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)
He was a student of Parmenides, and his arguments were in support of his master's doctrine of the One.
If there are many things, they must be both finite and infinite in number.
The very act of measurement implies a division into parts, which leads to infinite regress.
He showed that our everyday concepts of reality are fraught with logical difficulties.
His arguments are still debated today.
He was a pioneer in the field of logical paradoxes.
The problem of actual versus potential infinity.
He demonstrated that what seems obvious can be logically impossible.
His work is a testament to the power and limitations of human reason.
The paradoxes are not mere sophistry, but profound philosophical challenges.
That which is in locomotion must arrive at the halfway stage before it arrives at the goal.
The slower will never be overtaken by the quicker.
The sum of an even and odd number is odd.
Motion is impossible.
What is cannot not be; what is not cannot be.
Plurality is impossible.
If there are many, they must be both so small as not to have magnitude, and so large as to be infinite.
The whole has no magnitude.
Being cannot be divided.
There is no motion, because what moves must first reach the middle.
Contemporaries of Zeno of Elea
Other Philosophys born within 50 years of Zeno of Elea (-490–-430).