It's not just that the liar's paradox refers to itself, but that the evaluation of it as a proposition, true or false, depends on its evaluation as a true or false proposition. Since it does not have a stable evaluation, it is not a proposition. But then the problem arises, how do we know whether we have eliminated this troublesome sort of non-proposition from an argument? I hope it should be obvious, ... I hope? At first glance, the paradox seems odd but harmless. Are there any more subtle non-propositions lying in ambush for us?
I’m not sure whether this guy is trying to agree with you or refute you: https://open.substack.com/pub/fakenous/p/virtue-and-vice-among-the-infinite?r=8hnjy&utm_medium=ios&utm_campaign=post
It's not just that the liar's paradox refers to itself, but that the evaluation of it as a proposition, true or false, depends on its evaluation as a true or false proposition. Since it does not have a stable evaluation, it is not a proposition. But then the problem arises, how do we know whether we have eliminated this troublesome sort of non-proposition from an argument? I hope it should be obvious, ... I hope? At first glance, the paradox seems odd but harmless. Are there any more subtle non-propositions lying in ambush for us?