Zeno of Elea

Zenon shows the youth the gates of truth and falsehood, fresco in the library of the Escorial 1588-1595, Madrid

Zeno of Elea (Greek: Ζήνων Zḗnōn, Latin: Zeno, also Zeno the Elder; * c. 490 BC in Elea; † c. 430 BC probably in Elea or Syracuse) was a Greek philosopher from the time of the Pre-Socratics and a friend and student of Parmenides.

Zeno's paradoxes

Like all Eleatics, Zeno assumed the unity and immutability of being, according to which there should in truth be neither movement nor becoming and passing away in the world. As proof that there is also no multiplicity, he cites the paradox of multiplicity in the fragment "On Nature", which leads to a reductio ad absurdum:

„If there is much, then there must necessarily be just as many things as there really are, no more, no less. But if there are as many things as there are, they are limited [in number].
If there is much, then being is unlimited [in number]. For between the individual things there are always others and between those again others. And thus being is unlimited.“

– Zeno of Elea: The Fragments of the Pre-Socratics. Greek and German by Hermann Diels. Vol. 1, Berlin 1922, p. 175

Zenon was primarily concerned with the relations of space, time and motion and encountered a number of paradoxes. The best known of these is the paradox of Achilles and the tortoise, according to which the fast Achilles could never catch up with a slow tortoise in a race if he gave it a head start, because before he could reach it, it would already have advanced a little further - and so it goes on and on. Other similar paradoxes are the dichotomy paradox, the arrow paradox and the stadium paradox.

„Zeno seeks to deal with thought-experience in such a way that he points out the contradictions that arise in a worldview that sees a truth in the change of things, in the becoming, in the many things that the outer world shows. Of the contradictions to which he refers, let us mention only one. He thinks that the fastest runner (Achilles) cannot reach the tortoise, for however slowly it crawls, when Achilles reaches the place it has just occupied, it is already a little further on. By such contradictions Zeno indicates how an imagination that adheres to the external world cannot come to terms with itself; he points to the difficulty that thought encounters when it attempts to find the "truth. One will recognise the significance of this worldview, which is called the Eleatic (Parmenides and Zeno are from Elea), if one directs one's gaze to the fact that its bearers have progressed so far with the formation of thought-experience that they have shaped this experience into a special art, the so-called dialectic. In this "art of thought" the soul learns to feel itself in its independence and inner unity. Thus the reality of the soul is felt as what it is through its own being, and as what it feels itself to be through the fact that it no longer, as in the past, lives along with the general world-experience, but unfolds in itself a life - the thought-experience - which is rooted in it, and through which it can feel itself implanted in a purely spiritual world-ground. At first this feeling does not yet find expression in a clearly expressed thought; but one can feel it alive as a feeling in this age by the esteem in which it is held. According to one of Plato's "Conversations", Parmenides told the young Socrates that he should learn the art of thought from Zeno, otherwise truth would remain distant from him. This "art of thought" was felt to be a necessity for the human soul that wants to approach the spiritual primal grounds of existence.“ (Lit.:GA 18, p. 57f)

The problem with all of Zeno's paradoxes is that he did not yet know how to grasp the concept of infinity. Basically, it is always about the problem of divisibility: is the world an infinitely divisible continuum or are space and time divisible into a finite number of discrete units? To this end, the idea of empty space is also rejected, for if it contains nothing, it is nothing and consequently cannot exist. At about the same time, Leucipp and Democritus held exactly the opposite opinion with their atomism. Since Plato and Aristotle, Zeno's arguments have been refuted. Aristotle, for example, distinguished between infinite extension and infinite divisibility and concluded from this that a finite but infinitely divisible distance could very well be traversed in finite time.

Paradoxically, modern quantum theory tilts the scales back in Zeno's favour in practice. Thus, there is in fact no truly empty space, since within the limits of the Heisenberg uncertainty principle, it is filled with vacuum fluctuations formed by particle-antiparticle pairs that rapidly emerge and immediately decay. In addition, the so-called quantum Zeno effect, which is reminiscent of the arrow paradox and is based on the fact that the light emission of an excited atom can be stopped by a dense sequence of measurements, was experimentally confirmed at the Ludwig Maximilian University of Munich in 1994.

Literature

• Rudolf Steiner: Die Rätsel der Philosophie in ihrer Geschichte als Umriß dargestellt, GA 18 (1985), ISBN 3-7274-0180-X English: rsarchive.org German: pdf pdf(2) html mobi epub archive.org

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