Descartes argued that bodies differ from how they appear through senses. Colors, sounds, tastes, smells, heat, and cold are merely sensations existing in thought, and there is nothing in bodies that resembles them, just as there is nothing in bodies that resembles our sensation of pain. Instead the properties of bodies are those which are capable of being quantified, namely, extension and its modes, shape, size, and motion. He denied the existence of a vacuum, because what one would be inclined to call empty space meets his definition of body in virtue of being extended in three dimensions. All the phenomena in the created world external to human beings, such as gravity, magnetism, and the cohesion of bodies, as well as the complex functioning of living organisms including human bodies, he believed could be explained solely by mechanistic physics, that is, by the motions and collisions of bodies. He even denied that consciousness must be attributed to animals in order to explain their behavior. Although his laws of impact, his vortex theory of gravity, and his denial of a vacuum were rejected as physics developed, he deserves credit for one of the first formulations of the law of inertia, which he justified by appeal to the immutability of God.
In mathematics Descartes is famous for the unification of algebra and geometry, marked by the use of what are now known as Cartesian coordinates. He influenced not only the rationalist thinkers who were his immediate followers, but also the whole course of modern philosophical enquiry, and the Cartesian quest for certainty gave epistemology the central place in philosophical thought it has maintained to this day.


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