In part four, the most important part of the Discourse, Descartes describes the results of his meditations following the method he previously laid down. Whereas he had earlier undertaken to act decisively even when he was uncertain, he now takes the opposite course, and considers as false anything that is at all doubtful. This way, he can be sure that he holds on only to things that are indubitably certain. He abandons all sensory knowledge, since the senses can deceive, all demonstrative reasoning, since people often make errors in their reasoning, and imagines that everything that has ever entered his mind is just illusions brought on by dreams.
Even in doubting all this, however, he observes that he must be something in order to doubt. This doubt requires thought, and this thought confirms his existence, so he adopts the principle "I am thinking, therefore I exist," as the indubitable foundation upon which he will build. Since his knowledge of his existence hinges exclusively on his thinking, he concludes that he is essentially a thinking substance, and that his soul is totally distinct from, and easier to know than, the body.
In considering how he knows that "I am thinking, therefore I exist" is true, he notes that there is nothing persuasive about the proposition in itself, but that he sees clearly and distinctly that it is necessarily true. He thus adopts such clear and distinct perceptions as the guarantors of truth.
While it is possible that thoughts of external objects like the sky, the earth, light, and so on are all delusions of the mind, Descartes asserts that the same is not possible of God. These other thoughts are of imperfect objects, so they could easily be invented by an imperfect mind. However, it is inconceivable that Descartes's imperfect mind could invent the idea of a perfect God: that would mean that the existence of a perfect being depended on an imperfect being. Descartes concludes that God is a perfect mind, and that all the perfections in himself and in other bodies are due to God's perfection.
Descartes arrives at another proof of God's existence by way of geometry. He notes the certainty with which geometers can prove facts such as the fact that the angles in a triangle add up to 180 degrees. This is part of the essence of a triangle, and yet for all that, there is no assurance that one triangle actually exists in the world. When contemplating God, however, he recognizes that existence is as much an essential property of God's as having three angles that add up to 180 degrees is an essential property of triangles. God's existence is thus as certain as a geometric proof. Descartes remarks that people have difficulty with these proofs because they rely exclusively on their senses and imagination. God's existence can only be perceived by reason, and not by these other two faculties.
In fact, God's existence is more certain than anything else, since all other things are subject to the doubts that Descartes has already raised. These doubts can only be removed by the recognition that God exists. Thanks to God we can be assured that our clear and distinct perceptions are true, since those perceptions come to us from God, and we can rest assured that all our perceptions must be true to the extent to which they are clear and distinct. We perceive clearly and distinctly when we exercise our reason properly, and we are misled when we rely exclusively on our senses or imagination.
Part Four of the Discourse reads as a very brief summary of the first three Meditations (though the geometrical proof of God's existence is in the Fifth Meditation). A more detailed commentary on all these matters can be found in the SparkNote on the Meditations. This commentary will simply be a brief overview.
At the beginning of his investigation, Descartes undertakes to consider as false everything that he can possibly doubt. Such doubt effectively demolishes the whole enterprise of Aristotelian philosophy, which bases its claims on sensory experience and demonstrative reasoning. His goal is to sweep away the philosophical prejudices of the previous two thousand years and to start afresh. In doing so, he also manages to set the tone for the nearly four hundred years of philosophy that follow him. The questions of how we can know that there are objects external to our minds, that there are minds other than our own, and so on, have been hotly contested in the light of Descartes's new standard for what counts as certainty.
Perhaps Descartes's most significant contribution to philosophy is his revolutionary conception of what the human mind is. According to Aristotelian philosophy, only reason and understanding are distinctly mental properties. Sensing, imagination, and willing are not simply mental properties, since they connect the mind with objects in the world. Descartes overturns this conception, suggesting that our sense experience, imagination, and will are all a part of the mind alone, and are not linked to the world. In suggesting that we may be dreaming or otherwise deceived, Descartes argues that sensory experience is not necessarily a faithful report of what is actually in the world. Effectively, Descartes re-conceives the mind as a thing—the source of all the thoughts, sensations, imaginings, and so on that constitute our world—trapped inside our body. How our mind can connect with a world outside this body has been a pressing problem for all modern humans since Hamlet.
"I am thinking, therefore I exist" is Descartes's proposed way out. This famous phrase is less precisely translated as "I think, therefore I am." The fact that I am thinking right now, and not that I am capable of thought, is what confirms that I exist right now, and not that "I am" in general. Descartes cannot doubt that he exists, and so he claims to have certain knowledge of this fact. It is quite tricky, however, to determine the nature of this knowledge. Descartes has doubted the certainty of demonstrative reasoning, so it can't follow from a logical argument. Descartes's answer is that it is a "clear and distinct perception": it is not something he has to argue for; it is something that it is simply impossible to doubt.
Descartes seems to argue in a circle later in his discussion, when he claims that God confirms the truth of clear and distinct perceptions. This implies that without God, clear and distinct perceptions would not be true. But he has only managed to "prove" that God exists by appealing to a clear and distinct perception to that effect. What, then, is the foundation upon which Descartes builds? If God is the source of all truth, including the truth of clear and distinct perceptions, how can Descartes prove that God exists? And if clear and distinct perceptions are the source of all truth, then what role does God play in all this?
We should note that Descartes's "proofs" of God are neither original nor very satisfying. Unlike his revolutionary ideas about the nature of the mind and of certainty, his proofs of God are borrowed from the medieval scholastic tradition. The first proof claims that the idea of God, as an idea of perfection, must be caused by something as perfect as the idea itself. This proof relies on notions of causation that are questionable to say the least. The second proof claims that existence is a property of God just as geometrical figures have certain properties. Kant was the first to point out that "exists" is not a property in the way that "angles add up to 180 degrees" is. Having angles that add up to 180 degrees is a property of a triangle: it says something about the triangle. Existing, however, is not a property of God's so much as it is a property of the world: it is saying that the world is such that God exists in (or above) it.
The ideas presented in this part are difficult to engage with head on. They represent a particular worldview, both in their approach and in their conclusions. This worldview, this "method," has defined the shape of Western culture in ways that we are hardly even aware of any more.