This reverbalising is a most important “higher level problem”, that of how to form questions that are “well- posed”. If we had criteria for this then we should be able to distinguish what types of problems are susceptible to Jaynes’ principles and methods. So Bertrand’s paradox has led us to a much deeper problem; how to “well-pose” problems and how to determine which types of problems are well-posable. This is what I believe Jaynes means by the “Well-Posed Problem”. If this is solved then via Jaynes’ principles we may have a method that, whilst not guaranteeing that it produces the precise probability distributions, at least provides a method for finding distributions that are not definitely wrong, which is a step away from this century old paradox.
Bibliography: Bertrand, J. Calcus des Probabilités. Jaynes, E. T. The Well-Posed Problem. Stewart, I. Does God Play Dice? Rowbottom, D. P. Bertrand’s Paradox Revisited: Why Bertrand’s ‘Solutions’ Are All Inapplicable Mosteller, F. Fifty Challenging Problems in Probability Aerts, D. Solving the Hard Problem of Bertrand’s Paradox https://en.wikipedia.org/wiki/Bertrand_paradox_(probability)#Further_reading https://en.wikipedia.org/wiki/Principle_of_indifference
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