George Szpiro

For example, the liar's paradox.

If I tell you I'm a liar, I always tell lies.

So when I tell you I always tell lies, I actually said the truth.

And that's a paradox.

A paradox is something that usually sounds absurd.

And when you analyze it further, either you find out that it's not absurd, it just sounded absurd, but it's actually a true statement, or it's a statement that's based on incorrect assumptions, or the logical arguments are wrong, or something in the basic assumptions is

is incorrect.

But very importantly, paradoxes were the gateway for philosophers to think deeply about questions.

For example, the liar's paradox.

If I tell you I'm a liar, I always tell lies.

then the question is, did I just say a truth?

Because I am a liar.

I always say lies.

So when I tell you I always tell lies, I actually said the truth.

And that's a paradox.

It's important in order to understand our way of thinking, the theory of knowledge.

For example, the liar's paradox is,

The problem with the liar's paradox is that I'm violating a law, basic logical law, namely the law of non-contradiction.

A proposition cannot be true and false at the same time.

Now, if I say I always lie, then I'm saying something that's both true and false at the same time.