Studia Logica 98 (3):445-482 (2011)

Stefan Wintein
Erasmus University Rotterdam
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
Keywords Philosophy   Mathematical Logic and Foundations   Logic   Computational Linguistics
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DOI 10.1007/s11225-011-9343-1
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Truth and Paradox.Anil Gupta - 1982 - Journal of Philosophical Logic 11 (1):1-60.
The Hardest Logic Puzzle Ever.George Boolos - 1996 - The Harvard Review of Philosophy 6 (1):62-65.
Some Thoughts About the Hardest Logic Puzzle Ever.Tim S. Roberts - 2001 - Journal of Philosophical Logic 30 (6):609-612.

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