My apologies for being slow in replying.
So then I think, to focus my first reply here -- which is directed at partial untranslatability -- I'd say that we could learn two different paradigms (to keep Kuhn in sites) by using them. And then this would be how we'd be able to tell that the two different paradigms do not have the same meaning.
So here, I think we can say, language is presumed as you note. It was only on the topic of total
untranslatability that a criteria for languagehood was sought after -- which has some interesting implications, I think, like when you were talking about understanding dolphins and other alien intelligences. But I think I'm going after making sense of paradigms, here -- or making nonsense of them too, if that be the case.
So when I ask what more someone could want -- well, they could want as faithful a rendition of the meaning as possible, and recognition that the meaning is not exactly
the same. We want someone to recognize that there is value to the statement in its original language, that the resonances of meaning are lost in translation, that there is something valuable in not just translating one language into another but in learning the language from which some work of science or art comes from.
I think that for paradigms to work, though, I would have to go a step further. As you note this is about a comparison between words -- from words to words, meanings to meanings, and not from words and meanings to world. It would seem that in order to argue in favor of paradigmatic change in the interesting sense Davidson is talking about here (and not just in a sociological sense as we can also take Kuhn to be talking about) that not only would meanings have to differ, but the relationship between the world would have to be one of truth.
And that's the kicker. Is what is lost in translation not just the resonances of meaning, but also truth? And that's a somewhat cryptic phrasing -- maybe it's cleaner to say are there languages where some sentences cannot be translated into one another, but truth is retained in both instances? Which actually differs, a bit, from merely contradiction. It's not like there's a proposition P and ~P, one of which is expressible in one language and one of which is expressible in another where they are both true but cannot be translated between each language, but P is only expressible in L1, and ~P is only expressible in L2. We might call that a version of hard
paradigms. But all that would be required is that there is some sentence in a language that cannot be expressed in another language, and it also is true -- a sort of soft version of paradigms. So there's a proposition P which is expressible in L1, is true, and is not expressible in L2
And while it may be too early to tell at present it seems
that we have reason to believe that the differences between quantum mechanics and relativity give us some example of this smaller, partially untranslatable, and soft paradigm (here I have in mind their different characterizations of causality -- which, in spite of various attempts to make QM deterministic, the actual usage of causality in practice is stochastic and so I'd say we're safe in inferring a difference, even if we want to put that difference in different ways that harmonize more than not). How do we understand the two? Well, we use them in their respective contexts -- we learn their meanings. We then compare them and see that there are some sentences in one that are not translatable to the other, but are also true. Some people work on trying to bridge these two theories, but it is enough for my point that right now we do not have such a bridge. They could, after all, both be true in their respective ways. Perhaps the true sentences in one are just better equipped to deal with certain phenomena in certain contexts -- hence why one isn't expressible in terms of the other. They really do just mean different things and are useful in those respects because they are fine-tuned technical languages built for that express purpose, rather than to serve as a universal-sort of language of the universe.
Anytime we delve into specifics there's a host of interpretive difficulties that would take longer than a paragraph to go through, and may in fact just be distracting to our overall argument. Hopefully I've elucidated how we might understand a paradigm, at least, even if you disagree with the example -- the hard/soft version of paradigms, with a focus more on the soft because that's the easier one to defend, and really it's all that's required. Meaning may be ineffable, but surely we can at least recognize a difference in meaning in spite of not having a theory of meaning? And if that be the case then we should be able to point to examples of sentences which cannot be translated into at least one other language, and are true. And if that be the case then all that I might ask, at least, is for our translator to recognize that difference.