the "meaning", insofar as it involves "referring" to something, depends on stuff outside the mind of the speaker. That may seem obvious in retrospect, but it's pretty tempting to think otherwise
The idea produces non-obvious results if you apply it to, for example, mathematical concepts. They certainly refer to something, which is therefore outside the mind. Conclusion: Hylaean Theoric World.
Seems to me that you can dodge the Platonic implications (that Anathem was riffing on). You can talk about relations between objects, which depend on objects outside the mind of the speaker but have no independent physical existence in themselves; you need not only a shared referent but also some shared inference, but that's still quite achievable without needing to invoke some Form of, say, mathematical associativeness.
Thagard (2012) contains a nicely compact passage on thought experiments: