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- Brian Rabern & Landon Rabern, In Defense of the Two Question Solution to the Hardest Logic Puzzle Ever.In Rabern and Rabern (2008) we presented a two question solution to 'the hardest logic puzzle ever' (as presented in Boolos (1996)), which relied on self-referential questions. In this note we respond to several worries related to this solution. We clarify our claim that some yes-no questions cannot be answered by the gods and thus that asking such questions of the gods will result in head explosion. We argue that the inclusion of exploding head possibilities is neither cheating nor ad hoc but is instead forced upon us by principles related to Tarski’s theorem. We also respond to concerns that have been raised about our use of self-referential questions in support of the two question solution. In particular, we address the worry that there is a revenge problem lurking, which is analogous to revenge problems that arise for purported solutions to the liar paradox. And we make some further observations about the relationship between self-referential questions, truth- telling gods and the semantic paradoxes. In the appendix we give a two question solution to the modified puzzle (where Random randomly answers 'ja' or da').In my reading list | Discuss this article | Edit | Categorize |My bibliography
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We present the simplest solution ever to 'the hardest logic puzzle ever'. We then modify the puzzle to make it even harder and give a simple solution to the modified puzzle. The final sections investigate exploding god-heads and a two-question solution to the original puzzle.
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| | Other links: nottingham.ac.uk interscience.wiley.com | Scholar | More.. The Hardest Logic Puzzle Ever was first described by the late George Boolos in the Spring 1996 issue of the Harvard Review of Philosophy. Although not dissimilar in appearance from many other simpler puzzles involving gods (or tribesmen) who always tell the truth or always lie, this puzzle has several features that make the solution far from trivial. This paper examines the puzzle and describes a simpler solution than that originally proposed by Boolos.
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There is a little known paradox the solution to which is a guide to a much more thoroughgoing solution to a whole range of classic paradoxes. This is shown in this paper with respect to Berrys Paradox, Heterologicality, Russells Paradox, and the Paradox of Predication, also the Liar and the Strengthened Liar, using primarily the epsilon calculus. The solutions, however, show not only that the first-order predicate calculus derived from Frege is inadequate as a basis for a clear science, and (...)
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| | Other links: interscience.wiley.com | Scholar | More.. Abstract: I argue that the solution to the Red Hat Problem, a puzzle derived from interactive epistemic logic, requires S5. Interactive epis- temic logic is set out in formal terms, and an attempt to solve the red hat puzzle is made in K, K, and K, each of which fails, showing that a stronger system, K is required.
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