 Mancosu’s Good Companions to HP arise only because he shares with the HP-er a fundamental logical commitment: every singular term of the language must denote. This means that the logic furnishing the supposed logicist foundation for arithmetic is not a free logic. Every singular term formed by applying the number-abstraction operator to a predicate is taken to stand for some object. This refusal to adopt a free logic complicates matters unduly if ones sees as part of the logicist project the task of generating only epistemically justifiable commitment to numbers as abstract existents. We want, as it were, to be able to recognize only those numbers whose existential credentials are absolutely compelling. In particular, the logicist should be able to deliver only the natural numbers, when furnishing deeper logical derivations of the Dedekind-Peano postulates.