Feferman argued that Kreisel's autonomy condition is epistemically circular: recognizing a progression as finitistically legitimate already presupposes the ordinal comprehension it purports to generate.

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Autonomy condition(as Kreisel's specific proposal in mathematical reasoning): A rule or requirement that something should be able to stand on its own without needing outside help or assumptions to justify itself.
Epistemically circular(describing a logical problem with the argument): A situation where you're trying to prove something, but your proof assumes the very thing you're trying to prove—like trying to prove a book is true by quoting the book itself.
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.
Finitistically legitimate(as the standard being applied to mathematical methods): Acceptable or valid according to finitism, a strict approach to math that only accepts reasoning about things we can actually construct or compute in a finite number of steps.

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