It’s actually a matter of debate whether Peirce’s scholastic realism is compatible with his pragmatic maxim. I think it is but there are whole books that argue it isn’t.

Now it is true that how James pushed the pragmatic maxim took “use” in a broader more subjective psychological sense. But use even often for James is more verification as a way of ending debate.

-Borrowed from Rorty

I wonder if the decoupling of language and meanings you are discussing may be related to what we mean by ‘meanings’. If by ‘meaning’ we mean something which is pointed to by language (so, not “inside” the language so to say), then I think you are right. For sure things like rabbits, water (and possibly math theorems, change, time, space) are not in the language, though we can use language to talk about them.

If we on other side by ‘meaning’ we mean the relation between the language and those things, then it seems that there can’t be meaning without language, and that meanings are part of the language taken in general as a more or less established practice in the world.

Anyway, the issue of speaking the same language seems as very interesting question, if I understand what you are pointing to – we surely would be inclined to say that Neo knows to speak English when he gets out of the vat, though before we describe him the situation he doesn’t mean what we mean by lot of his words (‘water’, ‘rabbits’). But if he doesn’t speak English we couldn’t inform him about what is happening in first place, and it surely seems that we could tell Neo what is happening. So, it seems that we must accept that he know to speak English in the moment he leaves the vat.

I wonder if this has to do with the distinction of knowing how-to from knowing-that and knowing-X (in sense of being acquainted with X).

I don’t think we can individuate language. That’s sort of what I’m getting at. I want to say that we’re speaking the same language but clearly there are differences. But, as you suggest, we could typically say that of any two people. (Not just me and Shakespeare but say me and a trapper living off in the wilds of Canada) Many of the meanings of words I have will be different from other English speakers on the planet. Is that enough to constitute a difference? I’m not sure we can really say that. It seems that the path from one language into an other is somewhat continuous. Why do we call Porteugeuse and Spanish different languages while say the Argentine and Mexican forms of Spanish are merely dialects. It’s very blurry at best.

As to the bit about universals. If math is more than just a language then if we want to say that the alien and ourselves are both doing math we have to make sense of that. One obvious way is to say that math is real independent of what any particular person thinks about it. As I said that needn’t lead to Platonism as one could make that claim without arguing for existence.

I didn’t mean to imply this is the only way out of the delemma. I think that there are anti-realist approaches to mathematical foundationalism that would work. I’d mentioned at Brood Comb Intuitionism for instance.

As to whether the existence of universals (i.e. strong Platonism) makes a difference in what we say or do I’d have to think about that. I’m not sure I’ve even thought along those lines much, truth be told. I reject strong Platonism but more for complex reasons regarding time. But if they did exist… I just don’t really have an opinion one way or the other. I tend to reject it mainly because I don’t think there’s a good argument for the existence of universals. So I suppose I’ve always just taken Ockham’s Razor and assumed they aren’t existing. I probably could come up with a stronger argument but it’s just not something I’ve given much time to.