This paper shows that Bertrand's proposed ‘solutions’ to his own question, which generates his chord paradox, are inapplicable. It uses a simple analogy with cake cutting. The problem is that none of Bertrand's solutions considers all possible cuts. This is no solace for the defenders of the principle of indifference, however, because it emerges that the paradox is harder to solve than previously anticipated.
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Rowbottom, D. P. (2013). Bertrand's paradox revisited: Why Bertrand's 'solutions' are all inapplicable. Philosophia Mathematica, 21(1), 110-114. doi: 10.1093/philmat/nks028