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    It is not the case that Montague demonstrated that natural language has a rigorous compositional semantics expressible within intensional type theory without recourse to a separate Begriffsschrift.

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    Reasons For

    1 perspective
    Reason for
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    • 1.Natural language contains context-dependent, non-compositional meaning phenomena (e.g., idioms, metaphor, pragmatic implicature) that resist formal type-theoretic treatment.
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    • 2.Montague's approach artificially restricts natural language to a well-formed subset and presupposes logical structure not obviously present in actual linguistic competence.
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    • 3.The claim conflates formal modelability with explanation of actual cognitive processes; showing natural language *can* be formalized doesn't prove it *operates* that way.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Montague's framework successfully formalized quantification, intensionality, and scope ambiguities that previous logical systems handled inadequately.
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    • 2.Natural language compositionality—where sentence meaning derives from parts and structure—is empirically demonstrated through systematic productivity of new utterances.
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    • 3.Intensional type theory provides a unified framework for semantic phenomena without requiring external notation, proving formal elegance and foundational adequacy.
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