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    Feferman himself acknowledged that the autonomous conditi... — Carmelics
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    Challenges→Autonomous progressions of theories can characterize finitism and predicativism in a mathematically precise way

    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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    Key Terms

    Autonomous condition(as the condition Feferman discussed)
    A requirement or rule that stands on its own without needing help from outside sources—in this case, a mathematical principle that should work independently.
    Feferman(as a historical figure in logic and philosophy of mathematics)
    Solomon Feferman (1928–2016), a logician and philosopher who studied the foundations of mathematics and how different formal systems relate to each other.
    Formalized(as describing how scope fallacies have been studied in logic)
    Written out using a strict, systematic method (usually with symbols or mathematical notation) so it can be studied precisely.
    Legitimate(in epistemology)
    Accepted as valid or justified according to the standards and rules of a particular field or time period.

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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.

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    Proof of definition segments1 linkedModality & Possibility1 linked

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    Autonomous progressions of theories can characterize finitism and predicativism ...

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