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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that The Space Hierarchy Theorem presupposes that space-constructible functions are well-defined, but constructibility itself is a notion relative to a model of computation with no canonical metaphysical grounding.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Space Hierarchy Theorem proves results about all machines meeting abstract definition requirements, not any particular physical implementation.
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    • 2.Relative constructibility is philosophically unproblematic: empirical theorems also presuppose frameworks without requiring independent metaphysical grounding.
      ?

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    • 3.Model-dependence doesn't undermine validity; the theorem holds across all reasonable Turing-complete formalizations, establishing robust mathematical structure.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Space-constructibility depends on Turing machines, which lack universal physical instantiation across all possible universes or computational substrates.
      ?

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    • 2.Mathematical theorems about constructibility describe formal systems, not mind-independent reality, so grounding claims require external metaphysical assumptions.
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    • 3.Different computational models (cellular automata, lambda calculus, circuits) yield different constructibility notions, undermining canonical status.
      ?

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