Plato and Socrates: Influence of Pythagoreanism on Philosophy
**Plato’s Context and Philosophical Influences**
Parmenides’ influence on all later Greek philosophy, including Plato and Aristotle, is undeniable. He stated: *”We need to say and think that being is and that it is not.”* Only this way leads to truth. Being is *one, immutable, immovable, indivisible, timeless.* The reasons behind this description are purely logical. Being is **unique** because, if there were two beings, what would differentiate them? Would it be being? No, because that is what they have in common. Would it be non-being? Nor, if it is not, can it be the cause of the difference. Therefore, being is one. In addition, being cannot change: it cannot change into being, as it already is, and how could it shift to non-being, if non-being is not? Being is indivisible because only non-being could separate its parts. As it does not change, time, plurality, and emptiness are considered illusory. This introduces the distinction between truth and appearance, truth and opinion, and gives priority to reason over the senses. Parmenides claims that this world is an illusion; the senses deceive us, showing us a world of multiplicity subject to change. From this moment on, it is necessary to explain how, if being is immutable, reality is multiple and changing. Plato resolved this through the duality of worlds.
Plato’s thought is influenced by his teacher Socrates and Pythagorean doctrines he encountered in Italy. The early years of Socrates’ life coincided with the period of splendor of the Sophists in Athens. Philosophical interest then focused on man and society, abandoning the study of nature. For the Sophists, moral concepts are not amenable to a universal definition: they are the result of a convention, making what is just in one city potentially unjust in another. Socrates, however, is convinced that right must be the same in all cities and that its definition has universal validity. The quest for universal definition was intended to be achieved through an inductive method.
**Socrates’ Method: Irony and Maieutics**
Socrates developed a practical method based on dialogue and conversation, consisting of two phases: **irony and maieutics.**
- In the first phase, the main objective is, through the practical analysis of specific definitions, to acknowledge our ignorance of the definition we seek. Only by recognizing our ignorance are we able to seek the truth.
- The second phase would be the proper search for the truth, the universal definition, the reference model for all our moral judgments.
The truth is that in Plato’s Socratic dialogues, one never achieves that universal definition, so it is possible that the Socratic dialectic could be seen by some as annoying, puzzling, or even humiliating to those whose ignorance was manifested, without actually achieving that alleged universal definition that was sought. All this suggests that Socrates’ intention was practical: to discover knowledge that would serve for life. In this sense, Socratic ethics is called “intellectualist”: if we knew the good, we would act according to it; the lack of virtue in our actions is the result of ignorance.
In the year 399, Socrates, who had refused to cooperate with the regime of the Thirty Tyrants, was involved in a trial during the full restoration of democracy under the dual charge of “failing to honor the gods the city honors” and “corrupting the youth.” Sentenced to death by a majority of 280 to 220 votes, he refused to voluntarily accept exile or escape that his friends were preparing, saying that such action would be contrary to the laws of the city and his principles. On the appointed day, he drank the hemlock. Plato became disillusioned with democracy, which condemned the just man, and with the dictatorship of the Thirty Tyrants, of aristocratic character, who had committed abuses. Plato then began a series of trips that put him in contact with the Pythagoreans.
**Pythagoreanism: A Mystical and Mathematical Philosophy**
Beside the official religion of the Olympian gods, mystery cults in Greece were promising immortality of the individual through the purification of the soul. In Orphism, ecstasy was reached in which the soul is separated from the body.
Around 530 BC, Pythagoras settled in Crotona, a Greek colony in southern Italy, where he founded a movement of religious, political, and philosophical nature known as Pythagoreanism. It was a kind of sect whose symbol was the pentagram, it was secretive, and there was community property. The philosophy of Pythagoras is known only through the work of his students and seeks to reconcile the ancient mythical world with scientific explanation.
Pythagorean philosophy is developed in two ways: a mystical-religious one and a mathematical-scientific one.
**Mystical-Religious Aspect: Transmigration of Souls**
With respect to the first, the central axis is represented by the theory of transmigration of souls and the consequent assertion of kinship between all living beings. The idea of the immortality of the soul was new to the Greeks. The Universe is alive, and its soul is divine. Individual souls are fragments of the divine soul, which have fallen to Earth and are imprisoned in bodies. Souls are immortal entities that are forced to stay in bodies, reincarnating and passing from one to another for an indefinite period, until they overcome the reincarnation process through purification *(*catharsis*)*, culminating in the soul’s return to its place of origin. For this, it was necessary to observe many rules of purification, for example, abstinence from meat and various rituals and moral standards. The safest and most difficult path for liberation is the mathematical way, as the secrets of the universe are numerical.
**Mathematical-Scientific Aspect: Harmony of Numbers**
Analogy between music, the cosmos, and numbers: the Pythagoreans discovered that the loudness of a sound depends on the number, as it depends on the lengths of the strings, and they could represent the intervals of the scale with numerical reasons. Therefore, if musical harmony depends on a number, we may assume that the harmony of the universe also depends on the number. All things are numbers because they believed that numbers are things.
**The Tetraktys: The Perfect Number**
Aristotle reports that the Pythagoreans held that the elements of number are the even and odd, and that of these two elements, the first is unlimited and the second limited. One unit (because one is both even and odd) proceeds from both, and all numbers proceed from one, and the whole sky is a number. The unit is the point, two is the line, three is the surface, and four is the volume. This means that all bodies consist of points or units in space, which when taken together, represent a number. Ten, which is the sum of 1 + 2 + 3 + 4 (the sum of the first four numbers), is the perfect number or Tetraktys. This is the perfect number and the key to the doctrine.