Feferman himself acknowledged that the autonomous condition requires recognizing which ordinal notations are 'legitimate,' a judgment that cannot be formalized without circularity.
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Ordinal notations(as the labeling system used in the progression)
A system of symbols used to label and order infinite sequences and structures in a precise mathematical way.
circularity(as used in logic and epistemology)
A logical problem where an explanation depends on the very thing it's trying to explain, going in a circle rather than providing genuine support.
knowledge(Distinguished from mere true belief, which may be the product of indoctrination and need not exercise deliberative capacities.)
Justified true belief — true belief that has been arrived at through the exercise of deliberative capacities, including comparison of and deliberation among alternatives.