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    Constructibility requirements, as Blum's axioms show, are... — Carmelics
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    Challenges→NSPACE(f(n)) is a subset of TIME(2^O(f(n)))

    Constructibility requirements, as Blum's axioms show, are not purely formal but encode substantive constraints on what counts as a legitimate resource measure.

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    1 reason for
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    Reasons For

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    Reason for
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    • 1.Blum's axioms (linearity, symmetry, monotonicity) presuppose philosophical commitments about what makes computation 'fair' or 'meaningful.'
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    • 2.Different resource measures (time, space, reversible operations) cannot be purely formally equivalent; choosing between them reflects value judgments.
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    • 3.Axiom systems that claim formality always embed implicit assumptions about legitimate vs. illegitimate computational idealizations.
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    Reasons Against

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    Reason against
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    • 1.Blum's axioms are derivable from minimal assumptions about measure-theoretic structure, not substantive philosophical commitments about resources.
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    • 2.Constraints can be mathematically formal yet still constrain what's measurable—formality and substantivity are independent properties, not opposed.
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    • 3.The distinction between 'purely formal' and 'substantive' constraints is itself philosophically contested and may not carve nature at its joints.
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    Truth & Knowledge1 linkedModality & Possibility1 linked

    Related

    Axiom systems that claim formality always embed implicit assumptions about legit...Blum's axioms (linearity, symmetry, monotonicity) presuppose philosophical commi...Blum's axioms are derivable from minimal assumptions about measure-theoretic str...Constraints can be mathematically formal yet still constrain what's measurable—f...
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    Different resource measures (time, space, reversible operations) cannot be purel...NSPACE(f(n)) is a subset of TIME(2^O(f(n)))The distinction between 'purely formal' and 'substantive' constraints is itself ...

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