There remain many attributes of God, and many aspects of the nature of myself, or my mind, for me to investigate. But perhaps I shall return to these another time, and for the moment nothing appears more urgent (now that I have realized what to avoid and what to do in order to attain truth) than to attempt to extricate myself from the doubts I have fallen into during these past days, and to see whether any certainty is possible with respect to material things.
And indeed, before investigating whether any such things exist outside me, I should first consider the ideas of them, in so far as these ideas exist in my thought, and see which of them are distinct, and which confused.
I can certainly distinctly imagine the quantity that philosophers commonly call ‘continuous’: that is, the extension of this quantity (or rather, of the thing to which the quantity is attributed) in length, breadth, and depth. I can count various parts within it. To each of these parts I ascribe various magnitudes, shapes, positions, and local motions, and to the motions I ascribe various durations.
Not only are these things, considered in these general terms, clearly known and grasped by me: I also, if I pay close attention, perceive innumerable particular facts involving shape, number, motion,
and suchlike—facts so plainly true, and so much in conformity with
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my nature, that when I first discover them I do not seem to be learning anything new, but rather to be remembering something I knew before, or to be noticing for the first time something that was in me already, although I had not previously turned the gaze of my mind in its direction.
And what I think particularly needs to be considered here is this: that I find in myself innumerable ideas of certain things, that, even if, perhaps, they do not exist anywhere outside me, cannot yet be said to be nothing. And although, in a sense, whether I think of them or not is up to me, yet they are not inventions of my own mind, but they have true and immutable natures of their own. For instance, when I imagine a triangle, even if perhaps such a figure does not exist, and has never existed, anywhere at all outside my thought, it nonetheless certainly has a determinate nature, or essence, or form, that is immutable and eternal, which was not invented by me, and does not depend on my mind. This is clear from the fact that it is possible to demonstrate various properties of the triangle (for instance, that its three angles are equal to two right angles, and that the hypotenuse subtends the greatest angle, and so forth) which, whether I like it or not, I now clearly recognize to hold good, even if up to now I have never thought of them in any way when imagining a triangle. And therefore these properties were not invented by me.
It would make no difference if I were to say that perhaps this idea of a triangle has come to me from things outside myself via the sense-organs, because, that is, I have occasionally seen bodies of a triangular shape. For I can think up innumerable other shapes that it
is impossible to suspect ever reached me via the senses; and yet
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I can demonstrate several of their properties, just as I can with the triangle. And all of these properties are certainly true, since they are clearly known [cognoscuntur] by me, and therefore they are something, and not a pure nothing. For it is clear that everything that is true, is something; and I have already abundantly demonstrated that everything I clearly know [cognosco], is true. And even if I had not demonstrated this, the nature of my mind is such that I cannot in any case help assenting to the things I clearly perceive, at least, for as long as I clearly* perceive them; and I remember that even in past times, when I was as closely attached to the objects of the senses as it is possible to be, I always considered that truths of this kind that I clearly recognized, concerning shapes, or numbers, or other matters belonging to arithmetic or geometry or, in general, pure and abstract mathematics, were the most certain of all.
But now, if, from the fact alone that I can produce the idea of a given thing from my thought, it follows that everything I clearly and distinctly perceive to belong to the thing does in fact belong to it, cannot I also find here a further proof of the existence of God? Certainly, I find the idea of him, that is, of a supremely perfect being, in myself, just as much as I find the idea of any shape or number. And I clearly and distinctly understand that eternal existence belongs to his nature—just as clearly and distinctly as I understand that the properties I can demonstrate of some shape or number belong in fact to the nature of that shape or number. So that, even if not all the conclusions I have come to in my meditations over the past few days were true, I would still have to ascribe the same degree of certainty to
the existence of God that I up to now have ascribed to mathematical
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truths.
To be sure, this is not altogether evident at first sight: it appears to be something of a sophism. For since I am accustomed in all other things to distinguish existence from essence, I can easily convince myself that existence can be separated from the essence of God, and thus that God can be thought of as not existing. But if one considers the matter more closely, it becomes plain that existence can no more be separated from the essence of God than we can separate from the essence of a triangle that the sum of its three angles adds up to two right angles, or than we can separate the idea of a mountain from the idea of a valley.* So true is this that the thought of a God (that is, a supremely perfect being) who lacks existence (that is, who lacks a certain perfection) is no less contradictory than the thought of a mountain without a valley.
However, even if I can no more think of God without existence than I can think of a mountain without a valley, yet certainly, it does not follow from my thinking of a mountain as having a valley that any mountain exists in the world; similarly, from my thinking of God as existing, it does not seem to follow that God exists. For my thought imposes no necessity on things; and just as I am free to imagine a winged horse, even if no horse actually does have wings, so perhaps I can imagine the existence of a God, even though no God in fact exists.
No: this is where the sophism is lurking here. The point is not that, from my inability to think of a mountain except with a valley, it follows that a mountain and a valley exist somewhere, but only that
the mountain and the valley, whether they exist or not, cannot be
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separated from each other. Whereas from the fact that I cannot think of God except as existing, it follows that existence is inseparable from God, and therefore that he exists in reality. It is not that my thought brings his existence about, or that it imposes any necessity on anything, but, on the contrary, that the necessity of the thing itself, namely the existence of God, determines me to think it. Nor am I free to think of God without existence (that is, to think of the supremely perfect being without the supreme perfection), in the way I am free to imagine a horse with or without wings.
Nor can it be maintained that, although it is necessary to admit that God exists, once I have supposed him to possess all perfections, since existence is one of these perfections, the original supposition was not itself necessary* (just as it is not necessary for me to think that all quadrilateral shapes can be inscribed in a circle, but, supposing I do think this, I must admit that a rhombus can be inscribed in a circle, which, however, is patently impossible). For although it is not necessary that I should ever find myself thinking of God, nonetheless, whenever I choose to think about the first and supreme being, and bring forth the idea of him, so to speak, from the treasury of my mind, I must necessarily credit him with all perfections, even if at the time I neither list them all nor consider them individually. And this necessity is quite sufficient for me subsequently, when I recognize that existence is a perfection, to conclude, quite rightly, that the first and supreme being exists. In the same way, it is not necessary that I should ever imagine any triangle: but whenever I want to consider a straight-sided shape having only three angles, I must
necessarily credit it with properties from which it can be correctly
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inferred that the sum of its three angles does not exceed that of two right angles, even if I do not at the time realize this. On the other hand, when I am examining what shapes can be inscribed in a circle, there is absolutely no necessity for me to think that all quadrilaterals fall into this category: indeed, I cannot even imagine this to be true, as long as I am intending to accept only what I clearly and distinctly understand. Hence there is a great difference between false suppositions, such as this one, and true ideas innate within me, the first and most important of which is the idea of God. For indeed, I understand in many ways that this idea is not something fictitious that depends on my own thinking, but the image of a true and immutable nature: first, because no other thing can be conceived by me to the essence of which existence belongs, besides God himself; secondly, because I cannot conceive of two or more such Gods, and because, granted that one exists now, I plainly see that it is necessary both that he should have existed for all eternity up to now, and that he will continue to exist for an eternity in the future; and finally, because I perceive many other properties in God of which none can be subtracted or altered by me.
But indeed, whatever kind of proof I use, the issue always comes down to this: that nothing convinces me fully but what I clearly and distinctly perceive. It is true that, of the things I so perceive, although there are several that are obvious to anyone, there are others that can be discovered only by those who look into the matter more closely and examine it carefully. Once, however, these latter have been discovered, they are counted as no less certain than the former. Just as,
if we are dealing with a right-angled triangle, it does not so readily
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appear that that the square of the base is equal to the square of the sides as it does that the base is subtended by its greatest angle, nonetheless, once the first proposition has been grasped, it is as firmly believed as the second. But as far as God is concerned, certainly, if I were not overwhelmed by prejudices and if the images of sensible things were not pressing in on my thoughts from all directions, I should recognize nothing sooner and more readily than him. For what is more obvious in itself than that the supreme being exists, that is to say, that God, to whose essence alone existence belongs, exists?
And although careful consideration was required before I was capable of perceiving this truth, now, however, not only am I equally certain of it as I am of anything else that seems completely certain, but, moreover, I also observe that the certitude of all these other things depends on it so completely that without it nothing can ever be perfectly known [sciri].
For although my nature is such that, as long as I perceive something very clearly and distinctly, I cannot not believe that it is true, nonetheless, because my nature is also such that I cannot continuously fix the gaze of the mind on the same thing in order to perceive it clearly, and what often happens is that I remember judging something to be true, then, when I am no longer concentrating on the reasons for which I made that judgement, other reasons can be adduced that would easily (were I ignorant of God) shake me out of my opinion. And thus I should never have true and certain knowledge [scientia] of anything, but only vague and shifting opinions. Thus, for example, when I am considering the nature of a triangle, it certainly appears utterly evident to me (being, as I am, well versed in the principles of geometry) that its three angles are equal to two right
angles; and I cannot not believe this is true, as long as I am concentrating
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on the proof; but, as soon as I have turned the eye of the mind in a different direction, then however well I remember that I grasped the proof very clearly, I can still easily find myself doubting its truth, if I am ignorant of God. For I can persuade myself that I was so made by nature that I am sometimes deceived in matters which I think I perceive entirely clearly, especially since I remember counting many things as true and certain that later, when guided by other reasons, I judged to be false.
But once I have perceived that God exists, then because I grasped at the same time that everything else depends on him, and that he is no deceiver, and from this deduced that everything I clearly and distinctly perceive is necessarily true, then, even if I am no longer concentrating on the reasons why I judged this to be true, provided I remember that I did see it clearly and distinctly, no contrary reason can be adduced that can induce me to doubt it; and thus I have true and certain knowledge [scientia] of it. And not only of it, but of all the other propositions I remember demonstrating at some stage, such as the truths of geometry and others of the same kind. For what objections can now be raised against me? That I am so constituted as often to be deceived? But I know now [scio] that in matters I clearly understand, I cannot be deceived. That I once counted many things as true and certain that I later realized to be false? But I had perceived none of these clearly and distinctly, but, unaware as I was of this criterion of truth, perhaps I believed them for other reasons, which I later discovered to be less sound than I had thought. So what further objection can be raised? Perhaps (an objection I put to myself not long ago) I am sleeping, or all the things I am now thinking are no more true than the thoughts that occur to one who is asleep. But this makes no
difference. For certainly, even if I were sleeping, if something is evident
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to my understanding, then it is altogether true.
And so I plainly see that the certitude and truth of all knowledge [scientiae] depends on the knowledge [cognitione] of the true God alone: so much so, that before I had discovered this knowledge, I could have no perfect knowledge [scire] of anything else at all. But now innumerable truths, concerning both, on the one hand, God himself and other intellectual things and, on the other, the whole of this bodily nature which is the object of pure mathematics,* can be plainly known to me with certainty.