 Church concluded this version of CTA by noting that (4) and (5) are clearly not synonymous, since they convey different information to a German speaker who does not speak English. Church concluded that, therefore, (2) and (3) are not synonymous (1951a [BE: 294]). Church assumed, plausibly, that synonymy is an equivalence relation—reflexive, symmetric, and transitive. Hence, the basic structure of CTA is as follows: Assume that (2) and (3) are synonymous. Then (4) and (5) are synonymous. But (4) and (5) are not synonymous, and so neither are (2) and (3), and therefore (3) cannot serve as an analysis of (2).