I'm entirely unfamiliar with the syntax and corresponding semantics Davidson uses for the four equations at the beginning of Truth and Meaning(https://www.jstor.org/stable/20114563). He states that the following sentences are supposed to be equivalent in some invalid theory, but I'm not sure what two of them are even supposed to mean in the naive theory. The four sentences are:
(1) R (2) x̂(x=x.R)=x̂(x=x) (3) x̂(x=x.S)=x̂(x=x) (4) S
His conclusion is that the naive (possibly Fregean?) theory doesn't work because it says that all sentences with the same truth value must be synonymous. I get that that is an odd result, but I don't understand what these four equations are communicating to get that result. Thanks for the help!