If we take a look at the historical context of the Discourse on Method, it was written around the time the Thirty Years’ War was ravaging Europe, and the book was seen as some sort of reaction to this destructive event with a quest to establish an unshakeable foundation for order. The conflict from within of Christendom (Catholics pitted against Protestants) on who has the privileged access to divine truth was still ongoing, and Descartes presented a truly radical idea at this time: that the individual, the “I”, was the source of knowledge and is capable of reveling in the truth without the voice of some institution or order (by the word “radical”, one has to contextualize the situation into the times, where since the medieval period it had been the church that monopolized the truth-Descartes had been a revolutionary before becoming seen as a dogmatic, systemic philosopher by the later philosophers).
The Discourse on Method then presented a new, more mechanistic approach to knowledge, making it a prioritized text in the achievements of the Scientific Revolution.
In fact, this autobiography of sorts was originally meant to be a “preface” to three books on mechanistic physics and heliocentric conceptions, on geometry, and on meteorology. Throughout the text, Descartes identifies geometry and mathematics as certain things, and used them to build the foundation on what else in the world is to be considered as certain and true.
All these were preludes to the general feel of the Enlightenment period, where man and his reason were the masters, and nature was no longer mysterious, divine or sacred—it was now to be explored, mastered and manipulated.
Technological advances and voyage expeditions somehow embodied Descartes’ mathematical and geometrical type of reducing the seemingly complex physical systems into simple, universal and foundational principles.
As an autobiography and thinly veiled as a “this-is-MY-experience” sort of text (he was speaking out about his dissatisfaction with the how his schooling has given him more doubts than certainty), Descartes talks about this methodological doubt that he used to guide his reason and intellectual development. If he examined each possible belief carefully, and only accepted those about which there could be no doubt, then he’d know he was only believing true things. Beginning with certain principles and moral maxims, he set out to apply this methodological doubt over everything to discover what was true. These included to never to accept things with no evidences as true, and true to be a certain degree of being obedient to what the conventional rules are in practical life (which he differentiates from the contemplative life).
From this, it then follows that he is certain that he can doubt everything but not his own existence. Descartes claimed that he is a soul (NOT necessarily a physical body, because materiality and the senses are still subject under intensive scrutiny), whose very purpose is to think, and in that act of thinking and doubting, it is impossible that he would not exist. Also, because he can doubt, he deduced that doubting is itself an act of imperfection, and so he is imperfect, because it is a greater perfection to know than to doubt. God’s existence is proved in through the causal argument (that if he is imperfect, someone more perfect should have caused the existence of imperfect things) and through the ontological argument (that something totally perfect should exist, because it is a greater perfection to exist in the mind and in reality).
When one is to contextualize it, this method is initially for the set of scientific principles that he has developed as a contribution for the discoveries of the modern era, but the condemnation and excommunication of Galileo and his radical (and heretic) heliocentric conceptions have urged Descartes to discontinue the publication of his more science-inclined essays. However, Descartes’ questions with the method have started the shift of Western psychology and philosophy from Aristotelian scholasticism.
The general feel for the Discourse on Method is somewhat a preparatory course for his philosophy. He presents the principles and moral maxims that he has followed in order to go down the path of the methodological doubt, as well as what this has resulted for him, and, most importantly, that he has chosen to doubt everything he believed in because there were no propositions so doubtful entirely that no semblance of truth can be gathered from it.
The Meditations on First Philosophy, in contrast, was a more refined, serious philosophical work produced by Descartes that provided more details of the Method, spread out into a 6-part retreat to meditate and engage in spiritual exercises, and to probe much deeper into what he had studied previously in the Discourse, most especially in the Meditator’s existence and the existence of God.
By shaking at the foundations of what he has previously known, the Meditator rebuilds from the very starting point and up, withdrawing completely from his senses, because everything he thought he had ever known was given to him by his senses. The senses are very impressionable, either from God or from some evil demon-so how can he ascertain which is true from every little thing delivered to him by his senses?
The first certain principle established in the previous work, the Discourse on Method, is that for him to be able to doubt, he must exist. In order to determine what else exists, he must assure the existence of God, and that God is not deceiving him. His idea of God is one of a perfect being, and this idea cannot be created by his imperfect mind hence, God exists, a being so perfect that He would not deceive him of anything. Errors in perception and interpretation are not to be taken as God’s deception, but rather the fault of the limited intellect.
From this, the Meditator proceeds to scrutinize corporeal things. He instead turns to look at ideas regarding these material things than looking at the things themselves, and conclude that he has distinct ideas about size, shape, position, local motion, duration, and extension of its length, breadth and depth. Hence, this makes it possible for him to imagine triangles, even if, say, he has never seen one. He can distinctly imagine the triangle and other shapes without having previously experienced them with his senses (this line of reasoning was used to prove the existence of God). He then emphasizes the mind-body problem, where the mind is essentially thinking thing, and the body is something that is essentially an extended non-thinking thing (and the real possibility of one being able to exist without the other). The Meditator is then determined as a thinking thing and nothing else, and that because he has a distinct idea of the body as an extended thing, the mind is distinct form the body.
The argument for material objects comes last in 6th Meditation, where the arguments go like such: the Meditator is able to imagine himself without the possession of imagination or understanding or sense, but he is not able to comprehend imagination and sense without needing to attribute them to something that can think; the Meditator has the power of movement, and movement is a power only possessed by extended things.
Hence, it follows that even though he is a thinking thing, he is not only just a thinking thing. It must be that he has an extended body with the power of both passive (examining concepts in his mind) and active sense the latter requiring no intellection, because these ideas gathered by the body’s sense are brought to him against his will. Therefore, it follows that this faculty is not in the mind because he cannot control it, and that this faculty is in a substance that has as much reality as the objective reality of the ideas that it produces. This substance must then an external extended body, unless the Meditator is God (which he is not, as he has established). Therefore, material objects exist, though these objects may sometimes be incorrectly perceived by our senses.
The level at where the mind and body interact begins with the previous argument. The Meditator is intimately joined with the body, where any sensations of pain or pleasure are the confused perceptions arising from the mind’s union with the body. Also, though a lot of our ideas come from the sense, the nature of a thinking thing teaches it not to conclude anything without at least some form of intellectual inquiry. Only the mind is capable of knowing the truth (and certainly not the composite of mind and body), and the senses’ purpose is to determine what is necessary for the welfare of the composite of the mind and body. When it comes to the essences of things, this job is for the mind, and not for the senses that can get easily confused.
We can see the similarity of the Discourse on Method and Meditations on First Philosophy insofar as that they have the same ideas, just with one more refined than the other. While the Discourse is the paradigm shift from the then-standard scholastic Aristotelian concepts, the Meditations is the first step in modern Western philosophy.