The Core Logic Paradox

Joseph Vidal-Rosset (1)

1 LHSP - Laboratoire d'Histoire des Sciences et de Philosophie - Archives Henri Poincaré

This paper provides a proof that Tennant's logical system entails a paradox that is called "Core logic paradox", in reference to the new name given by Tennant to his intuitionistic relevant logic. The inconsistency theorem on which this paper ends is preceded by lemmas that prove syntactically and semantically that rule L⊤ is strongly admissible in the sequent calculus for propositional Core logic. This rule plays a key role in a consistency test on which Tennant's logical system fails.

Mots clés: intuitionistic logic; paradox

Domaines: Philosophie; Logique [math.LO]

Joseph Vidal-Rosset. The Core Logic Paradox. 2019. ⟨hal-02473031⟩