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Document Details : Title: Revisiting the Mutilated Chessboard or the Many Roles of a Picture Author(s): STARIKOVA, Irina , VAN BENDEGEM, Jean Paul Journal: Logique et Analyse Volume: 255 Date: 2021 Pages: 289-312 DOI: 10.2143/LEA.255.0.3290192 Abstract : As the title indicates, this paper revisits the famous mutilated chessboard problem (MCP). Our objective is to show that the power of this seminal example is underestimated. It not only helps to better understand the formal-informal distinction but also to put forward some ideas on the nature of mathematical explanation. As to the former, we analyse in detail Brown’s suggestion for a formal proof of the MCP and how this can be done in practice. This leads to an exploration of attempts to prove MCP using automated reasoning. As to the latter, we propose a gradual and contextual approach to explanation. The paper can also be read as a study of variations on the MCP, presenting a host of related problems and proofs, thereby showing that, instead of the MCP, we better speak of the rich family of MCP-related problems, proofs, issues and philosophical discussions. |
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