I'll restate these ideas in a more explicit claim. All symbols are defined via one's own subjective experience.
One's own understanding/definition of every word can be traced back to personal experience. Imagine your life as a timeline, like a video, from birth up until now. You can seek that timeline to find the moments/clips that contributed to your definition of any given word or even mathematical symbol. To give an example, when I say "apple", the corresponding idea in my head is based on every apple I've seen and every instance of the word "apple" I've seen being used or being taught to me in the past. Even when we try to define the phrase "this specific apple" while looking at the same apple on the same table in the same room, the light bounces off of it slightly differently from my angle of view vs yours, and we did not see the same sequence of "video frames" about the apple, and so our mental models of that apple would necessarily be slightly different.
This is probably why the hard problem of consciousness / unified theory of physics appear forever out of reach. If no two observers/observations are fully identical, then you cannot even define what an ideal observer is. But we tend to assume such an ideal definition exists.
This seems almost trivial in hindsight because "identical" can be defined as 1) "one and the same", based on one thing OR 2) "mostly similar", based on pairs of adjacent things one has seen in the past.
And to sort of echo the original post, it seems to me that a lot value comes from the interactive nature of argumentation. But I think the specific medium/modality of those interactions don't matter for most things, and even when it does, like in this case, valuable insights can still fall out of a discussion in text. I derived the precursor ideas which led to this conclusion of definitional non-equivalence in past offline arguments as well as simulated discussions in my head. And I derived the actual conclusion by arguing with people here on HN, which helped me truly internalize the idea that even the definition of consciousness/observation differs from one person to another. That comment thread can be seen here: https://news.ycombinator.com/item?id=49338029
It's worth mentioning that I am not too proud of that specific interaction because I got needlessly defensive and adversarial, and lied about my subjective experience of having undergone general anesthesia even though I haven't really, and it was especially egregious in a discussion about consciousness. My original reflex/motivation was I felt that many other people would likely prematurely dismiss some of those ideas if I admitted that one of the tangential premises were wrong. And regretfully, by lying that time, I've introduced a cancer in my mental pathways when considering the problem of consciousness and adjacent philosophical problems because I'd always have this nagging feeling to try to justify that past mistake, even now. But in truth, I was just being an intellectually dishonest little shit trying to win an argument. And yet, something valuable came out of that interaction.