In the First Meditation, Descartes lays out several arguments for doubting all of his previously held beliefs. He first observes that the senses sometimes deceive, for example, objects at a distance appear to be quite small, and surely it is not prudent to trust someone (or something) that has deceived us even once. However, although this may apply to sensations derived under certain circumstances, doesn’t it seem certain that “I am here, sitting by the fire, wearing a winter dressing gown, holding this piece of paper in my hands, and so on”? (AT VII 18: CSM II 13). Descartes’ point is that even though the senses deceive us some of the time, what basis for doubt exists for the immediate belief that, for example, you are reading this article? But maybe the belief of reading this article or of sitting by the fireplace is not based on true sensations at all but on the false sensations found in dreams. If such sensations are just dreams, then it is not really the case that you are reading this article but in fact you are in bed asleep. Since there is no principled way of distinguishing waking life from dreams, any belief based on sensation has been shown to be doubtful. This includes not only the mundane beliefs about reading articles or sitting by the fire but even the beliefs of experimental science are doubtful, because the observations upon which they are based may not be true but mere dream images. Therefore, all beliefs based on sensation have been called into doubt, because it might all be a dream.
This, however, does not pertain to mathematical beliefs, since they are not based on sensation but on reason. For even though one is dreaming, for example, that, 2 + 3 = 5, the certainty of this proposition is not called into doubt, because 2 + 3 = 5 whether the one believing it is awake or dreaming. Descartes continues to wonder about whether or not God could make him believe there is an earth, sky and other extended things when, in fact, these things do not exist at all. In fact, people sometimes make mistakes about things they think are most certain such as mathematical calculations. But maybe people are not mistaken just some of the time but all of the time such that believing that 2 + 3 = 5 is some kind of persistent and collective mistake, and so the sum of 2 + 3 is really something other than 5. However, such universal deception seems inconsistent with God’s supreme goodness. Indeed, even the occasional deception of mathematical miscalculation also seems inconsistent with God’s goodness, yet people do sometimes make mistakes. Then, in line with the skeptics, Descartes supposes, for the sake of his method, that God does not exist, but instead there is an evil demon with supreme power and cunning that puts all his efforts into deceiving him so that he is always mistaken about everything, including mathematics.
In this way, Descartes called all of his previous beliefs into doubt through some of the best skeptical arguments of his day But he was still not satisfied and decided to go a step further by considering false any belief that falls prey to even the slightest doubt. So, by the end of the First Meditation, Descartes finds himself in a whirlpool of false beliefs. However, it is important to realize that these doubts and the supposed falsehood of all his beliefs are for the sake of his method: he does not really believe that he is dreaming or is being deceived by an evil demon; he recognizes that his doubt is merely hyperbolic. But the point of this “methodological” or ‘hyperbolic” doubt is to clear the mind of preconceived opinions that might obscure the truth. The goal then is to find something that cannot be doubted even though an evil demon is deceiving him and even though he is dreaming. This first indubitable truth will then serve as an intuitively grasped metaphysical “axiom” from which absolutely certain knowledge can be deduced. For more, see Cartesian skepticism.