Gödel’s proposition is inherently a cycle, the incomplete proof tool actually just falls into the loop of making the main proposition Gödel created – Gödel created a circle with his proposition and then hid in that circle.
Gödel’s wrong as there’s a circle loop in his proof. The tool used for proving is incomplete.
Similar to the liar paradox, in the logical reasoning itself, the paradox of the statement “I am lying” is both true and false, but if you look outside the reasoning (outside the system), you will see that the statement “I am lying” is initially a lie, but through a logical transformation it becomes true, that is, 0 + 1 = 1, so this is the truth, there is no paradox at all. The paradox is that in the logical transformation itself, which is incomplete, it shows that the same statement “I am lying” is both true and false. The proof of Gödel’s Theorem suffers from such a loop error. Self-referencing and then drawing a conclusion.
The proof of Gödel’s Theorem contains serious logical errors: 1) Loop error: Gödel’s proposition itself causes a loop error G = “Cannot prove G”. The proof tool is incomplete, resulting in a return to the original statement (loop error); 2) Self-referentiality: From an incomplete system in the proof, Gödel attributes it to all logical systems; 3) Failure to distinguish between the two states “before logical inference” and “after logical inference”.
Tran, B. L. (2025). Explaining the Limits of Gödel’s Theorem from Its Proof. Zenodo. https://doi.org/10.5281/zenodo.17155727
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