Paradoxes without self-reference?

Question

Most paradoxes involves self-reference, the only exception known to me is Yablo's paradox, however it is still debated if it is really without self-reference. So, I was wondering, are there other known paradoxes that works without self-reference?

Answer 1

It is well known that the natural numbers have the property that if we have some non-empty set $A\subseteq\mathbb{N}$, then $A$ has a minimal element. Now let $$A = \{n\in\mathbb{N}|\,n\mathrm{\ can't\ be\ expressed\ with\ less\ than\ }100\mathrm{\ characters}\}$$ Let $a\in A$ be the smallest element in $A$. Then we can express $a$ as "$a$ is the smallest number that can't be expressed with less than $100$ characters". But this is an expression for $a$ containing less than $100$ characters, which would be a contradiction. We deduce that $A=\emptyset$. Thus every natural number can be expressed with less than $100$ characters. But there is only a limited number $n$ of characters, thus there are at most $n^{100}$ natural numbers.

This paradox is known with the name of Richard's paradox.

Answer 2

There's the Achilles and the tortoise paradox:
In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.

The Dichotomy paradox is in some sense a particular case of the above:
Suppose Homer wants to catch a stationary bus. Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before traveling a quarter, he must travel one-eighth; before an eighth, one-sixteenth; and so on.

Answer 3

A famous one was given by the Harvard logician WVO Quine (look up Quine's paradox for more information):

"Yields falsehood when preceded by its quotation" yields falsehood when preceded by its quotation.

When I first saw it I had to take a minute to parse what it was saying and why it wasn't self-referencing.