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    The prohibition on presupposing contingent truths conflat... — Carmelics
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    Challenges→Inductive logic should not presuppose the truth of contingent statements.

    The prohibition on presupposing contingent truths conflates the object-language content of hypotheses with the meta-level structural constraints that define a coherent probability space.

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    Reasons For

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    Reason for
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    • 1.Probability spaces require structural assumptions (σ-algebras, measure functions) independent of any specific hypothesis's truth value.
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    • 2.Conflating these levels leads to circular reasoning: using contingent facts to justify the framework that evaluates those facts.
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    • 3.Formal probability theory distinguishes sample space definition from event assignment, mirroring this object/meta-level distinction.
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    Reasons Against

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    Reason against
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    • 1.Some structural constraints (like exchangeability) are justified precisely by contingent empirical facts about symmetries in nature.
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    • 2.The distinction between 'object-level content' and 'meta-level structure' is itself philosophically contentious and context-dependent.
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    • 3.Rejecting all contingent presuppositions makes probability spaces arbitrary rather than principled, undermining their rational applicability.
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    Key Terms

    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.
    Presupposing(what the externalist secretly assumes in their reasoning)
    To assume something is already true without proving it, usually without realizing you're doing it.
    Probability space(The unified system where acts, states, and outcomes interact in Jeffrey's framework)
    A mathematical structure that shows all the possible outcomes of a situation and assigns probabilities (chances) to each one.
    coherent(de Finetti's usage in the context of the Dutch Book argument for probabilism)
    A subject is coherent if their unconditional degrees of belief do not permit a Dutch Book (a guaranteed loss through a combination of bets) to be made against them
    contingent truths(Contrasted with the modal collapse implied by sσ ⊃• □•sσ)
    Truths that are not necessarily determined; truths that could have been otherwise
    object-language(Davidsonian theory of meaning)
    The language to which a theory of meaning applies

    Connections

    2 topics

    Truth & Knowledge1 linkedSkepticism1 linked

    Related

    Conflating these levels leads to circular reasoning: using contingent facts to j...Formal probability theory distinguishes sample space definition from event assig...

    Details

    Type
    claim
    Perspectives
    2 (1 for, 1 against)
    Edits
    1 edit
    Inductive logic should not presuppose the truth of contingent statements.
    Probability spaces require structural assumptions (σ-algebras, measure functions...
    +3 moreShow less
    Rejecting all contingent presuppositions makes probability spaces arbitrary rath...Some structural constraints (like exchangeability) are justified precisely by co...The distinction between 'object-level content' and 'meta-level structure' is its...