Anandi Hattiangadi’s review of Yli-Vakkuri and Hawthorne’s “Narrow Content” neatly takes on the core of their Mirror Man argument.
Mirror Man is a symmetrical being living in an asymmetrical world. He has in his mental lexicon two names, which refer to (perceptually and otherwise to MM) indiscernible people, located on his right and left sides.
Y and H suggest that no purely internal assignment of content to those two names can get the truth values of MM’s thoughts right. Suppose that Leftie is a philosopher and Rightie is a scientist; then “Rightie is a scientist” is true and “Rightie is a scientist” is false. But the two thoughts are identical as far as narrow content goes, and they share all the relevant indexes (time, place, subject). So if content is narrow, and content (plus index) determines truth value, they should have the same truth value. The internalist can try to add parameters or indexes to distinguish them; but Y & H can just come up with more symmetries. (This last is the “parameter-proliferation” argument.)
AH responds that Y and are just assuming that “Rightie” and “Leftie" have distinct referents, and it’s not clear they are entitled to. For even an externalist about content thinks a name gets its reference via a mental act. Not any old causal contact with an object is a baptism; only ones accompanied by a deliberate use of a name for the object. (Similarly, transmission of names requires that the hearer intend to share the speaker’s reference.) But MM has no way of constructing a mental act that is about Leftie and not Rightie, or vice versa.
The internalist upshot is that “Rightie” and “Leftie" do not determinately refer to Rightie and Leftie. (Perhaps they don’t refer at all.) The result is that the two thoughts have the same (lack of) truth value, and the argument fails.
AH considers, as a possible externalist response, “hard-wiring” neural connections between “Leftie" and MM’s mental demonstration of Leftie. This move has neural connections play a sub-semantic role; although content cannot distinguish the objects of the demonstrations, something more brute can do the trick.
AH responds that such connections are agent-level, and so not suitable for neural individuation—thoughts about Leftie and Rightie might even be realised by the very same neurons, in a connectionist brain.
***
Now, I am not fond of talk about hard-wiring in general (neurons are plastic, and thoughts are implemented dynamically anyway). But I think AH misses the point here.
The key for most externalists is causal connection between term and referent. If a baptismal tokening of “Rightie” is in fact causally produced by a demonstration of Rightie and not by one of Leftie, and vice versa, then that is enough to break the tie. Presumably the two causal paths will run through neurons—one chain of activation running within the left side of MM’s brain, one on the right—but that doesn’t imply any neural hard-wiring, just actual connections. (Nor does it require the kind of overall functional isolation between MM’s two hemispheres that would make him two agents.)
And sure, the result will look weird in the case of MM, where the basis of the difference in reference is purely external. MM has no way of saying which of his names refer to which person. But MM is weird, and weird cases have weird consequences. The question is whether there’s a problem in principle with “Leftie" and “Rightie” referring distinctly while sharing internal content, and I don’t see one here.
For the record, I am not defending Y & H’s complete rejection of narrow content. I am an old-fashioned mixed-content fan. External connections are needed to get representation off the ground—you can’t define your way into meaning—and may well play a direct role in the semantics of natural-kind terms, etc. But narrow content—cognitive association between concepts—is also important. “Bachelors are unmarried” is true analytically, because the RHS is cognitively linked with the LHS in some appropriate way. What it’s an analytic truth about, on the other hand, has an ineliminable external element.