This is a "Write an LJ post instead of use a piece of scratch paper" exemplar. But you might find it interesting.
If Nelson lives in New York and Linda lives in Los Angeles and they're talking on the phone and Nelson says "Have you ever been here before?" Linda answers whether or not she's been in New York, even though she's been here all her life.
The full set of things any person would classify as BEAUTIFUL is probably close to unique. But even though reference differs wildly, we are perfectly able to understand someone's claim "That's a beautiful flower," even if we don't share the conclusion. A theory of concepts which requires publicity of BEAUTY is a theory which denies publicity in many cases.
Everyone has different extension for the concept MYSELF. While a Classical Theorist might thinkg MYSELF is defined as "the speaker," its reference flails wildly while the concept remains fixed across speakers.
It seems my best approach would be to argue that publicity isn't as important as potential publicity -- the ability for people to come to a shared concept when it matters, but let them have differing concepts for the same lexeme most of the time.