Does Curry's paradox have to be self-referential? This is kind of a logic question so I'm not exactly sure it belongs in math, but does Curry's paradox have to be self-referential?
For example, could this be considered an example of Curry's paradox, even though it isn't self-referential:
If I teach math, then elephants fly.
I teach math.
Therefore, elephants fly.
https://en.wikipedia.org/wiki/Curry%27s_paradox
 A: The point of self-referentiality is that it can force truth values to behave in a certain way. In general, if you just assert a sentence, there's no reason I can't say "But that's wrong!" For example, in this context disagreeing with the sentence "If I teach math, then elephants fly" defuses the paradox.
But self-referential statements can add a weird layer of complexity: by referring to their own truth, they can control their own truth value simply by virtue of existing! For instance, consider the sentence "This statement is false": the way it talks about itself, rules out the possibility of consistently saying that it's true or false.
The Curry paradox is an interesting variation on this: it is an example of a sentence which doesn't "explode," but rather just forces itself to be true; and moreover lets us cook up such examples with whatever consequences we want. It shows that there's more flexibility in self-reference than merely producing immediate contradictions (although of course we can use Curry to produce an immediate contradiction, the point is that we don't have to). 

For a (arguably) non-self-referential paradox, consider Yablo's paradox: let $p_n$ be the sentence "There is at least one $m>n$ such that $p_m$ is false", for $n\in\mathbb{N}$. Then how can we assign truth values to these sentences? Either we make infinitely many of them false, in which case all of them must be true; or we make only finitely many of them false, in which case all but finitely many of them are false.
In a sense, Yablo is an "unfolded Liar," but making this precise takes serious effort.
A: There is no paradox here, just a false statement. Given that elephants don't fly, if the sentence "I teach math" is true, the sentence "If I teach math, then elephants fly" is false.
