When saying that the aggregate is not-self are we not predicting the existence of a thing called self? Parmenides, a presocratic philosopher, said: 


  The only roads of inquiry there are to think of: one, that it is and
  that it is not possible for it not to be, this is the path of
  persuasion (for truth is its companion); the other, that it is not and
  that it must not be — this I say to you is a path wholly unknowable.


In short, we should bar our thought from an inquiry of what is not. Of course, we can say that "the apple is not red" there is nothing wrong with that, but unless a thing called an apple exist we can't say that "a thing is not an apple". 

In the same way, when we say " the aggregate is not self" unless there is a self our statement is a wrong inquiry because as Parmenides says "we can only speak about what is: what is not cannot be thought of, and what cannot be thought of cannot be."
When saying that the aggregate is not-self are we not predicting the existence of a thing called self?

I think that perhaps "we" are not predicting nor denying the existence of a thing called self: for details see for example How is it wrong to believe that a self exists, or that it doesn't?

Parmenides, a presocratic philosopher, said ...

I don't know him but it sounds like he's being a sophist. :-) I guess he's saying we should (or can) only talk truthfully about things that exist, because the non-existant is unknowable.

I think that Buddhism asks a slightly different question: i.e. is a belief beneficial, is it a skilful view?

unless a thing called an apple exist we can't say that "a thing is not an apple"

Can't we say that "a thing is not a unicorn"?

More importantly people generally do view the aggregates as self (at least more-or-less depending on what you mean by "self"): for example, "this is my body, it is mine, my body is me", and so on.

So if that's a common but an unskillful view (from which arises suffering and so on), perhaps it's worth contradicting.