Finest Partitions Do Not Solve Bertrands Paradox
Some claim (citation?) that the ambiguities which Betrand thought were unresolvable can be resolved by taking the sample space to be the finest partition of the set of possible outcomes.
The finest partition of squares and cubes is the set containing every square and every cube. That doesn’t help to solve Bertrand’s paradox.
The finest partition of possible worlds may (or even will generally?) have no cardinality, at least on Lewis’s model. So that doesn’t help to solve Bertrand’s paradox either.
What was number 3?
Maybe I spoke too soon about not putting this into the encyclopedia article, since the encyclopedia won’t come out for ages (I presume). Maybe the encyclopedia article should at least hint at these issues, and I should meanwhile be turning them into a paper. If you (Alan) could send me relevant bits of encyclopedia draft, that would be helpful. Jason
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Alan H’jek, Jason Grossman
