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Hintikka, Free Logician

Singular Terms in World Lines Semantics


The combination of quantifiers with a semantics for epistemic operators in a modal framework is one of the major contributions of Hintikka in intensional logic. Hintikka’s starting point is his diagnosis of the failure of existential generalization and the substitution of identicals in terms of referential multiplicity. In this paper, I introduce Hintikka as a free logician. Indeed, Hintikka’s first-order epistemic logic is grounded on a logic free of ontological presuppositions with respect to singular terms. It is also a logic free of presuppositions of uniqueness of reference. After having focused on the use of quantifiers and singular terms in Hintikka’s epistemic logic, I discuss some consequences from a semantico-logical perspective, but also from a philosophical one. By arguing against the so-called contingent a priori truths defended by Kripke, I conclude with a proposal in favour of Hintikka’s non-rigid interpretation of proper names.

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This work was completed with the support of the postdoctoral program of the FCT-Portugal (Grant Number SFRH/BPD/116494/2016). I am particularly thankful to Olga Pombo and Shahid Rahman for their support. I would also like to thank the organizers and participants of the workshop “Hintikka’s Logical Thought” which took place at Unilog 2018 (Vichy), as well as the editors and anonymous reviewers for their helpful comments and suggestions.

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Correspondence to Matthieu Fontaine.

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Fontaine, M. Hintikka, Free Logician. Log. Univers. 13, 179–201 (2019).

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Mathematics Subject Classification

  • Primary 03B45
  • Secondary 03C07
  • 03C10
  • 03C80


  • Modality
  • World lines
  • Identity
  • Existential generalization
  • Singular terms