Stadium paradox

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The paradox of the moving blocks or stadium paradox of Zeno of Elea , in contrast to his other paradoxes , a simple fallacy.

It is argued as follows: four blocks BBBB of the same size move along four stationary blocks AAAA of the same size, and four blocks CCCC of the same size move in the opposite direction as BBBB but at the same speed. BBBB will now pass two blocks of AAAA in the same time as four blocks of CCCC. Since the speed remains the same, and speed is measured as distance per time, half the time is twice the time.

Alexander von Aphrodisias illustrates Zeno's argument with the following diagram:

  AAAA
BBBB →
     ← CCCC

becomes

  AAAA
  BBBB →
  ← CCCC

The fallacy arises because the concept of relative movement is missing. The reasoning could be as follows:

If the right B block moves one block to the right - the distance E m far - at the speed of G m / s, it needs E / G s. The same movement requires the left C to move one block over the right B to the penultimate block B on the right, which corresponds to a distance of 2 E. Zeno concludes from this that since the Cs move with the speed G m / s, the movement also lasts 2E / G s. And so "half the time (E / G) is equal to double (2E / G)", because apparently a movement uses both times.

The paradox, however, is the first conception of the relativity of motion in ancient literature.

It uses a reconstruction of the paradox as an argument against a discontinuous structure of space and time. If there are smallest units of space and time, BBBB and CCCC, which have the smallest subunits, always move two blocks past each other in these minimal time intervals, but some (every second) of these blocks B and C move past each other without to happen.

Another reconstruction assumes that Aristotle paraphrases the paradox in order to make sense of Zenon's argument. The paradox does not assume three, but two moving blocks, with AAAA moving from the center of the stadium to the right edge and passing an infinite number of sections on its way, while BBBB moves at the same speed in the other direction from the right There is an equally infinite number of sections to the left of the stadium. Because of the same speed, the assumption that the two total sections of the route are the same size must lead to the absurdity that half time is all time. Zeno has discovered that with infinite quantities, the whole does not always have to be larger than the part.

swell

  1. ^ A b Kurt von Fritz about Zenon von Elea
  2. ↑ a b Mittelstrasse, philosophy and philosophy of science, paradoxes, zenonic
  3. ^ Stanford Encyclopedia of Philosophy, Zeno's Paradoxes

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