now what if we prove that A is provable or not provable

consider if unprovable statements are false:
- A: this statement is unprovable
- therefore, A is false

_except_ A has undefined truth value, so we can't infer things from it

...

the problem maybe is that Godel considers A to be clearly true.

But you know what? I can make a logic that defines statements in
another logic to be true or false arbitrary.
_The fact that something is true in a different logic does not relate
to its usefulness in reality unless that logic describes reality._

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