 is formally similar to the formulation of minimalism in terms of (GT) that Horwich rejects, but to avoid the circularity concerns driving that rejection, Hill’s (ibid., 18–22) idea is to offer introduction and elimination rules in the style of Gerhard Gentzen (1935 [1969]) as a means for defining the substitutional quantifiers. Horwich (1998a, 26) rejects even this inference-rule sort of approach, but he directs his critique against defining linguistic substitutional quantification this way. Hill takes his substitutional quantifiers to apply to thoughts (propositions) instead of sentences. But serious concerns have been raised regarding the coherence of this non-linguistic notion of substitutional quantification (cf. David 2006, Gupta 2006b, Simmons 2006). As a result, it is unclear that Hill’s account is an improvement on Horwich’s version of minimalism.