Eurogamer has a solid 3-page interview with BioShock Infinite lead artist Shaun Robertson, digging into the root of the game's inspiration, design and its place in the franchise.
Eurogamer: It seems like a dramatic departure. I wonder why it even has BioShock in the title.
Shaun Robertson: BioShock to us has always been more than the city of Rapture. When we sat down and we were thinking about what is BioShock? Is it Rapture? No-one felt BioShock was Rapture. BioShock is more than that. Then what is it?
Our core values for BioShock are making a fantastic place that's immersive, the player wants to visit and wants to be in and wants to explore, and take their time to explore. Even if there's no AIs and there's no external story, you would still understand elements of that city and why it was there because the environment is rich enough that you could pull a story from it at your own pace.
The other element is providing the player with a wide enough variety of tools and problems that they can use their imagination and the tool set in how they want solve these problems.
Eurogamer: That explains the BioShock part. What about the Infinite part?
Shaun Robertson: We couldn't call this BioShock 3 because it doesn't have anything... Or does it? Anything to do with 1 and 2. Like I said, BioShock is bigger than Rapture. Calling it 3 would just imply it's either a straight-up sequel or prequel to BioShock 1 and 2, which it's not.
We will reveal more in the future about the actual relationship, if there is one, between the other BioShocks. It's one of those things where ultimately the idea of BioShock transcends Rapture.