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Aristotle borrowed selectively from his teacher Plato and from those same predecessors, but his selection was different from Plato’s. 4. In particular, Plato adopted certain Pythagorean ideas about mathematics but rejected the idea that mathematical objects existed within the natural. 5. Aristotle rejected the idea that mathematics was central to knowledge of nature, except for optics, music, and astronomy, which he considered special cases. C. Aristotle’s theory of nature is dominated by a theory of change, and his physics, by a theory of motion as one type of change.
That mathematical forms are the essence of natural objects and processes was central to the teachings of Pythagoras and his followers. The orderliness of natural phenomena is a mathematical order, as in the difference between music and noise. Beginning with Pythagoras, Greek mathematics, based on geometry primarily, became the paradigm of using deductive reasoning to acquire philosophical knowledge. Archimedes used deduction and mathematics to solve problems in physics. Aristotle dismissed the value of mathematics for natural science, except for music, optics, and astronomy, but Renaissance philosophers, partly under the influence of Plato’s writings, restored mathematics to its Pythagorean position.
We’re going to be exploring that in the next lecture, and its consequences for modern science. ©2007 The Teaching Company 39 Lecture Five Mathematics as the Order of Nature Scope: Together with the experimental method and deductive reasoning, the use of mathematics is the hallmark of modern science. Mathematics is the language of scientific explanation because it is, in some sense, the “language” of nature. That mathematical forms are the essence of natural objects and processes was central to the teachings of Pythagoras and his followers.
course guidebook - Great Scientific Ideas That Changed the World by StevenGoldman