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Ancient Greece had a long and varied philosophical tradition, with many different thinkers and schools proposing different answers to the question of the fundamental nature of the universe. Greek philosophy is often considered to begin with Thales, whose thought has only come down to us in fragments quoted by later authors. One fragment ascribes the theory that "all is water" to him, suggesting that he believed this element was the basic component of reality. His student, Anaximenes, adopted the fundamental element view but changed the element, suggesting instead that air was most basic. Heraclitus, from whom we have more fragments than Thales, is nevertheless at least as mysterious a thinker. He emphasized the impermanent character of the perceptual world, but also said that "nature loved to hide," which may indicate he also accepted a basic regularity to the universe. There is some indication in his fragments that he thought fire was the force driving perceived change in nature. Others, such as Pythagoras and Parmenides, did not take an elemental view of the universe. Pythagoras, who seems to have been a sort of cult leader, is thought to have believed numbers (and form more generally) to have been at the basis of reality. Parmenides, in a poem some lines of which have survived, contrasts his view of "being" against the way of "non-being," seemingly taking this eternal, unanalyzable "being" to be the most basic element of existence. An interesting embellishment on these cosmological views comes from Empedocles, again in the form of a poem, and again only surviving in fragments (though more than Parmenides). In his poem, Empedocles describes a universe where the four basic elements (earth, fire, air, water), themselves eternal and unchanging, go from a state of complete separation to complete intermingling, and back again. This clearly draws a lot on the work of the preceding philosophers described above, unifying many of these theories into a picture of an eternal universe where change is nevertheless possible.

The philosophers above are all now termed "pre-Socratic", because they came before Socrates, who had a revolutionary impact on Greek philosophy that has continued to the present day. One other important philosopher preceded Socrates, however: Democritus, the founder of Greek atomism. The central insight of atomism is that there is a smallest unit of matter, which is termed an atom. Democritus speculated that all change was created by the motion and interaction of atoms. He further posited special soul atoms that were the basis for human thought. However, as this still provided a mechanistic explanation of thought and action, it contradicted the intuitive sense of free will and common-sense morality.

The atomist assault on free will may have been a large part of Socrates' inspiration, as his teaching focused on principles of justice and piety. Unfortunately, as Socrates never wrote any philosophical texts himself, it is impossible to know exactly what his views were, or whether he had a coherent cosmological view underlying his ethical and political views. His student, Plato, wrote many dialogues which include Socrates as a major character debating these issues with various interlocutors. However, these are generally better thought of as Plato putting his view in the mouth of his teacher, rather than accurately recording Socrates' thoughts. In various works, Plato puts forth a theory of forms, which have the permanence and perfection impossible to attain in the perceived world, and are accessible only through dialectical reason. This view seems to draw more clearly on the Parmenidean and Pythagorean traditions than the elemental or atomistic views.

With Plato's student Aristotle, we see a return to elemental theory. The Epicureans (named for their founder, Epicurus) endorse a broadly atomistic view, with the caveat that they believe atoms occasionally turn randomly in their motions, allowing for free will.

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Q: Which greek philospher says everything is made up of numbers?
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