 A few natural language examples provide a convenient illustration to clarify the difference between (1), that is a well-formed (but meaningless) expression and (2), which is a meaningful (but ill-formed) sentence. (The meaningfulness of (2), of course, should be taken with a grain of salt. In reality,  Kurt Gödel proved the system of PM to be incomplete in 1930. Thus (2) may be guessed—using syntactic and semantics clues—to be a distorted version of (2′) Peano arithmetic was proved to be incomplete by Gödel in 1930.)