When we say that A is B, aren't we either just calling it a different name or focusing on a different set of facts about it, a la morning and evening star? — Terrapin Station

I don't understand this. — AppLeo

So, one thing you said was, "You can call something a different name, but that doesn't change what it actually is."

Sure. And "A" and "B" can represent different names. So one thing we can be doing when we say that A is B is using the two different names. "Robert is Bob."

Another thing we can be doing--often in conjunction with different names--is focusing on a different set of facts about the thing in question.

For example, the morning star is the evening star. The different set of facts is that in the one case, we're talking about the "star" (it's not actually a star, though) we often see as the brightest star in the morning--it's often the last "star" we can see prior to sunrise, and in the other case, we're talking about the "star" we see in the evening--often the brightest/first star we can see at dusk. In both cases, we're actually referring to the planet Venus.

Another example there: Bruce Wayne is Batman. "Bruce Wayne" typically refers to the person in question in his everyday guise, as an uber-rich philanthropist businessman, etc. "Batman" typically refers to him in his crime-fighting superhero capacity. Each side, which is accompanied by different names, focuses on a different set of facts about the same person.

Those are examples where A is B. "The morning star is the evening star"--they both refer to the planet Venus. "Bruce Wayne is Batman"--they both refer to a particular person, as does "Robert is Bob."

Okay yes, I agree.

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