In this paper, I want to draw attention to a connection between rigid designation with its consequence that we are able to stipulate worlds and haecceitism, the doctrine that we have possible worlds alike in all qualitative features which nonetheless are metaphysically different, in that two individuals can have all their qualitative features swapped while remaining the same individuals. I shall argue that stipulation leads to haecceitism, which in turn depends upon commitment to haecceity ("primitive thisness"). Haecceitism is, I claim, (...) an unattractive doctrine, but there is one powerful argument for it, drawn from the desire to make sense of observed frequencies of probabilistic events in terms of possible configurations of phase spaces which may be taken to be a form of possible world. However, by paying close attention to classical and quantum statistics, we see that this argument fails. (shrink)