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The next step is to draw out the implications of asserting only that something is. The result is that we arrive at the qualities of the One, namely, that it is eternal, indivisible, unmoving, and round. The first implication of the path of assertion, then, is that whatever exists must be eternal, that is, uncreated and indestructible.

Or how could it come into being? If it came into being, then it is not. Nor is it, if it is going to be in the future. Thus is becoming extinguished and passing away not to be heard of. The second implication of the path of assertion is that whatever exists is indivisible. If we say that it has parts, then we maintain some of it is here, but not there. This, again, takes us down the impossible path of denial.

Parmenides writes,. For this reason it is wholly continuous; for what is, is in contact with what is. Third, the One is unmoving, since movement requires us to say that it is now in this position, but not in that position, yet again taking us down the path of denial. It is immovable in the bonds of mighty chains, without beginning and without end; since coming into being and passing away have been driven afar, and true belief has cast them away. It is the same, and it rests in the self-same place, abiding in itself.

And thus it remains constant in its place; for hard necessity keeps it in the bonds of the limit that holds it fast on every side. Finally, the One is round. If it was irregularly shaped, one part would be greater, and another part smaller; this would require us to say that this part is not like that part, yet again taking us down the path of denial.

According to Parmenides, then, what we can say about reality is that it is an eternal, single, unmoving, and round thing. Surprisingly, though, he had followers who staunchly defended his position, one of which was Zeno c. The motive of my book was to protect Parmenides against ridicule by showing that the hypothesis of the existence of the many involved greater absurdities than the hypothesis of the one.

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The book was a youthful composition of mine, which was stolen from me, and therefore I had no choice about the publication. We also believe that things in the world go through change: they come into existence, change configuration in innumerable ways, then go out of existence. Thus, those who disagree with Parmenides theory of the One by defending common sense appearances will find greater difficulties than those they were trying to avoid. While Zeno is reported to have produced more than 40 paradoxes in defense of Parmenides, little of his actual wording survives, and we are able to reconstruct only a handful of them.

One group of paradoxes targets the common sense conception of motion, that is, the basic view that things in the world around us move—such as leaves blowing around in the yard, a dog running down the street, a ball rolling across the floor. The first asserts the non-existence of motion on the ground that that which is in motion must arrive at the half-way stage before it arrives at the goal. This we have discussed above.

The third is that already given above, to the effect that the flying arrow is at rest [i. The first is called the paradox of the stadium runner. Imagine that a runner sets off on a race track. Before he can reach the finish line, he must pass the halfway point.

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The runner would have to cross an infinite number of way points in a finite time, and thus can never reach his goal. The second argument is called the paradox of Achilles and the Tortoise, and is similar in structure to the first. Achilles is the Greek mythological hero who could run like the wind. Suppose that Achilles was in a race with a much slower tortoise, and gave the tortoise a few second head start. Could Achilles overtake the tortoise? No, says Zeno. Suppose that the tortoise gets to point A on the road; Achilles will need to reach point A before overtaking the tortoise.

But, once Achilles reaches point A, the tortoise will have moved on to point B, and Achilles will need to reach point B before overtaking it. Again, though, once Achilles reaches point B, the tortoise will have moved on to point C, and so on. Since the tortoise is always on the move, regardless of how slowly, it will be moving on to an infinite number of points that Achilles will need to cross.

Thus, Achilles can never overtake the Tortoise.

The third paradox, regarding the motion of the arrow, takes a slightly different strategy than the above two and can be formulated as follows:. Second, we might point out that in real life runners do reach the finish line and overtake slower competitors.

The Presocratic Philosophers

The question under consideration is whether common sense reality is only an illusion. Of course it appears as though the runner reaches the finish line. However, the paradoxes of motion aim to show that our underlying assumptions about reality are seriously flawed, specifically our assumption that things actually move at all. The paradoxes are generated by the underlying assumption that it is impossible to touch infinitely many points in a finite amount of time. One possible solution is to deny that space is really infinitely divisible. According to traditional geometry, for any two points that you designate, there are an infinite number of points between them.

For centuries people assumed that this was true of the actual physical world too, and not just true in geometry. But is real space infinitely divisible?

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Many physicists today say no, and hold that the tiniest portions of space may involve indivisible segments. So, when we move across space we jump from one of these segments to the next, rather than sweeping over an infinite number of points. On the one hand, our ordinary view of the world is that it is composed of many things. Yet, on the other hand, there seems to be a unifying force behind all of this diversity.

How then do we reconcile these two views of reality? Rather than reduce all things to a single force or substance, why not instead reduce everything to a few basic forces or substances? This is the approach taken by two Presocratic philosophers, namely, Empedocles and Anaxagoras. Empedocles c. Born in Acragas, a Greek colony in Sicily, Empedocles had varied careers as a physician, politician, and even a magician. Empedocles also claimed to be a god who was exiled to earth for breaking his Pythagorean vow of vegetarianism.

Like Pythagoras, Empedocles too believed in reincarnation, and in fact argued that, as punishment for his sin, his soul transmigrated into the bodies of animals and even plants. To highlight his divine status, he wore bronze sandals, the purple robes of royalty, a garland around his head, and, as the story goes, even performed miracles.

He once prevented strong winds from destroying local crops by stretching out animal skins atop a hill to catch the wind.

Presocratic philosophy - Oxford Classical Dictionary

There is also an account of him raising someone from the dead. Empedocles modeled his poetic writing style upon that of Xenophanes and Parmenides, and his principal book, On Nature , was the longest philosophical work that appeared up until his time.

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  • There are various accounts of his death, one of which is that he died from a chariot injury while attending a festival. Another story describes how he planted his bronze sandal at the mouth of a volcano, making people think that he jumped in. First is his view that all things come from the four elements—or roots , as he calls them—of earth air, fire and water. While the four elements had been part of Greek thinking for some time, Empedocles expanded their role to be the four fundamental substances from which all things emerge, and this became the foundation of physics within Europe for the next 2, years.

    Second is his view that two forces are responsible for the mixing and unmixing of the four elements, namely Love and Strife, which function as physical forces of attraction and repulsion. He describes how the four elements and two forces first emerged from the cosmos:. I will tell you of a twofold process. At one time it [i.

    Fire and Water and Earth and the mighty height of Air. And also, apart from these, dreaded Strife of equal weight to each, and Love in their midst, equal in length and breadth. All these elements are equal and of the same age in their creation. But each presides over its own area, and each has its own character, and they dominate in turn in the course of time.

    All change that occurs in the cosmos results from the combination, separation and regrouping of these indestructible elements, depending on the amount of Love and Strife that is present. Empedocles continues explaining how the universe as we know it evolved from the original appearance of the four elements and two forces. Imagine that the cosmos is like a large kitchen blender that contains equal portions of earth, air, fire and water, all swirling around. Suppose, then, that the two forces of Love and Strife are thrown into the blender, where Love has the power to draw the elements together, and Strife has the power to have the elements separate from each other.

    As the mixture swirls around in the blender, it will exhibit four separate states, depending on how much Love and Strife are sucked into the mix. Consider first when Strife is pulled into the mix by itself, while Love sinks to the bottom of the blender. As Strife circulates through the four elements, it makes the four elements repel each other, sort of like mixing water and oil.

    Thus, all the earth collects together in one side of the blender, air on another side, fire on another and water on another. According to Empedocles, this was what the first stage of the cosmos was like. As Love churns into the mix, its attractive powers cause the four elements to blend together into one formless glob of stuff.

    Empedocles describes this phase of cosmic development here:. When Strife had fallen to the lowest depth of the vortex, and Love had reached to the center of the whirl, all things came together in it so as to be one only. This did not happen all at once, but they came together at their will each from different quarters. Third, consider what happens when a lot of Love, with just a little bit of Strife, mixes through the four elements.

    The problem, though, is that in this state the four elements are not separated quite enough, and the result is that some things become stuck together in grotesque ways, such as the faces of people being stuck to the bodies of animals. Empedocles describes this here:. Many creatures with faces and breasts looking in different directions were born.