Another question I got is how one determines whether a syntactic object “is bound with anything.”
I do want to make a clarification point here: there is an error in the question, and it’s actually something that often seems to be confusing to people. But binding is asymmetric. Even if X binds Y, you can’t suppose that Y also binds X. Things are not “bound with” each other, nor do you say X and Y “are bound” if either X binds Y or Y binds X. It’s a one-directional thing. X binds Y, Y is bound by X.1
But as for the question itself, the way you can tell by definition whether one thing binds another is to see whether X c-commands Y and then see if X and Y both have the same index.
Another way to answer that question is in fact to use Binding Theory and possible meanings—probably the safest way to do this is by checking judgments about Principle C: if you put “he” in for X and “John” in for Y and it’s ungrammatical (but would be fine if Y were “Mary”), then X almost certainly binds Y. That is:
Xi introduced Yi to Zi.
X binds Y and X binds Z, and Y binds Z.
If you put “He” in for X and “John” in for Y, it’s bad.
*Hei introduced Johni to Z.
But it’s fine with “Mary”:
Hei introduced Maryj to Z.
Similarly:
*Hei introduced Y to Johni.
Hei introduced Y to Maryj.
*X introduced himi to Johni.
X introduced himi to Maryj.
1 It is conceptually possible for X to bind Y and Y to simultaneously bind X if X and Y c-command each other— that is, if they are sisters. This situation will never arise, though. The only such combination Binding Theory would allow would be two anaphors combined together (“himself himself”) and you couldn’t Merge them together to form a larger object because it wouldn’t check any features or satisfy the Hierarchy of Projections. So, for all practical purposes, if X binds Y, Y does not bind X.