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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
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    It is not the case that Syntactic consistency cannot be equivalent to satisfiability when 'satisfiability' picks out different model classes depending on unresolved foundational choices about sort ontology.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    1 perspective
    Reason for
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    • 1.Completeness theorems show syntactic consistency reliably tracks satisfiability across standard model classes, regardless of foundational metaphysics.
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    • 2.Ontological indeterminacy about sorts doesn't make satisfiability meaningless—it just relativizes it to explicit framework choices we can specify.
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    • 3.Syntactic consistency itself presupposes logical rules whose legitimacy depends on the same foundational choices as model-class selection does.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Model-theoretic semantics requires fixed sort ontologies; without resolving what counts as a domain element, 'satisfiability' remains ambiguous.
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    • 2.Syntactic consistency is proof-theoretically determinate regardless of ontological commitments, making it independent of model-class variation.
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    • 3.Different foundational frameworks (constructivism vs. classical set theory) yield incompatible model classes for identical syntactic theories.
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