ABSTRACT
The exposition of the paradox in Chapter 3 shows that piecemeal attempts at the Well-posing strategy won’t succeed. What is required is an appeal to general principle. But there is a danger that proposed principles, whilst general in themselves, impose in their use a covert restriction on Bertrand’s question, thereby substituting a restriction of the problem for the general problem rather than comprehending the general problem.
In this chapter I look at three attempted solutions that make the appeal and fall for the danger. The first from Jaynes was historically and for a long time the prime contender for resolving the paradox using the Well-posing strategy: it was thought by van Fraassen to succeed. Jaynes makes use of a principle, essentially van Fraassen’s Symmetry requirement interpreted in terms of transformation groups, to produce an apparently unique probability. The second is from Wang and Jackson, who offer a definition of homogeneous chords to solve the paradox. The third is from Rizza, being the first radical mathematical treatment I address, who applies infinitesimals from Sergeyev’s arithmetic of infinity.
