According to Rudolph Carnap’s approach, x, y, and z can be variables of anything you want. Carnap might have simply said here that these are questions for the scientist or the ontologist. Quine, for example, let science (though not scientists) decide these matters.
If a priori or necessary truths are true simply via linguistic convention (in Carnap's scheme), then what’s the point of them? If they bear no relation to the world, the mind or a non-spatiotemporal realm (take your pick), what purpose do they serve? How do we get outside language or “schemes”? Do we even need to get outside language/convention? If not, why not?
Conventionalists may say that we have good reasons for adopting conventions. What are those reasons? And if they're reasons outside language and conventions, doesn’t the conventionalist stop being a conventionalist by adopting those reasons? I guess that realists would happily accept that we need conventions. No problem there. The realist can’t say anything without conventions; even if these conventions do indeed duplicate, in some way, the actual nature of the world.
As Karl Popper might have put it, if a conventionalist’s law becomes analytic and therefore unfalsifiable, then what’s the point of it? It may help you predict; though what if the predictions are incorrect or the laws postulate non-existents? If what's analytic becomes law-like in this respect, isn’t it a dangerous law in that it halts philosophical or scientific advancement?
It's true that conventions aren't forced on us by nature. (What would it mean to have a convention forced upon us?) Even realists would accept that nature doesn’t force itself on us. However, we have causal interactions with nature and these causal interactions impinge on us - even if they don’t force us to speak nature's very own language. Nothing forces the realist to say, “There are quarks and planets.” However, there are causal reasons for him to say what he says. If there are no restraints on the adoption of conventions, then anything goes and we have…well, relativism (if with lots of added logical symbols and fancy technical/scientific terms).
Why can’t the realist be a realist and still accept (with the conventionalist) that there's more than one description (or explanation) of a given “space-time point” (in Carnap's scheme), event or object? I don’t see why a realist must uphold a single “correct description” of a given space-time point. That, surely, isn't necessarily entailed by realism. (Think here of Husserl’s metaphysical “positions”.)
Again, of course conventions are freely chosen. I think that the realist can accept this. The "nature forcing itself on us” metaphor isn't very helpful in this debate. I don’t believe that, for example, realists were really horrified by Poincare's admission that contradictory scientific principles can be maintained. Why can't the realist accept Poincare’s position too? You could accept and still believe that your principle (or theory) is dis-confirmable in the future. The realist must accept and live with the alternative descriptions (or explanations) of the world even while accepting that, of course, some are correct and some are false. One can be a realist and say that “there is a way the world is” and still live with – many? – alternative descriptions (or explanations) of the world.
What being said here (if rather counter-intuitively) is that realists are conventionalists (in some ways, at least) and conventionalists are realists (in some ways, at least).
In theory T certain new terms are postulated (say, a, b, c…). Does a Carnapian need reasons for postulating a, b, c…? Is it the very nature of postulation that they're assumed without proof or even evidence? If they're postulated variables with objects, properties, classes, etc. as their extensions, then what is the Carnapian’s ontological position on these things? For example, what is to stop a Carnapian from saying that a’s reference or extension is a round square?
Does “anything go” if it's via stipulation? In addition, Carnapian analyticity makes it the case that what's analytic is analytic because the terms are so devised to be analytic (“by fiat”, as Quine put it). A priori analytic statements are true and analytic because they're constructed to be true and analytic. So didn't Carnap restrict the range of his own variables? Or would Carnap have said that his variables range over what scientists say they range over (as Quine did)? However, if philosophers accept everything that science (rather than a science or scientists) postulates, then why would science need philosophy at all (that's if it does need it)?
*) Carnap's "linguistic frameworks" approach can be found in various places. This piece is mainly based on the paper 'Empiricism, Semantics, and Ontology'; which was first published in 1950 and later found in Carnap's book Meaning and Necessity.