From Objection I (Caterus): (Objective Reality)

'Nevertheless', says our ingenious author, 'in order for a given idea to contain such and such objective reality it must surely derive it from some cause.' On the contrary, this requires no cause; for objective reality is a pure label, not anything actual. A cause imparts some real and actual influence; but what does not actually exist cannot take on anything, and so does not receive or require any actual causal influence. Hence, though I have ideas, there is no cause for these ideas, let alone some cause which is greater than I am, or which is infinite.

'But if you do not grant that ideas have a cause, you must at least explain why a given idea contains such and such objective reality.' Certainly; I do not normally stint my friends, but am as lavish as possible. I take the same general view about all ideas as M. Descartes takes of a triangle. He says: 'even if perhaps no such figure exists, or has ever existed, anywhere outside my thought, there is still a determinate nature or essence or form which is immutable and eternal'. What we have here is an eternal truth, which does not require a cause. A boat is a boat and nothing else. Davus is Davus and not Oedipus. But if you insist on having an explanation, the answer lies in the imperfection of our intellect, which is not infinite. For since it does not comprehend in one single grasp that totality that is all at once and once for all, it divides and separates out the universal good, and being unable to bring forth the totality, it conceives of it piecemeal, or, as they say, inadequately.

Descartes’s Response:

When the learned theologian says that there is an equivocation in what I say here, he apparently means to remind me of the point I have just made, in case I should forget it. He says, first of all, that when a thing exists in the intellect by means of an idea, it is not an actual entity, that is, it is not a being located outside the intellect; and this is quite true. Next he goes on to say that 'it is not something fictitious or a conceptual entity but something real which is distinctly conceived'; here he concedes everything which I have assumed. But he then adds 'since it is merely conceived and is not actual' - i.e. since it is merely an idea, and not a thing located outside the intellect- 'although it can be conceived it cannot in any way be caused'. This is to say that it does not require a cause enabling it to exist outside the intellect. This I accept; but it surely needs a cause enabling it to be conceived, which is the sole point at issue. Thus if someone possesses in his intellect the idea of a machine of a highly intricate design, it is perfectly fair to ask what is the cause of this idea. And it will not be an adequate reply to say that the idea is not anything outside the intellect and hence that it cannot be caused but can merely be conceived. For the precise question being raised is what is the cause of its being conceived. Nor will it suffice to say that the intellect itself is the cause of the idea, in so far as it is the cause of its own operations; for what is at issue is not this, but the cause of the objective intricacy which is in the idea. For in order for the idea of the machine to contain such and such objective intricacy, it must derive it from some cause; and what applies to the objective intricacy belonging to this idea also applies to the objective reality belonging to the idea of God. Now admittedly there could be various causes of the intricacy contained in the idea of the machine. Perhaps the cause was a real machine of this design which was seen on some previous occasion, thus producing an idea resembling the original. Or the cause might be an extensive knowledge of mechanics in the intellect of the person concerned, or perhaps a very subtle intelligence which enabled him to invent the idea without any previous knowledge. But notice that all the intricacy which is to be found merely objectively in the idea must necessarily be found, either formally or eminently, in its cause, whatever this turns out to be. And the same must apply to the objective reality in the idea of God. Yet where can the corresponding reality be found, if not in a really existing God? But my shrewd critic sees all this quite well, and he therefore concedes that we can ask why a given idea contains such and such objective reality. His answer is that, in the case of all ideas, what I wrote in connection with the idea of a triangle holds good, namely that 'even if perhaps a triangle does not exist anywhere, it still has a determinate nature or essence or form which is immutable and eternal'. And this, he says, does not require a cause. But he is well aware that this is not an adequate reply; for even if the nature of the triangle is immutable and eternal, it is still no less appropriate to ask why there is an idea of it within us. Hence he adds 'If you insist on having an explanation, the answer lies in the imperfection of our intellect', etc. In making this reply he simply means, I think, that those who have tried to take a different view from mine on this issue have no plausible reply to make. For surely to claim that the imperfection of our intellect is the cause of our having the idea of God is as implausible as claiming that lack of experience in mechanics is the cause of our imagining some very intricate machine as opposed to a more imperfect one. On the contrary, if someone possesses the idea of a machine, and contained in the idea is every imaginable intricacy of design, then the correct inference is plainly that this idea originally came from some cause in which every imaginable intricacy really did exist, even though the intricacy now has only objective existence in the idea. By the same token, since we have within us the idea of God, and contained in the idea is every perfection that can be thought of, the absolutely evident inference is that this idea depends on some cause in which all this perfection is indeed to be found, namely a really existing God. The latter inference would not present any more problems than the former, were it not the case that we all have the same ability to conceive of the idea of God, whereas everyone is not equally experienced in mechanics, and so not everyone can have an idea of a very intricate machine. Because the idea of God is implanted in the same way in the minds of all, we do not notice it coming into our minds from any external source, and so we suppose it belongs to the nature of our own intellect. This is correct enough, but we forget something else which is a most important consideration - indeed one on which the entire luminous power of the argument depends - namely that this ability to have within us the idea of God could not belong to our intellect if the intellect were simply a finite entity (as indeed it is) and did not have God as its cause. Hence I went on to inquire 'whether I could exist if God did not exist'. But my purpose here was not to produce a different proof from the preceding one, but rather to take the same proof and provide a more thorough explanation of it.

From Objection I (Caterus): (Idea of the infinite)

But now use this rule to make the inference you wanted. 'I am clearly and distinctly aware of an infinite being; hence this is a true entity and something real.' Yet will not someone ask 'Are you clearly and distinctly aware of an infinite being? What, in that case, is the meaning of that well-worn maxim which is common knowledge: the infinite qua infinite is unknown?' When I think of a chiliagon, and construct for myself a confused representation of some figure, I do not distinctly imagine the chiliagon itself, since I do not distinctly see the thousand sides. And if this is so, then the question obviously arises as to how the infinite can be thought of in a distinct as opposed to a confused manner, given that the infinite perfections that make it up cannot be seen clearly 'before the eyes' as it were.

Descartes’s Response:

At this point, however, he shrewdly asks whether I am 'clearly and distinctly aware of the infinite'. I did try to anticipate this objection, but it is one which occurs so spontaneously to everyone that it is worthwhile replying to it at some length. So let me say first of all that the infinite, qua infinite, can in no way be grasped. But it can still be understood, in so far as we can clearly and distinctly understand that something is such that no limitations can be found in it, and this amounts to understanding clearly that it is infinite.

Now I make a distinction here between the indefinite and the infinite. I apply the term 'infinite', in the strict sense, only to that in which no limits of any kind can be found; and in this sense God alone is infinite. But in cases like the extension of imaginary space, or the set of numbers, or the divisibility of the parts of a quantity, there is merely some respect in which I do not recognize a limit; so here I use the term 'indefinite' rather than 'infinite', because these items are not limitless in every respect.

Moreover, I distinguish between the formal concept of the infinite, or 'infinity', and the thing which is infinite. In the case of infinity, even if we understand it to be positive in the highest degree, nevertheless our way of understanding it is negative, because it depends on our not noticing any limitation in the thing. But in the case of the thing itself which is infinite, although our understanding is positive, it is not adequate, that is to say, we do not have a complete grasp of everything in it that is capable of being understood. When we look at the sea, our vision does not encompass its entirety, nor do we measure out its enormous vastness; but we are still said to 'see' it. In fact if we look from a distance so that our vision almost covers the entire sea at one time, we see it only in a confused manner, just as we have a confused picture of a chiliagon when we take in all its sides at once. But if we fix our gaze on some part of the sea at close quarters, then our view can be clear and distinct, just as our picture of a chiliagon can be, if it is confined to one or two of the sides. In the same way, God cannot be taken in by the human mind, and I admit this, along with all theologians. Moreover, God cannot be distinctly known by those who look from a distance as it were, and try to make their minds encompass his entirety all at once. This is the sense in which St Thomas says, in the passage quoted, that the knowledge of God is within us 'in a somewhat confused manner'. But those who try to attend to God's individual perfections and try not so much to take hold of them as to surrender to them, using all the strength of their intellect to contemplate them, will certainly find that God provides much more ample and straightforward subject-matter for clear and distinct knowledge than does any created thing.

From Objection IV (Arnauld): (Cartesian Circle)

I have one further worry, namely how the author avoids reasoning in a circle when he says that we are sure that what we clearly and distinctly perceive is true only because God exists.

But we can be sure that God exists only because we clearly and distinctly perceive this. Hence, before we can be sure that God exists, we ought to be able to be sure that whatever we perceive clearly and evidently is true.

Descartes’s Response:

Lastly, as to the fact that I was not guilty of circularity when I said that the only reason we have for being sure that what we clearly and distinctly perceive is true is the fact that God exists, but that we are sure that God exists only because we perceive this clearly: I have already given an adequate explanation of this point in my reply to the Second Objections, under the headings Thirdly and Fourthly, where I made a distinction between what we in fact perceive clearly and what we remember having perceived clearly on a previous occasion. To begin with, we are sure that God exists because we attend to the arguments which prove this; but subsequently it is enough for us to remember that we perceived something clearly in order for us to be certain that it is true. This would not be sufficient if we did not know that God exists and is not a deceiver.

As to the fact that there can be nothing in the mind, in so far as it is a thinking thing, of which it is not aware, this seems to me to be self-evident. For there is nothing that we can understand to be in the mind, regarded in this way, that is not a thought or dependent on a thought. If it were not a thought or dependent on a thought it would not belong to the mind qua thinking thing; and we cannot have any thought of which we are not aware at the very moment when it is in us. In view of this I do not doubt that the mind begins to think as soon as it is implanted in the body of an infant, and that it is immediately aware of its thoughts, even though it does not remember this afterwards because the impressions of these thoughts do not remain in the memory.

But it must be noted that, although we are always actually aware of the acts or operations of our minds, we are not always aware of the mind's faculties or powers, except potentially. By this I mean that when we concentrate on employing one of our faculties, then immediately, if the faculty in question resides in our mind, we become actually aware of it, and hence we may deny that it is in the mind if we are not capable of becoming aware of it.

From Objection IV (Arnauld): (Materially false ideas)

In the first part, the only thing I would criticize is this. The author first asserts that 'falsity in the strict sense can occur only in judgements'; but a little later he admits that ideas can be false - not 'formally false' but 'materially false', and this seems to me to be inconsistent with the author's own principles.

I am afraid that on a topic as obscure as this I may not be able to explain what I want to say with sufficient lucidity; but an example will clarify the issue. The author says that 'if cold is merely the absence of heat, the idea of cold which represents it to me as a positive thing will be materially false'.

But if cold is merely an absence, then there cannot be an idea of cold which represents it to me as a positive thing, and so our author is here confusing a judgement with an idea.

What is the idea of cold? It is coldness itself in so far as it exists objectively in the intellect. But if cold is an absence, it cannot exist objectively in the intellect by means of an idea whose objective existence is a positive entity. Therefore, if cold is merely an absence, there cannot ever be a positive idea of it, and hence there cannot be an idea which is materially false.

This is confirmed by the very argument that the author uses to prove that the idea of an infinite being cannot but be a true idea, since, though I can pretend that such a being does not exist, I cannot pretend that the idea of such a being does not represent anything real to me.

The same can plainly be said of any positive idea. For although it can be imagined that cold, which I suppose to be represented by a positive idea, is not something positive, it cannot be imagined that the positive idea does not represent anything real and positive to me. For an idea is called 'positive' not in virtue of the existence it has as a mode of thinking (for in that sense all ideas would be positive), but in virtue of the objective existence which it contains and which it represents to our mind. Hence the idea in question may perhaps not be the idea of cold, but it cannot be a false idea.

But, you may reply, it is false precisely because it is not the idea of cold. No: it is your judgement that is false, if you judge that it is the idea of cold. The idea itself, within you, is completely true. In the same way, the idea of God should never be called false - not even 'materially false', even though someone may transfer it to something which is not God, as idolaters have done.

Lastly, what does the idea of cold, which you say is materially false, represent to your mind? An absence? But in that case it is true. A positive entity? But in that case it is not the idea of cold. Again, what is the cause of the positive objective being which according to you is responsible for the idea's being materially false? 'The cause is myself', you may answer, 'in so far as I come from nothing.' But in that case, the positive objective being of an idea can come from nothing, which violates the author's most important principles.

Descartes’s Response:

But let us deal with the points more carefully one at a time. When M. Arnauld says 'if cold is merely an absence, there cannot be an idea of cold which represents it as a positive thing', it is clear that he is dealing solely with an idea taken in the formal sense. Since ideas are forms of a kind, and are not composed of any matter, when we think of them as representing something we are taking them not materially but formally. If, however, we were considering them not as representing this or that but simply as operations of the intellect, then it could be said that we were taking them materially, but in that case they would have no reference to the truth or falsity of their objects. So I think that the only sense in which an idea can be said to be 'materially false' is the one which I explained. Thus, whether cold is a positive thing or an absence does not affect the idea I have of it, which remains the same as it always was. It is this idea which, I claim, can provide subject-matter for error if it is in fact true that cold is an absence and does not have as much reality as heat; for if I consider the ideas of cold and heat just as I received them from my senses, I am unable to tell that one idea represents more reality to me than the other.

I certainly did not 'confuse a judgement with an idea'. For I said that the falsity to be found in an idea is material falsity, while the falsity involved in a judgement can only be formal.

When my critic says that the idea of cold 'is coldness itself in so far as it exists objectively in the intellect', I think we need to make a distinction. For it often happens in the case of obscure and confused ideas - and the ideas of heat and cold fall into this category - that an idea is referred to something other than that of which it is in fact the idea. Thus if cold is simply an absence, the idea of cold is not coldness itself as it exists objectively in the intellect, but something else, which I erroneously mistake for this absence, namely a sensation which in fact has no existence outside the intellect.

The same point does not apply to the idea of God, or at least to the idea of God which is clear and distinct, since it cannot be said to refer to something with which it does not correspond. But as for the confused ideas of gods which are concocted by idolaters, I see no reason why they too cannot be called materially false, in so far as they provide the idolaters with subject-matter for false judgements. Yet ideas which give the judgement little or no scope for error do not seem as much entitled to be called materially false as those which give great scope for error. It is easy to show by means of examples that some ideas provide much greater scope for error than others. Confused ideas which are made up at will by the mind, such as the ideas of false gods, do not provide as much scope for error as the confused ideas arriving from the senses, such as the ideas of colour and cold (if it is true, as I have said, that these ideas do not represent anything real). The greatest scope for error is provided by the ideas which arise from the sensations of appetite. Thus the idea of thirst which the patient with dropsy has does indeed give him subject-matter for error, since it can lead him to judge that a drink will do him good, when in fact it will do him harm.

But my critic asks what the idea of cold, which I described as materially false, represents to me. If it represents an absence, he says, it is true; and if it represents a positive entity, it is not the idea of cold. This is right; but my only reason for calling the idea 'materially false' is that, owing to the fact that it is obscure and confused, I am unable to judge whether or not what it represents to me is something positive which exists outside of my sensation. And hence I may be led to judge that it is something positive though in fact it may merely be an absence.

Hence in asking what is the cause of the positive objective being which, in my view, is responsible for the idea being materially false, my critic has raised an improper question. For I do not claim that an idea's material falsity results from some positive entity; it arises solely from the obscurity of the idea - although this does have something positive as its underlying subject, namely the actual sensation involved.

Now this positive entity exists in me, in so far as I am something real. But the obscurity of the idea is the only thing that leads me to judge that the idea of the sensation of cold represents some object called 'cold' which is located outside me; and this obscurity in the idea does not have a real cause but arises simply from the fact that my nature is not perfect in all respects.

This does not in any way violate my fundamental principles. One fear that I might have had, however, is that since I have never spent very much time reading philosophical texts, my calling ideas which I take to provide subject-matter for error 'materially false' might have involved too great a departure from standard philosophical usage. This might, I say, have worried me, had I not found the word 'materially' used in an identical sense to my own in the first philosophical author I came across, namely Suarez, in the Metaphysical Disputations, Part IX, Section 2, Number 4.