In defense of Bertrand: The non-restrictiveness of reasoning by example
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This note has three goals. First, we discuss a presentation of Bertrand's paradox in a recent issue of Philosophia Mathematica, which we believe to be a subtle but important misinterpretation of the problem. We compare claims made about Bertrand with his 1889 Calcul des Probabilités. Second, we use this source to understand Bertrand's true intention in describing what we now call his paradox, comparing it both to another problem he describes in the same section and to a modern treatment. Finally, we briefly consider the importance of knowing when a specific example represents a general case.
Klyve, D. (2013). In defense of Bertrand: the non-restrictiveness of reasoning by example. Philosophia Mathematica 21(3), 365-370. DOI: 10.1093/philmat/nkt028
Copyright © 2013 Dominic Klyve. Published by Oxford University Press. All rights reserved.