Explain how Descartes argues that we can gain a priori knowledge through intuition and deduction

I will begin by considering what apriori knowledge and then intuition and deduction are. On the basis of this I will explain how Descartes argues we can gain a priori knowledge through intuition and deduction. Descartes is a rationalist and therefore believes in a priori knowledge. A priori knowledge is knowledge that does not require sense (sense) experience to be known as true. In contrast a posteriori propositions are necessarily true on the basis of experience, for example 'all bachelors are unmarried men.' is necessarily true. This is a posteriori knowledge as it is established through our experience of the world. We know from our interaction with the world that a bachelor is a single man and therefore an unmarried man. This knowledge cannot be a priori as we could never gain an understanding of it without experience, babies are not aware that bachelors are unmarried men, nor could they be. We can however gain a priori knowledge through deduction. In a deductive argument the conclusion must follow the premise, thus if the premise is true the conclusion follows the proposition is true. In this way using reason you should be able to find truths just by thinking about them, with no reliance on knowledge from experience. The way one sees that the conclusion is true is through the use of 'rational intuition.' . Descrtes argues that we can establish the existence of the mind, the physical world and god through a priori reasoning. He believes we can do this through intuition and deduction. Similarly the a priori propositions discovered in this way are the only things we can truly be sure of. For example, how do you know you are not just a brain in a vat, where you are fed artificial sense experiences that give you the illusion of being a physical being interacting with a real physical world? Or the example Descartes uses, consider that all our sense experiences are produced by an evil demon who wants to deceive us. Both these examples according to Descartes illustrate that a posteriori knowledge is not a sufficient guide to knowing what exists. As such, Descartes uses pure reason to deduce that the only thing he can know is that he is exists, which I will illustrate below; Premise 1: I think (the only thing Descartes can be sure of, he cannot doubt that he thinks because doubting is necessarily thinking) Conclusion: I exist In contrast you cannot conclude that your body or the physical world exists through rational intuition. You may think you have a body due to being deceived by some other force it is not a conclusion you can deduce from thought alone, my belief that I have a body is based on my experience of the body through the senses and as such you cannot be sure of it.