If we deny the premise then the Liar can both successfully self-refer, and also be either truth or false. It would seem that in order for a sentence to be meaningful then, it must have truth conditions. None of these provide us with truth conditions for the Liar by itself. But its participation in the sentences above would seem impossible if the Liar were not at least meaningful and were either true or false. Since its discovery, all axiomatizations of set theory must somehow limit themselves to avoid paradox.
Most efforts seek to limit or restrict self-reference.
These same systems include a relatively free comprehension axiom. Only the intuition of comprehension is sacrificed.