Well, if I understand you correctly, you are hinting at the role that formal systems play in terms of truth.
I'm actually trying to get at something far simpler. For instance, the question "who was the President of the United States in the year 2,000?" has, by any definition, only one true answer which is knowable by anyone who can understand the question. It is ironic to have all those debates on truth when we deal with it on a daily basis.
The scientific methodologies aren't a pure formal system, but they are much more formal than casual discussion, and we use the methodologies of these formal enterprises to determine what is 'true'.
No, science has nothing to do with truth in principle. You can have true science and false science. In fact, science's power would be severely diminished if we weren't able to produce more false science than true science.
My view is that 'truth' must be treated as if it exists, but whether it actually exists (at least in any form that we would recognize) is another matter. The way the world actually is (ding an sich) does not appear to allow for trivialism (i.e., all contradictions are true), but it might allow for the non-existence of truth in terms of every so-called truth is just a useful approximation.
You are talking about something entirely different. There are no truths "in" the world, there are only truths "about" the world. Until someone opens their mouth and try to communicate an idea, the concept of truth has no application.
there might not exist one correct and final conceptual scheme Cx such that there is one final truth to the world. Change the conceptual scheme C1 to C2, and the 'facts' of P and not P change. This doesn't imply trivialism. For particular conceptual schemes (or a particular set of rules, as you said), the 'truth' is different.
What you are saying can be interpreted as this: a true statement in one language may be false when translated to another language. But if you take my definition of truth, your proposition becomes a non-sequitur, as only true ideas can be communicated. If a statement may be false upon translation, that means it is not true even in the original, it only appeared to be true. It was an illusion.
I'm not a proponent of (T2), but I allow for the possibility.
The trick is to come up with a definition of truth that makes T2 impossible. Admitting the possibility of T2, even if just in principle, is equivalent to saying truth does not exist. As I said before, "truth does not exist" is not a valid proposition in any language, formal system, conceptual scheme. Notice there's a difference between truth not existing and our not being able to say such a thing. For instance, I can conceive of a world in which I cannot make any assertions, but I cannot, at any time, assert that I'm not able to make assertions.