The biconditional conflates provability within a descriptive complexity framework with the truth of an independent computational conjecture, committing a use-mention error about mathematical equivalence.
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Provability(as the standard by which large cardinal hypotheses are being compared)
The ability to prove something is true using logical rules and established facts—whether a statement can be demonstrated with certainty.
use-mention error(fundamental logic error in arguments)
A logical mistake where you confuse using a word with talking about the word itself—like saying 'dog has three letters' when you meant the word 'dog' has three letters.