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)
The world as we perceive it is an illusion.
If there are many things, they must be separated from one another. If they are separated, there must be something between them. If there is something between them, there are more things.
The very idea of a 'point' in space or time leads to contradictions.
Continuity and discreteness are incompatible.
The concept of 'now' in time is problematic.
If motion exists, then a moving object must occupy a series of points. But if it occupies a point, it is at rest.
The sum of an infinite series of finite quantities can be finite.
My arguments are not meant to deny the existence of motion, but to expose the difficulties in understanding it.
If there is a plurality, then things are both limited and unlimited.
The problem of the continuum.
He was a master of dialectic.
He argued that if a thing has magnitude, it must have parts, and if it has parts, it is infinitely divisible.
The paradoxes force us to re-examine our fundamental assumptions.
He was the first to use the method of reductio ad absurdum.
His arguments are not easily dismissed.
The problem of infinitesimals.
He demonstrated the power of logical reasoning.
The concept of absolute space and time is challenged by his paradoxes.
His work laid the groundwork for later developments in mathematics and philosophy.
The paradoxes highlight the limitations of human intuition.
Contemporaries of Zeno of Elea
Other Philosophys born within 50 years of Zeno of Elea (-490–-430).