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    It is not the case that Putnam's model-theoretic argument establishes that formal consistency alone cannot fix intended reference, so 'polynomial-time computable' in M may not refer to the same class as in the standard model.

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    Reasons For

    1 perspective
    Reason for
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    • 1.Putnam's argument targets reference-fixing for general terms; 'polynomial-time computable' has clear extensional definition in standard models of arithmetic.
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    • 2.Model-theoretic indeterminacy affects existence claims but doesn't show meaning itself is indeterminate—we grasp 'polynomial-time' via algorithm structure.
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    • 3.Mathematical practice demonstrates robust inter-model agreement on computational classes; this convergence suggests determinate reference despite formal underdetermination.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Putnam showed that any formal system admits multiple models satisfying identical axioms, so syntax alone underdetermines which model is 'intended'.
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    • 2.Computational predicates like 'polynomial-time computable' depend on interpretation of primitive terms; formal consistency permits non-standard domains.
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    • 3.Without extra-formal constraints (use, causation, intentionality), we lack principled grounds to exclude non-standard interpretations of 'P vs NP' claims.
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