Nozick’s Tale of the Slave is online. You should go read it (it’s short) before continuing this post.
Okay, welcome back. Although the story ends with a question I think it’s clear that the intended answer is “none of them,” and that the sequence of cases is meant to be a kind of argument for that conclusion.
It’s important to see, then, that Nozick’s argument is not merely a Sorites argument.
A Sorites argument has the structure “A isn’t different enough from B to belong to a different category; B isn’t different enough from C to belong to a different category … and so on … so all the instances A through Z must belong to the same category.” Thus a pile of three pebbles isn’t a heap; a pile of four pebbles isn’t different enough from a pile of three pebbles to be categorised differently – so no number of pebbles can ever be large enough to count as a heap.
Although there’s philosophical disagreement as to how to describe exactly what’s gone wrong, that kind of argument is clearly fallacious; so if that’s all that Nozick’s argument were doing it wouldn’t be very impressive. But I think there’s a more charitable way of understanding the argument – namely that in each transition from one case to the next we are meant to recognise that the essence of slavery has not been affected – that slavery isn’t at all about how kindly or cruelly one is treated, for example. In a Sorites, each stage is a bit more heaplike than the next, whether it gets all the way to heaphood or not; but – Nozick wants us to see – each stage of his story is not any more freedomlike.