 Another and rather different line of criticism of the claim that HP is analytic can be found in Mancosu (2016: Chapter 4). Ironically, Mancosu advances what he calls a Good Company objection to HP. HP jostles for primacy with at least infinitely many ‘Good Companion’ abstraction principles. They are good because, like HP, they permit the logical derivation of the Dedekind-Peano axioms. They do so via their respective ‘number’-abstraction operators with predicates whose extensions are (Dedekind-)finite. They assign such extensions the right natural numbers as their cardinal numbers. When that operator is applied to a predicate whose extension is (Dedekind-)infinite, however, these other principles give results arbitrarily different from what one would expect from the more Cantorian principle HP. HP and these Good Companions get matters right on all finite extensions. But the Good Companions give rise to a confusing variety of ‘number’-assignments to infinite extensions. The problem for the HP-er, as Mancosu sees it, is how to maintain the case for the analyticity of HP in light of all this good company. We see here another manifestation of the epistemological worry that HP is of excessive consistency strength when the logicist project is simply to furnish a deeper but analytic foundation for Dedekind-Peano arithmetic. All that such a foundation requires is what HP and these competing Good Companion principles agree upon—namely, that predicates with (Dedekind-)finite extensions should get the right numbers assigned to them (i.e., the natural numbers). There is no need for the logicist about Dedekind-Peano arithmetic to make pronouncements about any infinite numbers.