All A is B and all A is C, therefore some B is C I still do not understand the question. We are discussing formal logic, what true conclusions we can--or rather, cannot--derive from that proposition, assuming that it is true. — aletheist
Either we're imagining As with property B in a domain, or there possibly are As in a domain, independent of our imagining.
If we're imagining As, we're imagining them to have property B, then it makes no sense to also imagine that there are no As in that domain. For one, we've already imagined As in that domain in order to imagine them having property B. If we imagine a domain with no As (if that's even really possible, it might not be), then there no As in that domain to have any property whatsoever.
If we're talking about a domain where As can obtain independent of our imagining, then we can't--especially logically--say what properties the independent As would have at all, as we could always be contingently wrong about that.
You could say "I'm only going to call x 'A' if x has property 'B'," but then we're talking about something we're imagining (in other words, these sorts of statements, statements about "essences" and the like, are statements about how we think about something), and we're stuck with the same problem as above. Our imagining is the domain in question, in which case we've imagined As with property B, and it doesn't make sense to say that we've both imagined that and imagined that same domain without any As.