Descartes Meditation Analysis

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
Since he cannot directly prove that we are not dreaming, he assumes the opposite is true, that we are indeed dreaming. It is assumed that if we were dreaming, then we were imagining all of the events and experiences. That would imply that we do not know anything to be real. However, he shows that there are some concepts that are real, such as arithmetic and geometry, which hold to be true regardless of any object's existence. Since he proves that there is some truth in all that we imagine or dream about, hence the idea that we are dreaming is false. Using this reasoning, he concludes that we are not