Zeno (c. 495 BCE) Zeno was a Stoic philosopher best known for his four ‘paradoxes.’
The two most popular paradoxes are:
1) Zeno asks how many grains of millet must fall before a sound is heard. One fallen grain makes no sound on impact, therefore it accounts for ‘nothing.’ A second grain (a second ‘nothing’) added to the first might also make no sound. But suppose a third grain (a third ‘nothing’) is added to the two grains and this does make a sound. This would result in a ‘something’ (audible sound) being made out of three ‘nothings.’
2) The great runner Achilles can never catch a slower tortoise in a race if the tortoise begins ahead of Achilles. By the time Achilles reaches the tortoise’s starting point, the tortoise has moved to a new position. And by the time Achilles reaches the tortoise’s new position, the tortoise has vacated it and moved on to another position. The distances between the two may become increasingly small but the tortoise always remains a fraction ahead of Achilles.
Philosophers still debate the import of the Achilles paradox but its solution might be simple. The problem seem to arise from Zeno’s use of logic divorced from observation.
The student of vectors will observe that a higher-velocity object gaining on and moving in the same direction as a lower-velocity object will at some point overtake the slower moving object.
Not so complicated.
But Zeno imaginatively ‘stops motion’ to observe the competitors in a series of equally imaginative points to say that Achilles will never reach the tortoise’s position. And this sheer act of imagination doesn’t correspond to what actually happens in observable reality.
Among other things, Zeno’s paradoxes illustrate how thinking about problems and their apparent solutions can be influenced, constrained and distorted by our use of a symbol system, such as language, logic or mathematics–especially when divorced from empiricism. » Achilles, Heap of Sand Paradox, Semiotics, Signifier, Signified, Stoicism
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