""self contradictory"" (Was: Analytic Truth-makers)

I have focused on analytic truth-makers where an expression of language x is shown to be true in language L by a sequence of truth preserving operations from the semantic meaning of x in L to x in L.
 In rare cases such as the Goldbach conjecture this may require an infinite sequence of truth preserving operations thus making analytic knowledge a subset of analytic truth. https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
 There are cases where there is no finite or infinite sequence of
truth preserving operations to x or ~x in L because x is self-
contradictory in L. In this case x is not a truth-bearer in L.