Forcing the Burden of Proof

Now, this is not my Area of Competence, but let's talk about whether you're a robot...

1) The causal theory of reference is an accurate portrayal of meaning (Assumption)
2) Consciousness is 'what it's like to be' from an arbitrary perspective (Definition)
3) Consciousness is reflexive and insulated (Problem of other Minds, 2)
4) Subjective personal consciousness has no causal link to external consciousness(es) (1,3)

It appears that this argument implies that meaning cannot be applied to consciousness unless the reference is reflexive. I doubt this will be solved here, especially noting the historically intractable nature of (3), but thinking about the problem led me to consider formulations of (3) which seem to fail:

(3x) Reflexive-Consciousness necessarily excludes relational consciousness

This seems to be saying that the fact of my consciousness excludes the possibility that I can causally interact with other consciousness(es). Does this seem reasonable? Is it necessary that if I am conscious then I cannot know 'what it's like' from another perspective?

(3y) Reflexive-Consciousness can exclude relational consciousness

This is weaker and seems to imply that it is possible for me to know what it's like from another perspective, but this seems to be precluded on the basis of (1) above. That is, there is no reason for me to infer from my consciousness that what I mean by 'consciousness' is the same as what others, purportedly, have (rigid designation across possible consciousnesses seems to be the motivation here). But then this seems to lead to some variation of (3) by definition, which is unappealing....

Obviously, I have not thought too much about the topic hence the rather informal discussion. Any thoughts internet?

I think you're pretty much right about the causal theory being insufficient, but for slightly different, technical reasons.

In my view, what prevents the causal theory of meaning being applied to the intentionality ("meaning") of consciousness isn't a kind of reference, strictly speaking, but modes of presentation. That is, the redness I see in an apple is caused by the apple's disposition to cause that color experience, but the redness itself is an intrinsic feature of my experience, not (wholly) a property of the apple. This is why I can hallucinate redness even when it isn't caused by the apple (against (1)). But that isn't to say that I'm reflexively referencing my experience, because this seems to cause an infinite regress (sense-data). Instead, the intrinsic, qualitative aspects of my experience are part of its mode of presentation, not reference. So reference "ain't in the head," as Putnam would say, but qualia is. This is why water and twin water look the same.

Sorry for the jargon, I'm basically taking after Chalmer's version of representationalism here:
http://consc.net/papers/representation.html

Now on other minds...
I can't know what it's like for someone else because although we can be conscious of the same things, the same referents, we don't have the same modes of presentation. (However, the Twin Earth example is set up so that my Twin and I are presented different information in the same way, because we're twins). I'm not sure if (4) means anything else besides the conclusion that we can't know what it's like for other minds. If that's what you mean, I would agree that (4) is true, though not in virtue of (1), but because (1) is insufficient for explaining (3).

Of course neither of our arguments imply that there aren't other minds, just that we can't "know" them. And I think it's reasonable to suppose that there are things which exist that we can't know (or prove) in principle.

There is certainly something deeply unsettling about how correct this view appears. While I have misgivings about dispositional properties, I can appreciate the weaving of modes of presentation (sense?) and reference together. Gilbert Ryle quickly pointed out the sense-datum regress to which I think you refer back in 1990 in the following way:
Take sensing some object X. If this requires perception of X, and X were perceived through X' (sense-datum) then we do not seem to have gotten anywhere.
Chalmers' view circumvents the regress by positing (it appears) sense in the head as a primitive. This makes 'sense' since experiences, or consciousness, does not appear to be something that needs justification on external grounds. I mean, my conscious experience at this moment, eating a Powerbar and typing, just is, as the kids say, what it is. Hmmm, but methinks I dost protest too little. Consider the following:
Holding the position that the redness of the apple exists outside in the real world (which it appears Chalmers' does not) leads apparently to the same circularity found in Ryle's argument contra sense-data (namely, redness explained in terms of experience, in terms of physical reality, etc). Holding the position that the redness of the apple exists intrinsically, however, seems to exclude any real objectivity. The redness of the apple is never the same between us, yet we reference it nonetheless (as you know, I am cool with this fundamentally, I have a sinking suspicion that the difference between sense-reference is vague and unclear and I am working on a proof to that effect, a real one this time...). Are we acting in some kind of error theoretical manner when we discuss color? Is 'This is red' false even though by my experience this is, in fact, red? As you may have noticed, this is less a criticism and more a request for clarification...

Now, you end by indicating that neither of our arguments imply that there are not other minds, just that we cannot know them, but to this I would respond skeptically. The argument does indeed imply that we cannot know other minds, but from here it seems reasonable to hold that if we cannot know these other minds, then what basis do we have for saying they exist or not? Analogy? Transpose the argument for a moment, to math. I have no experience of abstract mathematical objects (that I know of!), though I could take analogies from, say, the mathematics, and from here argue that such entities exists even though I have no experience of them. Similarly, I have no experience of other minds but I can infer from, say, behavioral arguments, and argue that other minds exist. The argument seems to rest on how dispensable the purported object is. Field showed that mathematical objects are dispensable for science. It seems that by analogy all one would have to do is show that other minds are dispensable for social interactions, society, etc. Easily done. Robots, zombies, whatever you like, can populate the world and nothing else change except the precluded minds. Would society continue on as before? It seems likely.

Now, to the statement that it is reasonable to suppose that there are things we can't know or prove in principle, that yet exist, I respond, by what reasonableness? Certainly not by analogy. How can a statement in this regard even be posed. There is, perhaps, a thing-in-itself which we cannot know, and which we are prevented, for whatever reason, from knowing? Who is to say that such a thing-in-itself even correlates with what we 'can't know?'

Consider: Brain in a vat stimulated to perceive everything in a matrix-like way. Nothing changes, it could be me typing right now, etc. Assuming that the thing-in-itself is the real world, which the BIV scientist imitates identically, why stop there? Why should the scientist imitate the real world at all? Perhaps we are, in fact, in such a matrix-like situation but the programmer is lazy and so only the directly perceivable aspects of reality line up with the thing-in-itself of the real world. When we get down to, say, the quantum level, the programmer just threw in some random code to ensure an infinite loop did not occur, but there is no real isomorphism between the real world and the BIV world at this level. Similarly for massive objects warping space-time. Moral? Postulating things that exist without having access, proof, knowledge, etc, is dangerous ground for philosophers, but perfect for creative writers.

Jeez, I wrote too long, I really have to get back to work, but I didn't want to leave you hanging!