I am taking issue with the so-called "falsity" of the "this statement is false". If you imagine that statement, and imagine that what you imagine is probable in the extreme, outside of your imagination, free, and unmolested by your probings, then "this statement is false" is always, only, incidental.
And don't come back saying saying "false" and "proven false" are different. I can compare strings!
Is your argument that the statement could possibly be false? Otherwise we're already in agreement... Nobody is suggesting the statement is false (I think).
Edit: to clarify, the statement in question is "this statement cannot be proven," not "this statement is false."
He says, "If it [the statement] is proven, then a false statement is proven." (Proven true or false?)
I am not interpreting the statement "this statement cannot be proven" as true, as you do, or false.
What I argue is that one's interpretation has an effect, without which the statement is neither true nor false, but, as I claim, incidental. We can imagine the statement, but what we imagine is not the statement, even if it looks and smells like it.
Thus, the Schrodinger Card trumps the Goedel. The trick here is that I am standing outside of "the system", not permitting myself to enter paradox land. If you so much as look at me, I'll get sucked in.