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    The claim therefore smuggles in classical assumptions abo... — Carmelics
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    Part of a larger discussion

    Challenges→In the Mostowski model, the set A of rationals can be linearly ordered but cannot be well-ordered.

    The claim therefore smuggles in classical assumptions about linear order that are not neutral across foundational frameworks, making its modal force framework-relative rather than absolute.

    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Classical logic assumes temporal/logical order is fundamental, but constructive and paraconsistent frameworks reject this assumption entirely.
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    • 2.Modal claims (necessity, possibility) derive their meaning from background logical structures, which differ across foundational frameworks.
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    • 3.A claim's modal force cannot be framework-neutral if the frameworks themselves are logically incompatible rather than merely different.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Some modal truths (e.g., logical contradictions are impossible) hold across frameworks because they constrain what any framework can be.
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    • 2.Claiming all modal force is framework-relative requires the meta-claim to be framework-relative too, creating performative contradiction.
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    • 3.Frameworks differ in *how* they establish necessity/possibility, but this doesn't prove no facts about modality transcend all frameworks.
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    Key Terms

    Absolute(1930 [1893]: 129)
    One system whose contents are nothing but sentient experience; a single and all-inclusive experience embracing every partial diversity in concord.
    Classical assumptions(what constructive logic challenges)
    The traditional rules of logic that have been used for centuries, which assume that every statement is either completely true or completely false.
    Foundational frameworks(mathematical philosophy)
    Different basic systems or sets of rules that mathematicians use to build and understand mathematics from the ground up.
    Framework-relative(philosophy of mathematics)
    Something that is true or makes sense only within a particular system or set of rules, rather than being true in all situations.
    Linear order(as used in mathematics and logic)
    An arrangement where things are lined up in a sequence from first to last, like numbers on a number line, so you can always say one thing comes before another.
    Smuggles in(argumentation and logic)
    Introduces something quietly or without acknowledgment, making it seem innocent when it's actually a controversial addition.
    modal force(as used in modal logic)
    The power or strength of a statement about necessity, possibility, or contingency—what makes something 'must be' versus 'might be'.

    Connections

    2 topics

    Truth & Knowledge1 linkedModality & Possibility1 linked

    Related

    A claim's modal force cannot be framework-neutral if the frameworks themselves a...Claiming all modal force is framework-relative requires the meta-claim to be fra...

    Details

    Type
    claim
    Perspectives
    2 (1 for, 1 against)
    Edits
    1 edit
    Classical logic assumes temporal/logical order is fundamental, but constructive ...
    Frameworks differ in *how* they establish necessity/possibility, but this doesn'...
    +3 moreShow less
    In the Mostowski model, the set A of rationals can be linearly ordered but canno...Modal claims (necessity, possibility) derive their meaning from background logic...Some modal truths (e.g., logical contradictions are impossible) hold across fram...