On the Behavior of True and False
- Stefan Wintein
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Uzquiano (Analysis 70:39–44, 2010) showed that the Hardest Logic Puzzle Ever (HLPE) [in its amended form due to Rabern and Rabern (Analysis 68:105–112, 2008)] has a solution in only two questions. Uzquiano concludes his paper by noting that his solution strategy naturally suggests a harder variation of the puzzle which, as he remarks, he does not know how to solve in two questions. Wheeler and Barahona (J Philos Logic, to appear, 2011) formulated a three question solution to Uzquiano’s puzzle and gave an information theoretic argument to establish that a two question solution for Uzquiano’s puzzle does not exist. However, their argument crucially relies on a certain conception of what it means to answer self-referential yes–no questions truly and falsely. We propose an alternative such conception which, as we show, allows one to solve Uzquiano’s puzzle in two questions. The solution strategy adopted suggests an even harder variation of Uzquiano’s puzzle which, as we will show, can also be solved in two questions. Just as all previous solutions to versions of HLPE, our solution is presented informally. The second part of the paper investigates the prospects of formally representing solutions to HLPE by exploiting theories of truth.
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- On the Behavior of True and False
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- Available under Open Access This content is freely available online to anyone, anywhere at any time.
Minds and Machines
Volume 22, Issue 1 , pp 1-24
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- Stefan Wintein (1)
- Author Affiliations
- 1. Department Wijsbegeerte and TiLPS, Universiteit van Tilburg, Warandelaan 2, Gebouw D136, 5000 LE, Tilburg, The Netherlands