Zeno's Paradoxes

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1. Zeno of Elea
   • his treatise

   • the logical method:
     • Is it absurd to argue as Parmenides did that all things are one and that change and motion are impossible?
     • even more absurd and counter-intuitive consequences follow from the assumption that Parmenides' Way of Truth is false

   • the arguments:
     • arguments against plurality (the many):
       • things must be both like and unlike, and this is absurd;
       • if there is a many, the many things must be "ones" (unities), and this is absurd;
       • the concept of size leads to an infinite regress;
       • the same things are limited and unlimited, because there is no smallest indivisible unit of space, and this is absurd;
     • arguments against motion:
       • the stadium
       • Achilles
       • the flying arrow
       • the moving rows
     • two more paradoxes:
       • where (in what place) is place?
       • the sound of the falling millet seed

   • fascination through the ages with Zeno's arguments

   • Visit Zeno's Coffeehouse

2. Melissus of Samos
   His clue to later philosophers: "If there were a many, they would have to be such as I say the one is" (Simplicius, Com. Arist. On the Heavens, 558.19=DK 30B8, McKirahan translation.)

3. Following Melissus' clue:
   • Qualitative Pluralists:
     • Empedocles of Acragas
     • Anaxagoras of Clazomenae

   • Quantitative Pluralists:
     • Leucippus
     • Democritus of Abdera

revised September 21, 1996


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