René Descartes

René Descartes (IPA: {{IPA |d?-'kärt}}, March 31, 1596 – February 11, 1650), also known as Cartesius, was a French philosopher, mathematician and part-time mercenary. He is noted equally for his groundbreaking work in philosophy and mathematics. As the inventor of the Cartesian coordinate system, he formulated the basis of modern geometry (analytic geometry), which in turn influenced the development of modern calculus.

Significance

Philosophical legacy

Often regarded as the first modern thinker for providing a philosophical framework for the natural sciences as these began to develop, Descartes in his Meditations on First Philosophy attempts to arrive at a fundamental set of principles that one can know as true without any doubt. To achieve this, he employs a method called methodological skepticism: he doubts any idea that can be doubted.

Related Topics:
Natural sciences - Methodological skepticism

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He gives the example of dreaming: in a dream, one's senses perceive things that seem real, but do not actually exist. (This idea is similar to what Chuang Tzu writes after dreaming that he is a butterfly.) Thus, one cannot rely on the data of the senses as necessarily true. Or, perhaps an "evil demon" exists: a supremely powerful and cunning being who sets out to try to deceive Descartes from knowing the true nature of reality. Given these possibilities, what can one know for certain?

Related Topics:
Dream - Chuang Tzu

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Initially, Descartes arrives at only a single principle: if I am being deceived, then surely "I" must exist. Most famously, this is known as cogito ergo sum, ("I think, therefore I am"). (These words do not appear in the Meditations, although he had written them in his earlier work Discourse on Method).

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Therefore, Descartes concludes that he can be certain that he exists. But in what form? You perceive your body through the use of the senses; however, these have previously proved unreliable. So Descartes concludes that at this point, he can only say that he is a thinking thing. Thinking is his essence as it is the only thing about him that cannot be doubted.

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To further demonstrate the limitations of the senses, Descartes proceeds with what is known as the Wax Argument. He considers a piece of wax: his senses inform him that it has certain characteristics, such as shape, texture, size, color, smell, and so forth. However, when he brings the wax towards a flame, these characteristics change completely. However, it seems that it is still the same thing: it is still a piece of wax, even though the data of the senses inform him that all of its characteristics are different. Therefore, in order to properly grasp the nature of the wax, he cannot use the senses: he must use his mind. Descartes concludes:

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:"Thus what I thought I had seen with my eyes, I actually grasped solely with the faculty of judgment, which is in my mind."

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In this manner, Descartes proceeds to construct a system of knowledge, discarding perception as unreliable and instead admitting only deduction as a method. Halfway through the Meditations, he also claims to prove the existence of a benevolent God, who, being benevolent, has provided him with a working mind and sensory system, and who cannot desire to deceive him, and thus, finally, he establishes the possibility of acquiring knowledge about the world based on deduction and perception.

Related Topics:
Perception - Deduction - God - Sensory system

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Mathematicians consider Descartes of the utmost importance for his discovery of analytic geometry. Up to Descartes's times, geometry, dealing with lines and shapes, and algebra, dealing with numbers, appeared as completely different subsets of mathematics. Descartes showed how to translate many problems in geometry into problems in algebra, by using a coordinate system to describe the problem.

Related Topics:
Mathematicians - Geometry - Algebra

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Mathematical legacy

Descartes's theory provided the basis for the calculus of Newton and Leibniz, by applying infinitesimal calculus to the tangent problem, thus permitting the evolution of that branch of modern mathematics {{ref|tangent_problem}}. This appears even more astounding when one keeps in mind that the work was just intended as an example to his Discours de la méthode pour bien conduire sa raison, et chercher la verité dans les sciences (Discourse on the Method to Rightly Conduct the Reason and Search for the Truth in Sciences, known better under the shortened title Discours de la méthode).

Related Topics:
Newton - Leibniz - Infinitesimal calculus - Tangent problem

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Descartes also made contributions in the field of Optics, for instance, he showed by geometrical construction using the Law of Refraction that the angular radius of a rainbow is 42° (i.e. the angle subtended at the eye by the edge of the rainbow and the ray passing from the sun through the rainbow's centre is 42°). {{ref|rainbow}}

Related Topics:
Optics - Law of Refraction

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Psychobiological Legacy

Throughtout his lifetime, Descartes was known for many things. One thing he covered and thought of in his life time was the idea that some ideas are innate within a being. Thus later leading to the field of psychobiology and further research into the effects of behavioral genetics.

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