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    If indices underdetermine totality, then the inference fr... — Carmelics
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    Challenges→The universal partial computable function υ(i,x) is not total (i.e., not computable everywhere)

    If indices underdetermine totality, then the inference from 'υ(i,x) is partial computable' to 'it cannot be total' conflates a representational limitation with a metaphysical one.

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    1 reason for
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    Reasons For

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    Reason for
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    • 1.An index is merely a notation system; what it represents may possess properties independent of representational constraints.
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    • 2.Partial computability describes our epistemic access, not necessarily the actual totality or partiality of the underlying function.
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    • 3.Confusing map limitations with territory properties is a systematic error in reasoning about computability and existence.
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    Reasons Against

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    • 1.If indices underdetermine totality, we cannot distinguish metaphysical facts from representational artifacts—making the distinction itself unclear.
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    • 2.Partial computability has formal consequences (halting behavior, domain restrictions) that constrain any realization, not mere representation.
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    • 3.Without independent access to the function beyond indexing, claiming totality exists 'metaphysically' is unfalsifiable speculation.
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    Related

    An index is merely a notation system; what it represents may possess properties ...Confusing map limitations with territory properties is a systematic error in rea...If indices underdetermine totality, we cannot distinguish metaphysical facts fro...Partial computability describes our epistemic access, not necessarily the actual...
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    Partial computability has formal consequences (halting behavior, domain restrict...The universal partial computable function υ(i,x) is not total (i.e., not computa...Without independent access to the function beyond indexing, claiming totality ex...

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