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Meditations on First Philosophy (1641) and Principles of Philosophy (1644), main works of French mathematician and scientist René Descartes, considered the father of analytic geometry and the founder of modern rationalism, include the famous dictum "I think, therefore I am."
A set of two perpendicular lines in a plane or three in space intersect at an origin in Cartesian coordinate system. Cartesian coordinate, a member of the set of numbers, distances, locates a point in this system. Cartesian coordinates describe all points of a Cartesian plane.
From given sets, {X} and {Y}, one can construct Cartesian product, a set of all pairs of elements (x, y), such that x belongs to {X} and y belongs to {Y}.
René Descartes, a writer, highly influenced society. People continue to study closely his writings and subsequently responded in the west. He of the key figures in the revolution also apparently influenced the named coordinate system, used in planes and algebra.
Descartes frequently sets his views apart from those of his predecessors. In the opening section of the Passions of the Soul, a treatise on the early version of now commonly called emotions, he goes so far to assert that he writes on his topic "as if no one had written on these matters before." Many elements in late Aristotelianism, the revived Stoicism of the 16th century, or earlier like Saint Augustine of Hippo provide precedents. Naturally, he differs from the schools on two major points: He rejects corporeal substance into matter and form and any appeal to divine or natural ends in explaining natural phenomena. In his theology, he insists on the absolute freedom of act of creation of God.
Baruch Spinoza and Baron Gottfried Wilhelm von Leibniz later advocated Descartes, a major figure in 17th century Continent, and the empiricist school of thought, consisting of Thomas Hobbes, John Locke, George Berkeley, and David Hume, opposed him. Leibniz and Descartes, all well versed like Spinoza, contributed greatly. Descartes, the crucial bridge with algebra, invented the coordinate system and calculus. Reflections of Descartes on mind and mechanism began the strain of western thought; much later, the invention of the electronic computer and the possibility of machine intelligence impelled this thought, which blossomed into the Turing test and related thought. His stated most in §7 of part I and in part IV of Discourse on the Method.
The seventeenth century saw a dramatic rise in mechanistic and mathematical explanations in science, descriptions of the natural world that referred only to the motion of matter (often in the form of mathematical formulas) in order to account for all observable phenomena. Descartes was not the first scientist to develop a mechanistic, mathematical science, though he was influential in its development and perhaps was the most ambitious scientist in terms of his scope. He was, however, the first to give a thorough and comprehensive philosophical response to the demands raised by this new way of viewing the world. His writings initiated a dramatic revision of philosophical method and concerns.
Descartes explains in the preface to the Principles why he felt the need to give a philosophical response to the new science in the first place. As he writes there, he viewed all of human knowledge as a tree, each part relying heavily on the others for vitality. The trunk of the tree he compared to physics, and the branches to the applied sciences of medicine, mechanics, and morals. The roots, giving support and nourishment to the entire system, he claimed, was metaphysics, the philosophical study of the nature of God, the world, and everything in it. The Principles was intended as a coherent picture of the entire tree, his magnum opus, which he hoped would serve as a textbook, should his work ever be taught at the universities.
In order to understand why Descartes felt that a new metaphysics was needed to ground his new physics, it is important to have a sense of the worldview he was reacting to. Both Descartes' philosophy and his physics are best viewed as a response to the Aristotelian-influenced Scholastics, who had dominated the intellectual scene for almost 2000 years. According to the Scholastic view, all of natural philosophy reduced to the study of change. Explanations relied heavily on the obscure metaphysical notions of "essence", the characteristic that makes something the sort of thing that it is, "matter," the thing that remains constant through change, and "form," the thing that changes when change occurs. Also crucial to these accounts of change were the four elements: earth, air, fire, and water. The most basic units of existence of this view, substances, are all various mixtures of these four elements. Descartes believed that the obscure metaphysical notions of matter, form, and the elements needlessly complicated the picture of the world. More specifically, the inclusion of such concepts made it impossible to give explanations purely in terms of the motion of matter (which is precisely what the new mechanistic physics sought to do). In order to clear the way for a new scientific outlook, Descartes had to dramatically simplify the metaphysical picture. Where the Scholastics had posited numerous types of substances, each with their own essence and each requiring their own type of explanation in terms of earth, air, fire, and water, Descartes argued that there were only two types of substances in the world. There was mental substance, whose essence was thinking, and there was physical substance, whose essence was extension. Since the entire observable world thus reduced to a single sort of substance (i.e. physical substance or body), all natural phenomena could be explained by relying on just a small number of principles, based entirely on the property of extension. Physics conveniently collapsed into geometry, the study of extended body.
Given his mechanistic picture of the world, on which all explanation could be given in terms of the extension of physical substance, Descartes also needed a new epistemology, or theory of cognition, to complement his new physics and metaphysics. Scholastic philosophers, following Aristotle, believed that all human knowledge comes through the senses. That is to say, they were empiricists. However, their empiricism was of a very naïve form; they believed that our senses are incapable of systematically deceiving us about the kinds of things that are in the world. If the senses tell us that there are colors, then there are colors. If the senses tell us that there are enduring objects, such as tables and chairs, then there are enduring objects. The trustworthiness of the senses was built into the conception of how perception operated: the one perceiving, on this view, took on the form of the thing perceived, became, in a very obscure sense, like the object of perception. Yet in Descartes' picture of the world, there was no such thing as color, sound, odor, taste, heat. There was only extension and the properties that arose from it, such as size, shape, and motion. In order to defend his physics and metaphysics, therefore, Descartes was forced to come up with a new understanding of where human knowledge comes from. Knowledge could not come from our senses, because our senses tell us that we live in a colorful, loud, odorous, tasty, hot, cold world.
In order to rid knowledge of sensory influence, Descartes' freed the intellect from the senses altogether. Where the Scholastics had claimed that nothing got into the intellect except through the senses, in Descartes' theory of cognition, certain concepts are present in the intellect at birth. According to Descartes, human beings are born with certain innate concepts, concepts such as "God," "extension," "triangle," and "something cannot come from nothing." Using these innate concepts, and our faculty of reason, we can trace chains of logical connections and unravel all the possible knowledge in the world. Both Descartes' metaphysics and his epistemology have been hugely influential in the history of philosophy. In fact, Descartes is largely responsible for setting the modern philosophical conversation in motion. John Locke, Baruch Spinoza, G.W. Leibniz, George Berkeley, and Immanuel Kant, all modeled their metaphysical positions on the Cartesian picture, presenting their own radically modified versions of Descartes' view. Even today, Descartes' theory of the nature of mind, and of mind's relation to body, continues to play a central role in philosophical debates. In epistemology, Descartes' terminology and his conception of a purely intellectual faculty found their way into the writings of John Locke, Blaise Pascal, Baruch Spinoza, and G.W. Leibniz. His concern with the limitations of human reason in its pursuit of knowledge was picked up by an even wider circle.
Descartes' theory of knowledge also gave rise to the most famous split in the history of modern philosophy, the divide between the rationalists and the empiricists. The rationalists (Nicolas Malebrance, Baruch Spinoza, and G.W. Leibniz) accepted the Cartesian idea that humans have a purely intellectual faculty that can serve as a reliable source of substantive knowledge about the world. The empiricists (most famously, John Locke, Thomas Reid, George Berkeley, and David Hume) also believed in the existence of Descartes' purely intellectual faculty, but they were dubious that this faculty could tell us anything, except tautological truths, without the help of the senses. This debate, too, rages on even today, with the two sides gaining and losing respectability at one another's expense, on a decades-long cycle.
I thought this was a really good read. A methodical step wise description of what Descartes knew. Using his method, he eliminated what he doubted and described in a linear fashion the things he was completely sure of.
I did not take the time (as he said I should!) of completely understanding it. But one can see how he has influenced mathematics and philosophy. This is probably must reading for philosophy majors. I can fully understand why.
Reading more than 20 times per page the word "God" is a red line, and so happens in this book. Interesting as an historical document to explain the influence of religion in certain thinkers.
I will read these books, and recommend those like me to read, to have a better understanding especially on the subjects of metaphysics, which is the first, and more relevant, part of this book. This is because basically you have to recall a lot of stuff from Aristotle's Metaphysics, which was hard to me since I am not an expert on the subject, so I would prefer to have someone do it for me, that, I expect, is already done in the books above.
A method of reasoning is explored, used to state many a fact, some more factual than others, concept by concept, layered upon each other as if they were bricks. Some of these concepts are simplified to the point that I question their veracity, along with the structure of the entire wall. The method itself, however, does have a logic to it and encourages the reader to think logically, a helpful practice, even when I can’t quite accept what the writer is saying. I wonder if part of the problem is this book being translated from French to English. Some of the essentials may have been lost or don’t quite have the same impact. The end result is at times awkward. This is still a good read, though, offering a window into a way of thinking in a particular place and time which spread out through Europe, encouraging other readers to examine and expand upon this method.
It is amazing to me how horrendously wrong the author's understanding of theology is which taints his application of that same theology in his philosophy. Sadly, few will have the discernment to read this and detect the flawed theology in order to understand the flawed philosophy.
God is in truth the only being who is absolutely wise, that is, who possesses a perfect knowledge of all things; but we may say that men are more or less wise as their knowledge of the most important truths is greater or less.
But to live without philosophizing is in truth the same as keeping the eyes closed without attempting to open them;
The brutes, which have only their bodies to conserve, are continually occupied in seeking sources of nourishment; but men, of whom the chief part is the mind, ought to make the search after wisdom their principal care, for wisdom is the true nourishment of the mind;
THAT in order to seek truth, it is necessary once in the course of our life, to doubt, as far as possible, of all things.
That we cannot doubt of our existence while we doubt, and that this is the first knowledge we acquire when we philosophize in order.
Accordingly, the knowledge, I THINK, THEREFORE I AM, is the first and most certain that occurs to one who philosophizes orderly.