Eleatics
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The Eleatics were a school of pre-Socratic philosophers at Elea, a Greek colony in Lucania, Italy. The group was founded in the early fifth century BCE by Parmenides. Other members of the school included Zeno of Elea and Melissus. Xenophanes is sometimes included in the list, though there is some dispute over this.
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History
The school took its name from Elea, a Greek city of lower Italy, the home of its chief exponents, Parmenides and Zeno. Its foundation is often attributed to Xenophanes of Colophon, but, although there is much in his speculations which formed part of the later Eleatic doctrine, it is probably more correct to regard Parmenides as the founder of the school.
Xenophanes had made the first attack on the mythology of early Greece in the middle of the 6th century, including an attack against the whole anthropomorphic system enshrined in the poems of Homer and Hesiod. In the hands of Parmenides this spirit of free thought developed on metaphysical lines. Subsequently, either because its speculation were offensive to the contemporary thought of Elea, or because of lapses in leadership, the school degenerated into verbal disputes as to the possibility of motion and other such academic matters. The best work of the school was absorbed into Platonic metaphysics.
Philosophy
The Eleatics rejected the epistemological validity of sense experience, and instead took mathematical standards of clarity and necessity to be the criteria of truth. Of the members, Parmenides and Melissus build arguments starting from indubitably sound premises. Zeno, on the other hand, primarily employed the reductio ad absurdum, attempting to destroy the arguments of others by showing their premises led to contradictions.
The main doctrines of the Eleatics were evolved in opposition to the theories of the early physicalist philosophers, who explained all existence in terms of primary matter, and to the theory of Heraclitus, which declared that all existence may be summed up as perpetual change. The Eleatics maintained that the true explanation of things lies in the conception of a universal unity of being. According to their doctrine, the senses cannot cognize this unity, because their reports are inconsistent; it is by thought alone that we can pass beyond the false appearances of sense and arrive at the knowledge of being, at the fundamental truth that the All is One. Furthermore, there can be no creation, for being cannot come from non-being, because a thing cannot arise from that which is different from it. They argued that errors on this point commonly arise from the ambiguous use of the verb to be, which may imply existence or be merely the copula which connects subject and predicate.
Though the conclusions of the Eleatics were rejected by the later Presocratics and Aristotle, their arguments were taken seriously, and they are generally credited with improving the standards of discourse and argument in their time. Their influence was likewise longlasting -- Gorgias, a Sophist, argued in the style of the Eleatics in his work "On Nature or What Is Not," and Plato acknowledged them in the Parmenides, the Sophist and the Politicus. Furthermore, much of the later philosophy of the ancient period borrowed from the methods and principles of the Eleatics.