Continuing on from yesterday's Jimquisition on the subject, I want to help a few people who are still confused about BioShock Infinite and, dismayingly, the English language. The general argument against the game seems to be that BioShock was the wrong name for the game, and if they wanted a spiritual successor, they should have removed the "Bio" bit.
Apparently, it must be called SkyShock, or some sort of variant, because BioShock is an explicit reference to either the ocean or the philosophical ideals of Andrew Ryan. I'd like to point out that you do not understand the English language if you believe this is the case. I don't know who told you this, but the "Bio" part of BioShock has nothing to do with philosophy or the ocean.
"Bio" is used to indicate life or living organisms. That's all it references. Nothing about Ayn Rand dystopias or underwater cities. In game terms, it specifically references genetic manipulation and man attempting to control life. If BioShock Infinite has anything like that in it -- and it appears that it does -- then the "Bio" part of BioShock is perfectly acceptable.
I know that for many of you, this is pathetically obvious, but I felt it a public duty to point it out for those who didn't finish first grade English. I hope that's cleared it up for you!