Single-case probabilities and the case of Monty Hall: Levy's view

In Baumann (2005) I argued that reflections on a variation of the Monty Hall problem throws a very general sceptical light on the idea of single-case probabilities. Levy (2007) puts forward some interesting objections which I answer here. The notion of probability is so important that we cannot do without it, neither in science nor in everyday life nor in philosophy. At the same time there is more than one interpretation of this notion (cf., e.g., Gillies 2000) and definitely many controversies about basic issues. One of them has to do with the question whether there is such a thing as single-case probabilities. In Baumann (2005) I argued that considerations concerning a problem that has been discussed widely and not just within philosophy, namely the Monty Hall Problem (cf., e.g., vos Savant 1992, 199-209), suggest that one should be skeptical with respect to the idea that there are single-case probabilities at all. After an exposition of the argument (I) I will discuss some interesting objections (II-IV) against my argument which have recently been made by Ken Levy in Levy (2007). My conclusion (V) will be that Levy ́s objections can be answered. The argument against single-case probabilities remains intact. But first to the exposition of my argument.