Turkey to join EU?

Apparently it's a distinct possibility. The European Union has opened membership talks with Turkey. Turkey's actually been interested in joining the EU for some time, but EU member states Greece, France, and Austria have always blocked any negotiations for admitting Turkey.

The possible inclusion of Turkey in the EU raises an interesting question: How does one define Europe? As I see it, there are two main possibilities: geographically and culturally.

As you can see in these maps, Turkey rests predominantly on the Asian continent. Okay, so a small portion of Turkey is in Europe. But really, geographically speaking, Turkey is in Asia. Ah, but Turkey is culturally more similar to Europe, you say. Well, if we're going to play that game, maybe the EU would like to admit Australia, which still has close cultural ties to the UK. So how does one solve this riddle? Assign various points depending on cultural similarity and geographic proximity? That seems like it might work, even if it turns any intuitive definition of Europe on its head.

Maybe it's time to just abandon the old nomenclature and come up with a new name for the Union. Anyone have an interesting idea? [NOTE: I am personally disallowing "The Union Formerly Known as EU" or any ridiculous symbols.] Feel free to share your thoughts in the comments.