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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that The least upper bound of the ordinal indices appearing in the finitist autonomous progression is the ordinal epsilon_0

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Tait's analysis of finitism identifies primitive recursive arithmetic (PRA) as the correct formalization, not Kreisel's autonomous progression.
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    • 2.PRA's proof-theoretic ordinal is omega^omega, which falls strictly below epsilon_0, undermining the claimed supremum.
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    Reason for 2 of 2
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    • 1.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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    • 2.If the autonomy condition is viciously circular, the progression cannot legitimately be said to converge on epsilon_0 as a finitistically meaningful bound.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Kreisel identified a specific autonomous progression of theories for finitism
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    • 2.Kreisel determined the supremum of ordinal indices in this finitist hierarchy
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    • 3.Epsilon_0 is also the proof-theoretic ordinal of Peano Arithmetic
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