Philosophy of Elea - Velia: Parmenide, Zeno and Melissus of Samos
Parmenide was born in Elea (Velia) between 510 and 435 b.C. He was very loved by his fellow-citizens and they asked him to write the laws of Elea (Velia). Citizens had to declare their fidelity to these laws when they were of age. He also went for a diplomatic mission to Athens in 450 b.C. to convince Pericles to sign an alliance. Parmenide went with his pupil, Zeno, and spent a lot of time talking with philosophers, also with Socrates. Plato narrated this event and showed the contrast between the ideals and the thoughts of a philosopher of a far peripheral town and the ones generated in Athens, the heart of Greek culture. Parmenide thought that human sense are deceptive. He was a real rationalist and thought that the Being was immutable, not generated, unique, homogeneous, and eternal. According to Parmenide, there was no creation. He thought that the Being was like a sphere. Also Einstein saw the universe as a sphere. According to Parmenide, thinking means being: if I think about a thing, then this object exists. If I think about a phantom, this phantom exists because thinking about it, I brought it to life, maybe only in my mind. (https://it.wikipedia.org/wiki/Parmenide)
Zeno was born and lived in Elea (Velia) around 490 b. C. He was a pupil of Parmenide. Some sources suggest the idea of a "physical relation" between them, a common relation between master and pupil at that age. He worked especially to strengthen the theories by his master inventing one of the most important mathematic methods in the demonstration of theorems, that is demonstrating the absurd. This method means that you have to consider the hypothesis that is contrary to what you want to demonstrate as the real one. Then you can realize that this hypothesis is absurd and so the other is the true one. Let's make a very simple example; there are two possible hypothesises: all mushrooms are poisonous and not all the species of mushrooms are poisonous. If I want to demonstrate that there are edible mushrooms and I want to do so using the method by Zeno, I declare that all mushrooms are poisonous, that is the contrary of what I actually want to demonstrate. Now I just have to take a sample of any species and let different guinea pig eat them. The guinea pigs that survive will show that not all the mushrooms are poisonous. As a philosopher, Zeno did not "invent" anything but as a dialectician he was very important, since he invented the methods later used by sophists and Socrates. Zeno thought that any reasoning has to respect the principle of "non contradiction" in all its parts. A line of reasoning cannot be correct if it shows to be fallacious in any of its parts, when you decompose it. The use of paradox was his winning arm. The most famous paradox was the one against motion. He describes the example of Achilles. Achilles (whose main gift was speed) leaves from a position called A to catch a turtle (whose main gift is slowness) in a position called B. Achilles covers the distance between A and B while the turtle covers a smaller distance and will be in another position, called C. When Achilles goes from B to C, the turtle will be in another position, D, and so on. Achilles will never catch the turtle because he will never reach it. Zeno wanted to show with his paradox that motion does not exist. This reasoning was good for ancient people, because they did not understand the concept of zero and of infinite and they did not have the concept of limit, an important part of mathematics today. So, while the intervals covered by the turtle increase, the covered distance will be near zero and so at a certain point.
Melissus of Samos
Melissus was born in Samos between 490 and 480 b.C. and he was the admiral of the fleet of Samos. He was a very strategic person and succeeded in creating problems to armies from Athens. We can imagine that Melissus was not considered much as a philosopher by Greek philosophers as a revenge. He tried to strengthen the thesis by Parmenide, but, unlike Zeno, he introduced some variants. He did not accept the idea of the Being as a sphere. According to Melissus, the Being cannot be limited and cannot have boundaries but is infinite. He defines the characteristics of the Being:
a) The Being is eternal because there was no creation, since what exists cannot be created by what does not exist.
b) If the Being is eternal cannot have other definitions, since any definition would imply a beginning and an end.
c) If the Being is eternal and infinite, it is one.
d) If the Being is eternal, infinite, one it is also homogeneous, because he could not be composed by different parts, otherwise it would not be one.
e) If the Being is eternal, infinite, one and homogeneous he will be also immovable because since it is infinite, he cannot go anywhere. It already is everywhere.
According to Melissus, the Being is also unchangeable, because if it changed (even if in a very slow manner), at the end it would destroy itself.