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)
That which, being added to another, does not make it larger, and, being taken away from another, does not make it smaller, is nothing.
If there are many things, they must be both small and large, so small as to have no magnitude, and so large as to be infinite.
If there is motion, the moving object must arrive at the half-way point before it arrives at the goal.
The flying arrow is at rest.
Everything that exists has a place. If place exists, it too must have a place, and so on ad infinitum.
If there are many things, they must be just as many as they are, and neither more nor fewer. Now, if they are as many as they are, they will be finite. If there are many things, they must be infinite.
The stadium paradox: In a race, the fastest runner can never overtake the slowest, because the pursuer must first reach the point from which the pursued started, so that the slower is always some distance ahead.
If a grain of millet makes no sound when it falls, then a bushel of millet makes no sound when it falls.
The senses deceive us.
There is no motion.
The one is not many.
If there is a plurality, then things are both like and unlike, and this is impossible.
The path to knowledge is through reason, not the senses.
To refute the common belief in motion and plurality.
My writings are a defense of Parmenides.
If a thing exists, it must be either finite or infinite in magnitude. If it is finite, it has parts. If it has parts, it is infinite.
The arguments are designed to show that the assumptions of common sense lead to contradictions.
If a thing exists, it must be in a place. If place exists, it must be in a place, and so on.
The concept of infinity is problematic.
Our understanding of space and time is flawed.
Contemporaries of Zeno of Elea
Other Philosophys born within 50 years of Zeno of Elea (-490–-430).