"I was led to believe that Descartes argued his new method should be added to existing ones rather than replace them entirely – am I wrong in thinking this way?"
Actually I think you are, but it is of course complicated. My read of the Discourse (certainly not original with me!) traces a sequence of subtle but nevertheless explicit rejections of each category of Descartes' own education: mathematics, physics, metaphysics, aesthetics, etc.
Descartes flatters his masters on the one hand while on the other "provisionally" rejecting every single one of them, never to return. This is the birth of modernism. The rejection of the past, the 'blank slate' of a hypothetical 'view from nowhere' acutely expressed in Descartes' notion of Radical Doubt (in the Meditations on First Philosophy). Descartes argues that, like a city built by multiple architects over many centuries, contemporary knowledge in the 17th Century was brilliant and confused all at once, at odds with itself and incapable of 'clear and distinct' ideas. Therefore he proposes that he himself embark on a provisional quest for certain knowledge, not because of his own genius, but because it is possible that a single philosopher with clarity of purpose can achieve what centuries of confused development cannot. It is an intoxicating proposition, and we moderns have yet to let go of its promise.
Awesome. With your interests and obvious clarity of expression, I'd suggest you pop the Discourse near the top of the queue! What's needful at this point in history, imo, is as many inquisitive, acute minds as possible re-engaging these debates in their original subtlety.
Actually I think you are, but it is of course complicated. My read of the Discourse (certainly not original with me!) traces a sequence of subtle but nevertheless explicit rejections of each category of Descartes' own education: mathematics, physics, metaphysics, aesthetics, etc.
Descartes flatters his masters on the one hand while on the other "provisionally" rejecting every single one of them, never to return. This is the birth of modernism. The rejection of the past, the 'blank slate' of a hypothetical 'view from nowhere' acutely expressed in Descartes' notion of Radical Doubt (in the Meditations on First Philosophy). Descartes argues that, like a city built by multiple architects over many centuries, contemporary knowledge in the 17th Century was brilliant and confused all at once, at odds with itself and incapable of 'clear and distinct' ideas. Therefore he proposes that he himself embark on a provisional quest for certain knowledge, not because of his own genius, but because it is possible that a single philosopher with clarity of purpose can achieve what centuries of confused development cannot. It is an intoxicating proposition, and we moderns have yet to let go of its promise.