Haecceitism and degrees of freedom

According to haecceitism as I shall understand it, there are vast numbers (probably infinitely many) possible worlds that are just like ours in all qualitative features but that differ in which particular entities fill which roles in the world. We should, however, prefer theories with fewer fundamental degrees of freedom. And haecceitism introduces many new fundamental degrees of freedom into the theory like the answer to "Who lived Einstein's life?"

This isn't an objection that haecceitism violates the Principle of Sufficient Reason. It might not. It might be that we can explain why Einstein rather than some other (actual or possible) person lived Einstein's life by supposing that the values of different individuals living a life are always incommensurable and that God freely chooses between these incommensurables. But even if (as I have argued) such a divine choice would be an explanation, it wouldn't be a very illuminating one. It would be a choice between vast (probably infinite) numbers of alternatives that are in an important sense on par. A theory that posits that is less attractive.