Concealed Carry of Guns on Private College Campuses?

Say Uncle has a short post on the issue of concealed carry on college campuses, and a distinction, commonly made in such discussions, is made here: Most states which allow carry on public university campuses allow private colleges and universities to ban such, on the theory that private owners should control their property.

Commenter 17, tho, brings up an interesting issue:

So a basic civil right can be eliminated on private property at the property owner’s whim? Why then can’t plantation owners keep slaves? Is the claim here that the 13th Amendment applies despite this “private property” thing, but the 2nd Amendment doesn’t?

Hmmmmmm.....