Descartes begins Part I of the Principles by calling all of our beliefs into doubt. This exercise is meant to free us from our reliance on the senses, so that we can begin to contemplate purely intellectual truths.
The doubting is initiated in two stages. In the first stage, all the beliefs we have ever received from sensory perceptions are called into doubt. In the second stage, even our intellectual beliefs are called into doubt.
Descartes presents two reasons for doubting that our sensory perceptions tell us the truth. First of all, our senses have been known to deceive us. Examples of the sort of systematic deception he has in mind here include phenomena such as the bent appearance of a straight stick when viewed in water and the optical illusion of smallness created by distance. The second doubt that Descartes brings to bear on sensory perceptions is more dramatic. Descartes claims that even in optimal viewing conditions (i.e. close by, no intervening water, etc.) we cannot trust our senses. The reason is that when we sleep we often have sensations indistinguishable from those that we have when we are awake. We admit that those dreaming sensations do not correspond to reality, so why are we any more certain of our waking sensations? How do we know that any particular sensation is not just a dream, a sensation stemming from causes unbeknownst to us? This second argument is popularly referred to as the "Dreamer Argument."
Descartes next casts doubt onto our mathematical demonstrations and other self- evident truths. In order to do this, he first points out that people are sometimes known to make mistakes when it comes to these subjects. In addition, he claims, for all we know, God (or some lesser being) is manipulating our thoughts, causing things to seem certain when really they are not. This argument is commonly referred to as the "Evil Demon Argument".
After attempting to undermine all of our beliefs, Descartes identifies one belief that resists all such attempts: the belief that I myself exist. This stage in Descartes' argument is called the cogito, derived from the Latin translation of "I think." It in only in the Principles that Descartes states the argument in its famous form: "I think, therefore I am." This oft- quoted and rarely understood argument is meant to be understood as follows: the very act of thought proves existence, because one cannot possibly think without existing.
The cogito is arguably the most famous argument in philosophy, but what is it really supposed to prove? What is Descartes' purpose in beginning his magnum opus with such a trivial piece of knowledge? In order to see the answer to this question, it is important to view the cogito in its context.
The cogito comes immediately on the heels of a battery of skeptical worries, meant to undermine our faith in our very methods of coming to know the world. Descartes shows that we cannot use our senses to come to know the world and then questions how far reason can get us. The cogito provides the answer: reason can get us somewhere so long as it attends to self-evident truths, truths that cannot be doubted. The cogito's primary importance is that it is our first instance of a truth that cannot possibly be doubted, what Descartes will come to call a clear and distinct perception. By showing that there is a truth that cannot be doubted, he is establishing a basis on which we can build a certain foundation for knowledge. Rather than relying on the doubtful senses, we can seek out these clear and distinct perceptions that are within our own mind (for many others do exist, this was simply the first one he hit upon). We can then use our reason to derive further knowledge from these clear and distinct perceptions. This is the method that Descartes will utilize throughout the rest of the text (and, in fact, in all his writings).
The mathematical demonstrations that Descartes calls into question in principle I.5 also count as self-evident truths, according to Descartes, so one might wonder why it was the cogito, and not one of these truths, that stopped the skeptical worries dead in their tracks. I cannot doubt that two plus two equals four, any more than I can doubt that I can exist, so why is it that only the latter, and not the former, resisted the skeptical onslaught? The reason is that it is only the cogito that is actually proved by the very act of doubting. To say that I doubt that two plus two equals four might make me sound a little stupid, but it is not logically incoherent. On the other hand, the statement "I doubt that I exist" is logically incoherent. I cannot have the capacity for doubt if I do not exist. The famous phrase, then, could just as easily be "I doubt, therefore I am." It is for this reason that the cogito stops the skeptical worries dead in their tracks, while the other clear and distinct impressions fall momentarily prey to doubt.
Many people, starting with Descartes' earliest readers, have questioned whether the cogito really works as an argument. Do you really know you exist, they ask, just from the act of thinking? There are various ways to go about attacking the argument, but all of these rest on a misreading. The cogito is one of those rare philosophical joys: an argument that simply cannot be refuted, so long as it is correctly understood. Most of the objections to the cogito arise because of misguided attempts to reconstruct the argument as a syllogism: (1) Whatever thinks exists, (2) I think, (3) therefore, I exist. Obviously, the argument in this form is not beyond doubt, and there is no certain reason to believe the truth of the first claim. The key to understanding Descartes' brilliant argument is to see that it is not a syllogism at all. There are only two steps to the argument: (1)I think, (2) therefore, I exist. It is the very act of thinking, or doubting, or believing, or sensing, or anything else mental one can do, that proves one's existence. The awareness that you are doing one of these things, amounts to the awareness that you exist, because you cannot do these things without existing.
Another common objection to the cogito asks why it is that only mental operations prove existence. Why, some people ask, can I not say "I jump, therefore I exist?" The reason is that the jumping itself can be doubted. We cannot, however, doubt that we are thinking, sensing, doubting etc. for obvious reasons. We may doubt that what we are sensing is real, or whether our thoughts are caused by an evil demon, but we cannot doubt that we have an awareness of these sensations or of these thoughts. This much, and only this much, is beyond all doubt.