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This paper addresses a proof of incompleteness published by George Boolos. An analysis of this proofs demonstrates that there is an elementary error in the proof; the proof relies on the unproven assumption that the formal system can self- reference its own formulas.
There are several similar proofs published by Chaitin involving the concept of information-theoretic complexity, and Chaitin claims that these are proof of the incompleteness of formal systems. An elementary analysis of these proofs demon- strates that the proofs are not in fact proofs of incompleteness
In many incompleteness proofs there is a claim that, given a Gödel numbering function that encodes sequences of symbols of a given formal system, there is a formula of that formal system that corresponds to that Gödel numbering function such that the formula itself can refer unambiguously to formulas of that formal system. This paper proves that this cannot be the case.