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The Eleatics refers to the pre-Socratic school of philosophy founded by Parmenides in the early fifth century BC in the ancient town of Elea. Other members of the school included Zeno of Elea and Melissus of Samos. Xenophanes is sometimes included in the list, though there is some dispute over this. Elea, whose modern-day appellation is Velia, was a Greek colony located in present-day Campania in southern Italy.
The school took its name from Elea (//; Greek: Ἐλέα), 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 espoused a belief that "God is one, supreme among gods and men, and not like mortals in body or in mind." Parmenides developed some of Xenophanes's metaphysical ideas. Subsequently the school debated the possibility of motion and other such fundamental questions. The work of the school was influential upon Platonic metaphysics.
The Eleatics rejected the epistemological validity of sense experience, and instead took logical standards of clarity and necessity to be the criteria of truth. Of the members, Parmenides and Melissus built 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 (Zeno's paradoxes).
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 On Nature or What Is Not, and Plato acknowledged them in the Parmenides, the Sophist and the Statesman. Furthermore, much of the later philosophy of the ancient period borrowed from the methods and principles of the Eleatics.
See also 
- Hugh Chrisholm, ed. (1911). Encyclopædia Britannica (11 ed.). Cambridge University Press.
- Zeller. Vorsokrastische Philosophie [Pre-Socratic Philosophy] (in German). p. 530, n.3.