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What is clear is that Parmenides is making a conscious attempt at some kind of a new start. Like Descartes, he is trying to find an unassailable starting-point on which something further can be built. This search is understandable, given the intellectual situation of the time. The principles of the Milesians had yielded no one clearly true system, but a number of rival ones — in itself a scandal. Heraclitus had made the whole of cosmology suspect by revealing deep-seated contradictions at its heart. In the background, the Pythagoreans were directly or indirectly stimulating new lines of thought and using them, perhaps, for their own mysterious purposes.
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Edward Hussey, in The Presocratics, Classical Life and Letters (1982), p. 105

 

Parmenides

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The Immortal Principle was first called water by Thales. Anaximenes called it air. The Pythagoreans called it number and were thus the first to see the Immortal Principle as something nonmaterial. Heraclitus called the Immortal Principle fire and introduced change as part of the Principle. He said the world exists as a conflict and tension of opposites. He said there is a One and there is a Many and the One is the universal law which is immanent in all things. Anaxagoras was the first to identify the One as nous, meaning "mind."
Parmenides made it clear for the first time that the Immortal Principle, the One, Truth, God, is separate from appearance and from opinion, and the importance of this separation and its effect upon subsequent history cannot be overstated. It's here that the classic mind, for the first time, took leave of its romantic origins and said, "The Good and the True are not necessarily the same," and goes its separate way. Anaxagoras and Parmenides had a listener named Socrates who carried their ideas into full fruition.

 

Robert M. Pirsig

 

Nothing is that which fills no space. If one single point placed in a circle may be the starting point of an infinite number of lines, and the termination of an infinite number of lines, there must be an infinite number of points separable from this point, and these when reunited become one again; whence it follows that the part may be equal to the whole.

 

Leonardo da Vinci

 

Parmenides made it clear for the first time that the Immortal Principle, the One, Truth, God, is separate from appearance and from opinion, and the importance of this separation and its effect upon subsequent history cannot be overstated. It's here that the classic mind, for the first time, took leave of its romantic origins and said, "The Good and the True are not necessarily the same," and goes its separate way. Anaxagoras and Parmenides had a listener named Socrates who carried their ideas into full fruition.

 

Parmenides

 

At present (around 1960-1970, fh) I make objects (whether a type-writer, wheelbarrow, bed or fishingboat..) very ‘hourloupés’. What I mean is that I am swimming upstream against the ‘l’Hourloupe’ current. I am approaching it from the opposite direction: instead of starting out with indeterminate lines that eventually give me a wheelbarrow, I start out with the idea of making a wheelbarrow and then add my indeterminate lines. In effect what I am doing is making the current run simultaneously in both directions at the same time.

 

Jean Dubuffet

 

I would inquire of reasonable persons whether this principle: Matter is naturally wholly incapable of thought, and this other: I think, therefore I am, are in fact the same in the mind of Descartes, and in that of St. Augustine, who said the same thing twelve hundred years before. ...I am far from affirming that Descartes is not the real author of it, even if he may have learned it only in reading this distinguished saint; for I know how much difference there is between writing a word by chance without making a longer and more extended reflection on it, and perceiving in this word an admirable series of conclusions, which prove the distinction between material and spiritual natures, and making of it a firm and sustained principle of a complete metaphysical system, as Descartes has pretended to do. ...it is on this supposition that I say that this expression is as different in his writings from the saying in others who have said it by chance, as in a man full of life and strength, from a corpse.

 

Augustine of Hippo