What exactly is “existential supremacy”?
I dunno, but it if applies to fire hydrants, I can’t imagine it being very prestigious.
Just speaking for myself, I’d love to have one.
I’m not sure I agree. Surely if we’re subjective beings we can relate subjectively? It may not be a “true” communication, but it is a method, as mangled as the results may be.
I would add that shared language would help this, but I don’t know the word i’m looking for. Language is essentially a shared subjectivity; it may hold no objective meaning, but a shared subjectivity means that the spokes are more the same. It may be that we can understand each other more than we do the objective being; though it sends the same signal, it’s mangled before we get to us, but with a spoke between each other the “smaller” hubs (ourselves) will send a better signal. We still have the problem of different hubs, but then we’re likely to be as different to each other as we are to an objective being.
I think I need a new monitor. I opened this thread because I was intrigued that Lib might think $5 was a logic tool.
Pretty much just what it says. One way to look at it is in terms of scope. How many contingencies would be required for X to exist? The fewer there are, the greater the existence of X. If there are exactly 0 contingencies, then the existence of X is said to be necessary, or supreme.
It is certainly the case that these logics are formed by adding axioms to K, and that these are cumulative for any S. But just as we normally take for granted such logical principles as A -> A, especially in informal discussions like this one, so also does it seem unecessary to spec out the entire axiomatic foundation for S5 each time reference is made to it.
I think your description makes it clear, however, that this is indeed the system of choice since the objective agent must have noncontigent access to every world (or at least every possible world). But what is unique about the Euclidean frame, (wRv & wRu) -> vRu, is of course “w”, through which v and u must “go” to for access. Hence, the hub and spoke analog. And although v might have direct access to u through some subsumed frame like transitivity, there is nothing to address the contingency of v’s relation to u. But where v and u are both contingent on w, their subjectivity becomes clear. And so again S5 is the system of choice.
I think this sub-discussion we’re having is pretty much a good example of what you’re describing. I’m not really sure just how mangled our communication is. I seem to agree with you on some levels and disagree with you on others, but the crux of it is a frustration in understanding really just what it is you’re getting at, so to speak. In other words, our communication is not clear enough that I can formulate the same context in my head that you have in yours. If I reach the same conclusion as you, it will be pure serendipity because I have no idea either where you’re coming from or where you’re going.
But just to address the matter of subjective access in particular, I would say that if A has access to B only subjectively — that is, A has a subjective perception of B — than what A really has access to is some B’ that is not B. I think this is what you’re calling not a true communication. And that’s fine, but it really isn’t the question I’m examining. I’m not wondering whether subjective worlds relate perfectly to other subjective worlds. Indeed I gladly concede they do not. I’m wondering whether the tool for describing their relations (however clear they may be) as well as their relations to the object viewpoint is most properly S5.
Ah, ok. Sorry to bring you on a tangent.
No, that’s fine. I’m not complaining, just describing. 
Ah. Then only logical-mathematical concepts would have existential supremacy.
More precisely, only analytic concepts would have it.
And God is not an analytic concept.
Actually, it so happens that He is. Not that that is pertinent here, but still.
(If God were a synthetic concept, you could observe Him with your senses.)
Analytic concepts have no mind or will.
If by mind you mean “brain”, then I agree. But will? By what rationale do you take such a renegade position? If the statement “X is supreme” is such that supremecy is entailed in X, then we have an analytic judgment. If the same is true of “X’ is willful”, then the proposition about X’ is also analytic. (This is the Kantian interpretation, but the Fregian interpretation doesn’t really change the point.) What you seem to be going for is making existential supremacy out to be an abstract concept (rather than an analytic one), which might be why you mentioned math originally. But math can be synthetic. For example, the statement “2 + 3 = 5” is a synthetic claim. The predicate, 5, is not contained in the subject, 2 + 3.
How can an analytic concept be non-abstract?
I guess my problem is that you haven’t defined R (at least as far as I can tell.) I agree that R being necessity is transitive, but in the second part of your post you used the transitivity of R in an argument about objectivity and subjectivity. Why would a necessary being be objective in your sense?
Well, it just means that the predicate of the concept is entailed in the subject. One way that a friend of mine looks at it (it helps him, so maybe it’ll help someone else) is the number 2 versus the numberal “2”. The number 2 is both analytic and abstract, but the numeral “2” is both analytic and representational.