Parmenides' principle

Abstract
The following is my interpretation of the philosophy of Parmenides of Elea , the Greek father of metaphysics. His only work, On Nature , is written in rather obscure verse, and so his thesis can be viewed from a variety of perspectives, of which mine is only one (although a fairly standard one). Parmenides' most important principle, hereafter called "Parmenides' Principle", was that anything rationally conceivable must exist. Nonbeing is not a thing and can neither be thought of nor spoken about in any meaningful or coherent way. Parmenides forbade talking as if there are possible things that nonetheless do not exist. He illustrated this principle by showing us three possible methods of inquiry, of which only one is valid. The following chart summarizes them.
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