So, you want to know what’s so special about a dodgy paradox?
No one knows precisely when Zeno of Elea had his paradox. It is in the nature of paradoxes to spring out at you unexpectedly. I like to think he was probably in the shower.
Anyway, he was already a middle-aged man when he met Socrates in around 450BC.
Zeno was tall and fair, and, in his early days, in had been in love with an older philosopher – Parmenides. Actually, that’s where it all begins, Zeno’s paradoxes really all go back to love. (and certainly not the first or last paradoxii to be born of love)
Parmenides was one of the most important of the early Greek philosophers. That may or may not have anything to do with Zeno’s infatuation. Anyway, Plato refers to him as the Father of true philosophy. His importance for us, and for Zeno’s paradox, lies in his teaching about the structure of the Universe. Parmenides believed that the Universe is not composed of lots of little pieces, it is One. That’s to say, it is in reality one, undifferentiated, endless whole. It is not a collection of little bits flying around, bumping into each other, and having a whale of a time.
I would not be at all surprised if you think that sounds completely barmy.
All our experience of life in this world seems to tell us that everything is made up of bits of stuff. I’m a bit of Man-stuff, and the computer is a bit of Cyber-stuff, and the tree is a bit of tree stuff, and we are all different bits and pieces. The Universe might be One Thing, in the sense of a combination of lots of bits, but from looking around it doesn’t seem apparent that it is just One Big Endless Bit. What would lead Parmenides to reach such a bizarre conclusion, and more interestingly, why would anyone else believe him?
Parmenides got there like this…
If there are lots of different pieces of stuff in the universe. There must also exist gaps in between the pieces. You can’t have separate things without space (even if it’s only very little) in between to separate them. So if the Universe is made up of lots of separate pieces of material then it would in fact consist of, Stuff and Spaces.
But, the Universe is the totality of all the things that really exist. On the other hand, the gaps in between the pieces – the Spaces – are nothing, just a void. And Parmenides wasn’t for an instant going to believe that Nothing Is. (You can’t say that ‘Nothing’ exists. It’s not the Never-Ending Story, we aren’t be chased by a Giant ‘Nothing’).
Nothing is nothing, it isn’t a thing, it doesn’t have existence.
And if the spaces between the pieces are filled with nothing, then they aren’t spaces, are they? And if the spaces aren’t spaces, then the pieces aren’t pieces. And so the Universe is just one giant endless blob. (it has to be endless because there can’t be any ‘nothing’ around the outside either).
If you thought Zeno’s Paradoxes were whacky… well personally, this makes me want to strip down and start chasing turtles in the sun.
Parmenides ‘interesting’ view of Reality is the basis for Zeno’s Paradox of Achilles and the Tortoise. Zeno dreamt it up in order to defend his Erastes (look it up if you dare) from the nasty bad men who made fun of him. If Parmenides is right, and the Universe is one endless blob, then it should be impossible to move around in it. Movement requires that there be different pieces of stuff that can change their relationship to each other. If you don’t believe me, try sitting in front of the tv and going down to the pub at the same time. There needs to be a distinction between objects in order for there to be movement.
Zeno’s paradox is meant to demonstrate that, despite appearances, movement is impossible. No matter what our senses and experience tell us about what would actually happen in a race between Achilles and a Tortoise, on (apparently) strictly logical grounds, it’s all nonsense.
You are therefore left with a problem:
If the Paradox is right, then the evidence of your senses and experience is rubbish.