 Geach begins by urging that a plain identity statement ‘\(x\) and \(y\) are the same’ is in need of a completing predicate: ‘\(x\) and \(y\) are the same \(F\)’. Frege had argued that statements of number such as ‘this is one’ require a completing predicate: ‘this is one \(F\)’, and so it is, Geach claims, with identity statements. This is a natural view for one who subscribes to RI. The latter cannot even be stated without the completing predicates. Nevertheless, both the claim itself and the analogy with Frege have been questioned. Some argue that the analogy with Frege is incorrect. For example, Carrara and Sacchi (2007) maintain that Frege’s position that any ascription of a number to something is always relative to a concept boils down to the claim that concepts are essential in cardinality statements because without them there is no specification of what is to be counted. Once this is settled, Frege would count by means of absolute identity. Others argued that while the analogy is correct, both Frege and Geach are wrong (Perry 1978 and Alston and Bennett 1984). These matters do not bear directly on the question of the coherence and truth of RI or the question of absolute identity. One who adopts the weak view would not want to follow Geach on this score. And one could maintain the “completing thesis” without being committed to RI. Furthermore, the completing thesis occupies a puzzling role in Geach’s dialectic. Immediately following his statement of the thesis, Geach formalizes FOL\(^=\) on the basis of the single formula: