Revisiting the Mutilated Chessboard or the Many Roles of a Picture

Much has been said and written about the famous example of the mutilated chessboard problem (MCP), up to the point where one might have the impression all has been said about it. It is our aim to show that that is not the case and, to support that claim, we will draw attention to two related questions. The first question deals with what it could mean to produce a “purely” formal proof and the second question what the connection is between proof and explanation. More specifically, we want to defend, regarding the former, that a “purely” formal proof does not exist and, regarding the latter, that the explanatory power of a proof is a gradual notion and not a yes-no feature, that is, either it is explanatory or it is not. Our focus is on the example of the mutilated chessboard but this should be seen as a case study, though we do believe that it can play the role of an exemplar.

Jaar van publicatie:2021

Trefwoorden:Mutilated chessboard problem, formal proof, informal proof, picture proof, James Robert Brown, automated reasoning, explanation