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<p>This paper presents a novel approach to a formal theory of validity compatible with an inferentialist theory of meaning based on an expressivist conception of logical vocabulary. The formal theory of validity is obtained by adapting Tennant’s requirement for natural deduction, that the major premise of an elimination rule must be an assumption, to the naturalised sequent calculus framework proposed by Hlobil. The result is an inconsistent theory of validity which rejects transitivity not only for object-theoretic but also meta-theoretic reasoning.</p>

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Implications of an implication with the premise “this implication is valid”

  • 期刊论文

  • 发表日期：

    2026年7月31日

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  • Andreas Fjellstad

摘要

This paper presents a novel approach to a formal theory of validity compatible with an inferentialist theory of meaning based on an expressivist conception of logical vocabulary. The formal theory of validity is obtained by adapting Tennant’s requirement for natural deduction, that the major premise of an elimination rule must be an assumption, to the naturalised sequent calculus framework proposed by Hlobil. The result is an inconsistent theory of validity which rejects transitivity not only for object-theoretic but also meta-theoretic reasoning.