Descartes is a remarkably good writer, and his dramatic progress in the first two Meditations seems natural and unpremediated. It is important to realize that Descartes is employing not just one but two methods (The methods of doubt and analysis) in his descent into the pit of skepticism and that his progress is thus very methodical. We will begin here by focusing on the Method of Doubt.

What is the Method of Doubt? Descartes says that he wishes to examine those things which he thinks to be true and set aside all those beliefs of which there might be some doubt. Examining all of one's beliefs, one by one, would be a very long, chancy and impractical process. So, Descartes needs a way to group beliefs together, which will allow him to call into question whole classes of beliefs by questioning their common character. He finds such a way to group beliefs by focusing on the faculty, such as the senses, the imagination or reason, from which beliefs are derived. He then deploys a series of more and more powerful skeptical hypotheses which call into question his claims to knowledge derived from these faculties. A method is a procedure for doing something which is repeated. Descartes method of doubt, then, is to deploy a skeptical hypothesis, see what can and what cannot be doubted on that hypothesis, and then if there is something which can be doubted, to deploy a still stronger skeptical hypothesis to see if that which could not be doubted on the earlier hypothesis can be called into question by a stronger skeptical hypothesis.

The following table represents the methodical progress which Descartes makes in the first two Meditations towards finding something which he cannot doubt, and thus knows for certain. The table demonstrates that Descartes is moving from one faculty to another, from the senses through the imagination to reason. Each of these faculties is the source of a whole vast set of propositions which one might claim to know. Each skeptical hypothesis acts like a sieve, some things it will not allow through -- these are the things which can be doubted on that hypothesis, while others it allows to pass -- those things which cannot be doubted on that hypothesis. Thus as each skeptical hypothesis is found to leave something which cannot be doubted, a new and more powerful skeptical hypothesis is deployed to try to bring those things which fomerly could not be doubted into doubt. Since those things which can be doubted are studied by various crafts and sciences, these sciences themselves are called into doubt as Descartes proceeds. Finally Descartes finds a truth, the truth that while he exists he cannot be deceived into thinking that he does not, which cannot be doubted on the most powerful of skeptical hypotheses ever deployed -- the Evil Genius hypothesis.
Skeptical Hypothesis What Can Be Doubted What Cannot be doubted Faculty Science
The Senses Deceive us at a distance The size of the sun and stars, the shape of towers and the color of mountains Things observed close at hand, e.g. that I am now seated in a room etc. The senses Astronomy
The Dream Hypothesis That I am seated in this room, that I am clothed, that I have hands, eyes or a body at all Truths of mathematics, eg. 2+2 = 4, squares have four sides etc. The imagination Physiology, physics, medicine etc.
The Evil Genius hypothesis 2 + 2 = 4, squares have four sides, etc. That I exist etc. Reason Mathematics, i.e. arithemetic , geometry etc.
Descartes' achievement in isolating a truth he cannot doubt by use of this method is to defeat the universal skeptical claims that nothing is known (except that one knows nothing) -- the claim of the Academic skeptic or alternatively that nothing is known (and one does not even know that) -- the claim of the Pyhronian skeptic. This is hardly the end of skepticism, however, since many other more limited skeptical arguments remain to be defeated.