From Objection I (Caterus): (Ontological Argument)

My own answer to M. Descartes, which is based on this passage, is briefly this. Even if it is granted that a supremely perfect being carries the implication of existence in virtue of its very title, it still does not follow that the existence in question is anything actual in the real world; all that follows is that the concept of existence is inseparably linked to the concept of a supreme being. So you cannot infer that the existence of God is anything actual unless you suppose that the supreme being actually exists; for then it will actually contain all perfections, including the perfection of real existence.

Pardon me, gentlemen: I am now rather tired and propose to have a little fun. The complex 'existing lion' includes both 'lion' and 'existence', and it includes them essentially, for if you take away either element it will not be the same complex. But now, has not God had clear and distinct knowledge of this composite from all eternity? And does not the idea of this composite, as a composite, involve both elements essentially? In other words, does not existence belong to the essence of the composite 'existing lion'? Nevertheless the distinct knowledge of God, the distinct knowledge he has from eternity, does not compel either element in the composite to exist, unless we assume that the composite itself exists (in which case it will contain all its essential perfections including actual existence). Similarly even if I have distinct knowledge of a supreme being, and even if the supremely perfect being includes existence as an essential part of the concept, it still does not follow that the existence in question is anything actual, unless we suppose that the supreme being exists (for in that case it will include actual existence along with all its other perfections). Accordingly we must look elsewhere for a proof that the supremely perfect being exists.

Descartes’s Response:

The author of the objections here again compares one of my arguments with one of St Thomas', thus as it were forcing me to explain how one argument can have any greater force than the other. I think I can do this without too much unpleasantness. For, first, St Thomas did not use the argument which he then puts forward as an objection to his own position conclusion as I do; and lastly, on this issue I do not differ from the Angelic Doctor in any respect. St Thomas asks whether the existence of God is self-evident as far as we are concerned, that is, whether it is obvious to everyone; and he answers, correctly, that it is not. The argument which he then puts forward as an objection to his own position can be stated as follows. 'Once we have understood the meaning of the word "God", we understand it to mean "that than which nothing greater can be conceived". But to exist in reality as well as in the intellect is greater than to exist in the intellect alone. Therefore, once we have understood the meaning of the word "God" we understand that God exists in reality as well as in the understanding.' In this form the argument is manifestly invalid, for the only conclusion that should have been drawn is: 'Therefore, once we have understood the meaning of the word "God" we understand that what is conveyed is that God exists in reality as well as in the understanding.' Yet because a word conveys something, that thing is not therefore shown to be true. My argument however was as follows: 'That which we clearly and distinctly understand to belong to the true and immutable nature, or essence, or form of something, can truly be asserted of that thing. But once we have made a sufficiently careful investigation of what God is, we clearly and distinctly understand that existence belongs to his true and immutable nature. Hence we can now truly assert of God that he does exist.' Here at least the conclusion does follow from the premisses. But, what is more, the major premiss cannot be denied, because it has already been conceded that whatever we clearly and distinctly understand is true. Hence only the minor premiss remains, and here I confess that there is considerable difficulty. In the first place we are so accustomed to distinguishing existence from essence in the case of all other things that we fail to notice how closely existence belongs to essence in the case of God as compared with that of other things. Next, we do not distinguish what belongs to the true and immutable essence of a thing from what is attributed to it merely by a fiction of the intellect. So, even if we observe clearly enough that existence belongs to the essence of God, we do not draw the conclusion that God exists, because we do not know whether his essence is immutable and true, or merely invented by us.

But to remove the first part of the difficulty we must distinguish between possible and necessary existence. It must be noted that possible existence is contained in the concept or idea of everything that we clearly and distinctly understand; but in no case is necessary existence so contained, except in the case of the idea of God. Those who carefully attend to this difference between the idea of God and every other idea will undoubtedly perceive that even though our understanding of other things always involves understanding them as if they were existing things, it does not follow that they do exist, but merely that they are capable of existing. For our understanding does not show us that it is necessary for actual existence to be conjoined with their other properties. But, from the fact that we understand that actual existence is necessarily and always conjoined with the other attributes of God, it certainly does follow that God exists.

To remove the second part of the difficulty, we must notice a point about ideas which do not contain true and immutable natures but merely ones which are invented and put together by the intellect. Such ideas can always be split up by the same intellect, not simply by an abstraction but by a clear and distinct intellectual operation, so that any ideas which the intellect cannot split up in this way were clearly not put together by the intellect. When, for example, I think of a winged horse or an actually existing lion, or a triangle inscribed in a square, I readily understand that I am also able to think of a horse without wings, or a lion which does not exist, or a triangle apart from a square, and so on; hence these things do not have true and immutable natures. But if I think of a triangle or a square (I will not now include the lion or the horse, since their natures are not transparently clear to us), then whatever I apprehend as being contained in the idea of a triangle - for example that its three angles are equal to two right angles - I can with truth assert of the triangle. And the same applies to the square with respect to whatever I apprehend as being contained in the idea of a square. For even if I can understand what a triangle is if I abstract the fact that its three angles are equal to two right angles, I cannot deny that this property applies to the triangle by a clear and distinct intellectual operation - that is, while at the same time understanding what I mean by my denial. Moreover, if I consider a triangle inscribed in a square, with a view not to attributing to the square properties that belong only to the triangle, or attributing to the triangle properties that belong to the square, but with a view to examining only the properties which arise out of the conjunction of the two, then the nature of this composite will be just as true and immutable as the nature of the triangle alone or the square alone. And hence it will be quite in order to maintain that the square is not less than double the area of the triangle inscribed within it, and to affirm other similar properties that belong to the nature of this composite figure.

But if I were to think that the idea of a supremely perfect body contained existence, on the grounds that it is a greater perfection to exist both in reality and in the intellect than it is to exist in the intellect alone, I could not infer from this that the supremely perfect body exists, but only that it is capable of existing. For I can see quite well that this idea has been put together by my own intellect which has linked together all bodily perfections; and existence does not arise out of the other bodily perfections because it can equally well be affirmed or denied of them. Indeed, when I examine the idea of a body, I perceive that a body has no power to create itself or maintain itself in existence; and I rightly conclude that necessary existence - and it is only necessary existence that is at issue here - no more belongs to the nature of a body, however perfect, than it belongs to the nature of a mountain to be without a valley, or to the nature of a triangle to have angles whose sum is greater than two right angles. But instead of a body, let us now take a thing - whatever this thing turns out to be - which possesses all the perfections which can exist together. If we ask whether existence should be included among these perfections, we will admittedly be in some doubt at first. For our mind, which is finite, normally thinks of these perfections only separately, and hence may not immediately notice the necessity of their being joined together. Yet if we attentively examine whether existence belongs to a supremely powerful being, and what sort of existence it is, we shall be able to perceive clearly and distinctly the following facts. First, possible existence, at the very least, belongs to such a being, just as it belongs to all the other things of which we have a distinct idea, even to those which are put together through a fiction of the intellect. Next, when we attend to the immense power of this being, we shall be unable to think of its existence as possible without also recognizing that it can exist by its own power; and we shall infer from this that this being does really exist and has existed from eternity, since it is quite evident by the natural light that what can exist by its own power always exists. So we shall come to understand that necessary existence is contained in the idea of a supremely powerful being, not by any fiction of the intellect, but because it belongs to the true and immutable nature of such a being that it exists. And we shall also easily perceive that this supremely powerful being cannot but possess within it all the other perfections that are contained in the idea of God; and hence these perfections exist in God and are joined together not by any fiction of the intellect but by their very nature.

All this is manifest if we give the matter our careful attention; and it does not differ from anything I have written before, except for the method of explanation adopted. This I have deliberately altered so as to appeal to a variety of different minds. But as I readily admit, it is the kind of argument which may easily be regarded as a sophism by those who do not keep in mind all the elements which make up the proof. For this reason I did have considerable doubts to begin with about whether I should use it; for I feared it might induce those who did not grasp it to have doubts about the rest of my reasoning. But there are only two ways of proving the existence of God, one by means of his effects, and the other by means of his nature or essence; and since I expounded the first method to the best of my ability in the Third Meditation, I thought that I should include the second method later on.

From Objection II (Mersenne): (Order of Presentation)

These, Sir, are the points which we wanted you to clarify, so as to enable everyone to derive the utmost benefit from reading your Meditations, which are argued with great subtlety and are also, in our opinion, true. And after giving your solutions to these difficulties it would be worthwhile if you set out the entire argument in geometrical fashion, starting from a number of definitions, postulates and axioms. You are highly experienced in employing this method, and it would enable you to fill the mind of each reader so that he could see everything as it were at a single glance, and be permeated with awareness of the divine power.

Descartes’s Response:

I now turn to your proposal that I should set out my arguments in geometrical fashion to enable the reader to perceive them 'as it were at a single glance'. It is worth explaining here how far I have already followed this method, and how far I think it should be followed in future. I make a distinction between two things which are involved in the geometrical manner of writing, namely, the order, and the method of demonstration.

The order consists simply in this. The items which are put forward first must be known entirely without the aid of what comes later; and the remaining items must be arranged in such a way that their demonstration depends solely on what has gone before. I did try to follow this order very carefully in my Meditations, and my adherence to it was the reason for my dealing with the distinction between the mind and the body only at the end, in the Sixth Meditation, rather than in the Second. It also explains why I deliberately and knowingly omitted many matters which would have required an explanation of an even larger number of things.

As for the method of demonstration, this divides into two varieties: the first proceeds by analysis and the second by synthesis.

Analysis shows the true way by means of which the thing in question was discovered methodically and as it were a priori, so that if the reader is willing to follow it and give sufficient attention to all points, he will make the thing his own and understand it just as perfectly as if he had discovered it for himself. But this method contains nothing to compel belief in an argumentative or inattentive reader; for if he fails to attend even to the smallest point, he will not see the necessity of the conclusion. Moreover there are many truths which - although it is vital to be aware of them - this method often scarcely mentions, since they are transparently clear to anyone who gives them his attention.

Synthesis, by contrast, employs a directly opposite method where the search is, as it were, a posteriori (though the proof itself is often more a priori than it is in the analytic method). It demonstrates the conclusion clearly and employs a long series of definitions, postulates, axioms, theorems and problems, so that if anyone denies one of the conclusions it can be shown at once that it is contained in what has gone before, and hence the reader, however argumentative or stubborn he may be, is compelled to give his assent. However, this method is not as satisfying as the method of analysis, nor does it engage the minds of those who are eager to learn, since it does not show how the thing in question was discovered.

It was synthesis alone that the ancient geometers usually employed in their writings. But in my view this was not because they were utterly ignorant of analysis, but because they had such a high regard for it that they kept it to themselves like a sacred mystery.

Now it is analysis which is the best and truest method of instruction, and it was this method alone which I employed in my Meditations. As for synthesis, which is undoubtedly what you are asking me to use here, it is a method which it may be very suitable to deploy in geometry as a follow-up to analysis, but it cannot so conveniently be applied to these metaphysical subjects.

The difference is that the primary notions which are presupposed for the demonstration of geometrical truths are readily accepted by anyone, since they accord with the use of our senses. Hence there is no difficulty there, except in the proper deduction of the consequences, which can be done even by the less attentive, provided they remember what has gone before. Moreover, the breaking down of propositions to their smallest elements is specifically designed to enable them to be recited with ease so that the student recalls them whether he wants to or not.

In metaphysics by contrast there is nothing which causes so much effort as making our perception of the primary notions clear and distinct. Admittedly, they are by their nature as evident as, or even more evident than, the primary notions which the geometers study; but they conflict with many preconceived opinions derived from the senses which we have got into the habit of holding from our earliest years, and so only those who really concentrate and meditate and withdraw their minds from corporeal things, so far as is possible, will achieve perfect knowledge of them. Indeed, if they were put forward in isolation, they could easily be denied by those who like to contradict just for the sake of it.

This is why I wrote 'Meditations' rather than 'Disputations', as the philosophers have done, or 'Theorems and Problems', as the geometers would have done. In so doing I wanted to make it clear that I would have nothing to do with anyone who was not willing to join me in meditating and giving the subject attentive consideration. For the very fact that someone braces himself to attack the truth makes him less suited to perceive it, since he will be withdrawing his consideration from the convincing arguments which support the truth in order to find counter-arguments against it.