Zeno of Elea
Famous for his paradoxes, which challenged the concepts of motion and plurality.
Most quoted
"If it is, each thing must have some magnitude and thickness, and part of it must be apart from the rest. And the same reasoning holds concerning the part which is in front. For that too will have magnitude and part of it will be in front. Now it is the same thing to say this once and to say it always. For no such part of it will be last, nor will there be one part not related to another. Therefore, if there are many things, they must be both small and large; so small as to have no magnitude, so large as to be infinite."
— from Paradoxes of Plurality
"If Being is divided, it is either divided into beings or into non-beings. But it cannot be divided into non-beings, for non-beings are nothing. And if into beings, then each of these beings is further divisible, and so on forever. So Being is infinitely divisible and thus has no ultimate parts."
— from Arguments against plurality
"If things are many, they must be just as many as they are, no more and no less. And if they are just as many as they are, they must be finite. But if things are many, they are infinite; for between things that are there are always others, and between those yet others. So things are infinite."
— from Paradoxes of Plurality
All quotes by Zeno of Elea (155)
Being knows no plurality.
Reason triumphs over empirical deceit.
The tortoise teaches eternal pursuit.
Stillness underlies all motion.
Infinite series mock completion.
Philosophy begins with denying the obvious.
That which is in locomotion must arrive at the half-way stage before it arrives at the goal.
If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless.
Achilles will never overtake the tortoise.
The slower runner will never be overtaken by the quicker; for that which is pursuing must first reach the point from which that which is fleeing started, so that the slower must always be some distance ahead.
If there are many, they must be both finite and infinite in number.
If there are many things, they must be both like and unlike.
If things are a many, they must be both small and large; so small as to have no magnitude, so large as to be infinite.
What has no magnitude, thickness, or mass cannot exist.
If it is, each thing must have some magnitude and thickness, and part of it must be apart from the rest. And the same reasoning holds concerning the part which is in front. For that too will have magnitude and part of it will be in front. Now it is the same thing to say this once and to say it always. For no such part of it will be last, nor will there be one part not related to another. Therefore, if there are many things, they must be both small and large; so small as to have no magnitude, so large as to be infinite.
If place exists, where is it? For everything that exists is in a place. Therefore, place is in a place. This goes on to infinity. Therefore, place does not exist.
If you say a millet seed makes a sound when it falls, does a ten-thousandth part of a millet seed make a sound?
Motion is impossible because that which is moving must reach the midpoint before it reaches the end.
The first [argument] asserts the non-existence of motion on the ground that that which is in locomotion must arrive at the half-way stage before it arrives at the goal.
Nothing moves because the moving object must first reach the halfway point, and before that the quarter point, and so on ad infinitum; thus motion can never begin.
Contemporaries of Zeno of Elea
Other Philosophys born within 50 years of Zeno of Elea (-490–-430).