Refutement of Gorgias' arguments?

Question

We were asked by our professor to refute Gorgias' arguments. His arguments are as follows:

I. Nothing exists

II. Even if something exists, nothing can be known about it.

III. Even if something could be known about it, knowledge about it can't be communicated to others.

Answer 1

Use the argument of existentialism.

Answer 2

I think you've summarized it well although I'm no philosophy student but just looking at his premise it fails because of the reality of life.  For everything that one experiences in life is real.  It doesn't matter what is in your mind or not or whether you believe in it or not.

One thing obvious to my mind is that if life were to remain as mysterious and unknowable as Gorgias says then that would nullify the usefulness or purposes of teachers or even experts in their fields as well.  No one is to be believed and as such any knowledge from them can be ignored.

Who would use is this argument any way?  A fool?