Yes, that’s it exactly. Meaning isn’t objective. Or better to avoid the word meaning and use the words intention and interpretation. By calling the string of words “meaningless” I mean I find no coherent way to interpret it into a thought in my mind. If one cannot interpret a string of words, one cannot even begin to evaluate it as an argument. (Yes, I know in propositional logic they let you do that; that is part and parcel of the whole system I find useless at best.)
Soundness, validity, etc. - it’s not useful terminology to me, so I may differ from your textbook from time to time.
In fact, all of propositional logic rests on a questionable foundation, for a reason you already seem to grasp: The meaning interpretation of a statement is not objective. Propositions (words) are not truth-apt until they are interpreted into thoughts. Propositional logic treats a sentence without considering the thought in the speaker that prompted it, and without considering how the listener interprets it - which are the only two things that matter for argumentation, conveying a theory, or any intellectual discourse.
It seems to me that what I am trying to do in intellectual discourse is this:
(1) I have a thought, and I would like to get other people to experience that same thought. Since we’re not telepathic, I am usually forced to (2) put the thought into words in hopes that other people will (3) interpret it into a thought that matches mine. It looks pretty simple: unless all three steps happen in order, it doesn’t seem useful to call it intellectual discourse, or an argument, or the conveying of a theory.
With that in mind, it might be easier to see why I say that if a proposition has a contradiction that prevents the listener from being able to interpret it, communication/discourse/argument simply has not happened yet. Steps 1 and 2 may have happened, but Step 3 hasn’t.
Now in the case of contradictions, there is question that comes even before that: What was the speaker thinking before he or she uttered the contradictory proposition? What was the initial thought (Step 1)? If it is truly impossible think a bona fide logical contradiction (not just the words, but the actual thought behind them), then the communication can’t even have started (Step 1 has been skipped), and the words hardly seem worth calling a “proposition” at all.
So when someone utters an apparent contradiction, the best idea would be ask the person to clarify. If they refuse, ask what they are even trying to do. Are they trying to get a thought from their mind into yours, or are they just making noises for some other reason?
This might seem mundane, but in fact there are many people who will try to espouse a theory while telling you flatly that they do not understand it, can’t visualize it, or that it has unthinkable elements in it. This means they are not communicating (they just told you Step 1 is impossible!), but rather they think the theory is sitting there in some kind of objective meaning in the words themselves. Those who speak of 4 or more spacial dimensions come to mind. Propositional logic can’t tell you how 11D space is a bogus idea, but the praxeology of communication can. I recommend it because it is both simpler and more broadly applicable than propositional logic. Plus it helps reveal word-based error, which propositional logic does not. Propositional logic won’t even catch equivocations or WTOs (in fact it renders them invisible), which are the real culprits in most fuzzy-headed thinking and so-called logical errors.