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    Conflating mathematical universality claims with Humean d... — Carmelics
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    Challenges→The No-Free-Lunch theorems are versions of the argument in Hume's first fork

    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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    Reasons For

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    Reason for
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    • 1.Mathematical universality describes algorithmic procedures, while Humean necessity describes epistemic modal facts—fundamentally different logical levels.
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    • 2.Conflating them treats formal provability (meta-level) as justifying metaphysical necessity (object-level), which requires additional bridge principles.
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    • 3.Category errors occur precisely when properties of one logical level are incorrectly attributed to another without explicit reduction principles.
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    Reasons Against

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    • 1.The distinction between 'meta-level' and 'object-level' claims itself requires justification—it may not be a fundamental divide in mathematics.
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    • 2.Mathematical universality and epistemic justification may overlap legitimately; calling this a category error assumes they're categorically distinct without proof.
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    • 3.Many successful theories (arithmetic, set theory) treat formal and modal properties as integrated, not separated by categorical boundaries.
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    Key Terms

    Algorithmic results(the type of result at the higher level of analysis)
    Conclusions that come from following a step-by-step procedure or set of rules, like the output you get from a computer program.
    Category error(as used in logic and philosophy of language)
    A logical mistake where you apply a rule or concept to something it doesn't actually fit, like using a math formula on a poem.
    Conflating
    Conflating means mixing together or treating two different things as if they were the same thing, when they're actually distinct. It's a logical error where someone blurs important differences between concepts, ideas, or situations to make an argument seem stronger than it is. For example, conflating "being critical of a policy" with "being disloyal to your country" wrongly equates two separate things.
    Demonstrative necessity(the second type of claim being confused in the statement)
    Something that absolutely must be true because it can be proven or shown to be true through reason alone, without needing to check it in the real world.
    Humean
    "Humean" refers to ideas based on the philosophy of David Hume, an 18th-century Scottish philosopher who argued that our knowledge comes from what we directly experience through our senses, not from abstract reasoning alone. A key Humean idea is that we cannot truly prove that cause and effect exist in the world—we only observe that one thing regularly follows another, and our minds make the connection. Hume's skeptical approach to knowledge and causation has influenced centuries of philosophical debate about how we understand reality.
    Mathematical universality claims(one type of claim being confused with another)
    Statements in math that say something is true for all cases without exception, like 'all triangles have three sides.'
    Meta-level(as used in logic and philosophy of language)
    A higher level of thinking where you analyze or talk about something itself, rather than using it directly—like discussing grammar rules rather than just speaking.
    epistemic justification(Cresto's framing of the justification condition she argues is not always necessary)
    A condition for knowledge that can be understood either in internalist or externalist terms
    object-level(Carlson's distinction among verb arguments in the semantics of generics)
    A classification of verb arguments referring to ordinary individual objects, as distinguished from kind-level arguments which refer to kinds or types.

    Connections

    2 topics

    Truth & Knowledge1 linkedSkepticism1 linked

    Related

    Category errors occur precisely when properties of one logical level are incorre...Conflating them treats formal provability (meta-level) as justifying metaphysica...

    Details

    Type
    claim
    Perspectives
    2 (1 for, 1 against)
    Edits
    1 edit
    Many successful theories (arithmetic, set theory) treat formal and modal propert...
    Mathematical universality and epistemic justification may overlap legitimately; ...
    +3 moreShow less
    Mathematical universality describes algorithmic procedures, while Humean necessi...The No-Free-Lunch theorems are versions of the argument in Hume's first forkThe distinction between 'meta-level' and 'object-level' claims itself requires j...