Before coming to the Propositions and their Demonstrations, I have thought it helpful to give a concise account as to why Descartes doubted everything, the way in which he laid the solid foundations of the sciences, and finally the means by which he freed himself from all doubts. I should indeed have arranged all this in mathematical order had I not considered that the prolixity involved in this form of presentation would be an obstacle to the proper understanding of all those things that ought to be beheld at a single glance, as in the case of a picture.
Descartes, then, so as to proceed with the greatest caution in his enquiry, attempted:
1. to put aside all prejudice,
2. to discover the foundations on which everything should be built,
3. to uncover the cause of error,
4. to understand everything clearly and distinctly.
To achieve his first, second, and third aims, he proceeded to call everything into doubt, not indeed like a Skeptic whose sole aim is to doubt, but to free his mind from all prejudice so that he might finally discover the firm and unshakable foundations of the sciences, which, if they existed, could thus not escape him. For the true principles of the sciences ought to be so clear and certain that they need no proof, are placed beyond all hazard of doubt, and without them nothing can be demonstrated. These principles, after a lengthy period of doubting, he discovered. Now when he had found them, it was not difficult for him to distinguish true from false, to uncover the cause of error, and so to take precautions against assuming as true and certain what was false and doubtful.
To achieve his fourth and final aim, that of understanding everything clearly and distinctly, his chief rule was to enumerate the simple ideas out of which all others are compounded and to scrutinize each one separately. For when he could perceive simple ideas clearly and distinctly, he would doubtless understand with the same clarity and distinctness all the other ideas compounded from those simple ideas. Having thus outlined my program, I shall briefly explain in what manner he called everything into doubt, discovered the true principles of the sciences, and extricated himself from the difficulties of doubt.
First, then, he reviewed all those things he had gathered from his senses—the sky, the earth, and the like, and even his own body—all of which he had hitherto regarded as belonging to reality. And he doubted their certainty because he had found that the senses occasionally deceived him, and in dreams he had often been convinced that many things truly existed externally to himself, discovering afterward that he had been deluded. And finally there was the fact that he had heard others, even when awake, declare that they felt pain in limbs they had lost long before.9 Therefore he was able to doubt, not without reason, even the existence of his own body. From all these considerations he could truly conclude that the senses are not a very strong foundation on which to build all science, for they can be called into doubt; certainty depends on other principles of which we can be more sure. Continuing his enquiry, in the second place he turned to the consideration of all universals, such as corporeal nature in general, its extension, likewise its figure, quantity, etc., and also all mathematical truths. Although these seemed to him more certain than any of the things he had gathered from his senses, yet he discovered a reason for doubting them.10 For others had erred even concerning these. And there was a particularly strong reason, an ancient belief, fixed in his mind, that there was an all-powerful God who had created him as he was, and so may have caused him to be deceived even regarding those things that seemed very clear to him.11 This, then, is the manner in which he called everything into doubt.
Now in order to discover the true principles of the sciences, he proceeded to enquire whether he had called into doubt everything that could come within the scope of his thought; thus he might find out whether there was not perchance still something left that he had not yet doubted. For if in the course of thus doubting he should find something that could not be called into doubt either for any of the previous reasons or for any other reason, he quite rightly considered that this must be established as a foundation on which he could build all his knowledge.12 And although he had already, as it seemed, doubted everything—for he had doubted not only what he had gathered from his senses but also what he had perceived by intellect alone—yet there was still something left to be examined, namely, himself who was doing the doubting, not insofar as he consisted of head, hands, and other bodily parts (since he had doubted these) but only insofar as he was doubting, thinking, etc. Examining this carefully, he realized that he could not doubt it for any of the foregoing reasons. For whether he is dreaming or awake as he thinks, nevertheless he thinks, and is.13 And although others, or even he himself, had erred with regard to other matters; nevertheless, because they were erring, they were. He could imagine no author of his being so cunning as to deceive him on that score; for it must be granted that he himself exists as long as it is supposed that he is being deceived. In short, whatever other reason for doubting be devised, there could be adduced none of such a kind as not at the same time to make him most certain of his existence. Indeed, the more reasons are adduced for doubting, the more arguments are simultaneously adduced to convince him of his own existence. So, in whatever direction he turns in order to doubt, he is nevertheless compelled to utter these words: “I doubt, I think, therefore I am.”14
Thus, in laying bare this truth, at the same time he also discovered the foundation of all the sciences, and also the measure and rule for all other truths—that whatever is perceived as clearly and distinctly as this, is true.15
It is abundantly clear from the preceding that there can be no other foundation for the sciences than this; everything else can quite easily be called into doubt, but this can by no means be doubted. However, with regard to this foundation, it should be particularly noted that the statement, “I doubt, I think, therefore I am,” is not a syllogism with the major premise omitted. If it were a syllogism, the premises should be clearer and better known than the conclusion ‘Therefore I am’, and so ‘I am’ would not be the prime basis of all knowledge. Furthermore, it would not be a certain conclusion, for its truth would depend on universal premises which the Author had already called into doubt. So ‘I think, therefore I am’ is a single independent proposition, equivalent to the following—‘I am, while thinking’.
To avoid confusion in what follows (for this is a matter that must be perceived clearly and distinctly), we must next know what we are. For when this has been clearly and distinctly understood, we shall not confuse our essence with others. In order to deduce this from what has gone before, our Author proceeds as follows.
He recalls to mind all thoughts that he once had about himself, that his soul is something tenuous like the wind or fire or the ether, infused among the denser parts of his body; that his body is better known to him than his soul; and that he perceives the former more clearly and distinctly.16 And he realizes that all this is clearly inconsistent with what he has so far understood. For he was able to doubt his body, but not his own essence insofar as he was thinking. Furthermore, he perceived these things neither clearly nor distinctly, and so, in accordance with the requirements of his method, he ought to reject them as false. Therefore, understanding that such things could not pertain to him insofar as he was as yet known to himself, he went on to ask what was that, pertaining peculiarly to his essence, which he had not been able to call into doubt and which had compelled him to conclude his own existence. Of this kind there were—that he wanted to take precautions against being deceived, that he desired to understand many things, that he doubted everything that he could not understand, that up to this point he affirmed one thing only and everything else he denied and rejected as false, that he imagined many things even against his will, and, finally, that he was conscious of many things as proceeding from his senses. Because he could infer his existence with equal certainty from each of these points and could list none of them as belonging to the things that he had called into doubt, and finally, because all these things can be conceived under the same attribute, it follows that all these things are true and pertain to his nature. And so whenever he said, “I think,” all the following modes of thinking were understood—doubting, understanding, affirming, denying, willing, non-willing, imagining, and sensing.17
Here it is important to note the following points, which will prove to be very useful later on when the distinction between mind and body is discussed. First, these modes of thinking are clearly and distinctly understood independently of other matters that are still in doubt. Second, the clear and distinct conception we have of them would be rendered obscure and confused if we were to intermingle with them any of the matters of which we are still in doubt.
Finally, to achieve certainty about what he had called into doubt and to remove all doubt, he proceeds to enquire into the nature of the most perfect Being, and whether such exists. For when he realizes that there exists a most perfect Being by whose power all things are produced and preserved and to whose nature it is contrary that he should be a deceiver, then this will remove the reason for doubting that resulted from his not knowing the cause of himself. For he will know that the faculty of distinguishing true from false was not given to him by a supremely good and truthful God in order that he might be deceived. And so mathematical truths, or all things that seem to him most evident, cannot be in the least suspect.18 Then, to remove the other causes for doubting, he goes on to enquire how it comes about that we sometimes err. When he discovered that this arises from our using our free will to assent even to what we have perceived only confusedly, he was immediately able to conclude that he can guard against error in the future provided that he gives assent only to what he clearly and distinctly perceives. This is something that each individual can easily obtain of himself because he has the power to control the will and thereby bring it about that it is restrained within the limits of the intellect.19 But since in our earliest days we have been imbued with many prejudices from which we are not easily freed, in order that we may be freed from them and accept nothing but what we clearly and distinctly perceive, he goes on to enumerate all the simple notions and ideas from which all our thoughts are compounded and to examine them one by one, so that he can observe in each of them what is clear and what is obscure. For thus he will easily be able to distinguish the clear from the obscure and to form clear and distinct thoughts. So he will easily discover the real distinction between soul and body, and what is clear and what is obscure in the deliverance of our senses, and lastly wherein dreaming differs from waking.20 Thereafter he could no longer doubt that he was awake nor could he be deceived by his senses. Thus he freed himself from all doubts listed previously.
However, before I here make an end, I think I ought to satisfy those who argue as follows: “Because the existence of God is not self-evident to us, it seems that we can never be certain of anything, nor can it ever be known to us that God exists. For from premises that are uncertain (and we have said that, as long as we do not know our own origin), nothing certain can be concluded.”
To remove this difficulty, Descartes replies in the following manner. From the fact that we do not as yet know whether the author of our origin may have created us such as to be deceived even in those matters that appear to us most certain, it by no means follows that we can doubt those things that we understand clearly and distinctly through themselves or through a process of reasoning, that is, as long as we are paying attention to it. We can doubt only those things previously demonstrated to be true, which we may remember when we are no longer attending to the reasoning from which we deduced them, and which we have thus forgotten. Therefore, although the existence of God can be known not through itself but only through something else, we can nevertheless attain certain knowledge of God’s existence provided that we carefully attend to all the premises from which we conclude it. See Principia Part 1 Article 13, and “Reply to Second Objections,” No. 3, and at the end of the “Fifth Meditation.”
However, because some do not find this reply satisfactory, I shall give another. When we were speaking previously of the certainty and sureness of our existence, we saw that we concluded it from the fact that, in whatever direction we turned the mind’s eye, we did not find any reason for doubting that did not by that very fact convince us of our existence. This was so whether we were considering our own nature, whether we were imagining the author of our nature to be a cunning deceiver—in short, whatever reason for doubting we invoked, external to ourselves. Hitherto we had not found this to be so in the case of any other matter. For example, while attending to the nature of a triangle, although we are compelled to conclude that its three angles are equal to two right angles, we cannot reach this same conclusion if we suppose that we may be deceived by the author of our nature. Yet this very supposition assured us of our existence with the utmost certainty. So it is not the case that, wherever we turn the mind’s eye, we are compelled to conclude that the three angles of a triangle are equal to two right angles; on the contrary, we find a reason for doubting it in that we do not possess an idea of God such as to render it impossible for us to think that God is a deceiver. For one who does not possess the true idea of God—which at the moment we suppose we do not possess—may quite as easily think that his author is a deceiver as think that he is not a deceiver, just as one who does not have the idea of a triangle may indifferently think its angles are equal or not equal to two right angles.
Therefore we concede that, except for our existence, we cannot be absolutely certain of anything, however earnestly we attend to its demonstration, as long as we do not have the clear and distinct conception of God that makes us affirm that God is supremely truthful, just as the idea we have of a triangle makes us conclude that its three angles are equal to two right angles. But we deny that, for this reason, we cannot attain knowledge of anything. For, as is evident from all that has already been said, the whole matter hinges on this alone, that we are able to form such a conception of God as so disposes us that it is not as easy for us to think that God is a deceiver as to think that he is not a deceiver, a conception that compels us to affirm that he is supremely truthful. When we have formed such an idea, the reason for doubting mathematical truths will be removed. For in whatever direction we now turn the mind’s eye with the purpose of doubting one of these truths, we shall not find anything that itself does not make us conclude that this truth is most certain, just as was the case with regard to our existence.
For example, if after discovering the idea of God we attend to the nature of a triangle, its idea will compel us to affirm that its three angles are equal to two right angles, whereas if we attend to the idea of God, this too will compel us to affirm that he is supremely truthful, the author and continuous preserver of our nature, and therefore that he is not deceiving us with regard to this truth. And attending to the idea of God (which we now suppose we have discovered), it will be just as impossible for us to think that he is a deceiver as to think, when attending to the idea of a triangle, that its three angles are not equal to two right angles. And just as we can form such an idea of a triangle in spite of not knowing whether the author of our nature is deceiving us, so too we can achieve a clear idea of God and set it before us even though also doubting whether the author of our nature is deceiving us in all things. And provided we possess this idea, in whatever way we may have acquired it, it will be enough to remove all doubts, as has just now been shown.
So having made these points, I reply as follows to the difficulty that has been raised. It is not as long as we do not know of God’s existence (for I have not spoken of that) but as long as we do not have a clear and distinct idea of God, that we cannot be certain of anything. Therefore, if anyone wishes to argue against me, his argument will have to be as follows: “We cannot be certain of anything until we have a clear and distinct idea of God. But we cannot have a clear and distinct idea of God as long as we do not know whether the author of our nature is deceiving us. Therefore, we cannot be certain of anything as long as we do not know whether the author of our nature is deceiving us, etc.” To this I reply by conceding the major premise and denying the minor. For we do have a clear and distinct idea of a triangle, although we do not know whether the author of our nature is deceiving us; and granted that we have such an idea of God, as I have just shown at some length, we cannot doubt his existence or any mathematical truth.
With this as preface, I now enter upon the work itself.
1. Under the word Thought, I include all that is in us and of which we are immediately conscious. Thus all operations of the will, intellect, imagination, and senses are thoughts. But I have added ‘immediately’ so as to exclude those things that are their consequences. For example, voluntary motion has thought for its starting point, but in itself it is still not thought.
2. By the word Idea, I understand the specific form (forma) of a thought, through the immediate perception of which I am conscious of that same thought.
So whenever I express something in words while understanding what I am saying, this very fact makes it certain that there is in me the idea of that which is meant by those words. And so I do not apply the term ‘ideas’ simply to images depicted in the fantasy; indeed I do not here term these ‘ideas’ at all, insofar as they are depicted in the corporeal fantasy (i.e., in some part of the brain) but only insofar as they communicate their form to the mind itself when this is directed toward that part of the brain.
3. By the objective reality of an idea, I understand the being of that which is presented through the idea, insofar as it is in the idea.21
In the same way one can speak of ‘objective perfection’ or ‘objective art’, etc. For whatever we perceive as being in the objects of ideas is objectively in the ideas themselves.
4. When things are, in themselves, such as we perceive them to be, they are said to be formally in the objects of ideas, and eminently when they are not just such in themselves as we perceive them to be but are more than sufficient to account fully for our perception.
Note that when I say that the cause contains eminently the perfections of its effect, I mean that the cause contains the perfections of the effect with a higher degree of excellence than does the effect itself. See also Axiom 8.
5. Everything in which there is something that we perceive as immediately inhering in a subject, or through which there exists something that we perceive (i.e., some property, quality or attribute whose real idea is in us), is called substance. For of substance itself, taken precisely, we have no other idea than that it is a thing in which there exists formally or eminently that something which we perceive (i.e., that something which is objectively in one of our ideas).
6. Substance in which thought immediately inheres is called Mind (Mens).
I here speak of ‘Mind’ rather than ‘Soul’ (anima) because the word ‘soul’ is equivocal, and is often used to mean a corporeal thing.
7. Substance that is the immediate subject of extension and of accidents that presuppose extension, such as figure, position, and local motion, is called Body.
Whether what is called Mind and what is called Body is one and the same substance, or two different substances, is something to be enquired into later.
8. Substance that we understand through itself to be supremely perfect, and in which we conceive nothing at all that involves any defect or limitation of perfection, is called God.
9. When we say that something is contained in the nature or conception of some thing, that is the same as saying that it is true of that thing or can be truly affirmed of it.22
10. Two substances are said to be distinct in reality when each one can exist without the other.
We have here omitted the Postulates of Descartes because in what follows we do not draw any conclusions from them. But we earnestly ask readers to read them through and to think them over carefully.23
1. We arrive at the knowledge and certainty of some unknown thing only through the knowledge and certainty of another thing that is prior to it in certainty and knowledge.
2. There are reasons that make us doubt the existence of our bodies.
This has in fact been shown in the Prolegomenon, and so is here posited as an axiom.
3. If we have anything besides mind and body, this is less known to us than mind and body.
It should be noted that these axioms do not affirm anything about things external to us, but only such things as we find within ourselves insofar as we are thinking things.
PROPOSITION 1
We cannot be absolutely certain of anything as long as we do not know that we exist.
Proof This proposition is self-evident; for he who absolutely does not know that he is likewise does not know that he is a being affirming or denying, that is, that he certainly affirms or denies.
Here it should be noted that although we may affirm or deny many things with great certainty while not attending to the fact that we exist, unless this is presupposed as indubitable, everything could be called into doubt.
PROPOSITION 2
‘I am’ must be self-evident.
Proof If this be denied, it will therefore be known only through something else, the knowledge and certainty of which will be prior in us to the statement ‘I am’ (Ax. 1). But this is absurd (Prop. 1). Therefore it must be self-evident. Q.E.D.
Proof There are certain things that make us doubt the existence of our body (Ax. 2). Therefore (Ax. 1) we shall not attain certainty of this except through the knowledge and certainty of something else that is prior to it in knowledge and certainty. Therefore the statement ‘I am’, insofar as ‘I’ am a thing consisting of body, is not a first principle and is not known through itself. Q.E.D.
PROPOSITION 4
‘I am’ cannot be the first known principle except insofar as we think.
Proof The statement ‘I am a corporeal thing, or a thing consisting of body’ is not a first-known principle (Prop. 3), nor again am I certain of my existence insofar as I consist of anything other than mind and body. For if we consist of anything different from mind and body, this is less well known to us than body (Ax. 3). Therefore ‘I am’ cannot be the first known thing except insofar as we think. Q.E.D.
Corollary From this it is obvious that mind, or a thinking thing, is better known than body.
But for a fuller explanation read Part 1 of the Principia Arts. 11 and 12.
Scholium Everyone perceives with the utmost certainty that he affirms, denies, doubts, understands, imagines, etc., or that he exists as doubting, understanding, affirming, etc.—in short, as thinking. Nor can this be called into doubt. Therefore the statement ‘I think’ or ‘I am, as thinking’ is the unique (Prop. 1) and most certain basis of all philosophy. Now in order to achieve the greatest certainty in the sciences, our aim and purpose can be no other than this, to deduce everything from the strongest first principles and to make the inferences as clear and distinct as the first principles from which they are deduced. It therefore clearly follows that we must consider as most certainly true everything that is equally evident to us and that we perceive with the same clearness and distinctness as the already discovered first principle, and also everything that so agrees with this first principle and so depends on it that we cannot doubt it without also having to doubt this first principle.
But to proceed with the utmost caution in reviewing these matters, at the first stage I shall admit as equally evident and equally clearly and distinctly perceived by us only those things that each of us observes in himself insofar as he is engaged in thinking. Such are, for example, that he wills this or that, that he has definite ideas of such-and-such a kind, and that one idea contains in itself more reality and perfection than another—namely, that the one that contains objectively the being and perfection of substance is far more perfect than one that contains only the objective perfection of some accident, and, finally, that the idea of a supremely perfect being is the most perfect of all. These things, I say, we perceive not merely with equal sureness and clarity but perhaps even more distinctly; for they affirm not only that we think but also how we think.
Further, we shall also say that those things that cannot be doubted without at the same time casting doubt on this unshakable foundation of ours are also in agreement with this first principle. For example, if anyone should doubt whether something can come from nothing, he will be able at the same time to doubt whether we, as long as we are thinking, are. For if I can affirm something of nothing—in effect, that nothing can be the cause of something—I can at the same time and with the same right affirm thought of nothing, and say that I, as long as I am thinking, am nothing. Because I find this impossible, it will also be impossible for me to think that something may come from nothing.
With these considerations in mind, I have decided at this point to list here in order those things that at present seem to us necessary for future progress, and to add to the number of axioms. For these are indeed set forth by Descartes as axioms at the end of his “Reply to the Second Set of Objections,” and I do not aim at greater accuracy than he. However, not to depart from the order we have been pursuing, I shall try to make them somewhat clearer, and to show how one depends on another and all on this one first principle, ‘I am, while thinking’, or how their certainty and reasonableness is of the same degree as that of the first principle.
4. There are different degrees of reality or being; for substance has more reality than accident or mode, and infinite substance, more than finite substance. Therefore there is more objective reality in the idea of substance than in the idea of accident, and in the idea of infinite substance than in the idea of finite substance.25
This axiom is known simply from contemplating our ideas, of whose existence we are certain because they are modes of thinking. For we know how much reality or perfection the idea of substance affirms of substance, and how much the idea of mode affirms of mode. This being so, we also necessarily realize that the idea of substance contains more objective reality than the idea of some accident, etc. See Scholium Prop. 4.
5. A thinking thing, if it knows of any perfections that it lacks, will immediately give these to itself, if they are within its power.26
This everyone observes in himself insofar as he is a thinking thing. Therefore (Scholium Prop. 4) we are most certain of it. And for the same reason, we are just as certain of the following:
6. In the idea or concept of every thing, there is contained either possible or necessary existence. (See Axiom 10, Descartes.)
Necessary existence is contained in the concept of God, or a supremely perfect being; for otherwise he would be conceived as imperfect, which is contrary to what is supposed to be conceived. Contingent or possible existence is contained in the concept of a limited thing.
7. No thing, nor any perfection of a thing actually existing, can have nothing, or a nonexisting thing, as the cause of its existence.
I have demonstrated in the Scholium Prop. 4 that this axiom is as clear to us as is ‘I am, when thinking’.
8. Whatever there is of reality or perfection in any thing exists formally or eminently in its first and adequate cause.27
By ‘eminently’ I understand: when the cause contains all the reality of the effect more perfectly than the effect itself. By ‘formally’: when the cause contains all the reality of the effect equally perfectly.
This axiom depends on the preceding one. For if it were supposed that there is nothing in the cause, or less in the cause than in the effect, then nothing in the cause would be the cause of the effect. But this is absurd (Ax. 7). Therefore it is not the case that anything whatsoever can be the cause of a certain effect; it must be precisely a thing in which there is eminently or at least formally all the perfection that is in the effect.
9. The objective reality of our ideas requires a cause in which that same reality is contained not only objectively but also formally or eminently.28
This axiom, although misused by many, is universally admitted, for when somebody conceives something new, everyone wants to know the cause of this concept or idea. Now when they can assign a cause in which is contained formally or eminently as much reality as is contained objectively in that concept, they are satisfied. This is made quite clear by the example of a machine, which Descartes adduces in Art. 17 Part 1 Principia.29 Similarly, if anyone were to ask whence it is that a man has the ideas of his thought and of his body, no one can fail to see that he has them from himself, as containing formally everything that his ideas contain objectively. Therefore if a man were to have some idea that contained more of objective reality than he himself contained of formal reality, then of necessity we should be driven by the natural light to seek another cause outside the man himself, a cause that contained all that perfection formally or eminently. And apart from that cause no one has ever assigned any other cause that he has conceived so clearly and distinctly.
Furthermore, as for the truth of this axiom, it depends on the previous ones. By Axiom 4 there are different degrees of reality or being in ideas. Therefore (Ax. 8) they need a more perfect cause in accordance with their degree of perfection. But because the degrees of reality that we observe in ideas are not in the ideas insofar as they are considered as modes of thinking but insofar as one presents substance and another merely a mode of substance—or, in brief, insofar as they are considered as images of things—hence it clearly follows that there can be granted no other first cause of ideas than that which, as we have just shown, all men understand clearly and distinctly by the natural light, namely, one in which is contained formally or eminently the same reality that the ideas have objectively.30
To make this conclusion more clearly understood, I shall illustrate it with one or two examples. If anyone sees some books (imagine one to be that of a distinguished philosopher and the other to be that of some trifler) written in one and the same hand, and if he pays no attention to the meaning of the words (i.e., insofar as they are symbols) but only to the shape of the writing and the order of the letters, he will find no distinction between them such as to compel him to seek different causes for them. They will appear to him to have proceeded from the same cause and in the same manner. But if he pays attention to the meaning of the words and of the language, he will find a considerable distinction between them. He will therefore conclude that the first cause of the one book was very different from the first cause of the other, and that the one cause was in fact more perfect than the other to the extent that the meaning of the language of the two books, or their words considered as symbols, are found to differ from one another.
I am speaking of the first cause of books, and there must necessarily be one although I admit—indeed, I take for granted—that one book can be transcribed from another, as is self-evident.
The same point can also be clearly illustrated by the example of a portrait, let us say, of some prince. If we pay attention only to the materials of which it is made, we shall not find any distinction between it and other portraits such as to compel us to look for different causes. Indeed, there will be nothing to prevent us from thinking that it was copied from another likeness, and that one again from another, and so ad infinitum. For we shall be quite satisfied that there need be no other cause for its production. But if we attend to the image insofar as it is the image of something, we shall immediately be compelled to seek a first cause such as formally or eminently contains what that image contains representatively. I do not see what more need be said to confirm and elucidate this axiom.
10. To preserve a thing, no lesser cause is required than to produce it in the first place.
From the fact that at this moment we are thinking, it does not necessarily follow that we shall hereafter be thinking. For the concept that we have of our thought does not involve, or does not contain, the necessary existence of the thought. I can clearly and distinctly conceive the thought even though I suppose it not to exist.31 Now the nature of every cause must contain in itself or involve the perfection of its effect (Ax. 8). Hence it clearly follows that there must be something in us or external to us that we have not yet understood, whose concept or nature involves existence, and that is the reason why our thought began to exist and also continues to exist. For although our thought began to exist, its nature and essence does not on that account involve necessary existence any the more than before it existed, and so in order to persevere in existing it stands in need of the same force that it needs to begin existing. And what we here say about thought must be said about every thing whose essence does not involve necessary existence.
11. Of every thing that exists, it can be asked what is the cause or reason why it exists. See Descartes, Axiom 1.
Because to exist is something positive, we cannot say that it has nothing for its cause (Ax. 7). Therefore we must assign some positive cause or reason why it exists. And this must be either external (i.e., outside the thing itself) or else internal (i.e., included in the nature and definition of the existing thing itself).
The four propositions that follow are taken from Descartes.
PROPOSITION 5
The existence of God is known solely from the consideration of his nature.
Proof To say that something is contained in the nature or concept of a thing is the same as to say that it is true of that thing (Def. 9). But necessary existence is contained in the concept of God (Ax. 6). Therefore it is true to say of God that there is necessary existence in him, or that he exists.32
Scholium From this proposition there follow many important consequences. Indeed, on this fact alone—that existence pertains to the nature of God, or that the concept of God involves necessary existence just as the concept of a triangle involves its three angles being equal to two right angles, or that his existence, just like his essence, is an eternal truth—depends almost all knowledge of the attributes of God through which we are brought to love of him and to the highest blessedness. Therefore it is much to be desired that mankind should come round to our opinion on this subject.
I do indeed admit that there are some prejudices that prevent this from being so easily understood by everyone.33 If anyone, moved by goodwill and by the simple love of truth and his own true advantage, comes to look at the matter closely and to reflect on what is contained in the “Fifth Meditation” and the end of “Replies to the First Set of Objections,” and also on what we say about Eternity in Chapter 1 Part 2 of our Appendix, he will undoubtedly understand the matter quite clearly and will in no way be able to doubt whether he has an idea of God (which is, of course, the first foundation of human blessedness). For when he realizes that God is completely different in kind from other things in respect of essence and existence, he will at once see clearly that the idea of God is far different from the ideas of other things. Therefore there is no need to detain the reader any longer on this subject.
Proof The objective reality of any of our ideas requires a cause in which that same reality is contained not just objectively but formally or eminently (Ax. 9). Now we do have the idea of God (Defs. 2 and 8), and the objective reality of this idea is not contained in us either formally or eminently (Ax. 4), nor can it be contained in anything other than God himself (Def. 8). Therefore this idea of God, which is in us, requires God for its cause, and therefore God exists (Ax. 7).34
Scholium There are some who deny that they have any idea of God, and yet, as they declare, they worship and love him. And though you were to set before them the definition of God and the attributes of God, you will meet with no more success than if you were to labor to teach a man blind from birth the differences of colors as we see them. However, except to consider them as a strange type of creature halfway between man and beast, we should pay small heed to their words. How else, I ask, can we show the idea of some thing than by giving its definition and explaining its attributes? Because this is what we are doing in the case of the idea of God, there is no reason for us to be concerned over the words of men who deny the idea of God simply on the grounds that they cannot form an image of him in their brain.
Furthermore, we should note that when Descartes quotes Axiom 4 to show that the objective reality of the idea of God is not contained in us either formally or eminently, he takes for granted that everyone knows that he is not an infinite substance, that is, supremely intelligent, supremely powerful, etc., and this he is entitled to do. For he who knows that he thinks, also knows that he doubts many things and that he does not understand everything clearly and distinctly.
Finally, we should note that it also follows clearly from Definition 8 that there cannot be a number of Gods, but only one God, as we clearly demonstrate in Proposition 11 of this Part, and in Part 2 of our Appendix, Chapter 2.
Proof If I had the force to preserve myself, I would be of such a nature that I would involve necessary existence (Lemma 2). Therefore (Corollary Lemma 1) my nature would contain all perfections. But I find in myself, insofar as I am a thinking thing, many imperfections—as that I doubt, desire, etc.—and of this I am certain (Scholium Prop. 4). Therefore I have no force to preserve myself. Nor can I say that the reason I now lack those perfections is that I now will to deny them to myself, for this would be clearly inconsistent with Lemma 1, and with what I clearly find in myself (Ax. 5).
Further, I cannot now exist, while I am existing, without being preserved either by myself—if indeed I have that force—or by something else that does have that force (Axioms 10 and 11). But I do exist (Scholium Prop. 4), and yet I do not have the force to preserve myself, as has just now been proved. Therefore I am preserved by something else. But not by something else that does not have the force to preserve itself (by the same reasoning whereby I have just demonstrated that I am not able to preserve myself). Therefore it must be by something else that has the force to preserve itself; that is (Lemma 2), something whose nature involves necessary existence; that is (Corollary Lemma 1), something that contains all the perfections that I clearly understand to pertain to a supremely perfect being. Therefore a supremely perfect being exists; that is (Def. 8), God exists. Q.E.D.
Scholium To demonstrate this proposition Descartes assumes the following two axioms:
1. That which can effect what is greater or more difficult can also effect what is less.
2. It is a greater thing to create or (Ax. 10) to preserve substance than the attributes or properties of substance.
What he means by these axioms I do not know. For what does he call easy, and what difficult? Nothing is said to be easy or difficult in an absolute sense, but only with respect to its cause. So one and the same thing can be said at the same time to be easy and difficult in respect of different causes.35 Now if, of things that can be effected by the same cause, he calls those difficult that need great effort and those easy that need less (e.g., the force that can raise fifty pounds can raise twenty-five pounds twice as easily) then surely the axiom is not absolutely true, nor can he prove from it what he aims to prove. For when he says, “If I had the force to preserve myself, I should also have the force to give myself all the perfections that I lack” (because this latter does not require as much power), I would grant him that the strength that I expend on preserving myself could effect many other things far more easily had I not needed it to preserve myself, but I deny that, as long as I am using it to preserve myself,36 I can direct it to effecting other things however much easier, as can clearly be seen in our example.
And the difficulty is not removed by saying that, because I am a thinking thing, I must necessarily know whether I am expending all my strength in preserving myself, and whether this is also the reason why I do not give myself the other perfections. For—apart from the fact that this point is not at issue, but only how the necessity of this proposition follows from this axiom—if I knew this, I should be a greater being and perhaps require greater strength than I have so as to preserve myself in that greater perfection. Again, I do not know whether it is a greater task to create or preserve substance than to create or preserve its attributes. That is, to speak more clearly and in more philosophic terms, I do not know whether a substance, so as to preserve its attributes, does not need the whole of its virtue and essence with which it may be preserving itself.
But let us leave this and examine further what our noble Author here intends; that is, what he understands by ‘easy’ and what by ‘difficult’. I do not think, nor can I in any way be convinced, that by ‘difficult’ he understands that which is impossible (and therefore cannot be conceived in any way as coming into being), and by ‘easy’, that which does not imply any contradiction (and therefore can readily be conceived as coming into being)—although in the “Third Meditation” he seems at first glance to mean this when he says: “Nor ought I to think that perhaps those things that I lack are more difficult to acquire than those that are already in me. For on the contrary it is obvious that it was far more difficult for me, a thinking thing or substance, to emerge from nothing than …”, etc.37 This would not be consistent with the Author’s words nor would it smack of his genius. For, passing over the first point, there is no relationship between the possible and the impossible, or between the intelligible and the nonintelligible, just as there is no relationship between something and nothing, and power has no more to do with impossible things than creation and generation, with nonentities; so there can be no comparison between them. Besides, I can compare things and understand their relationship only when I have a clear and distinct conception of them all. So I deny that it follows that he who can do the impossible can also do the possible. What sort of conclusion, I ask, would this be? That if someone can make a square circle, he will also be able to make a circle wherein all the lines drawn from the center to the circumference are equal. Or if someone can bring it about that ‘nothing’ can be acted upon, and can use it as material to produce something, he will also have the power to make something from something. For, as I have said, there is no agreement, or analogy, or comparison or any relationship whatsoever between these things and things like these. Anyone can see this, if only he gives a little attention to the matter. Therefore I think this quite irreconcilable with Descartes’s genius.
But if I attend to the second of the two axioms just now stated, it appears that what he means by ‘greater’ and ‘more difficult’ is ‘more perfect’, and by ‘lesser’ and ‘easier’, ‘less perfect’. Yet this, again, seems very obscure, for there is here the same difficulty as before. As before, I deny that he who can do the greater can, at the same time and with the same effort (as must be supposed in the proposition), do the lesser.
Again, when he says: “It is a greater thing to create or preserve substance than its attributes,” surely he cannot understand by attributes that which is formally contained in substance and differs from substance itself only by conceptual abstraction. For then it would be the same thing to create substance as to create attributes. Nor again, by the same reasoning, can he mean the properties of substance which necessarily follow from its essence and definition.
Far less can he mean—and yet he appears to—the properties and attributes of another substance. For instance, if I say that I have the power to preserve myself, a finite thinking substance, I cannot for that reason say that I also have the power to give myself the perfections of infinite substance, which differs totally in essence from my essence. For the force or essence whereby I preserve myself in my being is quite different in kind from the force or essence whereby absolutely infinite substance preserves itself, and from which its powers and properties are distinguishable only by abstract reason.38 So even though I were to suppose that I preserve myself, if I wanted to conceive that I could give myself the perfections of absolutely infinite substance, I should be supposing nothing other than this, that I could reduce my entire essence to nothing and create an infinite substance anew. This would be much more, surely, than merely to suppose that I can preserve myself, a finite substance.
Therefore, because by the terms ‘attributes’ or ‘properties’ he can mean none of these things, there remain only the qualities that substance itself contains eminently (as this or that thought in the mind, which I clearly perceive to be lacking in me), but not the qualities that another substance contains eminently (as this or that motion in extension; for such perfections are not perfections for me, a thinking thing, and therefore they are not lacking to me). But then what Descartes wants to prove—that if I am preserving myself, I also have the power to give myself all the perfections that I clearly see as pertaining to a most perfect being—can in no way be concluded from this axiom, as is quite clear from what I have said previously. However, not to leave the matter unproved, and to avoid all confusion, I have thought it advisable first of all to demonstrate the following Lemmas, and thereafter to construct on them the proof of Proposition 7.
Lemma 1 The more perfect a thing is by its own nature, the greater the existence it involves, and the more necessary is the existence. Conversely, the more a thing by its own nature involves necessary existence, the more perfect it is.
Proof Existence is contained in the idea or concept of everything (Ax.6). Then let it be supposed that A is a thing that has ten degrees of perfection. I say that its concept involves more existence than if it were supposed to contain only five degrees of perfection. Because we cannot affirm any existence of nothing (see Scholium Prop. 4), in proportion as we in thought subtract from its perfection and therefore conceive it as participating more and more in nothing, to that extent we also deny the possibility of its existence. So if we conceive its degrees of perfection to be reduced indefinitely to nought or zero, it will contain no existence, or absolutely impossible existence. But, on the other hand, if we increase its degrees of perfection indefinitely, we shall conceive it as involving the utmost existence, and therefore the most necessary existence. That was the first thing to be proved. Now since these two things can in no way be separated (as is quite clear from Axiom 6 and the whole of Part 1 of this work), what we proposed to prove in the second place clearly follows.
Note 1. Although many things are said to exist necessarily solely on the grounds that there is given a cause determined to produce them, it is not of this that we are here speaking; we are speaking only of that necessity and possibility that follows solely from consideration of the nature or essence of a thing, without taking any account of its cause.
Note 2. We are not here speaking of beauty and other ‘perfections’, which, out of superstition and ignorance, men have thought fit to call perfections; by perfection I understand only reality or being. For example, I perceive that more reality is contained in substance than in modes or accidents. So I understand clearly that substance contains more necessary and more perfect existence than is contained in accidents, as is well established from Axioms 4 and 6.
Corollary Hence it follows that whatever involves necessary existence is a supremely perfect being, or God.
Lemma 2 The nature of one who has the power to preserve himself involves necessary existence.
Proof He who has the force to preserve himself has also the force to create himself (Ax. 10); that is (as everyone will readily admit), he needs no external cause to exist, but his own nature alone will be a sufficient cause of his existence, either possibly (Ax. 10) or necessarily. But not possibly; for then (through what I have demonstrated with regard to Axiom 10) from the fact that he now existed it would not follow that he would thereafter exist (which is contrary to the hypothesis). Therefore necessarily; that is, his nature involves necessary existence. Q.E.D.
Corollary God can bring about every thing that we clearly perceive, just as we perceive it.
Proof All this follows clearly from the preceding proposition. For there God’s existence was proved from the fact that there must exist someone in whom are all the perfections of which there is an idea in us. Now there is in us the idea of a power so great that by him alone in whom it resides there can be made the sky, the earth, and all the other things that are understood by me as possible. Therefore, along with God’s existence, all these things, too, are proved of him.
PROPOSITION 8
Mind and body are distinct in reality.
Proof Whatever we clearly perceive can be brought about by God just as we perceive it (Corollary Prop. 7). But we clearly perceive mind, that is (Def. 6), a thinking substance, without body, that is (Def. 7), without any extended substance (Props. 3 and 4); and conversely we clearly perceive body without mind, as everyone readily admits. Therefore, at least through divine power, mind can be without body and body without mind.39
Now substances that can be without one another are distinct in reality (Def. 10). But mind and body are substances (Defs. 5, 6, and 7) that can exist without one another, as has just been proved. Therefore mind and body are distinct in reality.
See Proposition 4 at the end of Descartes’s “Replies to the Second Set of Objections,” and the passages in Principia Part 1 from Arts. 22–29. For I do not think it worthwhile to transcribe them here.
PROPOSITION 9
God is a supremely understanding being.
Proof If you deny this, then God will understand either nothing or not everything, that is, only some things. But to understand only some things and to be ignorant of the rest supposes a limited and imperfect intellect, which it is absurd to ascribe to God (Def. 8). And that God should understand nothing either indicates a lack of intellection in God—as it does with men who understand nothing—and involves imperfection (which, by the same definition, cannot be the case with God), or else it indicates that it is incompatible with God’s perfection that he should understand something. But because intellection is thus completely denied of God, he will not be able to create any intellect (Ax. 8). Now because intellect is clearly and distinctly perceived by us, God can be its cause (Cor. Prop. 7). Therefore it is far from true that it is incompatible with God’s perfection for him to understand something. Therefore he is a supremely understanding being. Q.E.D.
Scholium Although it must be granted that God is incorporeal, as is demonstrated in Prop. 16, this must not be taken to mean that all the perfections of extension are to be withdrawn from him. They are to be withdrawn from him only to the extent that the nature and properties of extension involve some imperfection. The same point is to be made concerning God’s intellection, as is admitted by all who seek wisdom beyond the common run of philosophers, and as will be fully explained in our Appendix Part 2 Chapter 7.
PROPOSITION 10
Whatever perfection is found in God, is from God.
Proof If you deny this, suppose that there is in God some perfection that is not from God. It will be in God either from itself, or from something different from God. If from itself, it will therefore have necessary existence, not merely possible existence (Lemma 2 Prop. 7), and so (Corollary Lemma 1 Prop. 7) it will be something supremely perfect, and therefore (Def. 8) it will be God. So if it be said that there is in God something that is from itself, at the same time it is said that this is from God. Q.E.D. But if it be from something different from God, then God cannot be conceived through himself as supremely perfect, contrary to Definition 8. Therefore whatever perfection is found in God, is from God. Q.E.D.
PROPOSITION 11
There cannot be more than one God.
Proof If you deny this, conceive, if you can, more than one God (e.g., A and B). Then of necessity (Prop. 9) both A and B will have the highest degree of understanding; that is, A will understand everything, himself and B, and in turn B will understand himself and A. But because A and B necessarily exist (Prop. 5), therefore the cause of the truth and the necessity of the idea of B, which is in A, is B; and conversely the cause of the truth and the necessity of the idea of A, which is in B, is A. Therefore there will be in A a perfection that is not from A, and in B a perfection that is not from B. Therefore (Prop. 10) neither A nor B will be a God, and so there cannot be more than one God. Q.E.D.
Here it should be noted that, from the mere fact that something of itself involves necessary existence—as is the case with God—it necessarily follows that it is unique. This is something that everyone can see for himself with careful thought, and I could have demonstrated it here, but not in a manner as comprehensible to all as is done in this proposition.
PROPOSITION 12
All things that exist are preserved solely by the power of God.
Proof If you deny this, suppose that something preserves itself. Therefore (Lemma 2 Prop. 7) its nature involves necessary existence. Thus (Corollary Lemma 1 Prop. 7) it would be God, and there would be more than one God, which is absurd (Prop. 11). Therefore everything that exists is preserved solely by the power of God. Q.E.D.
Corollary 1 God is the creator of all things.
Proof God preserves all things (Prop. 12); that is (Ax. 10), he has created, and still continuously creates, everything that exists.
Corollary 2 Things of themselves do not have any essence that is the cause of God’s knowledge. On the contrary, God is also the cause of things with respect to their essence.
Proof Because there is not to be found in God anything of perfection that is not from God (Prop. 10), things of themselves will not have any essence that can be the cause of God’s knowledge. On the contrary, because God has created all things wholly, not generating them from something else (Prop. 12 with Cor. 1), and because the act of creation acknowledges no other cause but the efficient cause (for this is how I define ‘creation’), which is God, it follows that before their creation things were nothing at all, and therefore God was also the cause of their essence. Q.E.D.
It should be noted that this corollary is also evident from the fact that God is the cause or creator of all things (Cor. 1) and that the cause must contain in itself all the perfections of the effect (Ax. 8), as everyone can readily see.
Corollary 3 Hence it clearly follows that God does not sense, nor, properly speaking, does he perceive. For his intellect is not determined by anything external to himself; all things derive from him.
Corollary 4 God is prior in causality to the essence and existence of things, as clearly follows from Corollaries 1 and 2 of this Proposition.
PROPOSITION 13
God is supremely truthful, and not at all a deceiver.40
Proof We cannot attribute to God anything in which we find any imperfection (Def. 8); and because (as is self-evident) all deception or will to deceive proceeds only from malice or fear, and fear supposes diminished power while malice supposes privation of goodness, no deception or will to deceive is to be ascribed to God, a being supremely powerful and supremely good. On the contrary, he must be said to be supremely truthful and not at all a deceiver. Q.E.D. See “Replies to the Second Set of Objections,” No. 4.41
PROPOSITION 14
Whatever we clearly and distinctly perceive is true.
Proof The faculty of distinguishing true from false, which is in us (as everyone can discover in himself, and as is obvious from all that has already been proved) has been created and is continuously preserved by God (Prop. 12 with Cor.), that is, by a being supremely truthful and not at all a deceiver (Prop. 13), and he has not bestowed on us (as everyone can discover in himself) any faculty for holding aloof from, or refusing assent to, those things that we clearly and distinctly perceive. Therefore if we were to be deceived in regard to them, we should be deceived entirely by God, and he would be a deceiver, which is absurd (Prop. 13). So whatever we clearly and distinctly perceive is true. Q.E.D.
Scholium Because those things to which we must necessarily assent when they are clearly and distinctly perceived by us are necessarily true, and because we have a faculty for withholding assent from those things that are obscure or doubtful or are not deduced from the most certain principles—as everyone can see in himself—it clearly follows that we can always take precautions against falling into error and against ever being deceived (a point that will be understood even more clearly from what follows), provided that we make an earnest resolution to affirm nothing that we do not clearly and distinctly perceive or that is not deduced from first principles clear and certain in themselves.
PROPOSITION 15
Error is not anything positive.
Proof If error were something positive, it would have as its cause only God, by whom it must be continuously created (Prop. 12). But this is absurd (Prop. 13). Therefore error is not anything positive. Q.E.D.
Scholium Because error is not anything positive in man, it can be nothing else than the privation of the right use of freedom (Schol. Prop. 14). Therefore God must not be said to be the cause of error, except in the sense in which we say that the absence of the sun is the cause of darkness, or that God, in making a child similar to others except for sight, is the cause of blindness. He is not to be said to be the cause of error in giving us an intellect that extends to only a few things. To understand this clearly, and also how error depends solely on the misuse of the will, and, finally, to understand how we may guard against error, let us recall to mind the modes of thinking that we possess, namely, all modes of perceiving (sensing, imagining, and pure understanding) and modes of willing (desiring, misliking, affirming, denying, and doubting); for they can all be subsumed under these two headings.
Now with regard to these modes we should note, first, that insofar as the mind understands things clearly and distinctly and assents to them, it cannot be deceived (Prop. 14); nor again can it be deceived insofar as it merely perceives things and does not assent to them. For although I may now perceive a winged horse, it is certain that this perception contains nothing false as long as I do not assent to the truth that there is a winged horse, nor again as long as I doubt whether there is a winged horse. And because to assent is nothing but to determine the will, it follows that error depends only on the use of the will.
To make this even clearer, we should note, secondly, that we have the power to assent not only to those things that we clearly and distinctly perceive but also to those things that we perceive in any other way. For our will is not determined by any limits. Everyone can clearly see this if only he attends to the following point, that if God had wished to make infinite our faculty of understanding, he would not have needed to give us a more extensive faculty of willing than that which we already possess in order to enable us to assent to all that we understand. That which we already possess would be sufficient for assenting to an infinite number of things.42 And in fact experience tells us, too, that we assent to many things that we have not deduced from sure first principles. Furthermore, these considerations make it clear that if the intellect extended as widely as the faculty of willing, or if the faculty of willing could not extend more widely than the intellect, or if, finally, we could restrict the faculty of willing within the limits of the intellect, we would never fall into error (Prop. 14).
But the first two possibilities lie beyond our power, for they would involve that the will should not be infinite and the intellect created finite. So it remains for us to consider the third possibility, namely, whether we have the power to restrict our faculty of willing within the limits of the intellect. Now because the will is free to determine itself, it follows that we do have the power to restrict the faculty of assenting within the limits of the intellect, therefore bringing it about that we do not fall into error. Hence it is quite manifest that our never being deceived depends entirely on the use of the freedom of the will. That our will is free is demonstrated in Art. 39 Part 1 of the Principia and in the “Fourth Meditation,” and is also shown at some length by me in the last chapter of my Appendix. And although, when we perceive a thing clearly and distinctly, we cannot refrain from assenting to it, that necessary assent depends not on the weakness but simply on the freedom and perfection of the will. For to assent to the truth is a perfection in us (as is self-evident), and the will is never more perfect and more free than when it completely determines itself. Because this can occur when the mind understands something clearly and distinctly, it will necessarily give itself this perfection at once (Ax. 3). Therefore we by no means understand ourselves to be less free because we are not at all indifferent in embracing truth. On the contrary, we take it as certain that the more indifferent we are, the less free we are.
So now it remains only to be explained how error is nothing but privation with respect to man, whereas with respect to God it is mere negation. This will easily be seen if we first observe that our perceiving many things besides those that we clearly understand makes us more perfect than if we did not perceive them. This is clearly established from the fact that, if it were supposed that we could perceive nothing clearly and distinctly but only confusedly, we should possess nothing more perfect than this perceiving things confusedly, nor would anything else be expected of our nature. Furthermore, to assent to things, however confused, insofar as it is also a kind of action, is a perfection. This will also be obvious to everyone if he supposes, as previously, that it is contrary to man’s nature to perceive things clearly and distinctly. For then it will become quite clear that it is far better for a man to assent to things, however confused, and to exercise his freedom, than to remain always indifferent, that is (as we have just shown), at the lowest grade of freedom. And if we also turn our attention to the needs and convenience of human life, we shall find this absolutely necessary, as experience teaches each of us every day.
Therefore, because all the modes of thinking that we possess are perfect insofar as they are regarded in themselves alone, to that extent that which constitutes the form of error cannot be in them. But if we attend to the way in which modes of willing differ from one another, we shall find that some are more perfect than others in that some render the will less indifferent (i.e., more free) than others. Again, we shall also see that, as long as we assent to confused things, we make our minds less apt to distinguish true from false, thereby depriving ourselves of the highest freedom. Therefore to assent to confused things, insofar as this is something positive, does not contain any imperfection or the form of error; it does so only insofar as we thus deprive our own selves of the highest freedom that is within reach of our nature and is within our power. So the imperfection of error will consist entirely merely in the privation of the highest freedom, a privation that is called error. Now it is called privation because we are deprived of a perfection that is compatible with our nature, and it is called error because it is our own fault that we lack this perfection, in that we fail to restrict the will within the limits of the intellect, as we are able to do. Therefore, because error is nothing else with respect to man but the privation of the perfect or correct use of freedom, it follows that it does not lie in any faculty that he has from God, nor again in any operation of his faculties insofar as this depends on God.43 Nor can we say that God has deprived us of the greater intellect that he might have given us and has thereby brought it about that we could fall into error. For no thing’s nature can demand anything from God, and nothing belongs to a thing except what the will of God has willed to bestow on it. For nothing existed, or can even be conceived, prior to God’s will (as is fully explained in our Appendix Part 2 Chapters 7 and 8). Therefore God has not deprived us of a greater intellect or a more perfect faculty of understanding any more than he has deprived a circle of the properties of a sphere, and a circumference of the properties of a spherical surface.
So because none of our faculties, in whatever way it be considered, can point to any imperfection in God, it clearly follows that the imperfection in which the form of error consists is privation only with respect to man. When related to God as its cause, it can be termed not privation, but only negation.
PROPOSITION 16
God is incorporeal.
Proof Body is the immediate subject of local motion (Def. 7). Therefore if God were corporeal, he would be divided into parts; and this, since it clearly involves imperfection, it is absurd to affirm of God (Def. 8).
Another Proof If God were corporeal, he could be divided into parts (Def. 7). Now either each single part could subsist of itself, or it could not. If the latter, it would be like the other things created by God, and thus, like every created thing, it would be continuously created by the same force by God (Prop. 10 and Ax. 11), and would not pertain to God’s nature any more than other created things, which is absurd (Prop. 5). But if each single part exists through itself, each single part must also involve necessary existence (Lemma 2 Prop. 7), and consequently each single part would be a supremely perfect being (Cor. Lemma 2 Prop. 7). But this, too, is absurd (Prop. 11). Therefore God is incorporeal. Q.E.D.
PROPOSITION 17
God is a completely simple being.
Proof If God were composed of parts, the parts (as all will readily grant) would have to be at least prior in nature to God, which is absurd (Cor. 4 Prop. 12). Therefore he is a completely simple being. Q.E.D.
Corollary Hence it follows that God’s intelligence, his will or decree, and his power are not distinguished from his essence, except by abstract reasoning.
PROPOSITION 18
God is immutable.
Proof If God were mutable, he could not change in part, but would have to change with respect to his whole essence (Prop. 17). But the essence of God exists necessarily (Props. 5, 6, and 7). Therefore God is immutable. Q.E.D.
Proof God is a supremely perfect being (Def. 8), from which it follows that he exists necessarily (Prop. 5). If now we attribute to him limited existence, the limits of his existence must necessarily be understood, if not by us, at any rate by God himself (Prop. 9), because he has understanding in the highest degree. Therefore God will understand himself (i.e. [Def. 8], a supremely perfect being) as not existing beyond these limits, which is absurd (Prop. 5). Therefore God has not a limited but an infinite existence, which we call eternity. See Chapter 1 Part 2 of our Appendix. Therefore God is eternal. Q.E.D.
PROPOSITION 20
God has preordained all things from eternity.
Proof Because God is eternal (Prop. 19), his understanding is eternal, because it pertains to his eternal essence (Cor. Prop. 17). But his intellect is not different in reality from his will or decree (Cor. Prop. 17). Therefore when we say that God has understood things from eternity, we are also saying that he has willed or decreed things thus from eternity. Q.E.D.
Corollary From this proposition it follows that God is in the highest degree constant in his works.
Proof That which is extended, as it is clearly and distinctly perceived by us, does not pertain to God’s nature (Prop. 16), but it can be created by God (Cor. Prop. 7 and Prop. 8). Furthermore, we clearly and distinctly perceive (as everyone can discover in himself, insofar as he thinks) that extended substance is a sufficient cause for producing in us pleasure, pain, and similar ideas or sensations, which are continually produced in us even against our will. But if we wish to suppose some other cause for our sensations apart from extended substance—say, God or an angel—we immediately destroy the clear and distinct concept that we have. Therefore,44 as long as we correctly attend to our perceptions so as to allow nothing but what we clearly and distinctly perceive, we shall be altogether inclined, or by no means uninclined, to accept that extended substance is the only cause of our sensations, and therefore to affirm that the extended thing exists, created by God. And in this we surely cannot be deceived (Prop. 14 with Schol.). Therefore it is truly affirmed that substance extended in length, breadth, and depth exists. This was the first point.45
Furthermore, among our sensations, which must be produced in us (as we have already proved) by extended substance, we observe a considerable difference, as when I say that I sense or see a tree or when I say that I am thirsty, or in pain, etc. But I clearly see that I cannot perceive the cause of this difference unless I first understand that I am closely united to one part of matter, and not so to other parts. Because I clearly and distinctly understand this, and I cannot perceive it in any other way, it is true (Prop. 14 with Schol.) that I am united to one part of matter. This was the second point. We have therefore proved what was to be proved.46
Note: Unless the reader here considers himself only as a thinking thing, lacking body, and unless he puts aside as prejudices all the reasons that he previously entertained for believing that body exists, his attempts to understand this proof will be in vain.
End of Part 1
9 [The first two arguments are given in Med1, 13–15 (AT7, 18–20) and PPH1A4, whereas the third is not given until Med6, 50 (AT7, 76–77).]
10 [Med1, 15 (AT7, 20).]
11 [Med1, 15–16 (AT7, 21–22).]
12 [Med2, 17 (AT7, 24).]
13 [Med2, 17–18 (AT7, 24–25).]
14 [Med2, 18 (AT7, 25); Discourse on Method 4 (AT6, 32–33).]
15 [Spinoza follows the Discourse on Method, rather than the Meditations or PPH, in deriving this principle directly from the cogito.]
16 [Med2, 18 (AT7, 25–26).]
17 [This enumeration is taken from Med2, 20 (AT7, 28).]
18 [Med3, 34–35 (AT7, 51–52); Med5, 46–47 (AT7, 70–71).]
19 [Med4, 35–42 (AT7, 52–62).]
20 [Med6, 47–59 (AT7, 71–90).]
21 [Cf. Med3, 27–28 (AT7, 40–41).]
22 [In each of the preceding eight definitions a word or phrase has been italicized to indicate the definiendum, but in this definition and the next there is no text italicized. It appears reasonable to assume that Def9 has as definiendum contained in the nature or conception of some thing and Def10 distinct in reality.]
23 [The seven postulates (AT7, 162–164) or demandes in the French version (AT9, 125–127) are not postulates in the Euclidean sense but are requests from Descartes to his readers to ponder carefully what can be doubted, the preceding definitions, and especially the distinction between clear, distinct perception and obscure, confused perception.]
24 [The first three axioms are not taken from Descartes; but Meyer, in his preface, has mentioned that Spinoza would expound Descartes’s opinions and demonstrations “just as they are found in his writings, or such as should validly be deduced from the foundations laid by him.”]
25 [Cf. Med3, 27–28 (AT7, 40–42).]
26 [Cf. Med3, 32–33 (AT7, 48).]
27 [Cf. Med3, 28 (AT7, 40–41).]
28 [Cf. Med3, 28 (AT7, 41–42).]
29 [Cf. Rep1, AT7, 104–106.]
30 We are also certain of this because we experience it ourselves insofar as we are thinking. See preceding Scholium.
31 This is something everyone discovers in himself, insofar as he is a thinking thing.
32 [Cf. Med5, 43–46 (AT7, 65–69); E1P11Dem1; KV1/1/1–2.]
33 Read Principia Part 1 Art. 16.
34 [Cf. Med3, 28–31 (AT7, 40–45).]
35 Take as only one example the spider, which easily weaves a web that men would find very difficult to weave. On the other hand, men find it quite easy to do many things that are perhaps impossible for angels.
36 [I have diverged from the punctuation of Gebhardt.—S.S.]
37 [Cf. Med3, 32–33 (AT7, 48).]
38 Note that the force by which substance preserves itself is nothing but its essence, differing from it only in name. This will be a particular feature of our discussion in the Appendix, concerning the power of God.
39 [Cf. Med6, 51 (AT7, 78).]
40 I have not included this axiom among the axioms because it was not at all necessary. I had no need of it except for the proof of this proposition alone, and furthermore, as long as I did not know God’s existence, I did not wish to assume as true anything more than what I could deduce from the first known thing, ‘I am’, as I said in the Scholium to Proposition 4. Again, I have not included among my definitions the definitions of fear and malice because everyone knows them, and I have no need of them except for this one proposition.
41 [AT7, 142–147.]
42 [Cf. Med4, 38 (AT7, 56–57).]
43 [Med4, 36–39 (AT7, 54–58).]
44 See the proof to Proposition 14 and the Scholium to Proposition 15.
45 [Cf. Med6, 51–52 (AT7, 78–80).]
46 [See Med6, 52–53 (AT7, 80–81).]