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    A translation that preserves truth value across indetermi... — Carmelics
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    Challenges→The translation from singular reference to 'the' singleton function into universal quantification over singleton functions introduces no inconsistency into mathematics.

    A translation that preserves truth value across indeterminate referents does not establish consistency but merely hides the ontological arbitrariness Benacerraf diagnosed.

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    Reasons For

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    Reason for
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    • 1.Benacerraf's indeterminacy problem shows mathematical objects lack determinate reference; translation cannot solve what is fundamentally metaphysical.
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    • 2.Preserving truth value across different ontologies merely redistributes the arbitrariness rather than justifying any particular ontological commitment.
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    • 3.Consistency is a logical property about formal systems, not evidence that our translation maps onto reality; it masks deeper ontological questions.
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    Reasons Against

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    • 1.If translations preserve truth value systematically, they achieve the practical goal of mathematics regardless of whether ontology is 'truly' justified.
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    • 2.Benacerraf's challenge assumes determinate reference is required for knowledge; but structural equivalence across models may be epistemically sufficient.
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    • 3.Calling consistency 'mere hiding' begs the question—consistency across indeterminate frameworks may actually resolve rather than conceal arbitrariness.
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    Modality & Possibility1 linkedPhilosophy of Language1 linked

    Related

    Benacerraf's challenge assumes determinate reference is required for knowledge; ...Benacerraf's indeterminacy problem shows mathematical objects lack determinate r...Calling consistency 'mere hiding' begs the question—consistency across indetermi...Consistency is a logical property about formal systems, not evidence that our tr...
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    If translations preserve truth value systematically, they achieve the practical ...Preserving truth value across different ontologies merely redistributes the arbi...The translation from singular reference to 'the' singleton function into univers...

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