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    The No-Free-Lunch theorems are versions of the argument i... — Carmelics
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    The No-Free-Lunch theorems are versions of the argument in Hume's first fork

    SkepticismTruth & Knowledge
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
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    • 1.Hume's first fork distinguishes demonstrative from probable reasoning, where demonstrative arguments require logical necessity
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    • 2.The No-Free-Lunch theorems show that no contradiction arises from an algorithm failing to perform well, ruling out logical necessity of good performance
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    Reasons Against

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    Reason against 1 of 2
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    • 1.Hume's first fork concerns the epistemic status of propositions, not the performance guarantees of computational procedures across problem distributions.
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    • 2.NFL theorems are mathematical results about aggregate performance over all possible functions, while Hume's fork addresses whether a single proposition's negation implies contradiction.
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    • 3.Conflating mathematical universality claims with Humean demonstrative necessity commits a category error between meta-level algorithmic results and object-level epistemic justification.
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    Reason against 2 of 2
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    • 1.Wolpert and Macready's NFL theorems presuppose a uniform prior over all possible target functions, a substantive assumption Hume's skeptical argument does not require.
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    • 2.Because NFL theorems are conditional on a specific probability measure over problem spaces, they yield a weaker, measure-dependent impossibility rather than Hume's unconditional logical gap between experience and necessity.
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    Related

    Because NFL theorems are conditional on a specific probability measure over prob...Conflating mathematical universality claims with Humean demonstrative necessity ...Hume's first fork concerns the epistemic status of propositions, not the perform...Hume's first fork distinguishes demonstrative from probable reasoning, where dem...
    +3 moreShow less
    NFL theorems are mathematical results about aggregate performance over all possi...The No-Free-Lunch theorems show that no contradiction arises from an algorithm f...Wolpert and Macready's NFL theorems presuppose a uniform prior over all possible...

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    The idea is also given formal expression in the so-called ‘No-Free-Lunch theorems’ (Wolpert 1992, 1996, 1997). These can be interpreted as versions of the argument in Hume’s first fork since they establish that there can be no contradiction in the algorithm not performing well, since there are a priori possible situations in which it does not (Sterkenburg and Grünwald 2021:9992). Given Hume’s premise P3, this rules out a demonstrative argument for its good performance.
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    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit