Can we learn anything positive about the nature of motion from Zeno’s paradoxes?
Can we learn anything positive about the nature of motion from Zeno’s paradoxes?
Answering this question requires a good treatment of all four paradoxes (that is, the dichotomy, Achilles and the tortoise, the stadium, and the arrow) before explaining their impact on the nature of motion. The second half of the question asks for an evaluation of the philosophical significance of the paradoxes with reference to motion. An outstanding answer can also discuss the Atomism’s reply that space and time are composed of indivisible atoms, and Aristotle’s twofold reply, first, that even if they are infinitely in division, they are not infinite in extension and, second, that the problem for the infinite should apply similarly to motion and time.
This question demands an ability to distinguish a series of somewhat different arguments, and to present them concisely and lucidly. Of these, the arrow paradox, in the form that presupposes that time consists of instants, is the simplest to state, and the paradox of the three rows the most complex. It is important to highlight that a race, for example, can never be terminated, but also that it can never even be started. Zeno needed the second claim, as well as the first, to exclude any motion. Aristotle inferred that motion is through a space that is infinitely divisible, but neither infinite in extent, nor actually infinitely divided. Bertrand Russell (in his early and brilliant book Our knowledge of the external world,) inferred that space and time form a continuum.
