Wes Salmon thinks the following "Leibniz Principle" is incompatible with the explanation of indeterministic phenomena:
if, on one occasion, the fact that circumstances of type C obtained is taken as a correct explanation of the fact that an event of type E occurred, then on another occasion, the fact that circumstances of type C obtained cannot correctly explain the fact that an event of type E' (incompatible with E) occurred.Salmon thinks that the Leibniz Principle is incompatible with explanations in indeterministic cases and hence false.
I don't know if the Leibniz Principle is false. But I do have an argument that it is compatible with explanations in indeterministic cases.
Consider an electron in a mixed (3/5)|up>+(4/5)|down> state. The electron then undergoes a process whereby it is measured whether it is in an up or down state, thereby requiring collapse. It has probability 9/25 of collapsing into |up> and 16/25 of collapsing into |down>. In fact it collapses into |up>. This is pretty much the hardest kind of real-life case for explanations of indeterministic cases, since it is the less likely outcome that happens. But it is also one where an explanation can be given that satisfies the Leibniz Principle.
Consider now the following circumstances:
- The electron is in a state such that the squared modulus of its probability amplitude for |up> is at least 9/25, and it was collapsed into |up> or |down>.
- The electron is in a state such that the squared modulus of its probability amplitude for |up> is 9/25 and the squared modulus of its probability amplitude for |down> is 16/25, and it was collapsed into |up> or |down>.
Now, if we accepted (2) as an explanation of the electron's collapsing to |up>, we would also have to accept it in another case as an explanation of the electron's collapsing to |down> (an even better one, since that is a likelier result), contrary to the Leibniz Principle. This is the sort of reason for which Salmon rejects the Leibniz Principle.
But (1) has no such unfortunate result. For while (1) does explain why the electron collapsed into |up>, it cannot explain why an electron collapsed into |down>.
One could also weaken the Leibniz Principle and take it to be a constraint on contrastive explanation (cf. this paper). If so, then the above would show that we can satisfy at least one desideratum for contrastive explanation in indeterministic cases (for a different approach, see this paper).