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    Kripke argued that BF's converse entails that actually ex... — Carmelics
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    Challenges→The Barcan Formula (BF) is valid in Simplest Quantified Modal Logic (SQML)

    Kripke argued that BF's converse entails that actually existing individuals are necessarily possible, but BF itself entails that possible individuals actually exist—a commitment many find ontologically profligate.

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
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    • 1.Possibilism avoids arbitrary distinctions: if possible worlds are real frameworks, denying possible objects an ontological status is inconsistent.
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    • 2.Modal intuitions support this: we meaningfully discuss non-actual people (e.g., 'your possible children'), suggesting they deserve genuine ontological commitment.
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    • 3.Kripke correctly identified that BF's converse creates asymmetry: actual things must be possible, but possible things need not be actual—an unjustified hierarchy.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Ontological parsimony remains fundamental: multiplying entities without necessity violates Occam's Razor and burdens theory with unmotivated commitments.
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    • 2.Discourse about possible non-actual individuals can be analyzed as quantification over abstract descriptions, not commitment to their real existence.
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    • 3.BF itself may be rejected rather than embraced: restricting quantifiers to actualia avoids both converse and commitment problems entirely.
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    Key Terms

    BF(Quantified modal logic)
    The Barcan Formula, a controversial principle provable in SQML but invalid in KQML
    Converse(referring to some claim being discussed)
    The flipped version of a statement; if the original says 'A implies B,' the converse says 'B implies A.'
    Kripke
    Kripke refers to Saul Kripke, an influential American philosopher and logician known for revolutionizing how we think about names, meaning, and possibility. He argued that names like "Albert Einstein" refer directly to the actual person rather than through descriptions of their properties, which changed philosophy fundamentally. His work also introduced "possible worlds" as a way to understand concepts like necessity and possibility, making him one of the most important philosophers of the 20th century.
    Necessarily possible(the conclusion drawn about how S5 treats possibility)
    Something that is not just possible in one situation, but *must* be possible in every conceivable situation—it's a guaranteed kind of possibility.
    Ontologically profligate(combining two concepts: ontology (study of what exists) and profligate (wasteful))
    Wasteful or excessive in terms of what you're claiming actually exists; adding too many things to your explanation when fewer would do.
    entails(describes a logical relationship between statements)
    Logically forces or guarantees; if A entails B, then whenever A is true, B must also be true.
    possible individuals(things that might exist but don't)
    Things (like people or objects) that could exist in some imaginable scenario, even if they don't actually exist in the real world right now.

    Connections

    1 topic

    Modality & Possibility1 linked

    Related

    BF itself may be rejected rather than embraced: restricting quantifiers to actua...Discourse about possible non-actual individuals can be analyzed as quantificatio...Kripke correctly identified that BF's converse creates asymmetry: actual things ...Modal intuitions support this: we meaningfully discuss non-actual people (e.g., ...

    Details

    Type
    claim
    Perspectives
    2 (1 for, 1 against)
    Edits
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    +3 moreShow less
    Ontological parsimony remains fundamental: multiplying entities without necessit...Possibilism avoids arbitrary distinctions: if possible worlds are real framework...The Barcan Formula (BF) is valid in Simplest Quantified Modal Logic (SQML)