The Barcan Formula (BF) is valid in Simplest Quantified M... — Carmelics

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The Barcan Formula (BF) is valid in Simplest Quantified Modal Logic (SQML)

Modality & Possibility

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1 reason for

2 reasons against

Reasons For

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Reason for

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1.In the model theory of SQML, the possibility operator ◇ is literally an existential quantifier ranging over all possible worlds
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2.In evaluating an existentially quantified formula ∃νφ at a possible world w, the quantifier ∃ν ranges unrestrictedly over all individuals
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3.When two existential quantifiers range over independent domains, switching their order does not alter the truth value of the formula
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Reasons Against

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Reason against 1 of 2

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1.SQML's constant domain assumption—that every individual exists in every possible world—is a substantive metaphysical commitment, not a logical truth.
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2.Once variable domains are permitted (as in Kripke's 1963 semantics), the universal instantiation axiom fails and BF is no longer valid.
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3.The validity of BF in SQML therefore reflects a built-in possibilist ontology, not a discovery about modal logic as such.
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Reason against 2 of 2

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