Simple question really, this one is hard to predict. If i had to take a guess at it, i think it will be compatible with PS2 but Sony will leave out PS3 compatibility in order to stretch out sales and lifespan for PS3.

What does everyone else think?  Any ideas on how backwards compatibility will be used for Sony's next console?   Maybe the full list of PS1,2 and 3 all built in the next console, or is that just a dream situation?

no theyll make you buy them again through downloads.

Nope, Could care less.. PS3 Compatible yes duhh

I agree with your very blatant answer.

No, they wiill make PS2 games available for download.

PS3 was PSX compatible and had the PSX classics on PSN.

So I say it's possible that PS4 has PS2 classics on PSN. But please make it PS3 compatible.

Yes that's what i am thinking as well, they will have the PS2 classics online but i also think they'll be b/c with PS2 discs as well. 

No. There's a reason Sony removed PS2 compatability in the move to PS3 Slim, to reduce costs.
A PS2 emulator would be too unstable so the best PS2 compatibility we will get in the future is PS2 games ported to work on PS3 like we're getting right now.

No but many PS2 titles will end up on the PSN.

I also think that you will be able to download PS2 titles, but you will probably not be able to play your old discs.
But... I'd love to be surprised and proven wrong!