I've been rethinking the generation thing, this particular discussion is a good one because it focuses on the actual console definition of "generation", not eyeballing and saying "This is next gen." The thing is that the generation will last longer than 6 or 7 years only because there is generally some generation spill over.
You could even look at decades as we interpret them and relate that to "next gen." The early 80s was technically still the late 70s until the a few years into the decade, the early 90s was still the late 80s until a bit into the decade when it came to television, film, (in some cases) music, fashion, and gaming.
The thing here is that 1. 7th generation will spill over into 8th generation while still running along it, 2. The console's life cycle doesn't really end until support ends and in the case of online play, most of the official online servers are ended. Now specific consoles could continue beyond that--the DC still had and will probably see more games put out by independent developers, 3. It's typically be PlayStation that extends a generation.
It's usually thought "Oh new console, time to completely abandon the last one and sell all your stuff from the previous. Two or three more years left for the last generation." In reality, this generation will last for along as whichever of the big three continues making games for their console. Once Sony, Microsoft, or Nintendo says "Okay, pencils down. Turn in your paper and prepare to use the 9th generation Scantron." Then that generation is officially done.