I'm teaching Parmenides, Zeno, and Gorgias tomorrow, and their arguments are so fun that I thought I might post them for discussion. Parmenides is generally seen as the founder of the Eleatic school of philosophy. Elea was a city on the Italic peninsula during the classical Greek period, and it was one of a few centers of philosophical thought in the pre-Socratic period. He argued that there really can't be multiple things but just one unchanging, eternal thing. What we perceive to be many, changing things is but illusion. He has a kind of dualism, because he speaks of what is (the unchanging one) and what is not (illusion, what we perceive). But since the second doesn't exist, there's really only one thing.
His student Zeno (not the same Zeno who founded the Stoic school a few centuries later) is famous for his paradoxes against motion, which served the purpose of supporting the overall Parmenidean thesis that there's no change. Gorgias the Sophist presented a parady of Parmenidean arguments, concluding that there isn't even one thing. There's just nothing. It's not clear if he does it to show that he thinks the whole discussion is stupid or if he thinks he's showing by parody what's wrong with Parmenides' arguments, but given that he was a Sophist who was famous for his claim that he could argue for any thesis, it's generally accepted that he wasn't endorsing his argument. I'll post a reconstruction of Parmenides' primary argument here. I may or may not post some Zeno stuff at some point, but I definitely want to do Gorgias' parody in a later post. So here's one way to capture Parmenides' argument.
Anything has to be in one of the four categories:
A. It is and it cannot not be.
B. It is not and it cannot be.
C. It is but can fail to be.
D. It is not but could have been in the past or could be in the future.
C and D are not options:
Against D: How could it possibly be that something exists but doesn't exist? If it exists, it exists. That's a necessary truth. It couldn't fail to be true. If it exists, it necessarily exists.
Against C: If something doesn't exist, then necessarily it doesn't exist. How could it not exist and exist? So it's got to be a necessary truth. That rules out C in a similar way.
That means that anything that doesn't exist cannot exist, and anything that does exist must exist. So the only possibilities are A and B.
He then argues that you can't think or speak about the non-existent, because something has to be possible to be thought of or spoken of. There's no possible thing to speak of or think of unless it's possible, and if it's possible then it's actual. So all there is is what does and must exist.
Now what does exist is what must exist, and that means it can't change. Change involves being one way and then no longer being that way. But if it exists, then it exists as it must be, because nothing is possible that isn't actual. So every way of being already is, and there's no room for change. Also, there can't be more than one thing, because two things mean there's a way to distinguish between them. If you can distinguish between Thing 1 and Thing 2, then that means Thing 1 is not Thing 2. But that can't be, because nothing can not be. Not being Thing 2 is a way of not being, and it's impossible to speak of something that's not Thing 2 if the thing you speak of (Thing 1) isn't Thing 2. So what he's already said leaves no room for multiplicity or change.
Therefore, there's only one unchanging thing, and all else that seems to be true is just illusion.