When saying that the aggregate is not-self are we not predicting the existence of a thing called self?
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.