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    Indispensability is a necessary condition for Quinean con... — Carmelics
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    Challenges→Mathematical theories are empirically confirmed

    Indispensability is a necessary condition for Quinean confirmational holism to extend empirical support to mathematics.

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    Reasons For

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    Reason for
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    • 1.If mathematical statements are woven into our best empirical theories, removing them would compromise predictive success and explanatory power.
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    • 2.Only indispensable components of a theory acquire empirical warrant through holistic confirmation; optional additions cannot inherit observational support.
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    • 3.Quine's rejection of the analytic-synthetic distinction requires that mathematics share confirmation-bearing status with physics if both are theory-internal.
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    Reasons Against

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    • 1.Mathematical theorems remain epistemically justified through proof and internal consistency, independent of whether they're indispensable to physics.
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    • 2.Indispensability conflates explanatory utility with evidential support; mathematics might be pragmatically necessary without being confirmable by observation.
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    • 3.Alternative mathematical frameworks could prove equally indispensable to empirical theories, suggesting indispensability underdetermines which mathematics gains support.
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    Connections

    1 linked claim · 2 topics

    Truth & Knowledge1 linkedModality & Possibility1 linked
    Mathematical theories are empirically confirmed

    Related

    Alternative mathematical frameworks could prove equally indispensable to empiric...If mathematical statements are woven into our best empirical theories, removing ...Indispensability conflates explanatory utility with evidential support; mathemat...Mathematical theorems remain epistemically justified through proof and internal ...
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    Mathematical theories are empirically confirmedOnly indispensable components of a theory acquire empirical warrant through holi...Quine's rejection of the analytic-synthetic distinction requires that mathematic...

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