Chris Leong

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Yes, you can posit that they are external references, my main point was that if they aren't external references but merely relabellings, then they don't change the system and so it's invalid to try to sneak in the connotations being attempted. Sometimes people try a motte and bailey where they say they are just making a definition and not positing something new; but then they act as though the thing they said was just a relabelling has its own existence.

So I don't see how your examples illustrate a relabeling vs. external reference distinction.

Part of what makes this so complex is that the same thing can be introduced as either a relabeling or an external reference. And people often do a half-and-half as I've described