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    Confirmational holism, as Sober argues against Quine, doe... — Carmelics
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    Challenges→We ought to be committed to the existence of mathematical entities.

    Confirmational holism, as Sober argues against Quine, does not extend to mathematical auxiliaries since they are not tested by any possible experimental outcome.

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    Reasons For

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    Reason for
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    • 1.Mathematical auxiliaries (like set theory axioms) are chosen for convenience and internal consistency, not empirical fit.
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    • 2.Experimental data underdetermines physics but not mathematics—no observation can falsify a purely formal system.
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    • 3.Sober's distinction preserves explanatory power: we can blame failed predictions on physics while keeping math reliable.
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    Reasons Against

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    Reason against
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    • 1.Mathematical auxiliaries are empirically testable indirectly: wrong math yields wrong predictions, triggering revision.
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    • 2.The boundary between mathematical and physical hypotheses is blurry—geometry was once thought mathematical, now empirical.
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    • 3.Quine's holism explains actual scientific practice: physicists do revise mathematical frameworks when experiments fail.
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    Related

    Experimental data underdetermines physics but not mathematics—no observation can...Mathematical auxiliaries (like set theory axioms) are chosen for convenience and...Mathematical auxiliaries are empirically testable indirectly: wrong math yields ...Quine's holism explains actual scientific practice: physicists do revise mathema...
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    Sober's distinction preserves explanatory power: we can blame failed predictions...The boundary between mathematical and physical hypotheses is blurry—geometry was...We ought to be committed to the existence of mathematical entities.

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