Let's examine the evidence, shall we?
Sony has made several interesting comments concerning the success of the PlayStation 4 this generation, and these comments tend to center on the "new" fans the system has acquired.
But if you read between the lines, one starts to wonder if Sony is simply regaining fans they lost with the PS3.
For instance, the company has said several times they're "welcoming back" Wii owners who skipped PS3 and Xbox 360 last generation. Now, some of those Wii owners maybe never owned a GameCube or original Xbox but I'm willing to bet that a great many did indeed own the PS2 (hell, 160 million people bought that damn thing). And let's not forget that PS3 and Wii launched at almost exactly the same time back in 2006 and while Sony struggled badly, Wii took off like a rocket. The fad soon stumbled and even though Wii hit 100 million in a few years, you couldn't give one away in the last few years…that's what fads are. And PS3 eventually rose to 80 million.
But the clear implication remains that a lot of gamers – many of whom probably owned PS2 – simply passed on PS3 and possibly snagged a Wii or 360. Don't forget that 360 got off to a pretty fast start last generation as well. Additionally, Sony has said many times that a lot of people who bought PS4 never had the PS3. In fact, at E3 this year, Sony said about half of PS4 owners never purchased the predecessor. Naughty Dog followed this up by saying that 80 percent of PS4 owners never played The Last Of Us (a PS3 exclusive). When you add all this information up, and combine it with the ridiculous success of PS2 – and the corresponding tiny market size of GameCube and Xbox – we can assume that a great many current PS4 owners simply skipped the PS3.
And hey, it fits. Maybe one of the reasons this generation feels a lot like the PS2 era (even though there's no chance of seeing that level of dominance again) is because Sony has successfully retrieved a great many, maybe millions, of fans they lost between 2006 and 2013. It makes sense.