Impredicativity

Okay kiddo, so impredicativity is when we try to define something using itself. Imagine you are trying to explain what a "big" thing is, but you use the word "big" in your explanation.

For example, let's say we want to define a set by saying it contains all the sets that don't contain themselves. But the problem is that in order to check whether a set isn't in itself, we have to look inside that set to check. And that means that our definition is using the very thing we are trying to define.

So, using impredicative definitions can lead to problems where we end up in a kind of circular reasoning that doesn't really give us any useful information. It's like trying to catch your own tail - you can keep going around in circles and never really getting anywhere.

Does that make sense, little one?