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Heraclitus
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Heraclitus was a contemporary of Pythagoras, Lao-tzu, Confucius, and Siddhartha, the Buddha; some say that the term "philosophy", love of wisdom, was first introduced by Pythagoras, who lived from approximately 580 BCE to 500 BCE. Pythagoras and his followers, the Pythagoreans, argued numbers to constitute the true nature of things and all relations to be numerical. Pythagoras is often regarded as the founder of modern mathematics and geometry. The Pythagorean Theorem states that in a right-angled triangle, the square of the hypothenuse (opposite side) is always equal to the sum of the squares of the other two sides. The Pythagoreans ... argued that earth was a sphere revolving around the sun in a predictable way.
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Although Heraclitus is not known to have had students, his writings seem to have been influential from an early time. He may have provoked Parmenides to develop a contrasting philosophy (Patin 1899; Graham 2002), although their views have much more in common than is generally recognized (Nehamas 2002). Empedocles seems to have invoked Heraclitean themes, and some Hippocratic treatises imitated Heraclitean language and presented applications of Heraclitean themes. Democritus echoed many of Heraclitus' ethical pronouncements in his own ethics. From an early time Heraclitus was seen as the representative of universal flux in contrast to Parmenides, the representative of universal stasis. Cratylus brought Heraclitus' philosophy to Athens, where Plato heard it. Plato seems to have used Heraclitus' theory (as interpreted by Cratylus) as a model for the sensible world, as he used Parmenides’ theory for the intelligible world.
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Heraclitus had an influence much broader than could be expected from his tiny corpus of sayings. Plato accepted his concept that matter was in endless change, but took this in an anti-materialist way to prove that there must be a better world of unchanging ideas. The Stoics, who were pantheists and materialists, regarded Heraclitus as a precursor. For his emphasis on development through the conflict of opposites, Marx and Engels viewed him as a harbinger of dialectical materialism.
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One thing seems certain: Heraclitus had an extremely negative reaction to Milesian thought. For the Milesians, what is real is fixed and permanent; change somehow had to be explained away. They understood changes as alterations of some basic, underlying, material stuff which is, in its own nature, unchanging. Heraclitus reversed this: change is what is real. Permanence is only apparent.
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Heraclitus provided some sort of discussion of meteorological and astronomical phenomena. He studied the disappearance and reappearance of the moon at the end and beginning of a month (Oxyrhynchus Papyri LIII 3710 ii. 43-47 and iii. 7-11–the clearest evidence that Heraclitus had a scientific interest in astronomy). He explained the sun and moon as bowls full of fire. As the moon's bowl rotated it caused the phases.
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Like the Milesian philosophers, Heraclitus focused on the material origins of the world. Moreover, he inspired the internal hidden rhythm of nature which moves and regulates things, namely, the logos. Heraclitus accepted only one material source of natural substances, fire (pyr). Fire is the manifestation of logos which creates an infinite and uncorrupted world, without beginning or end in time. In turn fire changes or transforms to water and earth.
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Heraclitus