Descartes hopes to come to one irrefutable truth on which he can build his philosophy. The truth that he eventually comes to is often called the “cogito argument,” after Descartes’ triumphant declaration in Discourse on the Method,Cogito ergo sum. Through this argument, he decides that he is a “thing that thinks.” In doing so, he reasons that we can only be certain of our minds and cannot be certain of our bodies’ existence.

With the wax argument, Descartes advances a new conception of the mind and its properties. Aristotle had held that the mind is only intellect and that sensation and imagination are properties of the body. Descartes insists that sensation and imagination, though they involve the body, are actually properties of the mind. Although we receive information through our senses when looking at unmelted wax and melted wax, neither our senses nor our imagination can tell us that both of these things are wax or that the wax started out unmelted and ended up melted. Only intellect can make that judgment. Without intellect, our perceptions and imaginings are meaningless and tell us nothing about the world.

The arguments expressed in meditation III are often called, derogatorily, “the Cartesian Circle.” Descartes argues that realizations such as Cogito ergo sum are “clear and distinct perceptions” and therefore certain. Essentially, Descartes claims that such perceptions are true because they are clear and distinct, and they are clear and distinct because it is obvious that they are true. This is called circular logic, and Descartes doesn’t want to be caught in this circle. He therefore attempts to legitimize all clear and distinct truths by claiming they are provided by God.

If God exists, then truth is possible, since God is truth and perfection. But Descartes attempts to prove that God exists by relying on his own clear and distinct perception of God’s existence. He is arguing that it is possible to have clear and distinct perception because we know that God exists and that we know that God exists because we have a clear and distinct perception of his existence. This logic is, again, circular. Descartes attempts to bolster this argument by saying that the idea of perfection, or God, must come from something outside of his own imperfect mind. He reasons that perfection must come from one source, and that source must be the perfect, all-powerful God. This argument has never held much philosophical weight, and it is tempting to see it as merely the result of caution on Descartes’ part about going too far with his doubt and exposing himself to censure.

Descartes’ idea that God can’t deceive us because God is good comes from ancient Greek ideas of virtue and truth, specifically from Plato. In this scheme, truth, existence, and virtue are inextricably linked. Good things are true and real, and bad things are unreal and false. Since God exists infinitely (the ultimate reality), we know that God cannot participate in deception. If Descartes makes mistakes, then it must be somehow helpful to the universe for mistakes to exist. Otherwise, they would not be allowed. A page torn from a book of poetry might seem meaningless, but when the page is in the book, the book as a whole makes sense.

Descartes makes an important distinction between the intellect and the human will. The intellect, crafted by God, is the source of understanding, sensation, and imagination. The will is our ability to either affirm or deny what our intellect tells us. If the will affirms something that is not true with the information the intellect delivers, then the will is always at fault, not the intellect. The difficulty lies in discerning when the will has made a mistake. Descartes, therefore, returns to the idea that we can only know what is true if we have had a clear and distinct perception. If we resolve to only ever believe what we have proved to ourselves, then we will be able to distinguish between what is clear and distinct and what is false and uncertain. Once we arrive at that point, the whole world of knowledge will open up to us.

Meditation V is an intermediary step in figuring out whether the material world exists. First, Descartes has to figure out whether he can believe even in things about which he has had clear and distinct perception. Naturally, he turns first to geometric and mathematical problems. Descartes, in the rationalist manner, argues that we learn the essence of things not through our interaction with them on a physical level but through our intellect. A triangle is a triangle because it has three sides, not because our senses tell us that a triangle has three sides. Because they are concepts and they exist in our intellect, we can be sure that triangles exist and have three sides. For Descartes, this is a “clear and distinct perception.” Essences of things are always clearly and distinctly perceived.

Turning to the physical world, Descartes asserts we can clearly and distinctly perceive that bodies are “extended.” Extended is a word that Descartes uses to describe something like “has physical mass” or “takes up space.” Therefore, if we so clearly perceive that bodies are extended, then extension must be an essential part of bodies. Part of their essence is to exist in the physical realm. His acceptance of the existence of the body and the physical world in meditation VI is similarly predicated on clear and distinct perceptions of them, ultimately provided by God.

We may find it strange that one of the greatest works of a genius who founded a revolutionary school of philosophy would conclude by agreeing that, yes, we do have bodies after all, but for Descartes, what matters is not the conclusion we reach but the method by which we reach it. His conclusion is the hard-won result of years of study. Obviously, Descartes’ years of study were not undertaken to prove that we have bodies and that the world exists. He never seriously doubted either of these things. His study was undertaken to prove that some form of truth existed and that it was possible to find it. He concludes with the truth that it is permissible to trust that our senses convey accurate information to our brains as long as we apply our intellect to all that information and rightly deduce information from it. And on this simple maxim, a whole new kind of thinking was born.