Spinoza did not significantly revise Parts I and II. We do not know precisely when Balling died. Clearly it was not before July 1664 (the date of Letter 17) and pretty certainly it was not later than 1669 (cf. AHW, 45), Akkerman (2, 152-153) thinks Balling must have died before June 1665, by which date Spinoza was writing to Bouwmeester about the possibility of his translating Part III. If this is correct, then the metaphysical and epistemological portions of the Ethics would have been in their final form some twelve years before they were published.

Gebhardt’s additions to the text from the NS create a problem for the translator. Shirley’s policy is to ignore them when they are in Dutch and to translate them when Gebhardt has translated them into Latin, but without indicating that what he is translating is an addition from the NS. But this seems to assume that Gebhardt has followed some defensible principle in deciding what to add in Dutch and what to add in Latin, an assumption I see no reason to make. In one way or another I have translated everything that Gebhardt adds from the NS (as well as some variations that Gebhardt does not seem to have noticed). Where it has seemed to me that an addition, even though it probably came originally from the NS translator, was pretty certainly correct and useful, I have generally followed Gebhardt in adding it to the text. I assume that a translator may take liberties that the editor of a critical edition may not. Where one of Gebhardt’s additions has seemed to me doubtfully correct, I have relegated it to a footnote. Wherever a bracketed addition comes from the NS, I have indicated that fact. There is some evidence that Spinoza may have had Balling’s translation of E I-II at his disposal, and indeed, that the copy of that translation used by the NS editors may have been Spinoza’s own (cf. Akkerman 2, 167-168). So additions made from the NS, even if they do originate from a translator, may have been seen and approved by Spinoza.

References to definitions, axioms, propositions, etc., that do not contain an explicit reference to an earlier part of the Ethics are to be understood as referring to the part in which they occur.

Ethics

DEMONSTRATED IN GEOMETRIC ORDER AND DIVIDED INTO FIVE PARTS, WHICH TREAT

I. Of God

II. Of the Nature and Origin of the Mind

III. Of the Origin and Nature of the Affects

IV. Of Human Bondage, or of the Powers of the Affects

V. Of the Power of the Intellect, or of Human Freedom1

[II/45] First Part Of the Ethics
On God

DEFINITIONS

[5] D1: By cause of itself I understand that whose essence involves existence, or that whose nature cannot be conceived except as existing.

D2: That thing is said to be finite in its own kind that can be limited by another of the same nature.

[10] For example, a body is called finite because we always conceive another that is greater. Thus a thought is limited by another thought. But a body is not limited by a thought nor a thought by a body.

D3: By substance I understand what is in itself and is conceived through [15] itself, i.e., that whose concept does not require the concept of another thing, from which it must be formed.

D4: By attribute I understand what the intellect perceives of a substance, as constituting its essence.2

[20] D5: By mode I understand the affections of a substance, or that which is in another through which it is also conceived.

D6: By God I understand a being absolutely infinite, i.e., a substance consisting of an infinity of attributes, of which each one expresses an3 [25] eternal and infinite essence.

[II/46] Exp.: I say absolutely infinite, not infinite in its own kind; for if something is only infinite in its own kind, we can deny infinite attributes of it [NS: (i.e., we can conceive infinite attributes which do not [5] pertain to its nature)];4 but if something is absolutely infinite, whatever expresses essence and involves no negation pertains to its essence.

D7: That thing is called free which exists from the necessity of its nature alone, and is determined to act by itself alone. But a thing is [10] called necessary, or rather compelled, which is determined by another to exist and to produce an effect in a certain and determinate manner.

D8: By eternity I understand existence itself, insofar as it is conceived [15] to follow necessarily from the definition alone of the eternal thing.

Exp.: For such existence, like the essence of a thing,5 is conceived as an eternal truth, and on that account cannot be explained6 by duration or time, even if the duration is conceived to be without beginning or end.

[20] AXIOMS

A1: Whatever is, is either in itself or in another.

A2: What cannot be conceived through another, must be conceived through itself.

A3: From a given determinate cause the effect follows necessarily; and [25] conversely, if there is no determinate cause, it is impossible for an effect to follow.

A4: The knowledge of an effect depends on, and involves, the knowledge of its cause.

A5: Things that have nothing in common with one another also cannot [30] be understood through one another, or the concept of the one does not involve the concept of the other.

[II/47] A6: A true idea must agree with its object.

A7: If a thing can be conceived as not existing, its essence does not involve existence.

[5] P1: A substance7 is prior in nature to its affections.

Dem.: This is evident from D3 and D5.

P2: Two substances having different attributes have nothing in common with [10] one another.8

Dem.: This also evident from D3. For each must be in itself and be conceived through itself, or the concept of the one does not involve the concept of the other.

[15] P3: If things have nothing in common with one another, one of them cannot be the cause of the other.

Dem.: If they have nothing in common with one another, then (by [20] A5) they cannot be understood through one another, and so (by A4) one cannot be the cause of the other, q.e.d.

P4: Two or more distinct things are distinguished from one another, either by a difference in the attributes of the substances or by a difference in their affections.

[25] Dem.: Whatever is, is either in itself or in another (by A1), i.e. (by D3 and D5), outside the intellect there is nothing except substances and their affections. Therefore, there is nothing outside the intellect [30] through which a number of things can be distinguished from one another [II/48] except substances, or what is the same (by D4), their attributes, and their affections,9 q.e.d.

P5: In nature there cannot be two or more substances of the same nature or [5] attribute.

Dem.: If there were two or more distinct substances, they would have to be distinguished from one another either by a difference in their attributes, or by a difference in their affections (by P4). If only by a difference in their attributes, then it will be conceded that there [10] is only one of the same attribute. But if by a difference in their affections, then since a substance is prior in nature to its affections (by P1), if the affections are put to one side and [the substance] is considered in itself, i.e. (by D3 and A6), considered truly, one cannot be conceived to be distinguished from another, i.e. (by P4), there cannot be [15] many, but only one [of the same nature or attribute],10 q.e.d.

P6: One substance cannot be produced by another substance.

Dem.: In nature there cannot be two substances of the same attribute [20] (by P5), i.e. (by P2), which have something in common with each other. Therefore (by P3) one cannot be the cause of the other, or cannot be produced by the other, q.e.d.

Cor.: From this it follows that a substance cannot be produced by [25] anything else. For in nature there is nothing except substances and their affections, as is evident from A1, D3, and D5. But it cannot be produced by a substance (by P6). Therefore, substance absolutely cannot be produced by anything else, q.e.d.

[30] Alternatively: This11 is demonstrated even more easily from the absurdity of its contradictory. For if a substance could be produced by something else, the knowledge of it would have to depend on the knowledge of its cause (by A4). And so (by D3) it would not be a substance.

[I/49] P7: It pertains to the nature of a substance to exist.

Dem.: A substance cannot be produced by anything else (by P6C); [5] therefore it will be the cause of itself, i.e. (by D1), its essence necessarily involves existence, or it pertains to its nature to exist, q.e.d.

P8: Every substance is necessarily infinite.

[10] Dem.: A substance of one attribute12 does not exist unless it is unique (P5), and it pertains to its nature to exist (P7). Of its nature, therefore, it will exist either as finite or as infinite. But not as finite. For then (by D2) it would have to be limited by something else of the same [15] nature, which would also have to exist necessarily (by P7), and so there would be two substances of the same attribute, which is absurd (by P5). Therefore, it exists as infinite, q.e.d.

Schol. 1: Since being finite is really, in part, a negation, and being [20] infinite is an absolute affirmation of the existence of some nature, it follows from P7 alone that every substance must be infinite. [NS: For if we assumed a finite substance, we would, in part, deny existence to its nature, which (by P7) is absurd.]13

[25] Schol. 2:14 I do not doubt that the demonstration of P7 will be difficult to conceive for all who judge things confusedly, and have not been accustomed to know things through their first causes—because they do not distinguish between the modifications15 of substances and the substances themselves, nor do they know how things are produced. [30] So it happens that they fictitiously ascribe to substances the beginning which they see that natural things have; for those who do not know the true causes of things confuse everything and without any conflict of mind feign that both trees and men speak, imagine that men are formed both from stones and from seed, and that any form [35] whatever is changed into any other.16 So also, those who confuse the divine nature with the human easily ascribe human affects to God, particularly so long as they are also ignorant of how those affects are [II/50] produced in the mind.

But if men would attend to the nature of substance, they would have no doubt at all of the truth of P7. Indeed, this proposition would be an axiom for everyone, and would be numbered among the common notions. For by substance they would understand what is in itself [5] and is conceived through itself, i.e., that the knowledge of which does not require the knowledge of any other thing.17 But by modifications they would understand what is in another, those things whose concept is formed from the concept of the thing in which they are.

This is how we can have true ideas of modifications which do not exist; for though they do not actually exist outside the intellect, nevertheless [10] their essences are comprehended in another in such a way that they can be conceived through it. But the truth of substances is not outside the intellect unless it is in them themselves,18 because they are conceived through themselves.

Hence, if someone were to say that he had a clear and distinct, i.e., true, idea of a substance, and nevertheless doubted whether such a substance existed, that would indeed be the same as if he were to say [15] that he had a true idea, and nevertheless doubted whether it was false (as is evident to anyone who is sufficiently attentive). Or if someone maintains that a substance is created,19 he maintains at the same time that a false idea has become true.20 Of course nothing more absurd can be conceived. So it must be confessed that the existence of a substance, like its essence, is an eternal truth.

[20] And from this we can infer in another way that there is only one [substance] of the same nature, which I have considered it worth the trouble of showing here.21 But to do this in order, it must be noted,

I. that the true definition of each thing neither involves nor expresses anything except the nature of the thing defined.

From which it follows,

II. that no definition involves or expresses any certain number of [25] individuals,[a]

since it expresses nothing other than the nature of the thing defined. E.g., the definition of the triangle expresses nothing but the simple nature of the triangle, but not any certain number of triangles. It is to be noted,

III. that there must be, for each existing thing, a certain cause22 on account of which it exists.

[30] Finally, it is to be noted,

IV. that this cause, on account of which a thing exists, either must be contained in the very nature and definition of the existing thing (viz. that it pertains to its nature to exist) or must be outside it.

From these propositions it follows that if, in nature, a certain number [35] of individuals exists, there must be a cause why those individuals, and [II/51] why neither more nor fewer, exist.

For example, if 20 men exist in nature (to make the matter clearer, I assume that they exist at the same time, and that no others previously existed in nature), it will not be enough (i.e., to give a reason why 20 men exist) [5] to show the cause of human nature in general; but it will be necessary in addition to show the cause why not more and not fewer than 20 exist. For (by III) there must necessarily be a cause why each [NS: particular man] exists. But this cause (by II and III) cannot be contained in human nature itself, since the true definition of man does [10] not involve the number 20. So (by IV) the cause why these 20 men exist, and consequently, why each of them exists, must necessarily be outside each of them.

For that reason it is to be inferred absolutely that whatever is of such a nature that there can be many individuals [of that nature] must, to exist, have an external cause to exist. Now since it pertains to the [15] nature of a substance to exist (by what we have already shown in this Scholium),23 its definition must involve necessary existence, and consequently its existence must be inferred from its definition alone. But from its definition (as we have shown from II and III) the existence of a number of substances cannot follow. Therefore it follows necessarily [20] from this, that there exists only one of the same nature, as was proposed.

P9: The more reality or being each thing has, the more attributes belong to it.

[25] Dem.: This is evident from D4.

P10: Each attribute of a substance must be conceived through itself.

[30] Dem.: For an attribute is what the intellect perceives concerning a substance, as constituting its essence (by D4); so (by D3) it must be conceived through itself, q.e.d.

[II/52] Schol.: From these propositions it is evident that although two attributes may be conceived to be really distinct (i.e., one may be conceived without the aid of the other), we still can not infer from that that they constitute two beings, or two different substances.24 For it [5] is of the nature of a substance that each of its attributes is conceived through itself, since all the attributes it has have always been in it together, and one could not be produced by another, but each expresses the reality, or being of substance.

So it is far from absurd to attribute many attributes to one substance. [10] Indeed, nothing in nature is clearer than that each being must be conceived under some attribute, and the more reality, or being it has, the more it has attributes which express necessity, or eternity, and infinity. And consequently there is also nothing clearer than that [15] a being absolutely infinite must be defined (as we taught in D6) as a being that consists of infinite attributes, each of which expresses a certain eternal and infinite essence.25

But if someone now asks by what sign we shall be able to distinguish the diversity of substances, let him read the following propositions, which show that in Nature there exists only one substance, and [20] that it is absolutely infinite. So that sign would be sought in vain.

P11: God, or a substance consisting of infinite attributes, each of which expresses [25] eternal and infinite essence, necessarily exists.

Dem.: If you deny this, conceive, if you can, that God does not exist. Therefore (by A7) his essence does not involve existence. But this (by P7) is absurd. Therefore God necessarily exists, q.e.d.

[30] Alternatively: For each thing there must be assigned a cause, or reason, as much for its existence as for its nonexistence. For example, if a triangle exists, there must be a reason or cause why it exists; but [II/53] if it does not exist, there must also be a reason or cause which prevents it from existing, or which takes its existence away.

But this reason, or cause, must either be contained in the nature of the thing, or be outside it. E.g., the very nature of a square circle indicates the reason why it does not exist, viz. because it involves a [5] contradiction. On the other hand, the reason why a substance exists also follows from its nature alone, because it involves existence (see P7). But the reason why a circle or triangle exists, or why it does not exist, does not follow from the nature of these things, but from the order of the whole of corporeal Nature. For from this [order] it must follow either that the triangle necessarily exists now or that it is impossible [10] for it to exist now.26

These things are evident through themselves, but from them it follows that a thing necessarily exists if there is no reason or cause which prevents it from existing. Therefore, if there is no reason or cause which prevents God from existing, or which takes his existence away, it must certainly be inferred that he necessarily exists.

[15] But if there were such a reason, or cause, it would have to be either in God’s very nature or outside it, i.e., in another substance of another nature. For if it were of the same nature, that very supposition would concede that God exists. But a substance which was of another nature [NS: than the divine] would have nothing in common with God (by [20] P2), and therefore could neither give him existence nor take it away.27

Since, then, there can be, outside the divine nature, no reason, or, cause which takes away the divine existence, the reason will necessarily have to be in his nature itself, if indeed he does not exist. That is, his nature would involve a contradiction [NS: as in our second Example]. [25] But it is absurd to affirm this of a Being absolutely infinite and supremely perfect. Therefore, there is no cause, or reason, either in God or outside God, which takes his existence away. And therefore, God necessarily exists, q.e.d.

Alternatively: To be able not to exist is to lack power, and conversely, [30] to be able to exist is to have power28 (as is known through itself). So, if what now necessarily exists are only finite beings, then finite beings are more powerful than an absolutely infinite Being. But this, as is known through itself, is absurd. So, either nothing exists or an absolutely infinite Being also exists. But we exist, either in ourselves, or in something else, which necessarily exists (see A1 and P7). [35] Therefore an absolutely infinite Being—i.e. (by D6), God—necessarily exists, q.e.d.

[II/54] Schol.: In this last demonstration I wanted to show God’s existence a posteriori, so that the demonstration would be perceived more easily—but not because God’s existence does not follow a priori from the [5] same foundation. For since being able to exist is power, it follows that the more reality belongs to the nature of a thing, the more powers it has, of itself, to exist. Therefore, an absolutely infinite Being, or God, has, of himself, an absolutely infinite power of existing. For that reason, he exists absolutely.

Still, there may be many who will not easily be able to see how [10] evident this demonstration is, because they have been accustomed to contemplate only those things that flow from external causes. And of these, they see that those which quickly come to be, i.e., which easily exist,29 also easily perish. And conversely, they judge that those things to which they conceive more things to pertain are more difficult to do, [15] i.e., that they do not exist so easily.30 But to free them from these prejudices, I have no need to show here in what manner this proposition—what quickly comes to be, quickly perishes—is true, nor whether or not all things are equally easy in respect to the whole of Nature. It is sufficient to note only this, that I am not here speaking of things that come to be from external causes, but only of substances that (by P6) [20] can be produced by no external cause.

For things that come to be from external causes—whether they consist of many parts or of few—owe all the perfection or reality they have to the power of the external cause; and therefore their existence arises only from the perfection of their external cause, and not from their own perfection. On the other hand, whatever perfection substance [25] has is not owed to any external cause. So its existence must follow from its nature alone; hence its existence is nothing but its essence.

Perfection, therefore, does not take away the existence of a thing, but on the contrary asserts it. But imperfection takes it away. So there is nothing of whose existence we can be more certain than we are of [30] the existence of an absolutely infinite, or perfect, Being—i.e., God. For since his essence excludes all imperfection, and involves absolute perfection, by that very fact it takes away every cause of doubting his existence, and gives the greatest certainty concerning it. I believe this will be clear even to those who are only moderately attentive.

[II/55] P12: No attribute of a substance can be truly conceived from which it follows that the substance can be divided.

[5] Dem.: For the parts into which a substance so conceived would be divided either will retain the nature of the substance or will not. If the first [NS: viz. they retain the nature of the substance], then (by P8) each part will have to be infinite, and (by P7)31 its own cause, and (by P5) each part will have to consist of a different attribute. And so [10] many substances will be able to be formed from one, which is absurd (by P6). Furthermore, the parts (by P2) would have nothing in common with their whole, and the whole (by D4 and P10) could both be and be conceived without its parts, which is absurd, as no one will be able to doubt.

[15] But if the second is asserted, viz. that the parts will not retain the nature of substance, then since the whole substance would be divided into equal parts,32 it would lose the nature of substance, and would cease to be, which (by P7) is absurd.

[20] P13: A substance which is absolutely infinite is indivisible.

Dem.: For if it were divisible, the parts into which it would be divided will either retain the nature of an absolutely infinite substance or they will not. If the first, then there will be a number of substances [26] of the same nature, which (by P5) is absurd. But if the second is asserted, then (as above [NS: P12]), an absolutely infinite substance will be able to cease to be, which (by P11) is also absurd.

Cor.: From these [propositions] it follows that no substance, and consequently no corporeal substance, insofar as it is a substance,33 is [30] divisible.

Schol.: That substance is indivisible, is understood more simply merely from this, that the nature of substance cannot be conceived unless as infinite, and that by a part of substance nothing can be [II/56] understood except a finite substance, which (by P8) implies a plain contradiction.

P14: Except God, no substance can be or be conceived.

[5] Dem.: Since God is an absolutely infinite being, of whom no attribute which expresses an essence of substance can be denied (by D6), and he necessarily exists (by P11), if there were any substance except God, it would have to be explained through some attribute of God, [10] and so two substances of the same attribute would exist, which (by P5) is absurd. And so except God, no substance can be or, consequently, be conceived. For if it could be conceived, it would have to be conceived as existing. But this (by the first part of this demonstration) is absurd. Therefore, except for God no substance can be or be [15] conceived, q.e.d.

Cor. 1: From this it follows most clearly, first, that God is unique,34 i.e. (by D6), that in Nature there is only one substance, and that it is absolutely infinite (as we indicated in P10S).

[20] Cor. 2: It follows, second, that an extended thing and a thinking thing are either attributes of God, or (by A1) affections of God’s attributes.

[25] P15: Whatever is, is in God, and nothing can be or be conceived without God.

Dem.: Except for God, there neither is, nor can be conceived, any substance (by P14), i.e. (by D3), thing that is in itself and is conceived through itself. But modes (by D5) can neither be nor be conceived [30] without substance. So they can be in the divine nature alone, and can be conceived through it alone. But except for substances and modes [II/57] there is nothing (by A1). Therefore, [NS: everything is in God and] nothing can be or be conceived without God, q.e.d.

Schol.: [I.]35 There are those who feign a God, like man, consisting [5] of a body and a mind, and subject to passions. But how far they wander from the true knowledge of God, is sufficiently established by what has already been demonstrated. Them I dismiss. For everyone who has to any extent contemplated the divine nature denies that God is corporeal. They prove this best from the fact that by body we [10] understand any quantity, with length, breadth, and depth, limited by some certain figure. Nothing more absurd than this can be said of God, viz. of a being absolutely infinite.

But meanwhile, by the other arguments by which they strive to demonstrate this same conclusion they clearly show that they entirely remove corporeal, or extended,36 substance itself from the divine nature. And they maintain that it has been created by God. But by what [15] divine power could it be created? They are completely ignorant of that. And this shows clearly that they do not understand what they themselves say.

At any rate, I have demonstrated clearly enough—in my judgment, at least—that no substance can be produced or created by any other (see P6C and P8S2). Next, we have shown (P14) that except for God, [20] no substance can either be or be conceived, and hence [in P14C2]37 we have concluded that extended substance is one of God’s infinite attributes. But to provide a fuller explanation, I shall refute my opponents’ arguments, which all reduce to these.

[25] [II.] First, they think that corporeal substance, insofar as it is substance, consists of parts. And therefore they deny that it can be infinite, and consequently, that it can pertain to God. They explain this by many examples, of which I shall mention one or two.38

[i] If corporeal substance is infinite, they say, let us conceive it to be divided in two parts.39 Each part will be either finite or infinite. If [30] the former, then an infinite is composed of two finite parts, which is absurd. If the latter [NS: i.e., if each part is infinite], then there is one infinite twice as large as another, which is also absurd, [ii] Again, if an infinite quantity is measured by parts [each] equal to a foot, it [35] will consist of infinitely many such parts, as it will also, if it is measured by parts [each] equal to an inch. And therefore, one infinite number will be twelve times greater than another [NS: which is no less absurd], [iii] Finally, if we conceive that from one point of a certain [II/58] infinite quantity two lines, say AB and AC, are extended to infinity, it is certain that, although in the beginning they are a certain, determinate distance [5] apart, the distance between B and C is continuously increased, and at last, from being determinate, it will become indeterminable. Since these absurdities follow—so they think—from the fact that an infinite quantity is supposed, they infer that corporeal substance must be finite, and consequently cannot pertain to God’s essence.

[10] [III.] Their second argument is also drawn from God’s supreme perfection. For God, they say, since he is a supremely perfect being, cannot be acted on. But corporeal substance, since it is divisible, can be acted on. It follows, therefore, that it does not pertain to God’s essence.40

[IV.] These are the arguments which I find authors using, to try to [15] show that corporeal substance is unworthy of the divine nature, and cannot pertain to it. But anyone who is properly attentive will find that I have already replied to them, since these arguments are founded only on their supposition that corporeal substance is composed of parts, which I have already (P12 and P13C) shown to be absurd. And then [20] anyone who wishes to consider the matter rightly will see that all those absurdities (if indeed they are all absurd, which I am not now disputing), from which they wish to infer that extended substance is finite, do not follow at all from the fact that an infinite quantity is supposed, but from the fact that they suppose an infinite quantity to be measurable [25] and composed of finite parts. So from the absurdities which follow from that they can infer only that infinite quantity is not measurable, and that it is not composed of finite parts. This is the same thing we have already demonstrated above (P12, etc.). So the weapon they aim at us, they really turn against themselves.

[30] If, therefore, they still wish to infer from this absurdity of theirs that extended substance must be finite, they are indeed doing nothing more than if someone feigned that a circle has the properties of a square, and inferred from that the circle has no center, from which all lines drawn to the circumference are equal. For corporeal substance, [35] which cannot be conceived except as infinite, unique, and indivisible [II/59] (see P8, 5 and 12), they conceive to be composed of finite parts, to be many, and to be divisible, in order to infer that it is finite.

So also others, after they feign that a line is composed of points, [5] know how to invent many arguments, by which they show that a line cannot be divided to infinity. And indeed it is no less absurd to assert that corporeal substance is composed of bodies, or parts, than that a body is composed of surfaces, the surfaces of lines, and the lines, finally, of points.

[10] All those who know that clear reason is infallible must confess this—particularly those who deny that there is a vacuum. For if corporeal substance could be so divided that its parts were really distinct, why, then, could one part not be annihilated, the rest remaining connected with one another as before? And why must they all be so fitted together that there is no vacuum? Truly, of things which are really [15] distinct from one another, one can be, and remain in its condition, without the other. Since, therefore, there is no vacuum in nature (a subject I discuss elsewhere),41 but all its parts must so concur that there is no vacuum, it follows also that they cannot be really distinguished, i.e., that corporeal substance, insofar as it is a substance, cannot be divided.

[20] [V.] If someone should now ask why we are, by nature, so inclined to divide quantity, I shall answer that we conceive quantity in two ways: abstractly, or superficially,42 as we [NS: commonly] imagine it, or as substance, which is done by the intellect alone [NS: without the [25] help of the imagination]. So if we attend to quantity as it is in the imagination, which we do often and more easily, it will be found to be finite, divisible, and composed of parts; but if we attend to it as it is in the intellect, and conceive it insofar as it is a substance, which happens [NS: seldom and] with great difficulty, then (as we have already sufficiently demonstrated) it will be found to be infinite, unique, [30] and indivisible.

This will be sufficiently plain to everyone who knows how to distinguish between the intellect and the imagination—particularly if it is also noted that matter is everywhere the same, and that parts are distinguished in it only insofar as we conceive matter to be affected in different ways, so that its parts are distinguished only modally, but [35] not really.

[II/60] For example, we conceive that water is divided and its parts separated from one another—insofar as it is water, but not insofar as it is corporeal substance. For insofar as it is substance, it is neither separated nor divided. Again, water, insofar as it is water, is generated and corrupted, but insofar as it is substance, it is neither generated nor corrupted.

[5] [VI.] And with this I think I have replied to the second argument also, since it is based on the supposition that matter, insofar as it is substance, is divisible, and composed of parts. Even if this [reply] were not [sufficient], I do not know why [divisibility] would be unworthy of the divine nature. For (by P14) apart from God there can [10] be no substance by which [the divine nature] would be acted on. All things, I say, are in God, and all things that happen, happen only through the laws of God’s infinite nature and follow (as I shall show) from the necessity of his essence. So it cannot be said in any way that God is acted on by another, or that extended substance is unworthy of the divine nature, even if it is supposed to be divisible, so long as [15] it is granted to be eternal and infinite. But enough of this for the present.

P16: From the necessity of the divine nature there must follow infinitely many things in infinitely many modes,43 (i.e., everything which can fall under an infinite intellect.)44

[20] Dem.: This Proposition must be plain to anyone, provided he attends to the fact that the intellect infers from the given definition of any thing a number of properties that really do follow necessarily from it (i.e., from the very essence of the thing); and that it infers more [25] properties the more the definition of the thing expresses reality, i.e., the more reality the essence of the defined thing involves. But since the divine nature has absolutely infinite attributes (by D6), each of which also expresses an essence infinite in its own kind, from its necessity there must follow infinitely many things in infinite modes (i.e., [30] everything which can fall under an infinite intellect), q.e.d.

Cor. 1: From this it follows that God is the efficient cause of all things which can fall under an infinite intellect.

[II/61] Cor. 2: It follows, secondly, that God is a cause through himself and not an accidental cause.45

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

[5] P17: God acts from the laws of his nature alone, and is compelled by no one.

Dem.: We have just shown (P16) that from the necessity of the divine nature alone, or (what is the same thing) from the laws of his [10] nature alone, absolutely infinite things follow, and in P15 we have demonstrated that nothing can be or be conceived without God, but that all things are in God. So there can be nothing outside him by which he is determined or compelled to act. Therefore, God acts from [15] the laws of his nature alone, and is compelled by no one, q.e.d.

Cor. 1: From this it follows, first, that there is no cause, either extrinsically or intrinsically, which prompts God to action, except the [20] perfection of his nature.46

Cor. 2: It follows, secondly, that God alone is a free cause. For God alone exists only from the necessity of his nature (by P11 and P14C1), and acts from the necessity of his nature (by P17). Therefore (by D7) [25] God alone is a free cause, q.e.d.

Schol.: [I.] Others47 think that God is a free cause because he can (so they think) bring it about that the things which we have said follow from his nature (i.e., which are in his power) do not happen or are not [30] produced by him. But this is the same as if they were to say that God can bring it about that it would not follow from the nature of a triangle that its three angles are equal to two right angles; or that from a given [II/62] cause the effect would not follow—which is absurd.

Further, I shall show later, without the aid of this Proposition, that neither intellect nor will pertain to God’s nature. Of course I know there are many who think they can demonstrate that a supreme intellect [5] and a free will pertain to God’s nature. For they say they know nothing they can ascribe to God more perfect than what is the highest perfection in us.

Moreover, even if they conceive God to actually understand in the highest degree, they still do not believe that he can bring it about that all the things he actually understands exist. For they think that in that [10] way they would destroy God’s power. If he had created all the things in his intellect (they say), then he would have been able to create nothing more, which they believe to be incompatible with God’s omnipotence. So they preferred to maintain that God is indifferent to all things, not creating anything except what he has decreed to create by some absolute will.

[15] But I think I have shown clearly enough (see P16) that from God’s supreme power, or infinite nature, infinitely many things in infinitely many modes, i.e., all things, have necessarily flowed, or always follow, by the same necessity and in the same way as from the nature of a triangle it follows, from eternity and to eternity, that its three angles are equal to two right angles. So God’s omnipotence48 has been actual [20] from eternity and will remain in the same actuality to eternity. And in this way, at least in my opinion, God’s omnipotence is maintained far more perfectly.

Indeed—to speak openly—my opponents seem to deny God’s omnipotence. For they are forced to confess that God understands infinitely many creatable things, which nevertheless he will never be able [25] to create. For otherwise, if he created everything he understood [NS: to be creatable] he would (according to them) exhaust his omnipotence and render himself imperfect. Therefore to maintain that God is perfect, they are driven to maintain at the same time that he cannot bring about everything to which his power extends. I do not see what could be feigned which would be more absurd than this or more contrary to [30] God’s omnipotence.

[II.] Further—to say something here also about the intellect and will which we commonly attribute to God—if will and intellect do pertain to the eternal essence of God,49 we must of course understand by each of these attributes something different from what men commonly understand. [35] For the intellect and will which would constitute God’s essence [II/63] would have to differ entirely from our intellect and will, and could not agree with them in anything except the name. They would not agree with one another any more than do the dog that is a heavenly constellation and the dog that is a barking animal. I shall demonstrate this.

If intellect pertains to the divine nature, it will not be able to be [5] (like our intellect) by nature either posterior to (as most would have it), or simultaneous with, the things understood, since God is prior in causality to all things (by P16C1). On the contrary, the truth and formal essence of things is what it is because it exists objectively in that way in God’s intellect.50 So God’s intellect, insofar as it is conceived [10] to constitute God’s essence, is really the cause both of the essence and of the existence of things. This seems also to have been noticed by those who asserted that God’s intellect, will and power are one and the same.

Therefore, since God’s intellect is the only cause of things (viz. as [15] we have shown, both of their essence and of their existence), he must necessarily differ from them both as to his essence and as to his existence. For what is caused differs from its cause precisely in what it has from the cause [NS: for that reason it is called the effect of such a cause].51 E.g., a man is the cause of the existence of another man, but not of his essence, for the latter is an eternal truth. Hence, they can [20] agree entirely according to their essence. But in existing they must differ. And for that reason, if the existence of one perishes, the other’s existence will not thereby perish. But if the essence of one could be destroyed, and become false, the other’s essence would also be destroyed [NS: and become false].

So the thing that is the cause both of the essence and of the existence [25] of some effect, must differ from such an effect, both as to its essence and as to its existence. But God’s intellect is the cause both of the essence and of the existence of our intellect. Therefore, God’s intellect, insofar as it is conceived to constitute the divine essence, differs from our intellect both as to its essence and as to its existence, [30] and cannot agree with it in anything except in name, as we supposed. The proof proceeds in the same way concerning the will, as anyone can easily see.

P18: God is the immanent, not the transitive, cause of all things.

[II/64] Dem.: Everything that is, is in God, and must be conceived through God (by P15), and so (by P16C1) God is the cause of [NS: all] things, which are in him. That is the first [thing to be proven]. And then [5] outside God there can be no substance (by P14), i.e. (by D3), thing which is in itself outside God. That was the second. God, therefore, is the immanent, not the transitive cause of all things,52 q.e.d.

P19: God is eternal, or all God’s attributes are eternal.

[10] Dem.: For God (by D6) is substance, which (by P11) necessarily exists, i.e. (by P7), to whose nature it pertains to exist, or (what is the same) from whose definition it follows that he exists; and therefore (by D8), he is eternal.

[15] Next, by God’s attributes are to be understood what (by D4) expresses an essence of the Divine substance, i.e., what pertains to substance. The attributes themselves, I say, must involve it itself. But eternity pertains to the nature of substance (as I have already demonstrated from P7). Therefore each of the attributes must involve eternity, [20] and so, they are all eternal, q.e.d.

Schol.: This Proposition is also as clear as possible from the way I have demonstrated God’s existence (P11). For from that demonstration, I say, it is established that God’s existence, like his essence, is an eternal truth. And then I have also demonstrated God’s eternity in [25] another way (Descartes’ Principles IP19), and there is no need to repeat it here.

P20: God’s existence and his essence are one and the same.

[30] Dem.: God (by P19) and all of his attributes are eternal, i.e. (by D8), each of his attributes expresses existence. Therefore, the same attributes of God which (by D4) explain God’s eternal essence at the [35] same time explain his eternal existence, i.e., that itself which constitutes [II/65] God’s essence at the same time constitutes his existence. So his existence and his essence are one and the same, q.e.d.

Cor. 1: From this it follows, first, that God’s existence, like his [5] essence, is an eternal truth.

Cor. 2: It follows, secondly, that God, or all of God’s attributes, are immutable. For if they changed as to their existence, they would also (by P20) change as to their essence, i.e. (as is known through itself), [10] from being true become false, which is absurd.

P21: All the things which follow from the absolute nature of any of God’s attributes have always53 had to exist and be infinite, or are, through the same attribute, eternal and infinite.

[15] Dem.: If you deny this, then conceive (if you can) that in some attribute of God there follows from its absolute nature something that is finite and has a determinate existence, or duration, e.g., God’s idea54 in thought. Now since thought is supposed to be an attribute of God, [20] it is necessarily (by P11) infinite by its nature. But insofar as it has God’s idea, [thought] is supposed to be finite. But (by D2) [thought] cannot be conceived to be finite unless it is determined through thought itself. But [thought can] not [be determined] through thought itself, insofar as it constitutes God’s idea, for to that extent [thought] is supposed to be finite. Therefore, [thought must be determined] through [25] thought insofar as it does not constitute God’s idea, which [thought] nevertheless (by P11) must necessarily exist. Therefore, there is thought55 which does not constitute God’s idea, and on that account God’s idea does not follow necessarily from the nature [of this thought] insofar as it is absolute thought (for [thought] is conceived both as constituting God’s idea and as not constituting it). [That God’s idea does not follow from thought, insofar as it is absolute thought] is contrary to the hypothesis. [30] So if God’s idea in thought, or anything else in any attribute of God (for it does not matter what example is taken, since the demonstration is universal), follows from the necessity of the absolute nature of the attribute itself, it must necessarily be infinite. This was the first thing to be proven.

Next, what follows in this way from the necessity of the nature of [II/66] any attribute cannot have a determinate [NS: existence, or] duration. For if you deny this, then suppose there is, in some attribute of God, a thing which follows from the necessity of the nature of that attribute—e.g., God’s idea in thought—and suppose that at some time [this [5] idea] did not exist or will not exist. But since thought is supposed to be an attribute of God, it must exist necessarily and be immutable56 (by P11 and P20C2). So beyond the limits of the duration of God’s idea (for it is supposed that at some time [this idea] did not exist or will not exist) thought will have to exist without God’s idea. But this is contrary to the hypothesis, for it is supposed that God’s idea follows [10] necessarily from the given thought. Therefore, God’s idea in thought, or anything else which follows necessarily from the absolute nature of some attribute of God, cannot have a determinate duration, but through the same attribute is eternal. This was the second thing [NS: to be proven]. Note that the same is to be affirmed of any thing which, in [15] some attribute of God, follows necessarily from God’s absolute nature.

P22: Whatever follows from some attribute of God insofar as it is modified by a modification which, through the same attribute, exists necessarily and is [20] infinite, must also exist necessarily and be infinite.57

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

[25] P23: Every mode which exists necessarily and is infinite has necessarily had to follow either from the absolute nature of some attribute of God, or from some attribute, modified by a modification which exists necessarily and is infinite.

[30] Dem.: For a mode is in another, through which it must be conceived (by D5), i.e. (by P15), it is in God alone, and can be conceived [II/67] through God alone. So if a mode is conceived to exist necessarily and be infinite, [its necessary existence and infinitude] must necessarily be inferred, or perceived through some attribute of God, insofar as that attribute is conceived to express infinity and necessity of existence, or [5] (what is the same, by D8) eternity, i.e. (by D6 and P19), insofar as it is considered absolutely. Therefore, the mode, which exists necessarily and is infinite, has had to follow from the absolute nature of some attribute of God—either immediately (see P21) or by some mediating modification, which follows from its absolute nature, i.e. (by P22), [10] which exists necessarily and is infinite, q.e.d.

P24: The essence of things produced by God does not involve existence.

Dem.: This is evident from D1. For that whose nature involves [15] existence (considered in itself), is its own cause, and exists only from the necessity of its nature.

Cor.: From this it follows that God is not only the cause of things’ beginning to exist, but also of their persevering in existing, or (to use [20] a Scholastic term) God is the cause of the being of things. For—whether the things [NS: produced] exist or not—so long as we attend to their essence, we shall find that it involves neither existence nor duration. So their essence can be the cause neither of their existence nor of their duration, but only God, to whose nature alone it pertains to exist [25] [,can be the cause] (by P14C1).

P25: God is the efficient cause, not only of the existence of things, but also of their essence.

[30] Dem.: If you deny this, then God is not the cause of the essence of things; and so (by A4) the essence of things can be conceived without [II/68] God. But (by P15) this is absurd. Therefore God is also the cause of the essence of things, q.e.d.

Schol.: This Proposition follows more clearly from P16. For from [5] that it follows that from the given divine nature both the essence of things and their existence must necessarily be inferred; and in a word, God must be called the cause of all things in the same sense in which he is called the cause of himself. This will be established still more clearly from the following corollary.

[10] Cor.: Particular things are nothing but affections of God’s attributes, or modes by which God’s attributes are expressed in a certain and determinate way. The demonstration is evident from P15 and D5.

[15] P26: A thing which has been determined to produce an effect has necessarily been determined in this way by God; and one which has not been determined by God cannot determine itself to produce an effect.

Dem.: That through which things are said to be determined to produce [20] an effect must be something positive (as is known through itself). And so, God, from the necessity of his nature, is the efficient cause both of its essence and of its existence (by P25 & 16); this was the first thing. And from it the second thing asserted also follows very clearly. For if a thing which has not been determined by God could determine itself, the first part of this [NS: proposition] would be false, which is [25] absurd, as we have shown.

P27: A thing which has been determined by God to produce an effect, cannot render itself undetermined.

[30] Dem.: This proposition is evident from A3.

[II/69] P28: Every singular thing, or any thing which is finite and has a determinate existence, can neither exist nor be determined to produce an effect unless it is [5] determined to exist and produce an effect by another cause, which is also finite and has a determinate existence; and again, this cause also can neither exist nor be determined to produce an effect unless it is determined to exist and produce an effect by another, which is also finite and has a determinate existence, and so on, to infinity.58

[10] Dem.: Whatever has been determined to exist and produce an effect has been so determined by God (by P26 and P24C). But what is finite and has a determinate existence could not have been produced by the absolute nature of an attribute of God; for whatever follows from the [15] absolute nature of an attribute of God is eternal and infinite (by P21). It had, therefore, to follow either from God or from an attribute of God insofar as it is considered to be affected by some mode. For there is nothing except substance and its modes (by A1, D3, and D5) and [20] modes (by P25C) are nothing but affections of God’s attributes. But it also could not follow from God, or from an attribute of God, insofar as it is affected by a modification which is eternal and infinite (by P22). It had, therefore, to follow from, or be determined to exist and produce an effect by God or an attribute of God insofar as it is modified [25] by a modification which is finite and has a determinate existence. This was the first thing to be proven.

And in turn, this cause, or this mode (by the same reasoning by which we have already demonstrated the first part of this proposition) had also to be determined by another, which is also finite and has a determinate existence; and again, this last (by the same reasoning) by [30] another, and so always (by the same reasoning) to infinity, q.e.d.

[II/70] Schol.: Since certain things had to be produced by God immediately, viz. those which follow necessarily from his absolute nature, and others (which nevertheless can neither be nor be conceived without God) had to be produced by the mediation of these first things,59 it follows:

[5] I. That God is absolutely the proximate cause of the things produced immediately by him, and not [a proximate cause] in his own kind, as they say.60 For God’s effects can neither be nor be conceived without their cause (by P15 and P24C).

II. That God cannot properly be called the remote cause of singular [10] things, except perhaps so that we may distinguish them from those things that he has produced immediately, or rather, that follow from his absolute nature. For by a remote cause we understand one which is not conjoined in any way with its effect. But all things that are, are in God, and so depend on God that they can neither be nor be conceived [15] without him.

P29: In nature there is nothing contingent, but all things have been determined from the necessity of the divine nature to exist and produce an effect in a certain way.

[20] Dem.: Whatever is, is in God (by P15); but God cannot be called a contingent thing. For (by P11) he exists necessarily, not contingently. Next, the modes of the divine nature have also followed from it necessarily and not contingently (by P16)—either insofar as the divine [25] nature is considered absolutely (by P21) or insofar as it is considered to be determined to act in a certain way (by P28).61 Further, God is the cause of these modes not only insofar as they simply exist (by P24C), but also (by P26) insofar as they are considered to be determined [30] to produce an effect. For if they have not been determined by God, then (by P26) it is impossible, not contingent, that they should [II/71] determine themselves. Conversely (by P27) if they have been determined by God, it is not contingent, but impossible, that they should render themselves undetermined. So all things have been determined from the necessity of the divine nature, not only to exist, but to exist in a certain way, and to produce effects in a certain way. There is nothing contingent, q.e.d.

[5] Schol.: Before I proceed further, I wish to explain here—or rather to advise [the reader]—what we must understand by Natura naturans and Natura naturata. For from the preceding I think it is already established that by Natura naturans we must understand what is in itself [10] and is conceived through itself, or such attributes of substance as express an eternal and infinite essence, i.e. (by P14C1 and P17C2), God, insofar as he is considered as a free cause.

But by Natura naturata I understand whatever follows from the necessity of God’s nature, or from any of God’s attributes, i.e., all the [15] modes of God’s attributes insofar as they are considered as things which are in God, and can neither be nor be conceived without God.

P30: An actual intellect, whether finite or infinite,62 must comprehend God’s attributes and God’s affections, and nothing else.

[20] Dem.: A true idea must agree with its object (by A6), i.e. (as is known through itself), what is contained objectively in the intellect must necessarily be in nature. But in nature (by P14C1) there is only one substance, viz. God, and there are no affections other than those [25] which are in God (by P15) and which can neither be nor be conceived without God (by P15). Therefore, an actual intellect, whether finite or infinite, must comprehend God’s attributes and God’s affections, and nothing else, q.e.d.

[30] P31: The actual intellect, whether finite or infinite, like will, desire, love, etc., must be referred to Natura naturata, not to Natura naturans.63

[II/72] Dem.: By intellect (as is known through itself) we understand not absolute thought, but only a certain mode of thinking, which mode differs from the others, such as desire, love, etc., and so (by D5) must [5] be conceived through absolute thought, i.e. (by P15 and D6), it must be so conceived through an attribute of God, which expresses the eternal and infinite essence of thought, that can neither be nor be conceived without [that attribute]; and so (by P29S), like the other modes of thinking, it must be referred to Natura naturata, not to Natura [10] naturans, q.e.d.

Schol.: The reason why I speak here of actual intellect is not because I concede that there is any potential intellect, but because, wishing to avoid all confusion, I wanted to speak only of what we perceive [15] as clearly as possible, i.e., of the intellection itself. We perceive nothing more clearly than that. For we can understand nothing that does not lead to more perfect knowledge of the intellection.

[20] P32: The will cannot be called a free cause, but only a necessary one.

Dem.: The will, like the intellect,64 is only a certain mode of thinking. And so (by P28) each volition can neither exist nor be determined to produce an effect unless it is determined by another cause, and this [25] cause again by another, and so on, to infinity. Even if the will be supposed to be infinite,65 it must still be determined to exist and produce an effect by God, not insofar as he is an absolutely infinite substance, but insofar as he has an attribute that expresses the infinite and eternal essence of thought (by P23). So in whatever way it is [30] conceived, whether as finite or as infinite, it requires a cause by which it is determined to exist and produce an effect. And so (by D7) it cannot be called a free cause, but only a necessary or compelled one, q.e.d.

[II/73] Cor. 1: From this it follows, first, that God does not produce any effect by freedom of the will.

Cor. 2: It follows, secondly, that will and intellect are related to [5] God’s nature as motion and rest are, and as are absolutely all natural things, which (by P29) must be determined by God to exist and produce an effect in a certain way. For the will, like all other things, requires a cause by which it is determined to exist and produce an effect in a certain way. And although from a given will, or intellect [10] infinitely many things may follow, God still cannot be said, on that account, to act from freedom of the will, any more than he can be said to act from freedom of motion and rest on account of those things that follow from motion and rest (for infinitely many things also follow from motion and rest). So will does not pertain to God’s nature any more than do the other natural things, but is related to him in the [15] same way as motion and rest, and all the other things which, as we have shown, follow from the necessity of the divine nature and are determined by it to exist and produce an effect in a certain way.

P33: Things could have been produced by God in no other way, and in no [20] other order than they have been produced.

Dem.: For all things have necessarily followed from God’s given nature (by P16), and have been determined from the necessity of God’s nature to exist and produce an effect in a certain way (by P29). Therefore, [25] if things could have been of another nature, or could have been determined to produce an effect in another way, so that the order of Nature was different, then God’s nature could also have been other than it is now, and therefore (by P11) that [other nature] would also have had to exist, and consequently, there could have been two or more Gods, which is absurd (by P14C1). So things could have been [30] produced in no other way and no other order, etc., q.e.d.

[II/74] Schol. 1: Since by these propositions I have shown more clearly than the noon light that there is absolutely nothing in things on account of which they can be called contingent, I wish now to explain briefly what we must understand by contingent—but first, what [we [5] must understand] by necessary and impossible.

A thing is called necessary either by reason of its essence or by reason of its cause. For a thing’s existence follows necessarily either from its essence and definition or from a given efficient cause. And a thing is also called impossible from these same causes—viz. either because [10] its essence, or definition, involves a contradiction, or because there is no external cause which has been determined to produce such a thing.

But a thing is called contingent only because of a defect of our knowledge. For if we do not know that the thing’s essence involves a contradiction, or if we do know very well that its essence does not [15] involve a contradiction, and nevertheless can affirm nothing certainly about its existence, because the order of causes is hidden from us, it can never seem to us either necessary or impossible. So we call it contingent or possible.66

[20] Schol. 2: From the preceding it clearly follows that things have been produced by God with the highest perfection, since they have followed necessarily from a given most perfect nature. Nor does this convict God of any imperfection, for his perfection compels us to affirm this. Indeed, from the opposite, it would clearly follow (as I [25] have just shown), that God is not supremely perfect; because if things had been produced by God in another way, we would have to attribute to God another nature, different from that which we have been compelled to attribute to him from the consideration of the most perfect Being.

Of course, I have no doubt that many will reject this opinion as [30] absurd, without even being willing to examine it—for no other reason than because they have been accustomed to attribute another freedom to God, far different from that we have taught (D7), viz. an absolute will. But I also have no doubt that, if they are willing to reflect on the matter, and consider properly the chain of our demonstrations, in the [II/75] end they will utterly reject the freedom they now attribute to God, not only as futile, but as a great obstacle to science. Nor is it necessary for me to repeat here what I said in P17S.

Nevertheless, to please them, I shall show that even if it is conceded [5] that will pertains to God’s essence,67 it still follows from his perfection that things could have been created by God in no other way or order. It will be easy to show this if we consider, first, what they themselves concede, viz. that it depends on God’s decree and will alone that each thing is what it is. For otherwise God would not be the cause of all [10] things. Next, that all God’s decrees have been established by God himself from eternity. For otherwise he would be convicted of imperfection and inconstancy. But since, in eternity, there is neither when, nor before, nor after, it follows, from God’s perfection alone, that he can never decree anything different, and never could have, or that God [15] was not before his decrees, and cannot be without them.

But they will say that even if it were supposed that God had made another nature of things, or that from eternity he had decreed something else concerning nature and its order, no imperfection in God would follow from that.

Still, if they say this, they will concede at the same time that God [20] can change his decrees. For if God had decreed, concerning nature and its order, something other than what he did decree, i.e., had willed and conceived something else concerning nature, he would necessarily have had an intellect other than he now has, and a will other than he now has. And if it is permitted to attribute to God another intellect and another will, without any change of his essence and of [25] his perfection, why can he not now change his decrees concerning created things, and nevertheless remain equally perfect? For his intellect and will concerning created things and their order are the same in respect to his essence and his perfection, however his will and intellect may be conceived.

[30] Further, all the Philosophers I have seen concede that in God there is no potential intellect,68 but only an actual one. But since his intellect and his will are not distinguished from his essence, as they all also concede, it follows that if God had had another actual intellect, and [35] another will, his essence would also necessarily be other. And therefore [II/76] (as I inferred at the beginning) if things had been produced by God otherwise than they now are, God’s intellect and his will, i.e. (as is conceded), his essence, would have to be different [NS: from what it now is]. And this is absurd.

Therefore, since things could have been produced by God in no [5] other way, and no other order, and since it follows from God’s supreme perfection that this is true, no truly sound reason can persuade us to believe that God did not will to create all the things that are in his intellect, with that same perfection with which he understands them.

But they will say that there is no perfection or imperfection in things; [10] what is in them, on account of which they are perfect or imperfect, and are called good or bad,69 depends only on God’s will. And so, if God had willed, he could have brought it about that what is now perfection would have been the greatest imperfection, and conversely [NS: that what is now an imperfection in things would have been the [15] most perfect]. How would this be different from saying openly that God, who necessarily understands what he wills, can bring it about by his will that he understands things in another way than he does understand them? As I have just shown, this is a great absurdity.

So I can turn the argument against them in the following way. All [20] things depend on God’s power. So in order for things to be able to be different, God’s will would necessarily also have to be different. But God’s will cannot be different (as we have just shown most evidently from God’s perfection). So things also cannot be different.

I confess that this opinion,70 which subjects all things to a certain [25] indifferent will of God, and makes all things depend on his good pleasure, is nearer the truth than that of those who maintain that God does all things for the sake of the good. For they seem to place something outside God, which does not depend on God, to which God attends, [30] as a model, in what he does, and at which he aims, as at a certain goal. This is simply to subject God to fate. Nothing more absurd can be maintained about God, whom we have shown to be the first and only free cause, both of the essence of all things, and of their existence. So I shall waste no time in refuting this absurdity.

[35] P34: God’s power is his essence itself.

[II/77] Dem.: For from the necessity alone of God’s essence it follows that God is the cause of himself (by P11) and (by P16 and P16C) of all things. Therefore, God’s power, by which he and all things are and [5] act, is his essence itself, q.e.d.

P35: Whatever we conceive to be in God’s power, necessarily exists.

Dem.: For whatever is in God’s power must (by P34) be so comprehended by his essence that it necessarily follows from it, and therefore [10] necessarily exists, q.e.d.

P36: Nothing exists from whose nature some effect does not follow.

[15] Dem: Whatever exists expresses the nature, or essence of God in a certain and determinate way (by P25C), i.e. (by P34), whatever exists expresses in a certain and determinate way the power of God, which is the cause of all things. So (by P16), from [NS: everything that exists] some effect must follow, q.e.d.

[20] APPENDIX

With these [demonstrations] I have explained God’s nature and properties: that he exists necessarily; that he is unique; that he is and acts from the necessity alone of his nature; that (and how) he is the free cause of all things; that all things are in God and so depend on him [25] that without him they can neither be nor be conceived; and finally, that all things have been predetermined by God, not from freedom of the will or absolute good pleasure, but from God’s absolute nature, or infinite power.

Further, I have taken care, whenever the occasion arose, to remove prejudices that could prevent my demonstrations from being perceived. [30] But because many prejudices remain that could, and can, be a great obstacle to men’s understanding the connection of things in the way I have explained it, I considered it worthwhile to submit them [II/78] here to the scrutiny of reason. All the prejudices I here undertake to expose depend on this one: that men commonly suppose that all natural things act, as men do, on account of an end; indeed, they maintain as certain that God himself directs all things to some certain end, [5] for they say that God has made all things for man, and man that he might worship God.

So I shall begin by considering this one prejudice, asking first [I] why most people are satisfied that it is true, and why all are so inclined by nature to embrace it. Then [II] I shall show its falsity, and [10] finally [III] how, from this, prejudices have arisen concerning good and evil, merit and sin, praise and blame, order and confusion, beauty and ugliness, and other things of this kind.71

[I.] Of course this is not the place to deduce these things from the nature of the human mind. It will be sufficient here if I take as a [15] foundation what everyone must acknowledge: that all men are born ignorant of the causes of things, and that they all want to seek their own advantage, and are conscious of this appetite.

From these [assumptions] it follows, first, that men think themselves free, because they are conscious of their volitions and their appetite, and do not think, even in their dreams, of the causes by which they [20] are disposed to wanting and willing, because they are ignorant of [those causes]. It follows, secondly, that men act always on account of an end, viz. on account of their advantage, which they want. Hence they seek to know only the final causes of what has been done, and when they have heard them, they are satisfied, because they have no reason to [25] doubt further. But if they cannot hear them from another, nothing remains for them but to turn toward themselves, and reflect on the ends by which they are usually determined to do such things; so they necessarily judge the temperament of other men from their own temperament.

Furthermore, they find—both in themselves and outside themselves—many [30] means that are very helpful in seeking their own advantage, e.g., eyes for seeing, teeth for chewing, plants and animals for food, the sun for light, the sea for supporting fish [NS: and so with almost all other things whose natural causes they have no reason to [35] doubt].72 Hence, they consider all natural things as means to their own advantage. And knowing that they had found these means, not provided them for themselves, they had reason to believe that there was someone else who had prepared those means for their use. For after [II/79] they considered things as means, they could not believe that the things had made themselves; but from the means they were accustomed to prepare for themselves, they had to infer that there was a ruler, or a number of rulers of nature, endowed with human freedom, who had taken care of all things for them, and made all things for their use.

[5] And since they had never heard anything about the temperament of these rulers, they had to judge it from their own. Hence, they maintained that the Gods direct all things for the use of men in order to bind men to them and be held by men in the highest honor. So it has happened that each of them has thought up from his own temperament [10] different ways of worshipping God, so that God might love them above all the rest, and direct the whole of Nature according to the needs of their blind desire and insatiable greed. Thus this prejudice was changed into superstition, and struck deep roots in their minds. This was why each of them strove with great diligence to understand [15] and explain the final causes of all things.

But while they sought to show that nature does nothing in vain (i.e., nothing which is not of use to men), they seem to have shown only that nature and the Gods are as mad as men. See, I ask you, how the matter has turned out in the end! Among so many conveniences in [20] nature they had to find many inconveniences: storms, earthquakes, diseases, etc. These, they maintain, happen because the Gods [NS: (whom they judge to be of the same nature as themselves)]73 are angry on account of wrongs done to them by men, or on account of sins committed in their worship. And though their daily experience contradicted this, and though infinitely many examples showed that conveniences [25] and inconveniences happen indiscriminately to the pious and the impious alike, they did not on that account give up their longstanding prejudice. It was easier for them to put this among the other unknown things, whose use they were ignorant of, and so remain in the state of ignorance in which they had been born, than to destroy that whole construction, and think up a new one.

[30] So they maintained it as certain that the judgments of the Gods far surpass man’s grasp. This alone, of course, would have caused the truth to be hidden from the human race to eternity, if Mathematics, which is concerned not with ends, but only with the essences and properties of figures, had not shown men another standard of truth. [35] And besides Mathematics, we can assign other causes also (which it is unnecessary to enumerate here), which were able to bring it about that men [NS:—but very few, in relation to the whole human race—]74 [II/80] would notice these common prejudices and be led to the true knowledge of things.

[II.] With this I have sufficiently explained what I promised in the first place [viz. why men are so inclined to believe that all things act for an end]. Not many words will be required now to show that Nature has no end set before it, and that all final causes are nothing but [5] human fictions. For I believe I have already sufficiently established it, both by the foundations and causes from which I have shown this prejudice to have had its origin, and also by P16, P32C1 and C2, and all those [propositions] by which I have shown that all things proceed by a certain eternal necessity of nature, and with the greatest perfection.

[10] I shall, however, add this: this doctrine concerning the end turns nature completely upside down. For what is really a cause, it considers as an effect, and conversely [NS: what is an effect it considers as a cause]. What is by nature prior, it makes posterior. And finally, what is supreme and most perfect, it makes imperfect.

[15] For—to pass over the first two, since they are manifest through themselves—as has been established in PP21-23, that effect is most perfect which is produced immediately by God, and the more something requires intermediate causes to produce it, the more imperfect it is. But if the things which have been produced immediately by God [20] had been made so that God would achieve his end, then the last things, for the sake of which the first would have been made, would be the most excellent of all.

Again, this doctrine takes away God’s perfection. For if God acts for the sake of an end, he necessarily wants something which he lacks. And though the Theologians and Metaphysicians distinguish between [25] an end of need and an end of assimilation,75 they nevertheless confess that God did all things for his own sake, not for the sake of the things to be created. For before creation they can assign nothing except God for whose sake God would act. And so they are necessarily compelled to confess that God lacked those things for the sake of which he willed to prepare means, and that he desired them. This is clear through itself.

[30] Nor ought we here to pass over the fact that the Followers of this doctrine, who have wanted to show off their cleverness in assigning the ends of things, have introduced—to prove this doctrine of theirs—a new way of arguing: by reducing things, not to the impossible, but to ignorance. This shows that no other way of defending their doctrine was open to them.

[35] For example, if a stone has fallen from a roof onto someone’s head and killed him, they will show, in the following way, that the stone fell in order to kill the man. For if it did not fall to that end, God [II/81] willing it, how could so many circumstances have concurred by chance (for often many circumstances do concur at once)? Perhaps you will answer that it happened because the wind was blowing hard and the man was walking that way. But they will persist: why was the wind [5] blowing hard at that time? why was the man walking that way at that same time? If you answer again that the wind arose then because on the preceding day, while the weather was still calm, the sea began to toss, and that the man had been invited by a friend, they will press on—for there is no end to the questions which can be asked: but why was the sea tossing? why was the man invited at just that time? And [10] so they will not stop asking for the causes of causes until you take refuge in the will of God, i.e., the sanctuary of ignorance.

Similarly, when they see the structure of the human body, they are struck by a foolish wonder, and because they do not know the causes of so great an art, they infer that it is constructed, not by mechanical, but by divine, or supernatural art, and constituted in such a way that [15] one part does not injure another.76

Hence it happens that one who seeks the true causes of miracles, and is eager, like an educated man, to understand natural things, not to wonder at them, like a fool, is generally considered and denounced as an impious heretic by those whom the people honor as interpreters [20] of nature and the Gods. For they know that if ignorance77 is taken away, then foolish wonder, the only means they have of arguing and defending their authority, is also taken away. But I leave these things,78 and pass on to what I have decided to treat here in the third place.

[25] [III.] After men persuaded themselves that everything that happens, happens on their account, they had to judge that what is most important in each thing is what is most useful to them, and to rate as most excellent all those things by which they were most pleased. Hence, they had to form these notions, by which they explained natural things: [30] good, evil, order, confusion, warm, cold, beauty, ugliness. And because they think themselves free, those notions have arisen: praise and blame, sin and merit. The latter I shall explain after I have treated human nature;79 but the former I shall briefly explain here.

Whatever conduces to health and the worship of God, they have [35] called good; but what is contrary to these, evil.

And because those who do not understand the nature of things, but only imagine them, affirm nothing concerning things, and take the [II/82] imagination for the intellect, they firmly believe, in their ignorance of things and of their own nature, that there is an order in things. For when things are so disposed that, when they are presented to us through the senses, we can easily imagine them, and so can easily remember [5] them, we say that they are well-ordered;80 but if the opposite is true, we say that they are badly ordered, or confused.

And since those things we can easily imagine are especially pleasing to us, men prefer order to confusion, as if order were anything in nature more than a relation to our imagination. They also say that [10] God has created all things in order, and so, unknowingly attribute imagination to God—unless, perhaps, they mean that God, to provide for human imagination, has disposed all things so that men can very easily imagine them. Nor will it, perhaps, give them pause that infinitely many things are found which far surpass our imagination, and [15] a great many which confuse it on account of its weakness. But enough of this.

The other notions are also nothing but modes of imagining, by which the imagination is variously affected; and yet the ignorant consider them the chief attributes of things, because, as we have already said, [20] they believe all things have been made for their sake, and call the nature of a thing good or evil, sound or rotten and corrupt, as they are affected by it. For example, if the motion the nerves receive from objects presented through the eyes is conducive to health, the objects by which it is caused are called beautiful; those which cause a contrary [25] motion are called ugly. Those which move the sense through the nose, they call pleasant-smelling or stinking; through the tongue, sweet or bitter, tasty or tasteless; through touch, hard or soft, rough or smooth, etc.; and finally, those which move the ears are said to produce noise, sound or harmony. Men have been so mad as to believe that God is [30] pleased by harmony. Indeed there are Philosophers who have persuaded themselves that the motions of the heavens produce a harmony.

All of these things show sufficiently that each one has judged things according to the disposition of his brain; or rather, has accepted affections of the imagination as things. So it is no wonder (to note this, [35] too, in passing) that we find so many controversies to have arisen among men, and that they have finally given rise to Skepticism. For although human bodies agree in many things, they still differ in very [II/83] many. And for that reason what seems good to one, seems bad to another; what seems ordered to one, seems confused to another; what seems pleasing to one, seems displeasing to another, and so on.

I pass over the [other notions] here, both because this is not the place to treat them at length, and because everyone has experienced [5] this [variability] sufficiently for himself. That is why we have such sayings as “So many heads, so many attitudes,” “everyone finds his own judgment more than enough,” and “there are as many differences of brains as of palates.” These proverbs show sufficiently that men judge things according to the disposition of their brain, and imagine, rather than understand them. For if men had understood them, the things would at least convince them all, even if they did not attract [10] them all, as the example of mathematics shows.

We see, therefore, that all the notions by which ordinary people are accustomed to explain nature are only modes of imagining, and do not indicate the nature of anything, only the constitution of the imagination. And because they have names, as if they were [notions] of beings [15] existing outside the imagination, I call them beings, not of reason, but of imagination. So all the arguments in which people try to use such notions against us can easily be warded off.

For many are accustomed to arguing in this way: if all things have followed from the necessity of God’s most perfect nature, why are [20] there so many imperfections in nature? why are things corrupt to the point where they stink? so ugly that they produce nausea? why is there confusion, evil, and sin?

As I have just said, those who argue in this way are easily answered. For the perfection of things is to be judged solely from their nature and power; things are not more or less perfect because they please or [25] offend men’s senses, or because they are of use to, or are incompatible with, human nature.

But to those who ask “why God did not create all men so that they would be governed by the command of reason?” I answer only “because he did not lack material to create all things, from the highest [30] degree of perfection to the lowest;” or, to speak more properly, “because the laws of his nature have been so ample that they sufficed for producing all things which can be conceived by an infinite intellect” (as I have demonstrated in P16).

These are the prejudices I undertook to note here. If any of this [35] kind still remain, they can be corrected by anyone with only a little meditation. [NS: And so I find no reason to devote more time to these matters, etc.]81

[II/84] Second Part of the Ethics On the Nature and Origin of the Mind

I pass now to explaining those things which must necessarily follow from the essence of God, or the infinite and eternal Being—not, indeed, all of them, for [10] we have demonstrated (IP 16) that infinitely many things must follow from it in infinitely many modes, but only those that can lead us, by the hand, as it were, to the knowledge of the human Mind and its highest blessedness.

DEFINITIONS

D1: By body I understand a mode that in a certain and determinate [15] way expresses God’s essence insofar as he is considered as an extended thing (see IP25C).

D2: I say that to the essence of any thing belongs that which, being given, the thing is [NS: also] necessarily posited and which, being taken away, the thing is necessarily [NS: also] taken away; or that without which the thing can neither be nor be conceived, and which [20] can neither be nor be conceived without the thing.1

D3: By idea I understand a concept of the Mind that the Mind forms because it is a thinking thing.

[25] Exp.: I say concept rather than perception, because the word perception [II/85] seems to indicate that the Mind is acted on by the object. But concept seems to express an action of the Mind.

D4: By adequate idea I understand an idea which, insofar as it is [5] considered in itself, without relation to an object, has all the properties, or intrinsic denominations of a true idea.

Exp.: I say intrinsic to exclude what is extrinsic, viz. the agreement of the idea with its object.

[10] D5: Duration is an indefinite continuation of existing.

Exp.: I say indefinite because it cannot be determined at all through the very nature of the existing thing, nor even by the efficient cause, which necessarily posits the existence of the thing, and does not take it away.

[15] D6: By reality and perfection I understand the same thing.

D7: By singular things I understand things that are finite and have a determinate existence. And if a number of Individuals2 so concur in one action that together they are all the cause of one effect, I consider [20] them all, to that extent, as one singular thing.

AXIOMS

A1: The essence of man does not involve necessary existence, i.e., from the order of nature it can happen equally that this or that man does exist, or that he does not exist.

[25] A2: Man thinks.3

A3: There are no modes of thinking, such as love, desire, or whatever [II/86] is designated by the word affects of the mind, unless there is in the same Individual4 the idea of the thing loved, desired, etc. But there can be an idea, even though there is no other mode of thinking.

[5] A4: We feel that a certain body5 is affected in many ways.

A5: We neither feel nor perceive any singular things [NS: or anything of natura naturata],6 except bodies and modes of thinking. See the postulates after P13.

[10] P1: Thought is an attribute of God, or God is a thinking thing.

Dem.: Singular thoughts, or this or that thought, are modes that express God’s nature in a certain and determinate way (by IP25C). [15] Therefore (by ID5) there belongs to God an attribute whose concept all singular thoughts involve, and through which they are also conceived. Therefore, Thought is one of God’s infinite attributes, which expresses an eternal and infinite essence of God (see ID6), or God is a thinking thing, q.e.d.

[20] Schol.: This Proposition is also evident from the fact that we can conceive an infinite thinking being. For the more things a thinking being can think, the more reality, or perfection, we conceive it to contain. Therefore, a being that can think infinitely many things in [25] infinitely many ways is necessarily infinite in its power of thinking. So since we can conceive an infinite Being by attending to thought alone, Thought (by ID4 and D6) is necessarily one of God’s infinite attributes, as we maintained.

[30] P2: Extension is an attribute of God, or God is an extended thing.

[II/87] Dem: The demonstration of this proceeds in the same way as that of the preceding Proposition.

[5] P3: In God there is necessarily an idea, both of his essence and of everything that necessarily follows from his essence.

Dem.: For God (by P1) can think infinitely many things in infinitely many modes, or (what is the same, by IP16) can form the idea of his [10] essence and of all the things which necessarily follow from it. But whatever is in God’s power necessarily exists (by IP35); therefore, there is necessarily such an idea, and (by IP15) it is only in God, q.e.d.

[15] Schol.: By God’s power ordinary people understand God’s free will and his right over all things which are, things which on that account are commonly considered to be contingent. For they say that God has the power of destroying all things and reducing them to nothing. Further, they very often compare God’s power with the power of Kings.7

[20] But we have refuted this in IP32C1 and C2, and we have shown in IP16 that God acts with the same necessity by which he understands himself, i.e., just as it follows from the necessity of the divine nature (as everyone maintains unanimously) that God understands himself, with the same necessity it also follows that God does infinitely many [25] things in infinitely many modes. And then we have shown in IP34 that God’s power is nothing except God’s active essence. And so it is as impossible for us to conceive that God does not act as it is to conceive that he does not exist.

Again, if it were agreeable to pursue these matters further, I could also show here that that power which ordinary people fictitiously ascribe [30] to God is not only human (which shows that ordinary people conceive God as a man, or as like a man), but also involves lack of power. But I do not wish to speak so often about the same topic. I [II/88] only ask the reader to reflect repeatedly on what is said concerning this matter in Part I, from P16 to the end. For no one will be able to perceive rightly the things I maintain unless he takes great care not to [5] confuse God’s power with the human power or right of Kings.

P4: God’s idea, from which infinitely many things follow in infinitely many modes, must be unique.

[10] Dem.: An infinite intellect comprehends nothing except God’s attributes and his affections (by IP30). But God is unique (by IP14C1). Therefore God’s idea, from which infinitely many things follow in infinitely many modes, must be unique, q.e.d.

[15] P5: The formal being of ideas admits God as a cause only insofar as he is considered as a thinking thing, and not insofar as he is explained by any other attribute. I.e., ideas, both of God’s attributes and of singular things, admit not the objects themselves, or the things perceived, as their efficient cause, but [20] God himself, insofar as he is a thinking thing.

Dem.: This is evident from P3. For there we inferred that God can form the idea of his essence, and of all the things that follow necessarily [25] from it, solely from the fact that God is a thinking thing, and not from the fact that he is the object of his own idea. So the formal being of ideas admits God as its cause insofar8 as he is a thinking thing.

But another way of demonstrating this is the following. The formal being of ideas is a mode of thinking (as is known through itself), i.e. (by IP25C), a mode that expresses, in a certain way, God’s nature [30] insofar as he is a thinking thing. And so (by IP10) it involves the concept of no other attribute of God, and consequently (by IA4) is the effect of no other attribute than thought. And so the formal being [II/89] of ideas admits God as its cause insofar as he is considered only as a thinking thing, etc., q.e.d.

P6: The modes of each attribute have God for their cause only insofar as he is [5] considered under the attribute of which they are modes, and not insofar as he is considered under any other attribute.

Dem.: For each attribute is conceived through itself without any other (by IP10). So the modes of each attribute involve the concept of [10] their own attribute, but not of another one; and so (by IA4) they have God for their cause only insofar as he is considered under the attribute of which they are modes, and not insofar as he is considered under any other, q.e.d.

[15] Cor.: From this it follows that the formal being of things which are not modes of thinking does not follow from the divine nature because [God] has first known the things; rather the objects of ideas follow and are inferred from their attributes9 in the same way and by the same necessity as that with which we have shown ideas to follow from the attribute of Thought.

[20] P7: The order and connection of ideas is the same as the order and connection of things.

Dem.: This is clear from IA4. For the idea of each thing caused [25] depends on the knowledge of the cause of which it is the effect.

Cor.: From this it follows that God’s [NS: actual] power of thinking is equal to his actual power of acting. I.e., whatever follows formally from God’s infinite nature follows objectively in God from his idea in [30] the same order and with the same connection.

[II/90] Schol.: Before we proceed further, we must recall here what we showed [NS: in the First Part], viz. that whatever can be perceived by an infinite intellect as constituting an10 essence of substance pertains [5] to one substance only, and consequently that the thinking substance and the extended substance are one and the same substance, which is now comprehended under this attribute, now under that. So also a mode of extension and the idea of that mode are one and the same thing, but expressed in two ways. Some of the Hebrews11 seem [10] to have seen this, as if through a cloud, when they maintained that God, God’s intellect, and the things understood by him are one and the same.

For example, a circle existing in nature and the idea of the existing circle, which is also in God, are one and the same thing, which is explained through different attributes. Therefore, whether we conceive [15] nature under the attribute of Extension, or under the attribute of Thought, or under any other attribute, we shall find one and the same order, or one and the same connection of causes, i.e., that the same things follow one another.12

When I said [NS: before] that God is the cause of the idea, say of a circle, only insofar as he is a thinking thing, and [the cause] of the [20] circle, only insofar as he is an extended thing, this was for no other reason than because the formal being of the idea of the circle can be perceived only through another mode of thinking, as its proximate cause, and that mode again through another, and so on, to infinity. Hence, so long as things are considered as modes of thinking, we must explain the order of the whole of nature, or the connection of causes, [25] through the attribute of Thought alone. And insofar as they are considered as modes of Extension, the order of the whole of nature must be explained through the attribute of Extension alone. I understand the same concerning the other attributes.

So of things as they are in themselves, God is really the cause insofar as he consists of infinite attributes. For the present, I cannot [30] explain these matters more clearly.13

P8: The ideas of singular things, or of modes, that do not exist must be comprehended in God’s infinite idea in the same way as the formal essences of the [35] singular things, or modes, are contained in God’s attributes.

[II/91] Dem.: This Proposition is evident from the preceding one, but is understood more clearly from the preceding scholium.

[5] Cor.: From this it follows that so long as singular things do not exist, except insofar as they are comprehended in God’s attributes, their objective being, or ideas, do not exist except insofar as God’s infinite idea exists. And when singular things are said to exist, not only insofar as they are comprehended in God’s attributes, but insofar [10] also as they are said to have duration, their ideas also involve the existence through which they are said to have duration.

Schol.: If anyone wishes me to explain this further by an example, I will, of course, not be able to give one which adequately explains what I speak of here, since it [15] is unique. Still I shall try as far as possible to illustrate the matter:14 the circle is of such a nature that the rectangles formed from the segments of all the straight lines intersecting in it are equal to one another.15 So in a circle there are contained infinitely many rectangles that are equal to one another. Nevertheless, [20] none of them can be said to exist except insofar as the circle exists, nor also can the idea of any of these rectangles be said to exist except insofar as it is comprehended in the idea of the circle. Now of these infinitely many [rectangles] let two only, viz. [those formed from the segments of lines]16 D and E, exist. Of course their ideas also exist [25] now, not only insofar as they are only comprehended in the idea of the circle, but also insofar as they involve the existence of those rectangles. By this they are distinguished from the other ideas of the other rectangles.

[30] P9: The idea of a singular thing which actually exists has God for a cause not [II/92] insofar as he is infinite,17 but insofar as he is considered to be affected by another idea of a singular thing which actually exists; and of this [idea] God is also the cause, insofar as he is affected by another third [NS: idea], and so on, to infinity.

Dem.: The idea of a singular thing which actually exists is a singular [5] mode of thinking, and distinct from the others (by P8C and S), and so (by P6) has God for a cause only insofar as he is a thinking thing. But not (by IP28) insofar as he is a thing thinking absolutely;18 rather insofar as he is considered to be affected by another [NS: determinate] mode of thinking.19 And God is also the cause of this mode, insofar [10] as he is affected by another [NS: determinate mode of thinking], and so on, to infinity. But the order and connection of ideas (by P7) is the same as the order and connection of causes.20 Therefore, the cause of one singular idea is another idea, or God, insofar as he is considered to be affected by another idea; and of this also [God is the cause], insofar as he is affected by another, and so on, to infinity, q.e.d.

[15] Cor.: Whatever happens in the singular object of any idea, there is knowledge of it in God, only insofar as he has the idea of the same object.

[20] Dem.: Whatever happens in the object of any idea, there is an idea of it in God (by P3), not insofar as he is infinite, but insofar as he is considered to be affected by another idea of [NS: an existing] singular thing (by P9); but the order and connection of ideas (by P7) is the same as the order and connection of things; therefore, knowledge of [25] what happens in a singular object will be in God only insofar as he has the idea of the same object, q.e.d.

P10: The being of substance does not pertain to the essence of man,21 or substance does not constitute the form of man.

[30] Dem.: For the being of substance involves necessary existence (by IP7). Therefore, if the being of substance pertained to the essence of man, then substance being given, man would necessarily be given (by [II/93] D2), and consequently man would exist necessarily, which (by A1) is absurd, q.e.d.

Schol.: This proposition is also demonstrated from IP5, viz. that [5] there are not two substances of the same nature. Since a number of men can exist,22 what constitutes the form of man is not the being of substance. Further, this proposition is evident from the other properties of substance, viz. that substance is, by its nature, infinite, immutable, [10] indivisible, etc., as anyone can easily see.

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

[15] Dem.: For the being of substance does not pertain to the essence of man (by P10). Therefore, it is something (by IP15) which is in God, and which can neither be nor be conceived without God, or (by IP25C) an affection, or mode, which expresses God’s nature in a certain and determinate way.

[20] Schol.: Everyone, of course, must concede that nothing can either be or be conceived without God. For all confess that God is the only cause of all things, both of their essence and of their existence.23 I.e., God is not only the cause of the coming to be of things, as they say, but also of their being.

[25] But in the meantime many say that anything without which a thing can neither be nor be conceived pertains to the nature of the thing.24 And so they believe either that the nature of God pertains to the essence of created things, or that created things can be or be conceived without God—or what is more certain, they are not sufficiently consistent.

[30] The cause of this, I believe, was that they did not observe the [proper] order of Philosophizing.25 For they believed that the divine nature, which they should have contemplated before all else (because it is prior both in knowledge and in nature) is last in the order of knowledge, and that the things that are called objects of the senses are prior [35] to all. That is why, when they contemplated natural things, they thought of nothing less than they did of the divine nature; and when afterwards [II/94] they directed their minds to contemplating the divine nature, they could think of nothing less than of their first fictions, on which they had built the knowledge of natural things, because these could not assist knowledge of the divine nature. So it is no wonder that they have generally contradicted themselves.

[5] But I pass over this. For my intent here was only to give a reason26 why I did not say that anything without which a thing can neither be nor be conceived pertains to its nature—viz. because singular things can neither be nor be conceived without God, and nevertheless, God [10] does not pertain to their essence. But I have said that what necessarily constitutes the essence of a thing is that which, if it is given, the thing is posited, and if it is taken away, the thing is taken away, i.e., the essence is what the thing can neither be nor be conceived without, and vice versa, what can neither be nor be conceived without the thing.

P11: The first thing that constitutes the actual being of a human Mind is [15] nothing but the idea of a singular thing which actually exists.

Dem.: The essence of man (by P10C) is constituted by certain modes of God’s attributes, viz. (by A2) by modes of thinking, of all of which (by A3) the idea is prior in nature, and when it is given, the other [20] modes (to which the idea is prior in nature) must be in the same individual (by A3).27 And therefore an idea is the first thing that constitutes the being of a human Mind. But not the idea of a thing which does not exist. For then (by P8C) the idea itself could not be said to exist. Therefore, it will be the idea of a thing which actually exists. [25] But not of an infinite thing. For an infinite thing (by IP21 and 22) must always exist necessarily. But (by A1) it is absurd [that this idea should be of a necessarily existing object]. Therefore, the first thing that constitutes the actual being of a human Mind is the idea of a singular thing which actually exists, q.e.d.

[30] Cor.: From this it follows that the human Mind is a part of the infinite intellect of God. Therefore, when we say that the human Mind perceives this or that, we are saying nothing but that God, not insofar as he is infinite, but insofar as he is explained through the nature of [II/95] the human Mind, or insofar as he constitutes the essence of the human Mind, has this or that idea; and when we say that God has this or that idea, not only insofar as he constitutes the nature of the human Mind, but insofar as he also has the idea of another thing together with the human Mind, then we say that the human Mind perceives [5] the thing only partially, or inadequately.

Schol.: Here, no doubt, my readers will come to a halt, and think of many things which will give them pause. For this reason I ask them [10] to continue on with me slowly, step by step, and to make no judgment on these matters until they have read through them all.

P12: Whatever happens in the object of the idea constituting the human Mind must be perceived by the human Mind, or there will necessarily be an idea of [15] that thing in the Mind; i.e., if the object of the idea constituting a human Mind is a body, nothing can happen in that body which is not perceived by the Mind.28

[20] Dem.: For whatever happens in the object of any idea, the knowledge of that thing is necessarily in God (by P9C), insofar as he is considered to be affected by the idea of the same object, i.e. (by P11), insofar as he constitutes the mind of some thing. Therefore, whatever happens in the object of the idea constituting the human Mind, the [25] knowledge of it is necessarily in God insofar as he constitutes the nature of the human Mind, i.e. (by P11C), knowledge of this thing will necessarily be in the Mind, or the Mind will perceive it, q.e.d.

[35] Schol.: This Proposition is also evident, and more clearly understood from P7S, which you should consult.

[II/96] P13: The object of the idea constituting the human Mind is the Body,29 or a certain mode of Extension which actually exists, and nothing else.

[5] Dem.: For if the object of the human Mind were not the Body, the ideas of the affections of the Body would not be in God (by P9C) insofar as he constituted our Mind, but insofar as he constituted the mind of another thing, i.e. (by P11C), the ideas of the affections of the Body would not be in our Mind; but (by A4) we have ideas of the [10] affections of the body. Therefore, the object of the idea that constitutes the human Mind is the Body, and it (by P11) actually exists.

Next, if the object of the Mind were something else also, in addition to the Body, then since (by IP36) nothing exists from which there does not follow some effect, there would necessarily (by P12) be an [15] idea in our Mind of some effect of it. But (by A5) there is no idea of it. Therefore, the object of our Mind is the existing Body and nothing else, q.e.d.

Cor.: From this it follows that man consists of a Mind and a Body, [20] and that the human Body exists, as we are aware of it.30

Schol.: From these [propositions] we understand not only that the human Mind is united to the Body, but also what should be understood by the union of Mind and Body. But no one will be able to [25] understand it adequately, or distinctly, unless he first knows adequately the nature of our Body. For the things we have shown so far are completely general and do not pertain more to man than to other Individuals, all of which, though in different degrees, are nevertheless animate.31 For of each thing there is necessarily an idea in God, of [30] which God is the cause in the same way as he is of the idea of the human Body. And so, whatever we have said of the idea of the human Body must also be said of the idea of any thing.

[II/97] However, we also cannot deny that ideas differ among themselves, as the objects themselves do, and that one is more excellent than the other, and contains more reality, just as the object of the one is more excellent than the object of the other and contains more reality. And so to determine what is the difference between the human Mind and [5] the others, and how it surpasses them, it is necessary for us, as we have said, to know the nature of its object, i.e., of the human Body. I cannot explain this here, nor is that necessary for the things I wish to demonstrate. Nevertheless, I say this in general, that in proportion as a Body is more capable than others of doing many things at once, or being acted on in many ways at once, so its Mind is more capable [10] than others of perceiving many things at once. And in proportion as the actions of a body depend more on itself alone, and as other bodies concur with it less in acting, so its mind is more capable of understanding distinctly. And from these [truths] we can know the excellence of one mind over the others, and also see the cause why we have [15] only a completely confused knowledge of our Body, and many other things which I shall deduce from them in the following [propositions]. For this reason I have thought it worthwhile to explain and demonstrate these things more accurately. To do this it is necessary to premise a few things concerning the nature of bodies.

[20] A1′:32 All bodies either move or are at rest.

A2′: Each body moves now more slowly, now more quickly.

[25] L1: Bodies are distinguished from one another by reason of motion and rest, speed and slowness, and not by reason of substance.

Dem.: I suppose that the first part of this is known through itself. But that bodies are not distinguished by reason of substance is evident [30] both from IP5 and from IP8. But it is more clearly evident from those things which are said in IP15S.

[II/98] L2: All bodies agree in certain things.

Dem.: For all bodies agree in that they involve the concept of one [5] and the same attribute (by D1), and in that they can move now more slowly, now more quickly, and absolutely, that now they move, now they are at rest.

L3: A body which moves or is at rest must be determined to motion or rest by [10] another body, which has also been determined to motion or rest by another, and that again by another, and so on, to infinity.

Dem.: Bodies (by D1) are singular things which (by LI) are distinguished [15] from one another by reason of motion and rest; and so (by IP28), each must be determined necessarily to motion or rest by another singular thing, viz. (by P6) by another body, which (by A1′) either moves or is at rest. But this body also (by the same reasoning) [20] could not move or be at rest if it had not been determined by another to motion or rest, and this again (by the same reasoning) by another, and so on, to infinity, q.e.d.

Cor.: From this it follows that a body in motion moves until it is [25] determined by another body to rest; and that a body at rest also remains at rest until it is determined to motion by another.

This is also known through itself. For when I suppose that body A, say, is at rest, and do not attend to any other body in motion, I can say nothing about body A except that it is at rest. If afterwards it [30] happens that body A moves, that of course could not have come about from the fact that it was at rest. For from that nothing else could follow but that body A would be at rest.33

[II/99] If, on the other hand, A is supposed to move, then as often as we attend only to A, we shall be able to affirm nothing concerning it except that it moves. If afterwards it happens that A is at rest, that of course also could not have come about from the motion it had. For from the motion nothing else could follow but that A would move. [5] Therefore, it happens by a thing which was not in A, viz. by an external cause, by which [NS: the Body in motion, A] has been determined to rest.

A1″:34 All modes by which a body is affected by another body follow [10] both from the nature of the body affected and at the same time from the nature of the affecting body, so that one and the same body may be moved differently according to differences in the nature of the bodies moving it. And conversely, different bodies may be moved differently by one and the same body.

[15] A2″: When a body in motion strikes against another which is at rest and cannot give way, then it is reflected, so that it continues to move, and the angle of the line of the reflected motion with the surface of the body at rest [20] which it struck against will be equal to the angle which the line of the incident motion makes with the same surface.35

This will be sufficient concerning the simplest bodies, which are distinguished from one another only by motion and rest, speed and [25] slowness. Now let us move up to composite bodies.

Definition: When a number of bodies, whether of the same or of different size, are so constrained by other bodies that they lie upon one another, or if they so [II/100] move, whether with the same degree or different degrees of speed, that they communicate their motions to each other in a certain fixed manner, we shall say that those bodies are united with one another and that they all together compose one body or Individual, which is distinguished from the others by this [5] union of bodies.

A3″: As the parts of an Individual, or composite body, lie upon one another over a larger or smaller surface, so they can be forced to change [10] their position with more or less difficulty; and consequently the more or less will be the difficulty of bringing it about that the Individual changes its shape. And therefore the bodies whose parts lie upon one another over a large surface, I shall call hard; those whose parts lie upon one another over a small surface, I shall call soft; and finally those [15] whose parts are in motion, I shall call fluid.

L4: If, of a body, or of an Individual, which is composed of a number of bodies, some are removed, and at the same time as many others of the same nature take their place, the [NS: body, or the] Individual will retain its [20] nature, as before, without any change of its form.

Dem.: For (by LI) bodies are not distinguished in respect to substance; what constitutes the form of the Individual consists [NS: only] in the union of the bodies (by the preceding definition). But this [NS: [25] union] (by hypothesis) is retained even if a continual change of bodies occurs. Therefore, the Individual will retain its nature, as before, both in respect to substance, and in respect to mode, q.e.d.

[30] L5: If the parts composing an Individual become greater or less, but in such a [II/101] proportion that they all keep the same ratio of motion and rest to each other as before, then the Individual will likewise retain its nature, as before, without any change of form.

[5] Dem.: The demonstration of this is the same as that of the preceding Lemma.

L6: If certain bodies composing an Individual are compelled to alter the [10] motion they have from one direction to another, but so that they can continue their motions and communicate them to each other in the same ratio as before, the Individual will likewise retain its nature, without any change of form.

Dem.: This is evident through itself. For it is supposed that it retains [15] everything which, in its definition, we said constitutes its form. [NS: See the Definition before L4.]36

L7: Furthermore, the Individual so composed retains its nature, whether it, [20] as a whole, moves or is at rest, or whether it moves in this or that direction, so long as each part retains its motion, and communicates it, as before, to the others.

Dem.: This [NS: also] is evident from the definition preceding L4.

[25] Schol.: By this, then, we see how a composite Individual can be affected in many ways, and still preserve its nature. So far we have conceived an Individual which is composed only of bodies which are distinguished from one another only by motion and rest, speed and [30] slowness, i.e., which is composed of the simplest bodies.37 But if we [II/102] should now conceive of another, composed of a number of Individuals of a different nature, we shall find that it can be affected in a great many other ways, and still preserve its nature. For since each part of [5] it is composed of a number of bodies, each part will therefore (by L7) be able, without any change of its nature, to move now more slowly, now more quickly, and consequently communicate its motion more quickly or more slowly to the others.

But if we should further conceive a third kind of Individual, composed [10] [NS: of many individuals] of this second kind, we shall find that it can be affected in many other ways, without any change of its form. And if we proceed in this way to infinity, we shall easily conceive that the whole of nature is one Individual, whose parts, i.e., all bodies, vary in infinite ways, without any change of the whole Individual.38

If it had been my intention to deal expressly with body,39 I ought [15] to have explained and demonstrated these things more fully. But I have already said that I intended something else, and brought these things forward only because I can easily deduce from them the things I have decided to demonstrate.

POSTULATES

[20] I. The human Body is composed of a great many individuals of different natures, each of which is highly composite.

II. Some of the individuals of which the human Body is composed [25] are fluid, some soft, and others, finally are hard.

III. The individuals composing the human Body, and consequently, the human Body itself, are affected by external bodies in very many ways.

IV. The human Body, to be preserved, requires a great many other [30] bodies, by which it is, as it were, continually regenerated.

V. When a fluid part of the human Body is determined by an external [II/103] body so that it frequently thrusts against a soft part [of the Body], it changes its surface and, as it were, impresses on [the soft part] certain traces of the external body striking against [the fluid part].

VI. The human Body can move and dispose external bodies in a [5] great many ways.

P14: The human Mind is capable of perceiving a great many things, and is the more capable, the more its body can be disposed in a great many ways.

[10] Dem.: For the human Body (by Post. 3 and 6) is affected in a great many ways by external bodies, and is disposed to affect external bodies in a great many ways. But the human Mind must perceive everything which happens in the human body (by P12). Therefore, the human Mind is capable of perceiving a great many things, and is the [15] more capable [, NS: as the human Body is more capable],40 q.e.d.

P15: The idea that constitutes the formal being [esse] of the human Mind is not simple, but composed of a great many ideas.

[20] Dem.: The idea that constitutes the formal being of the human Mind is the idea of a body (by P13), which (by Post. 1) is composed of a great many highly composite Individuals. But of each Individual composing the body, there is necessarily (by P8C)41 an idea in God. [25] Therefore (by P7), the idea of the human Body is composed of these many ideas of the parts composing the Body, q.e.d.

P16: The idea of any mode in which the human Body is affected by external bodies must involve the nature of the human Body and at the same time the [30] nature of the external body.

[II/104] Dem.: For all the modes in which a body is affected follow from the nature of the affected body, and at the same time from the nature [5] of the affecting body (by A1″ [II/99]). So the idea of them (by IA4) will necessarily involve the nature of each body. And so the idea of each mode in which the human Body is affected by an external body involves the nature of the human Body and of the external body, q.e.d.

[10] Cor. 1: From this it follows, first, that the human Mind perceives the nature of a great many bodies together with the nature of its own body.

Cor. 2: It follows, second, that the ideas which we have of external [15] bodies indicate the condition of our own body more than42 the nature of the external bodies. I have explained this by many examples in the Appendix of Part I.

P17: If the human Body is affected with a mode that involves the nature of [20] an external body, the human Mind will regard the same external body as actually existing, or as present to it, until the Body is affected by an affect43 that excludes the existence or presence of that body.

Dem.: This is evident. For so long as the human Body is so affected, [25] the human Mind (by P12) will regard this affection of the body, i.e. (by P16), it will have the idea of a mode that actually exists, an idea that involves the nature of the external body, i.e., an idea that does not exclude, but posits, the existence or presence of the nature of the external body. And so the Mind (by P16C1) will regard the [30] external body as actually existing, or as present, until it is affected, etc., q.e.d.