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<p>In this paper, we offer an account of a paradox analogous to Fitch’s paradox of knowability, elaborated around knowledge of <i>necessary</i> truths—such as mathematical or logical truths. In particular, we highlight at which semantic levels the paradox does and does not rise, and explain why that happens. The account employs a novel modal operator and language, which present some distinctive semantic features, such as being unable to characterise many frame properties characterisable in normal modal logic, a fact which may be used in interesting ways to study the logics of the proposed language. Following recent studies, this work may be seen as a case study of semantically insensitive non-normal modal logics.</p>

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Logics of Unknowable (Necessary) Truths

  • 期刊论文

  • 发表日期：

    2026年6月30日

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  • Pedro Teixeira Yago,
  • Giorgio Venturi

摘要

In this paper, we offer an account of a paradox analogous to Fitch’s paradox of knowability, elaborated around knowledge of necessary truths—such as mathematical or logical truths. In particular, we highlight at which semantic levels the paradox does and does not rise, and explain why that happens. The account employs a novel modal operator and language, which present some distinctive semantic features, such as being unable to characterise many frame properties characterisable in normal modal logic, a fact which may be used in interesting ways to study the logics of the proposed language. Following recent studies, this work may be seen as a case study of semantically insensitive non-normal modal logics.