One of the main challenges of Descartes’s commentators is the extent and potency of Descartes hyperbolic doubts. This matter is important since it determines whether Descartes argues in circle or not.
Descartes is ambiguous on whether he doubts his existence or not. In fact, his Meditations suggest both. However, if Descartes doubts his own existence and in order to respond to his doubt, he presents cogito as a form of argument—I think, therefore I am— then he would be in deep trouble. This formulation of cogito does not appear in the Meditations, but in his Principles of Philosophy. Although cogito is presented in the form of argument; however, it does not have characteristics of a valid argument. In fact, if cogito is Descartes’s response to his doubt, then his argument is circular.
In the beginning of Third Meditation, it seems that Descartes goes through radical doubts to the extent of doubting himself. However, I think that in the beginning of the Third Meditation, he merely explains how he knows that he is a thinking thing through intuition. It is through immediate impression, not through an inductive reasoning, that he knows he has a set of beliefs, perceptions, and feelings. As a result, if he applies his truth-maker or certainty-generator principle, i.e., clear and distinct perception, to assess the validity of his intuition of his own existence would not be problematic. As he mentions, “Now some of these perceptions are so transparently clear and at the same time so simple that we cannot ever think of them without believing them to be true. The fact that I exist so long as I am thinking, or that what is done cannot be done, are examples of truths in respect of which we manifestly posses this kind of certainty. For we cannot doubt them unless we think of them; but we cannot think of them without at the same time believing they are true, as was supposed. Hence, we cannot doubt them without at the same time believing hey are true; that is, we can never doubt them” (CSM 104). Therefore, the intuition of self-existence is certain and cannot legitimately be a subject of doubt. In fact, his intuition of his own existence is a doubt-exempt locus of his meditations. That’s why he can safely build the rest of his beliefs on cogito.
Another move is to make a distinction between Descartes as the meditator and Descartes as the writer. Based on this account, Descartes the meditator doubts his existence whereas Descartes the writer never doubts his existence. Descartes, to show that self-doubt is not a legitimate move, makes the meditator to doubt his own existence. After the meditator’s doubts, Descartes shows that these doubts are not legitimate, since Descartes himself knew that knowledge of self is an intuitive knowledge and cannot be doubted rightfully. The knowledge of the self is clear and distinct; therefore, Descartes can respond to the meditator, and people who are supposed to think along with the meditator, that the intuition that give rise to knowledge of the self is certain and trustworthy.
However, the question is that why does Descartes think it is necessary to respond to the doubts about self. Descartes’s purpose is to lay down a new foundation for science. I think that Descartes, to lay a robust foundation for a new science, was compelled to respond to the strongest doubts in order to justify the new foundations. To Descartes, knowledge requires ruling out relevant radical doubts. Descartes’ foundationalism requires finding a robust base for his new science, and this project requires responding to hyperbolic doubts. For this reason, it is doubtful that he personally believed in those doubts. Descartes claims that his philosophical inquiry is a geometrical way of arguing which each proof relies on the validity of the former proof. He thinks that employing geometrical writing in philosophical inquiry is a new path that he has started. However, his hyperbolic doubts along with his new approach of inquiry and his ambitious aim to build new robust foundations all represent his revolutionary sentiment in philosophy.
 On cogito, he says, “I have convinced myself that there is absolutely nothing in the world, no sky, no earth, no minds, no bodies. Does it now follow that I too do not exist? No: if I convinced myself of something then I certainly existed. But there is a deceiver of supreme power and cunning who is deliberately and constantly deceiving me. In that case I too undoubtedly exist, if he is deceiving me; and let him deceive me as much as he can, he will never bring it about that I am nothing so long as I think that I am something. So after considering everything very thoroughly, I must finally conclude that this proposition, I am, I exist, is necessarily true whenever it is put forward by me or conceived in my mind.” (Med. 2, AT 7:25)