 Collectives are abstract mathematical objects that are not empirically instantiated, but that are nonetheless posited by von Mises to explain the stabilities of relative frequencies in the behavior of actual sequences of outcomes of a repeatable random experiment. Church (1940) renders precise the notion of a place selection as a recursive function. Nevertheless, the reference sequence problem remains: probabilities must always be relativized to a collective, and for a given attribute such as ‘heads’ there are infinitely many. Von Mises embraces this consequence, insisting that the notion of probability only makes sense relative to a collective. In particular, he regards single case probabilities as nonsense: “We can say nothing about the probability of death of an individual even if we know his condition of life and health in detail. The phrase ‘probability of death’, when it refers to a single person, has no meaning at all for us” (11). Some critics believe that rather than solving the problem of the single case, this merely ignores it. And note that von Mises drastically understates the commitments of his theory: by his lights, the phrase ‘probability of death’ also has no meaning at all when it refers to a million people, or a billion, or any finite number — after all, collectives are infinite. More generally, it seems that von Mises’ theory has the unwelcome consequence that probability statements never have meaning in the real world, for apparently all sequences of attributes are finite. He introduced the notion of a collective because he believed that the regularities in the behavior of certain actual sequences of outcomes are best explained by the hypothesis that those sequences are initial segments of collectives. But this is curious: we know for any actual sequence of outcomes that they are not initial segments of collectives, since we know that they are not initial segments of infinite sequences. 