Paradox of Motion: Physics & Math Explained

[VazScep]

Yes, I'll say vague -- I've never been impressed by any presentation of Zeno's arguments.
Compare with, say, the Liar's paradox, in which I can formally derive a contradiction:
If P is the statement "P is false", then we have:
P = T or P = F
P = T --> P = F
P = T --> P = T and P = F
P = F --> P = T
P = F --> P = T and P = F
P = T and P = F
This is a real paradox. It, and other similar paradoxes, are the reason why the usual formal logic is designed in such a way that statements cannot refer to themselves (even indirectly!)

I know this is from several months ago, but:

Statements can refer to themselves. In theories of arithmetic, you can code all statements as Gödel numbers, so that statements are essentially capable of making assertions about other statements. A theorem known as the Fixed Point Theorem then shows that for any expressible property p, there is a statement which says "This sentence satisfies property p".

The liar's paradox is avoided because the property of being a true statement is not expressible in theories of arithmetic. This is known as Tarski's Theorem.

 

[michealsmith]

doesnt it just past each point in an infintesmal amount of time

 

[Ubern0va]

I understand his problem quite well, because I've thought of it while sitting in Math class a fiew times, but quickly dismissed it via the anthropic principle :P