Zeno's Paradoxes:

Motion, as a manifestation of causality, is the main concern behind all the theories of physics, from the pre-Socratics through Newton's theory of gravity to the most recent theories of quantum mechanics and quantum gravity. Yet there are a number of famous philosophers who have doubted that there could be any motion at all, despite our daily experience. As is well known, those philosophers expressed perspectives similar to Ibn ‘Arabî's. Most notably, Parmenides of Elea (b. 510 BC) affirmed cosmological conceptions remarkably similar to Ibn ‘Arabî's doctrine of the oneness of being: he held 'the One' unchanging existence to be alone true, while multitude and change were said to be an appearance without reality. This doctrine was defended by his pupil Zeno (b. ~488 BC) whose philosophy of monism claimed that the many things which appear to exist are merely a single eternal reality which he called Being (a term Ibn ‘Arabî also applies to the Single Monad). The complex and rigorous adaptation of Parmenides' hypotheses in Plato's Parmenides—constantly elaborated by the later Neoplatonists—offer even closer analogies to Ibn ‘Arabî's overall ontological system. Zeno wrote a book containing forty paradoxes, and although his book was lost, four of those paradoxes were discussed by Aristotle in his Physics: the Dichotomy, the Achilles, the Arrow, and the Stadium. Each of those four paradoxes challenge all claims that there is real motion (Heath 1981: 273-83; Sorensen 2003: 44-57; Darling 2004: 351; Leiber 1993: 77; Erickson 1998: 218-20).

The Dichotomy paradox concludes that there is no motion because that which is moved must arrive at the middle of its course before it arrives at the end. In order to traverse a line segment it is necessary to reach its midpoint. To do this, one must reach the one-fourth point; to do this, one must reach the one-eighth point, and so on ad infinitum. Hence motion can never begin, because the sum 1/2 + 1/4 + 1/8 + ... equals one, but only after infinite number of additions, and therefore it actually approaches one but never reaches it. Even more perplexing to the human mind is the attempt to sum 1/2 + 1/4 + 1/8 + ... backwards: for we can never get started, since we are trying to build up this infinite sum from the wrong end!

The paradox of Achilles attempts to show that even though Achilles runs faster than the tortoise, he will never catch her! Let us suppose that Achilles runs at ten meters per second and the tortoise at only one meter per second, and that when the race started the tortoise was ten meters ahead. After one second Achilles would arrive at the point where the tortoise was when the race started, but the tortoise would have moved one meter further—so that by the time the Achilles covers this one meter, the tortoise would have advanced again 0.1 meter, and so on. Thus the Achilles can never catch the tortoise.

Zeno bases the above two arguments on the fact that once a thing is divisible, then it is infinitely divisible. One could counter the above two paradoxes by postulating an atomic theory in which matter (or space) is composed of many small indivisible elements. However the remaining two paradoxes cause problems only if we consider that space is made up of indivisible elements that may be cut in indivisible durations of time.

Turning to the third paradox of the Arrow: if we consider the path of an arrow in flight: at each instant of its path, the arrow occupies some position in space; this is what it means to say that space is discrete. But to occupy some position in space is to be at rest in this position. So throughout the entire path of the arrow through space, it is in fact at rest! Or if in an indivisible instant of time the arrow moved, then indeed this instant of time would be divisible (for example, in a smaller instant of time the arrow would have moved half that distance).

The fourth paradox of the Stadium is a little bit more complicated, but it leads to the same result as the above—i.e., that time and space can not be discrete. While on the contrary, we have seen that the first two paradoxes may only be resolved if we assume that time and space are not continuous

The above four paradoxes not only challenge all scientific theories of motion, but also our everyday experience. For this reason they have often been dismissed as logical nonsense. Many attempts, however, have also been made to dispose of them by means of mathematical theorems, such as the theory of convergent series or the theory of sets. Aristotle did not fully appreciate the significance of Zeno's arguments, since he called them 'fallacies', without actually being able to refute them. Many modern scientists like to believe that axiomatic mathematics has dispelled Zeno's paradoxes, where now it is possible to talk about limits and infinity without reaching any mathematical contradiction and it can be proven that the sum of an infinite number of halving intervals is finite. But some recent philosophers such as Bertrand Russell persisted with such arguments, and recently similar puzzling phenomena (called the 'quantum Zeno effect') have been observed in radioactive atoms (Misra 1977: 756; Grossing 1991: 321-26).

With Ibn ‘Arabî's re-creation principle, we would have no difficulty at all in resolving Zeno's paradoxes and reconciling his conclusion that there is no motion with our daily perceptions. So although there is no real motion in the sense that the object gradually leaves its position to a new one, but rather it is re-created in ever new positions so that we imagine it moving between these places. For example, when we watch a 'movie' on the TV, we have no doubt that nothing really moves on the screen, but it is only a succession of different frames. According to Ibn ‘Arabî's cosmological perspective, the whole world is exactly like that (see section VI.8 above). As we noted in section II.6, Ibn ‘Arabî plainly stated that the object that we see moving actually is re-created in the distinct places between its start and destination one after another and does not really 'move' between them [II.457.31], so there is never any real motion in such a way that the object 'gradually moves' along its path. Thus Ibn ‘Arabî, like Zeno and Parmenides, believes that the whole world is a manifestation of a single entity which alone can be described to have a real existence. But Ibn ‘Arabî's distinctive contribution is to show how the multiplicity of the world emerges from/within the Single Monad.

## Zeno's Paradoxes

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