 CTA—as formulated in Church’s (1950a)—is specifically directed at Carnap’s (1947) analysis of sentences like (1) and (2), which in turn appeals to a particular notion of synonymy. However, since Church has shown that Carnap’s notion of synonymy is incorrect (via an argument described in  supplement E),  we can safely omit the details of Carnap’s notion for present purposes and speak simply in terms of synonymy. Now, according to Carnap’s analysis, (2) is synonymous with