  Two avenues of resistance to the line of thought in this section suggest themselves. The first is to maintain that, despite the truth of determinism for the baker’s transformation and classical physics (modulo worries to be addressed in the following section), there are still, or at there least may be, non-trivial chances in these theories. The proposal is that the possibility remains of deterministic chance, so that from the fact of determinism alone it does not follow that we have a counterexample to RCT. The outcomes may be determined to happen by the prior conditions, but (so the suggestion goes) they may still happen by chance. This radical proposal is discussed below, in  §7.  It should be noted, however, that even if it is true that deterministic chance is possible, that observation is far from establishing that the physical theories under discussion here are ones in which deterministic chance features. That some deterministic theories may have chances is no argument that all will, and particularly in very simple cases like the baker’s transformation, there doesn’t seem much point in an invocation of deterministic chance: chances will be trivial or redundant if classical physics is true. The second avenue of resistance is to claim that there really is chance here—it is chance of the initial conditions which is recapitulated in the random sequence of outcomes. While the Lebesgue measure over the set of initial conditions in our models is formally like a probability function, to assume it yields genuine chances is a fairly controversial thesis (for a contrary opinion, see Clark 1987). Other initial conditions could have obtained; still it seems wrong to think that (somehow) there was a chance process which terminated in the selection of the initial conditions which happened in fact to obtain at our world. Rather, that the initial conditions are what they are seems to be a brute fact. If there are to be chances, then, they cannot be dynamical chances, the kind that is familiar from physics, and from our discussion in  §1.2.  Some recent arguments in favour of the possibility of chancy initial conditions are discussed in the following supplementary document: