I admit I stated an opinion above. It's just my opinion and you can disagree. But I will stick with it.
Douglas (not Daniel) Hofstader went way beyond the coctail party philosophy in that book. I never read it, but Wiki says:
Through illustration and analysis, the book discusses how self-reference and formal rules allow systems to acquire meaning despite being made of "meaningless" elements. It also discusses what it means to communicate, how knowledge can be represented and stored, the methods and limitations of symbolic representation, and even the fundamental notion of "meaning" itself.
In response to confusion over the book's theme, Hofstadter has emphasized that GEB is not about mathematics, art, and music but rather about how cognition and thinking emerge from well-hidden neurological mechanisms. In the book, he presents an analogy about how the individual neurons of the brain coordinate to create a unified sense of a coherent mind by comparing it to the social organization displayed in a colony of ants .
I think that makes Hofstader's book relate to philosophy a bit like Andy Warhol's pieces relate to art. It is pop art, it is pop philosophy. I bet Hofstader would be in agreement that statements like "This statement is not true" belong to cocktail parties. It's probably where most of that philosophy takes place.
Here's another take on philosophy: You may not be experiencing life at all as you think. You could just be a brain in a vat, kept alive chemically and electricly. Instead of actually doing things, you might just have certain areas of your brain stimulated to think you are experiencing them. The "brain in a vat" philosophy has been extended to a whole new level nowadays: It is highly likely that human experiences may, in the future be able to be reproduced in a computer and no actual living people are needed to "play" these experiences. Since it would seem real to the personalities involved, and since it would be common in the future, odds are that "we" are all just part of one of those computer simulations right now.
I tell you what I think of such philosophy. If it were real, there's nothing I could do about it, so I must live my life as if it's real. I am offended at politicians ducking truths with legalese and I am just as offended when I realize people's beliefs are based on semantics or extreme definitions or obscure thoughts. It offends my senses when believers say that "You can't prove that God exists." Just as I must live as if I am not a brain in a vat, I must live in what I perceive as the real world where God doesn't show up, and I must live in a world where self-contradiction might seem real in people's minds and in religion, but I must learn better and move on.
What you say in your short version is important. Religious conversation is in and of itself a "trick of semantics". But instead of thinking we waste our time with "prove" or "truth," I think it's important to force the issue sometimes to force the mind to see that it's just a trick.
Flying Spaghetti Monster was a serious rebuttal to teaching Intelligent Design in school, but I can tell you this: No serious debates are taking place where someone actually believes FSM is real. There are some people who haven't gotten that. So the ridiculousness of the point prevails until they figure out that it is deliberate ridiculousness to help them see the same kind of ridiculousness in their view.
I didn't dwell on the "cocktail party" comment, but moved right into "Legalese." I don't think most Jehovah's Witnesses are caught in illogic similar to your "This statement is not true" discussion, nor are most people with Bible-based beliefs. There's a little bit of that in stuff like "It's impossible for God to lie." But Bible-based doctrine typically picks and chooses scriptures to bolster one claim that fits an agenda and then redefines the statements that contradict their doctrines. They use Legalese tactics to say, "No, the Bible doesn't say that, because that Hebrew word meant something completely different 4000 years ago."
I have said quite a bit here that could be taken apart and used against me. But we are just a couple of guys shooting the breeze at a cocktail party here. You get the general idea of what I am saying. In short, I don't think it's a waste of our breath to point out contradictions to our JW loved ones' (or other loved ones') way of thinking. I think we need to help them see how silly the matter is when their cognitive dissonance leads them astray, then we can help them empower themselves to think better.
It is like using metric wrenches to work on an American made automobile.
People do the opposite of that all the time. They use American Standard wrenches to work on metric-sized autos. They might get the job done sometimes with no harm, but will often run into trouble doing this, especially when it comes to tightening and torque. It's not a waste of time to help them see they are using the wrong tools. Similar with thinking, but it's harder to make them see they are using the wrong thoughts.