In Descartes Meditation I, he casts doubt as to whether or not we are dreaming. He first uses modus tollens to cast doubt to our senses. He then he uses redictio ad absurdum to show that even if we are dreaming, there are some things that are still real.
Descartes begins with establishing the key idea of laying a strong foundation for his ideas. He acknowledges that he has preconceived ideas about the world in which he can doubt their truth. He sees this collection of ideas as a pyramid, where his core values and opinions serve as the base for every other idea. He proposes that he should scrutinize his foundation, namely his existence, because proving it false will undermine the truth of any idea built on it. He is saying that if he could destroy the base of the pyramid, then every brick resting on it will collapse.
Descartes then states that all of his beliefs have either been obtained through his senses or through interpretations of his senses. However, he finds that his senses are not reliable, giving an example of a naked madman claiming to be wearing clothes. Using modus tollens, the madman believes that he is wearing clothes; it is obvious from his nakedness that he is not wearing anything. Clearly, the madman's senses are deceiving him, and thus cannot be relied on. Descartes then applies the idea of distorted senses to a more common application of dreams. In dreams, the dreamer cannot be sure of whether or not he is dreaming. Although he may try to test his senses, such as touch or movement or vividness, Descartes claims that he has done similar tests while he was actually dreaming. It is possible that a dreamer can have his senses experience the exact same feelings as if he were in the real world, while he was dreamin ...