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From Epistemic Paradox to Doxastic Arithmetic

  • V. Alexis PeluceEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10703)

Abstract

The logical analysis of epistemic paradoxes—including, for example, the Moore and Gödel-Buridan paradoxes—has traditionally been performed assuming the whole range of corresponding modal logic principles: \(\lbrace \mathsf{D, T, 4, 5}\rbrace \). In this paper, it is discovered precisely which of those principles (including also the law of excluded middle, LEM) are responsible for the paradoxical behavior of the Moore, Gödel-Buridan, Dual Moore, and Commissive Moore sentences. Further, by reproducing these paradoxes intuitionistically we reject a conjecture that these paradoxes are caused by the LEM. An exploration of the Gödel-Buridan sentence prompts the inquiry into a system, Doxastic Arithmetic, \(\mathsf{DA}\), designed to represent the arithmetical beliefs of an agent who accepts all specific arithmetical proofs and yet believes in the consistency of their own beliefs. For these reasons, \(\mathsf{DA}\) may be regarded as an epistemic way to circumvent limitations of Gödel’s Second Incompleteness Theorem.

Keywords

Modal logic Epistemology Paradoxes Doxastic arithmetic 

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.The Graduate Center of the City University of New YorkNew York CityUSA

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