Philosophical Problems January 13, 2015 Zeno's Paradoxes

The Eleatics Elea was a small colony in southern Italy. It is now called Velia.

‘Greek’ Philosophy Much of what we call Greek philosophy came from philosophers who were not born in the territory of modern Greece. Indeed, the origins of ‘classical’ Western philosophy are in Asia. More specifically, they are in towns along the western coast of Turkey.

Map of ancient Turkey

Pythagorus He was born on Samos, eventually settled in southern Italy. He had a major influence on philosophers there.

Metaphysics Among other things, he influenced them to take metaphysics seriously. Metaphysics is the study of being.

Meta Originally, 'meta' meant after. Now, at least in English, it means more like 'about. So a meta-debate is a debate about the qualities of a debate. – It invovles questions like: Should we even be talking about this?

Metaphysical Questions Are there properties in the world, or just individuals? Is the world entirely physical? Is there a God? How many things are there?

Parmenides Answer One. There is just one thing, and it doesn't change. This is the doctrine called monism.

Parmenides on Existence Everything exists. Not only is this true, it seems almost definitional. To be a thing is to be existing. So it doesn't make sense to talk about something not existing.

Parmenides on Creation 1.If something was created, then it exists at one time and did not exist at an earlier time. 2.If something did not exist at an earlier time, it had non-being at that earlier time. 3.But everything exists; nothing has non-being. So, nothing is ever created.

What Went Wrong? A.Premise 1 is false. B.Premise 2 is false. C.Premise 3 is false. D.All premises are true, but the conclusion does not follow. E.Nothing is wrong; Parmenides is right.

Parmenides and Change Maybe I can't be created, but I can change, right? Not so fast says Parmenides. Imagine that I stand up. Then the state of affairs I am standing is created. But nothing is created. So nothing can change.

Parmenides and Cosmology Parmenides is obviously wrong. Look, the slides just changed! But the questions he asks are relevant to thinking about how to think about whether anything preceded the Big Bang. And it turns out that getting theories of change, and of creation, is hard.

Zeno Zeno was a follower of Parmenides. He was famous for a book of forty paradoxes. Sadly, only a few of these have survived. But they are pretty neat paradoxes.

The Racecourse Achilles is running a race. It's one lap of a track. You'd think he could finish - he's Achilles! But think about what it takes to finish. He has to run half the course, then half of what's left, then half of what's left, then... And this sequence can never be finished.

The Racecourse as an Argument. 1.To finish the race, Achilles must complete an infinity of tasks. 2.No one, not even Achilles, can complete an infinity of tasks. So Achilles cannot finish the race.

What’s Wrong? A.Premise 1 is false. B.Premise 2 is false. C.The premises are true, but do not support the conclusion. D.Nothing is wrong; Achilles cannot finish the race.

Zeno, Parmenides and Calculus Zeno intended to support Parmenides’s argument that nothing changes. He didn't convince many people! But he did pose the kind of problem that was very important to setting up the modern calculus.

Achilles and the Tortoise. Achilles runs faster than the Tortoise. (Assume each moves at a constant pace.) So he gives the Tortoise a head start. You'd think he would catch the Tortoise. But whenever he gets to where the Tortoise was, the Tortoise has moved on. So Achilles can never catch the Tortoise.

The Tortoise and Tasks Achilles starts a mile behind the Tortoise. He completes his first task when he runs a mile, getting to where the Tortoise starts. From then on, he completes the next task when he gets to where the Tortoise was when Achilles completed the previous task. Achilles must complete infinitely many such tasks to catch the Tortoise. But no one can do infinitely many things.

What went wrong?

Zeno’s Arrow This is a very different kind of argument for a similar conclusion. Again, Zeno wants to argue that nothing moves. And the argument fails, but figuring out how it fails is fascinating.

Moving Pictures Think about a movie of an arrow in flight. It looks like the arrow is moving. But really it is just one still after another.

Zeno’s Argument At every instant of time, the arrow is not moving. For the arrow to move in an interval, it must move at some instant. So, the arrow does not move over the interval.

What Went Wrong? A.Premise 1 is false. B.Premise 2 is false. C.The premises are true, but do not support the conclusion. D.Nothing is wrong; arrows never move.

Two Theories of Motion ‘At-at’: motion is a matter of being at one place then at another. ‘Instantanous velocity’: motion is a matter of having a vector-valued motion property.

Theories and Zeno On the instantaneous velocity theory, premise 1 is false. You can’t see the arrow moving in a picture, but even in an instant it is moving.

Theories and Zeno On the ‘at-at’ theory, premise 2 is false. Motion isn't something that happens at any one time. So to be in motion over an interval doesn't require being in motion at some time.

Which Theory is Right? That's a hard question! It turns out there are surprising problems for each theory. If you push on all the problems, you can be led back to the Arrow paradox. Whatever theory you endorse, motion ends up being somewhat less intuitive than it seemed.

For Next Time Read the Crito. Socrates refuses an offer to escape from Death Row.