 Is this regress objectionable? Arguably it depends on what we want from an account of predication. If what you want is an analysis of predication, then arguably this regress is objectionable. If you start off not understanding predication—if you find it just utterly mysterious what ‘\(A\) is \(F\)’ is meant to mean, given that this ‘is’ is not identity—then this regress means that this account is not going to help you, for each answer simply invokes another predication, which is exactly what you don’t understand. If you don’t understand ‘\(A\) is \(F\)’, you’re not going to understand ‘\(A\) is bound to \(F\)-ness’, or ‘Instantiation is bound to \(A\) and \(F\)-ness’, or etc., since the ‘is’ in those claims is also not the ‘is’ of identity but the ‘is’ of predication, which you find a mystery. However, if you understand predication perfectly fine and want simply an ontological account of it—an account of what in the world makes true the true predications—then arguably the regress is not objectionable, because while there are infinitely many true predications, these can all be made true by the one underlying state of the world: the state of affairs of the particular \(A\) being bound to the property \(F\)-ness. Just as this state of affairs makes it true that \(A\) is \(F\), so does it make it true that \(A\) is bound to \(F\)-ness, and that this binding holds between \(A\) and \(F\)-ness, and etc. We would have one ontological underpinning for the infinitely many true predications. As Nolan (2008a, 182) puts it, we have “Ontology for each truth, and no infinite regress of [states of affairs], but only of descriptions of [states of affairs]: and it should never be thought that an infinite regress of descriptions is something to worry about per se”. (Cf. Armstrong 1974 and 1997 (157–8).) So whether or not we will find this regress objectionable depends on what we demand of an account of predication. We can all agree that the regress shows that the account does not yield an analysis of predication. Is this a theoretical vice? It depends on whether or not predication requires an analysis, and that depends on our theoretical goals.