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A Framework for Riddles about Truth that do not involve Self-Reference

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Abstract

In this paper, we present a framework in which we analyze three riddles about truth that are all (originally) due to Smullyan. We start with the riddle of the yes-no brothers and then the somewhat more complicated riddle of the da-ja brothers is studied. Finally, we study the Hardest Logic Puzzle Ever (HLPE). We present the respective riddles as sets of sentences of quotational languages, which are interpreted by sentence-structures. Using a revision-process the consistency of these sets is established. In our formal framework we observe some interesting dissimilarities between HLPE’s available solutions that were hidden due to their previous formulation in natural language. Finally, we discuss more recent solutions to HLPE which, by means of self-referential questions, reduce the number of questions that have to be asked in order to solve HLPE. Although the essence of the paper is to introduce a framework that allows us to formalize riddles about truth that do not involve self-reference, we will also shed some formal light on the self-referential solutions to HLPE.

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Authors and Affiliations

  1. Tilburg Center for Logic and Philosophy of Science (TiLPS), Tilburg University, 5037 AB, Tilburg, The Netherlands

    Stefan Wintein

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  1. Stefan Wintein
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Correspondence to Stefan Wintein.

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Wintein, S. A Framework for Riddles about Truth that do not involve Self-Reference. Stud Logica 98, 445–482 (2011). https://doi.org/10.1007/s11225-011-9343-1

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  • DOI: https://doi.org/10.1007/s11225-011-9343-1

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