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Like the Pythagoreans, Plato (c. 427–c. 347 BC) found the ordering principle of the universe in mathematics, specifically in geometry. A later account has it that Plato had inscribed at the entrance to his school, the Academy, "Let no man ignorant of geometry enter."[13] The story is a myth, but like all myths it has a grain of truth, for in his writings Plato repeatedly tell us of the importance of geometry. Plato is known more for his contributions to the philosophical basis of scientific method than to particular scientific concepts. He maintained that all things in the material world are imperfect reflections of eternal unchanging ideas, just as all mathematical diagrams are reflections of eternal unchanging mathematical truths. Since Plato believed that material things had an inferior kind of reality, he considered that we don't achieve demonstrative knowledge – that kind of knowledge we call science — by looking at the imperfect material world. Truth is to be found through rational demonstrations, analogous to the demonstrations of geometry.[14] Applying this concept, Plato recommended that astronomy be studied in terms of geometrical models[15] and proposed that the elements were particles constructed on a geometrical basis.[16] Aristotle (384–322 BC) disagreed with his teacher, Plato, in several important respects. While Aristotle agreed with Plato that truth must be eternal and unchanging, he maintained that we come to know the truth through the external world which we perceive with our senses. For Aristotle, directly observable things are real; ideas (or as he called them, forms) only exist as they express themselves in matter or in the mind of an observer or artisan.[17] This theory of reality led to a radically different approach to science: First, Aristotle emphasized observation of the material entities which embody the forms. Second, he played down the importance of mathematics. Third, he emphasized the process of change where Plato had emphasized eternal unchanging ideas. Fourth, he reduced the importance of Plato's ideas to one of four causal factors. As this last point suggests, Aristotle's concept of causes was less limited than ours. Among causes he included: the matter of which a thing was made (the material cause). the form into which it was made (the formal cause; something similar to Plato's ideas). the agent who made the thing (the moving or efficient cause). the purpose for which the thing was made (the final cause). Aristotle's emphasis upon causes fundamentally shaped the later development of science by insisting that scientific knowledge, what the Greeks called episteme and the Romans scientia, is knowledge of necessary causes. He and his followers would not accept mere description or prediction as science. In view of this disagreement with Plato, Aristotle established his own school, the Lyceum, which further developed and transmitted his approach to the investigation of nature. Most characteristic of Aristotle's causes is his final cause, the purpose for which a thing is made. He came to this insight through his biological researches, in which he noted that the organs of animals serve a particular function. The absence of chance and the serving of ends are found in the works of nature especially. And the end for the sake of which a thing has been constructed or has come to be belongs to what is beautiful.[18] Thus Aristotle was one of the most prolific natural philosophers of Antiquity. He made countless observations of nature, especially of the structure and habits of plants and animals. He also made many observations about the large-scale workings of the universe, which led to his development of a comprehensive theory of physics. For example, he developed a version of the classical theory of the elements (earth, water, fire, air, and aether). In his theory, the light elements (fire and air) have a natural tendency to move away from the center of the universe while the heavy elements (earth and water) have a natural tendency to move toward the center of the universe, thereby forming a spherical earth. Since the celestial bodies – that is, the planets and stars – were seen to move in circles, he concluded that they must be made of a fifth element, which he called Aether.[19] Aristotle could point to the falling stone, rising flames, or pouring water to illustrate his theory. His laws of motion emphasized the common observation that friction was an omnipresent phenomenon – that any body in motion would, unless acted upon, come to rest. He also proposed that heavier objects fall faster, and that voids were impossible. |
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