In Part Four, Descartes had applied his 4-step method of investigation to some basic problems in philosophy. He did this because he wished to "seek truth in the sciences" (as the title of the Discourse indicates), and he held that the sciences took their basic principles from philosophy.(1)
The basic principles that Descartes discovered in Part Four, the two main things he concluded had to be true, were
Descartes argued that these principles had to be true because his conceptions of them were very clear and distinct, and argued that clear and distinct ideas were guaranteed to be true by the divine being. (In Part Four he also presented an argument to show that a benevolent, all-powerful, infinite, eternal, all-knowing divine being exists.)
So you may be thinking, "OK, but what do those principles have to do with science? What does 'I think, therefore I am' have to do with 'For every action there is an equal and opposite reaction' or Mendel's laws of genetics or the Ideal Gas Law?"
That is the subject of Part Five.
In Part Five, Descartes reports that he used his 4-step method to discover laws of nature:
But what does Descartes mean by "nature"? We can see from the quotations above that it has something to do with matter. In fact, as we will see below, it has everything to do with matter; the human mind, for example, is not subject to the laws of nature. (The human mind is subject to some laws, of course; but Descartes will preserve the idea that the human mind can make its own choices.)
Bodies are made of matter (Paragraph 4). Descartes says that he examined human and non-human bodies (it's not clear how much direct observation was involved; Descartes mainly describes a process of reasoning). He considered the functions that would occur in a body made out of the kinds of matter he had previously found, and says that the functions he discovered were "precisely all the things that could be in us without our thinking of them, and hence without our soul (that is, that part distinct from the body of which I have said that its nature is only to think) contributing to them, and these are all the same so that one can say that nonrational animals resemble us. But I could not on that account find any of those things that, being dependent on thought, are the only things that belong to us insofar as we are men, although I found them all later when I supposed that God created a rational soul and joined it to this body..." (Paragraph 4)
In other words, bodies (human and non-human) are made of matter and thus are subject to laws of nature. No bodily functions (digestion, respiration, circulation, etc.) are caused by the human mind, according to Descartes.(1) He comes to this conclusion because he does not observe any bodily processes that he finds must be explained as having been caused by thought.
In other words, since D. cannot observe anything in body that would have to have been caused by what he thinks thought involves, he concludes that no body processes are caused by thought. This is very similar to the way he had concluded in Part Four that nothing in thinking was due to body: he had not observed anything in thinking that he felt had to be due to body. Once again, the principle of reasoning seems to be: if no influence is noticeable, then no influence is present. This is not necessarily a sound principle!
However, by this means Descartes has established a conceptual separation of what he calls "body" or "matter" (roughly, what can be sensed with the five senses or with instruments that are more delicate than our senses) on the one hand, and "mind" (roughly, those aspects of human experience and consciousness that are not able to be sensed with the five senses). Natural science is the science of "nature," and for Descartes that means the study of those things that are subject to "laws of nature." The things that are subject to "laws of nature" are bodies, matter. Thus modern natural science studies matter. (Modern natural science studies energy too, but in Descartes' time people did not have a clear idea of what that was, and assumed that it was a property or function of matter. Still, energy is supposed to be something we can detect with the five senses or with instruments, so the basic idea of the subject of science is defined in a way Descartes would accept.)
What does all of this have to do with "I think therefore I am"? -- Well, recall that "I think, therefore I am" was the first step in Descartes' "discovery" of the mind's independence from body. And Descartes' idea of science is predicated on a strict separation between mind and body. So is much of natural science today, though that is beginning to change. Still, recall that basic physics books begin by telling you that physics studies matter and energy; basic chemistry books begin by talking about "substances" which are all material; basic biology books begin by describing the "building blocks of life" which are chemical compounds, or by describing the "life functions" which are observable with the five senses or measurable with instruments.
Now, you may be asking, "How does Descartes account for the difference between a living thing and a dead or non-living thing? After all, the Greeks said that 'soul' -- something unmeasurable -- was responsible for that, both in humans and in non-humans." The answer is that Descartes does not subscribe to the Greek idea of soul; he considers the "soul" to be essentially mind. How then does he account for the difference between living things and non-living things? -- He says that bodily processes associated with life (circulation, heat, respiration, digestion) are just things that matter can go through when properly arranged. For example, in Paragraph 4 he attributes body heat to something like fermentation going on in the body (due apparently to chemical reactions from digestion). He thinks circulation may be caused at least in part by this heat, and by other mechanical expansions and contractions. He does not think that any of these things are caused by, or cause, mind.
1.Philosophy was supposed to address the ultimate nature of everything, and the sciences address parts or aspects of what exists. Also, the sciences often start from certain hypotheses and suppositions about what is most basic: physics even today begins by accepting certain definitions of matter and energy, and by assuming that what exists in the universe is matter, energy, and empty space -- nothing else. Unless and until some major problems arise (the discovery of data that cannot fit the hypothesis, failures of prediction, etc.), physicists do not need to ask whether anything exists besides matter, energy, and empty space; whether the accepted definitions of matter and energy make sense or are accurate, etc.
The point is that according to Descartes and most philosophers and scientists of his time, those basic principles that the physicists start from should be checked out by philosophy, and should be explained by principles philosophy had discovered to be true.
1. In other works Descartes deals with the fact that sometimes body and mind affect one another: if we think of something scary we may start physically shaking or get queasy; or if we have bodily ailments such as fevers we may have hallucinations. Although he allows that body and mind can affect one another, he does not think that any life functions in the body are CAUSED by mind (for example, we cannot decide whether to digest or not), or that any mind functions are CAUSED by body (for example, even if the body can affect what we think, D. does not believe the body can CAUSE us to be able to think).