Abstract: Basic to the idea of logical probability is the principle of indifference: equal possibilities are to be assigned equal probabilities. This principle appeared on the one hand to yield surprisingly fruitful results and on the other hand to engender paradoxes—the first, for example, in eighteenth- century empirical examples (Buffon's needle problem) and cosmological explanations (data concerning planets and comets), and the second, richly displayed by Joseph Bertrand. It is argued here, with reference to work by Henri Poincaré, Edwin Jaynes, Roger Rosencrantz, and others, that though refinable and restrictable in various useful ways, the principle of indifference cannot be salvaged so as to yield a foundation for probability judgements.

Keywords: Joseph Bertrand, Buffon, Edwin Jaynes, logical probability, needle problem, Henri Poincaré, principle of indifference, Roger Rosencrantz,