Zeno of Elea, Master of Paradoxes

Zeno of Elea (490 BC – 430 BC) was born in Elea in Lower Italy and was the son of Telutagoras and the favorite student of Parmenides. He was the third chronological leader of the philosophical school, which flourished in Elea for almost a century. Zeno devoted all his energy to explaining and developing the philosophical system of Parmenides.

Plato mentions that Zeno was 25 years younger than Parmenides, and wrote a defense of his philosophical system at a very young age, supporting Parmenides’ theory from a sidetrack. In other words, he negated the common perception of reality with such sharpness that Aristotle called him the father of dialectics and vigorously criticized his work.

Plato, in his dialogue “Parmenides”, describing the visit of Zeno and his teacher Parmenides to Athens, for the great Panathenaia, mentions that “Parmenides was at a very advanced age, sixty-five years old with gray hair, but with a noble countenance . Zeno was then about forty, tall and handsome. The two settled in the house of Pythodoros, outside the walls, in Kerameikos. Socrates went there and many others with him, wanting to hear Zeno’s writing, because it was the first time that Parmenides and Zeno had brought it to Athens. At that time Socrates was still very young.”

Zeno’s life developed initially in his homeland, the colony of Phocaea, which was too small and out of proportion to his intellectual stature and dialectical militancy, and so he exiled himself to Athens, where he taught for a fee, which was often unwieldy. It seems that this was the sophist, who is mentioned in the “Apology” and to whom Kallias, the son of Hipponikus, paid a hundred mnas for the upbringing of his two children.

As a personality he differs from his teachers and predecessors as the Sophists differ from the Ionian philosophers. Although he lacks the moral authority and mysterious depth of thought of those, he exercises over his environment an unlimited but purely individual imposition, and his intellectual acumen astonishes and compels the assent of his hearers.

His philosophy, although intended to indirectly support the unified metaphysical doctrines of the school, constantly moves to the level of analytical intellect and logic. In common with the sophists, he also has that of political employment, which he takes more idealistically than those and finally sacrifices his life in an attempt against a tyrant of his particular homeland, Nearchus or Diodemon.

What was handed down to us from his teaching are all reasonings, typically strict, that lead to absurd conclusions, because they start from the hypothetical assumption of a self-evident doctrine of the common mind or of the partly generally accepted philosophy of Heraclitus at the time. The services he offered in this way to the dialectical refinement of even the simplest propositions of the simplistic theory of knowledge are incalculable, and Aristotle rightly calls him the inventor and father of dialectics.

His purpose, however, in all the questions or dilemmas, to which he brings the common mind, was to prove by means of it in an absurd abduction the impossibility of any metaphysical theory contrary to the Eleatic principles. These questions or “reasons” deny all multiplicity, change and movement, prove the antinomies, which are introduced into the concept of space and time through the concept of infinity, and are the first model in the history of Western philosophy of the “Antinomies” of Cant.

Zeno, supporting the position of his teacher, insists on the existence of one Being and rejects the existence of many things by the method of abductive abduction. With a series of opposing thoughts, he led the listener to the conclusion he wanted to reach, proving the correctness of his argument.

Simplicius in his work “Eis Of course” gives us a characteristic passage of Zeno’s thought: “If there are many, then all that is necessary is necessary, neither more nor less. But if they are what they are, then they are finite. If there are many, then the things that exist are infinite, because there are always other things among the things that exist, and between those things again. Therefore, the things that exist are infinite.’

From Plato we learn that in the “Letters”, the collection of his youth, where he had included most of these proofs and which was disseminated without his permission, each “discourse”, that is, each section dealing with a certain subject, was subdivided into several cases, in each of which a doctrine of the simplistic and unexamined worldview was also taken as a basis.

The goal of most of his paradigmatic thoughts was to prove the immobility of bodies, a theory completely opposed to the Heraclean position of perpetual motion. Here the differences between the Eleatic and Ionian schools become clear.

Although we don’t know the reasoning he followed in his writings, we can define that the paradoxes of motion described by Aristotle in the Physics are four, namely the “Stadium” and the “Achilles”, where Zeno accepted that space and time are divided into infinity and the “Arrow” and “Moving Series”, where he accepted that space and time are made up of indivisible fractions. Zeno, through these considerations, seems to define the idea, firstly of absolute motion and secondly of the relative motion of bodies.

Zeno’s paradoxes

1. If the many exist, they must be at the same time infinitely small and infinitely large; but infinitely small, because they are reduced after every temporal division to parts indivisible and without size, particularly large, because in order to separate any two parts from each other, they must be parentheses countless others.

2. The many must be numerically both finite and infinite.

3. If everything that exists is in space, then space itself, as existing, must be in another containing medium, that is, in another space, and so on ad infinitum.

4. If a cloud of wheat, being scattered on the floor, makes a noise, it must, by analogy, not only every grain, but also every infinitesimal of the grain cause a noise; but this is not exact; therefore the whole cloud does not make a noise. The above reasoning stems from the assumption that true knowledge cannot be based on the senses, because the senses deceive us.

5. For a body to move from one point to another, it must first travel half of the space, and even earlier half of the half, and so on ad infinitum, so that the body does not move except in infinite time, so it does not move at all. Expressing this sophistry more demonstratively, it is that of “Achilles”, who cannot reach a tortoise that is ahead of him by even one step.

6. A body is in a certain position, but by moving it changes it; it is therefore in a position where it is not; a thing without place,

7. As long as a body is in a certain position, it is at rest; the thrown arrow is at every moment of its flight in a certain position; therefore the thrown arrow is at rest every moment of its journey.

8. Two bodies moving in opposite directions will meet at twice the speed than they would meet a body at rest at the end of their trajectory; so this distance is covered simultaneously with speed a and with speed 2a, which is absurd.

Doctrine of Rationalism

The doctrine of rationalism that the source of truth is the mind and of error the senses, is most clearly expressed in the perceptions of Zeno, who validates the idealistic and mystical character of the philosophy of the Eleats. With Zeno’s dialectic the theory was generalized and logically supported, that the immediate data of the senses are insufficient and illusory, and with the Sophists, and especially with Protagoras and Gorgias.

This tendency invented a critical and skeptical mood which in many ways simulated to the latest pragmatist or humanist movement in philosophy, which for a time threatened even this existence of metaphysical theory, until Plato reconstructed it by the commanding insight of his idealistic metaphysical system and traced it back to its first source, the theories of Parmenides , overlooking the skepticism of reasoning.

These reasonings are really understood by Zeno only as a means to support the ontological claims of Parmenides, but in terms of meaning, they are attributed not so much to the affirmation, but to the denial of the opposites, and lead silently to faith through the omnipotence of criticism and intellectual self-cultivation regardless of the conclusions.

Proving that every multiplicity, every change and finally every crisis of this or that kind are, simply, incomprehensible things, they do not support the forced acceptance of their opposites, and appear in the form of paradoxology, they amaze and deeply impress. Bertrand Russell interprets and defends them fervently, while Bergson sees in the sophistry of “Achilles” and the “arrow” the first intuition about the uncatalyzed opposition of the continuous to the discontinuous, the rational to the living.

Another paradox going back to Zeno, without explicitly mentioning his name, is the claim that it is impossible to accuse anything of anything, because either the predicate means the same thing about the subject, in which case it is a tautology, or it means something another, so the subject ceases to be what it was.

This problem occupied Plato a lot and a century or so later it was used by the Cynics as a reconstruction of the principle of contradiction, and they ended up declaring every predicate unacceptable, except the tautological one. The consistent development of these paradoxologies to the end certainly leads to the denial of the possibility of any agreement and any logic. But Gorgias also drew these conclusions with passion and without any fear. Zeno, however, recognizes the necessity of logic, and wrestles earnestly with the most serious and immediate logical problems, which have now ceased to make any impression, not because they have been solved but because their formulation has become commonplace.

The thorough preoccupation of the ancient Greeks with the problems of the infinitely small (or infinitely large) as well as with the problems of continuity and discontinuity, leads to the formulation of the hypothesis that a quantity is infinitely divisible or that, on the contrary, it is a composition of very small indivisible parts. The Platonic school formulates this view with the idea of the infinite divisibility of magnitudes, while the school of Democritus of Abderitis (460-370 BC) and his students rejects the idea of continuity and is based on the famous theory of ” vapors’ (atoms).

The position of the Eleates opposes these two schools considering the problem of continuity and discontinuity as a pseudo-problem, which has no meaning, since it refers to the incorrect appearance of the world and not to the “really being”. According to the Eleatians, not only does the world appear to be different from what it is, but also the world that appears is different from the world that is.