Given that God is not a deceiver, Descartes next asks, how is it possible that human beings come to make mistakes? The answer, as Descartes shows in principles I.32 through I.44, is that error results only when we form judgments about perceptions that are not clear and distinct. So long as we only assent to clear and distinct perceptions, we will never fall into error.
The fact that we err, then, cannot be seen as an imperfection in the way that God made us. God made us as perfectly as was possible. He gave us, first of all, an infinite will so that we could act voluntarily and thus be considered responsible for our own actions. He also gave us an understanding, capable of showing us clear and distinct perceptions. Our understanding, though, unlike our will, is not infinite. We only understand what we have already reasoned correctly about.
Descartes' claim that God gave us an infinite will leads him into a brief discussion of the problem of free will, in principles I.40 and I.41. Since we know that God is omnipotent and the author of all that occurs, we know that everything that happens is preordained by God. How, then, he asks, can we reconcile this with the idea that we are free to act however we choose? Descartes' answer is surprisingly disappointing. We can reconcile it, he says, by realizing that we do not understand everything about God. In other words, he has no idea how to reconcile it, but that does not mean that it is irreconcilable.
In principle I.40 Descartes moves back from God to clear and distinct perceptions themselves. First he tells us precisely what he means by the term "clear and distinct perception." By calling a perception "clear" he means to say that we fully grasp what is contained in it. To perceive an idea clearly is much like seeing an object in good light. A perception is "distinct," on the other hand, when we also fully grasp what it does not include. A perception can be clear without being distinct, but not vice versa. Pain, to use Descartes' own example, is very clear. It is not, however, always distinct, because people often think that pain is some actual thing existing in the part of the body that feels painful. They do not realize that pain is only a sensation. So though they clearly feel the pain, they do not distinctly perceive what is and is not included in this sensation.
Descartes now begins the main project of the text. He has established his method (i.e. find clear and distinct perceptions, use these to logically derive further clear and distinct perceptions, and so on), and now he is going to implement it. In I.47 he begins an inventory of all of our ideas and asking which of them are clear and distinct. In other words, he is trying to find some more of these all- important ideas so that he can use them to build up his system of certain knowledge. (Remember that up until this point, all he knew for certain was his own existence, God's existence and nature, and a few truths of mathematics).
The first step to this inventory is the division of all ideas into three categories. All of our ideas, Descartes tells us in I.47, belong to one of three types: either they are ideas of things (i.e. substances), the ideas of affections of things (i.e. properties or qualities of substances), or the ideas of eternal truths.
He turns first to the last category, eternal truths, because these are the simplest. Examples of eternal truths include the truths of mathematics and propositions such as, "It is impossible for the same thing to be and not to be at the same time" or "He who thinks cannot but exist while he thinks." These are statements of fact that, we perceive, cannot fail to be true. Though they do not have any concrete existence in the world, Descartes urges us, they certainly must be said to exist in some way.
Eternal truths are very important to Descartes' project. These are the purely intellectual ideas that he wants us to be discovering now, and they are the truths to which we all have access, so long as we withdraw from the senses. He, therefore, wants to give them some sort of real existence in the world. However, though Descartes is adamant that eternal truths exist in some way, he is not entirely clear on how, exactly, they are supposed to exist. There are several options available to him.
First, these truths might exist as their instantiations in the world. So, for instance, the truth "two plus two equals four" would exist as pairs of things in the world that together create quads. Descartes, however, would not be happy with this route. Even if there were no pairs of things in the world, Descartes would still want to say that "two plus two equals four" holds true. He would not want the existence of these truths to depend so heavily on the way the world actually is.
Another option Descartes has, and one that it often looks like he is taking, is to say that eternal truths only exist on our mind. In principle I.49 Descartes refers to them as "eternal truths which reside in our mind." This makes it sound as if eternal truths only exist insofar as someone is thinking about them. If there were no minds to believe "two plus two equals four" then there would be no such truth. Obviously, Descartes would not want this to be the case, any more than he would want the existence of eternal truths to depend on worldly instantiations. In addition, there is a second problem with this option: it makes eternal truths far too subjective. If eternal truths only exist insofar as they are in someone's mind, then whose thought matters? Do they only exist insofar as they are in my mind, in all our minds, or in God's mind? Can they exist for some people and not for others? Eternal truths are supposed to be the same for all of us, so how could they belong to our subjective minds? A final, related, problem with this view is that it makes it sound as if eternal truths are just properties of mind, since thoughts themselves are just properties of mind. Clearly, Descartes does not want eternal truths to exist as properties.
Luckily, there is a third route open to Descartes, and this is the route that he really seems to take. Eternal truths do not have any concrete existence. Instead they have a special sort of intentional existence, which is to say that they exist as the possible objects of thought. They are the things that we think about when we think about geometry, physics, mathematics, essences, etc. They do not need to actually be thought in order to exist, rather they exist as things of which can be thought.