George Szpiro

And that's the basic basis of this paradox.

And it teaches us something about logical thinking, that we cannot pronounce assertions or statements that are both true and false.

And if I say I'm a liar, then I just violated that law.

I pronounce the statement that is both true and wrong and untrue.

A very famous paradox is about Achilles and the turtle.

It goes like this.

If the turtle stands 10 feet in front of Achilles and they start running, Achilles can never reach and never overtake the turtle.

Why?

Because by the time he reaches Achilles,

where the turtle started out, the turtle will have moved on a bit.

And when Achilles reaches that point, the turtle will have moved on a bit more and so on and so on.

And so the Greeks, the ancient Greeks said, well, in that case, Achilles could never reach the turtle.

But obviously Achilles can reach the turtle and he can overtake the turtle.

So that was a conundrum.

They didn't know how to solve it.

And actually, the solution to that paradox is that you cannot subdivide the steps of Achilles into smaller and smaller steps.

The whole assertion that he'll always reach where the turtle was, and in that time space, the turtle will have gone a fraction further.

And when Achilles overcomes that fraction, the turtle will have gone a bit further and so on.

It's actually wrong because Achilles cannot take that small steps.

And this paradox was only solved when Isaac Newton came up with infinitesimal mathematics with calculus, where you speak about the infinitely small.