I am attracted to accounts of the liar paradox on which "This sentence is false" does not express a proposition. Here is one line of thought in that direction. Roughly speaking, speaker meaning is essential to language. Unless a scribble or a noise has speaker meaning, it is just a scribble or a noise, rather than a sentence, even if it looks just like a sentence. Now, for a sentence to have speaker meaning, the speaker must either understand something by it, or else must be referring the words back to an earlier speaker who meant something by them. But nobody really has any idea what they are saying when they utter the liar "sentence". Hence nobody is saying anything in doing so, and hence the liar "sentence" is not a sentence.