A statement asserts that a statement is a statement that is false.
The statement violates an axiom of logic, so it doesn’t really matter whether the ostensible statement the so-called liar, really is a statement or has a truth value.
When I endeavored some years ago to examine the so-called “liar paradox” from what I take to be a pragmatic, semiotic, sign relational standpoint, I arrived at a way of understanding it that dispelled, for me, every air of paradox about it. I wrote out an outline of that analysis under the same title I’m using here and shared it in several discussion groups. The couplet above is a bare bones rendering of that analysis.
The more rambling version can be found at the following locations.