 In this context, there are two things to notice about (GT). First, it is not a schema but a universally quantified formula. For this reason, it is possible to derive a generalization like \(\beta\) from it. Second, the existential quantifier, ‘\(\Sigma\)’, in (GT) must be a higher-order quantifier (see the entry on  second-order and higher-order logic)  that quantifies into sentential positions. We mentioned above an approach that takes this quantifier as a substitutional one, where the substitution class consists of sentences. We also mentioned Hill’s (2002) alternative version that takes the substitution class to be the set of all propositions. Künne (2003) suggests a different approach that takes ‘\(\Sigma\)’ to be an objectual (domain and values) quantifier ranging over propositions. However, parallel to Horwich’s rejection of (GT) discussed in Section 3.1, all of these approaches have drawn criticism on the grounds that the use of higher-order quantifiers to define truth is circular (cf. Platts 1980, McGrath 2000), and may get the extension of the concept of truth wrong (cf. Sosa 1993).