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The existence of a complete, Paretian, and finite anonymous ordering in the set of infinite utility streams implies the existence of a non-Ramsey set (a nonconstructive object the existence of which needs the axiom of choice). Therefore, each Paretian and finite anonymous social welfare relation either is incomplete or does not have an explicit description. Furthermore, the strongest anonymity condition that is compatible with Pareto involves a free ultrafilter on the lattice of partitions of positive integers. These results confirm a conjecture of Fleurbaey and Michel (2003) and further disentangle the theorems of Diamond (1965), Basu and Mitra (2003), and Svensson (1980).