Substructural logics are interesting tools to analyse philosophical problems that concern logic. In this chapter, we will take a philosophical approach to the logics presented earlier in this book. We will show how substructural approaches provide uniform solutions to the paradoxes involving the truth predicate—Liar and Curry paradoxes—and the paradox involving the validity predicate—the validity paradox. Concretely, we will consider non-transitive, non-reflexive, non-contractive and non-monotonic solutions to these antinomies. Giving a uniform solution to the semantic paradoxes is arguably a virtue of substructural logics when it comes to their applications in the face of other non-classical approaches, such as \(\mathbb {L}\mathbb {P}\) and \(\mathbb {K3}\) . However, this is not enough. For this reason, we explore philosophical interpretations that make sense of the failures of structural properties of these logics. In particular, we argue that these substructural logics can receive dialogical interpretations. Besides blocking the paradoxes of truth and validity and having interesting philosophical interpretations, it is required of these substructural theories that their validity predicate be sound with respect to their base logic, internalizing in their object-language their valid metainferences. Then, we address these questions for some of the substructural solutions. We will be particularly concerned with the most discussed validity theories, such as non-contractive and non-transitive.

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Philosophical Applications

  • Edson Bezerra,
  • Jonathan Erenfryd

摘要

Substructural logics are interesting tools to analyse philosophical problems that concern logic. In this chapter, we will take a philosophical approach to the logics presented earlier in this book. We will show how substructural approaches provide uniform solutions to the paradoxes involving the truth predicate—Liar and Curry paradoxes—and the paradox involving the validity predicate—the validity paradox. Concretely, we will consider non-transitive, non-reflexive, non-contractive and non-monotonic solutions to these antinomies. Giving a uniform solution to the semantic paradoxes is arguably a virtue of substructural logics when it comes to their applications in the face of other non-classical approaches, such as \(\mathbb {L}\mathbb {P}\) and \(\mathbb {K3}\) . However, this is not enough. For this reason, we explore philosophical interpretations that make sense of the failures of structural properties of these logics. In particular, we argue that these substructural logics can receive dialogical interpretations. Besides blocking the paradoxes of truth and validity and having interesting philosophical interpretations, it is required of these substructural theories that their validity predicate be sound with respect to their base logic, internalizing in their object-language their valid metainferences. Then, we address these questions for some of the substructural solutions. We will be particularly concerned with the most discussed validity theories, such as non-contractive and non-transitive.