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)