> I think the problem with insisting on using "is" that way is that you then can't distinguish between two things you might reasonably want to express, i.e. "is isomorphic to"/"has the same structure as" and "refers to the same object".
It’s reasonable to want to express that difference in specific circumstances, but it would be completely unreasonable to make this the default.
For example, I can say that Z is a subset of Q, and Q is a subset of R. I can do this, but maybe you cannot—you’ve expressed a preference for a more rigid and inflexible terminology, and I don’t think you’re prepared to deal with the consequences.
It’s reasonable to want to express that difference in specific circumstances, but it would be completely unreasonable to make this the default.
For example, I can say that Z is a subset of Q, and Q is a subset of R. I can do this, but maybe you cannot—you’ve expressed a preference for a more rigid and inflexible terminology, and I don’t think you’re prepared to deal with the consequences.