When equally confident testimony-based methods systematically yield contradictory conclusions, no non-circular criterion drawn from within any single tradition can adjudicate between them.

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Adjudicate(describing what functionalism can or cannot do regarding the disagreement): To judge, decide, or settle a dispute between two competing views.
Epistemic relativism / relativism about knowledge(the philosophical problem this statement is addressing): The idea that what counts as true or knowable might depend on your perspective, tradition, or framework rather than being absolute.
Non-circular criterion(a method for deciding between competing claims without begging the question): A fair, independent way to judge between options that doesn't just assume the answer you're trying to prove.
Systematically yield contradictory conclusions(describing what happens when different reliable approaches give conflicting results): Regularly and consistently produce opposite answers to the same question.

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