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    A conservative extension result is only as robust as the ... — Carmelics
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    Challenges→Predicativist analysis is a conservative extension of Peano Arithmetic

    A conservative extension result is only as robust as the reconstruction it presupposes, so disputed reconstructions yield disputed conservation results.

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    1 reason for
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    Reasons For

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    Reason for
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    • 1.Conservative extension theorems rest on formal mappings between theories; ambiguous reconstructions create multiple possible mappings.
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    • 2.If two reconstructions differ on which formulas count as theorems, they yield different conservation results for the same theory pair.
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    • 3.Without consensus on reconstruction, there's no fact of the matter about what the original theory actually claimed or entailed.
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    Reasons Against

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    Reason against
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    • 1.Some conservation results hold across all reasonable reconstructions, making them robust despite reconstruction disputes.
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    • 2.A reconstruction can be epistemically uncertain yet still correctly track logical consequences if the disputed elements are irrelevant.
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    • 3.Robustness degrees exist: results resistant to small reconstruction changes differ from those sensitive to minor reinterpretations.
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    Connections

    1 linked claim · 2 topics

    Truth & Knowledge1 linkedModality & Possibility1 linked
    Predicativist analysis is a conservative extension of Peano Arithmetic

    Related

    A reconstruction can be epistemically uncertain yet still correctly track logica...Conservative extension theorems rest on formal mappings between theories; ambigu...If two reconstructions differ on which formulas count as theorems, they yield di...Predicativist analysis is a conservative extension of Peano Arithmetic
    +3 moreShow less
    Robustness degrees exist: results resistant to small reconstruction changes diff...Some conservation results hold across all reasonable reconstructions, making the...Without consensus on reconstruction, there's no fact of the matter about what th...

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