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<p>I discuss two possible ways for dealing with a constructive, proof-based notion of logical consequence. The first, qualified as <i>extensional</i>, amounts to the idea that a given proof-structure is <i>justifiable</i> under every interpretation of the non-logical terminology it involves. The second, qualified as <i>intensional</i>, requires on the contrary that the given proof-structure be <i>justified</i> independently of its non-logical meaning. Contrarily to the extensional approach, the intensional account calls for a prior treatment of the notion of identity of proofs. Identity can be in turn addressed in an <i>extensional</i> or <i>intensional</i> way. Although these issues are obviously of a more general interest, I investigate them in a framework which seems to me to be particularly well-suited for the purpose, i.e., Prawitz’s (non-monotonic) Theory of Grounds.</p>

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Intensionality of Consequence and Identity of Proofs in Prawitz’s Theory of Grounds

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • Antonio Piccolomini d’Aragona

摘要

I discuss two possible ways for dealing with a constructive, proof-based notion of logical consequence. The first, qualified as extensional, amounts to the idea that a given proof-structure is justifiable under every interpretation of the non-logical terminology it involves. The second, qualified as intensional, requires on the contrary that the given proof-structure be justified independently of its non-logical meaning. Contrarily to the extensional approach, the intensional account calls for a prior treatment of the notion of identity of proofs. Identity can be in turn addressed in an extensional or intensional way. Although these issues are obviously of a more general interest, I investigate them in a framework which seems to me to be particularly well-suited for the purpose, i.e., Prawitz’s (non-monotonic) Theory of Grounds.