If the second incompleteness theorem's scope is predicate-relative, then Rosser's predicate reveals the theorem's dependence on representational choices, not a defect in the predicate itself.

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Predicate-relative(describing whether the theorem's conclusion varies with different logical choices): Meaning that something depends on or changes based on which specific logical formula (predicate) you choose to use.
Representational Choices(referring to how mathematicians can encode the same concepts in multiple ways): The different ways you can express or represent the same mathematical idea using different symbols or formulas—like how you can write the same number as a fraction or a decimal.
Rosser's predicate(as used in mathematical logic): A logical tool created by mathematician J. Barkley Rosser that defines consistency (the quality of having no contradictions) in a different way than the standard definition, while still capturing the same essential idea.
Second Incompleteness Theorem(Gödel's incompleteness theorems): A theorem showing that the consistency of arithmetic cannot be proved in arithmetic itself

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