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Making The ‘Hardest Logic Puzzle Ever’ a Bit Harder

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Raymond Smullyan on Self Reference

Part of the book series: Outstanding Contributions to Logic ((OCTR,volume 14))

Abstract

This paper intends to propose new forms of logic puzzles by adopting a pluralist perspective. Not only can this expanded view lead to more challenging puzzles, but it also helps the understanding of novel forms of reasoning. In 1996, George Boolos published a famous puzzle, known as the ‘hardest logic puzzle ever’. This puzzle has been modified several times, and is known not to be ‘the most difficult of all logical puzzles’. I argue that modified versions of this famous puzzle can be made even harder by using non-standard logics. As a study case, I introduce a version of the puzzle based on the three-valued paraconsistent logic LFI1 and show how it can be solved in three questions, leaving the conjecture that this three-valued puzzle cannot be solved in fewer than three questions.

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Notes

  1. 1.

    Whatever it is, not only English: gods are not monolingual.

  2. 2.

    This is seriously discussed e.g. in Rauser (2002).

  3. 3.

    Just by coincidence, da, \({ {ja}}\) and ta correspond to yes in, respectively, Russian, German and colloquial Portuguese.

  4. 4.

    It is debatable whether the a priori validity of Arithmetic and the impossibility of its empirical falsification can be demonstrated, but for the purpose of this puzzle let us honor this idea which Kant had already defended in the 18th century.

  5. 5.

    Logics of this family are called Logics of Formal Inconsistency (LFIs) and are thoroughly discussed in Carnielli et al. (2007). A full account of such logics is found in Carnielli and Coniglio (2016).

  6. 6.

    Clearly, a function \(E'(q)\): “If I asked you ‘q would you say x?”, where x is \({ {ja}}\), da or ta produces a similar effect, in the sense that a response of x indicates that the correct answer to q is affirmative, but E(q) suffices to the solution.

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Acknowledgements

I acknowledge support from FAPESP Thematic Project LogCons 2010/51038-0, Brazil, from the National Council for Scientific and Technological Development (CNPq), Brazil, and from the Centre for Research on Architecture of Information, University of Brasilia. I am thankful to the two referees for their sharp comments and criticisms. Special thanks to Karen Kletter for her invaluable help in editing this paper.

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Authors and Affiliations

  1. Department of Philosophy and Centre for Logic Epistemology and the History of Science, University of Campinas – UNICAMP, Campinas, SP, Brazil

    Walter Carnielli

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  1. Walter Carnielli
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Correspondence to Walter Carnielli .

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Editors and Affiliations

  1. City University of New York (CUNY) System, City University of New York, New York City, New York, USA

    Melvin Fitting

  2. NYC Department of Education, Brooklyn, New York, USA

    Brian Rayman

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Carnielli, W. (2017). Making The ‘Hardest Logic Puzzle Ever’ a Bit Harder. In: Fitting, M., Rayman, B. (eds) Raymond Smullyan on Self Reference. Outstanding Contributions to Logic, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-319-68732-2_11

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