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<p>It is shown that one common formulation of Stalnaker’s semantics for conditionals is incomplete: it has no sound and (strongly) complete proof system. At first, this seems to conflict with well-known completeness results for this semantics (e.g., Stalnaker and Thomason <CitationRef CitationID="CR22">1967</CitationRef>, Stalnaker <CitationRef CitationID="CR18">1970</CitationRef> and Lewis <CitationRef CitationID="CR11">1973</CitationRef>, ch.&#xa0;6). As it turns out, it does not: these completeness results rely on another closely-related formulation of the semantics that is provably complete. Specifically, the difference comes down to how the Limit Assumption is stated. I close with some remarks about what this means for the logic of conditionals.</p>

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Is Stalnaker’s Semantics Complete?

  • 期刊论文

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  • 发表日期：

    2025年2月18日

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  • Alexander W. Kocurek

摘要

It is shown that one common formulation of Stalnaker’s semantics for conditionals is incomplete: it has no sound and (strongly) complete proof system. At first, this seems to conflict with well-known completeness results for this semantics (e.g., Stalnaker and Thomason 1967, Stalnaker 1970 and Lewis 1973, ch. 6). As it turns out, it does not: these completeness results rely on another closely-related formulation of the semantics that is provably complete. Specifically, the difference comes down to how the Limit Assumption is stated. I close with some remarks about what this means for the logic of conditionals.