Parmenides and Plato were both concerned with ontology (from the Greek onta or being) and questioned the nature of the true. They both concluded that the world around is a woolgather or an illusion and that the senses, as opposed to reason, cannot aid us in our quest for truth.
Parmenides was the first of the ancient philosophers to make intention of deductive argument and he did this in order to stress the dichotomy between what was commonly believed to be true (i.e. change, transaction and growth etc) and what the reason illuminates as real. In Parmenides own dustup:
But the decision about these matters lies in this: it is or it is not.
What is not cannot be for is not is simply a privation of is; it is not a fragment of Being with matter and form. That which is is necessarily corporeal, as J Burnet explains: in that respect is no real doubt that this is what we call a body. It is certainly regarded as being spatially extended for it is quite seriously verbalize of as a sphere.
For Parmenides this perfect sphere of being is eternal, unchanging and immovable. There is no more of it in one part than another, it is absolutely equal and hence there can be no room for movement or growth.
Melissus and Zeno developed such arguments, Zeno gorgeously postulating the paradox of motion; if a tortoise were given a spike start in a race with Achilles, Achilles would not logically be able to overtake the tortoise, despite being faster, because by the time he reaches the point where the tortoise was the tortoise leave alone have travel ahead of that point. As long as the tortoise keeps moving it will always stay ahead, no matter how small the lead.
By the equivalent principle...
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