That is not at all what the incompleteness theorems say.
The first incompleteness theorem says that for any consistent formal system T (with a recursively enumerable set of axioms) capable expressing of elementary arithmetic, T can express a statement which it can neither prove nor disprove.
The second incompleteness theorem says that T can't prove the statement "T is consistent". (I've still glossed over a number of technical details here; pick up a book on model theory if you want all the messy internals.)
First order logic is notably not capable of expressing elementary arithmetic. And observers aren't involved in any way.
The first incompleteness theorem says that for any consistent formal system T (with a recursively enumerable set of axioms) capable expressing of elementary arithmetic, T can express a statement which it can neither prove nor disprove.
The second incompleteness theorem says that T can't prove the statement "T is consistent". (I've still glossed over a number of technical details here; pick up a book on model theory if you want all the messy internals.)
First order logic is notably not capable of expressing elementary arithmetic. And observers aren't involved in any way.