I'd be amazed more than anything since it would be next to impossible for Sony to emulate the PS3's CELL architecture on the PS4... hence the reason why so many PS3 games have been getting the "remastered" treatment on PS4.

To the people claiming that it's impossible to run PS3 games on PS4, you're really not providing any reasons why, you're just making unsupported claims.

In reality the issues involved are the programming languages used by PS3 (RISC in PPC and ISA on it's SPEs) and location where certain tasks are processed.
Translating RISC/ISA to CISC isn't impossible, it's no different than translating one language to another.

PS3's Power PC unit in the Cell Broadband Engine is only a single 2 threaded core, the 360's is 3X more powerful than PS3's PPC, yet XB1 has no issues in handling that code, this would be even easier for PS4, because it's only a single core's worth of work.
Code that runs on SPEs can be moved over to PS4's GPU using a virtual machine, translated from ISA to CISC.

Microsoft has already shown with their 360 BC that an NVidia GPU can be emulated easily by an ATI GPU, since RSX is a very weak NVidia GPU roughly a decade old at this point it could easily be emulated by modern AMD GPU technology.

Designing a virtual machine to do all of this isn't impossible, it would just require Sony to dedicate the programming resources to tackling each problem.

You can say anything is impossible if you're unwilling to try to tackle the task, but really when you break down each issue it becomes perfectly feasible that they can be resolved.

This! The dual pack of Symphonia Chronicles and Graces F, Valkyria Chronicles, dat Paradox game, and other non-Jrpgs.

I'd be shocked that they actually managed to software emulate it! Then I'd be very happy. And finally I'd pop in a PS3 disc into the PS4 and look for differences in games. I'd have a lot of fun with all of that actually! :)

I wouldn't care, I have a PS3 that Plays PS2 games, so I have to still use it anyways. No way would I stop using it for Dark Cloud 2

Nothing it'd be a useless announcement. I didn't buy a PS4 to play PS3 games.

I can assure you it has nothing to do with hardware sales. PS3's sales (just like the 360's) are pretty much non-existent at this point. It may to some extent have to do with Sony wanting to remaster some titles from the PS3, but more than anything it's because BC reduces software sales. If you can play all your last gen games on your current gen console, you may buy fewer current get games, which in turn leads to less cash to Sony. Couple that with the fact that it would require and abnorm amount of effort and resources to do so (resources which could've been put into other stuff, like making more new games for the PS4), it doesn't make sense for Sony, in any way. I'd rather them use that effort to create more new PS4 games, than trying to create an emulator for PS3 games. Remasters at least provide a financial return for Sony, and gives them resources they could put in other projects, backwards compatability is just a loss project.

This is the part you're underestimating.  Sony would have to find matching op codes for the SPU assembly and make sure they 1. produce the same behaviour, and 2. execute the entirety of the instructions at the same time.  Part 1 is extremely time-consuming and may not be worth the effort since there's an issue with part 2.  Interpreting  code which makes timing difficult to match, and if games are being interpreted, may make it impossible to run on the PS4.  Naughty dog ran into issues when doing part 1 at the high level and only achieved part 2 because the game was recompiled into a complete binary.  I've personally never understood why Sony hasn't taken the time to just write a low level recompiler and just feed their previous console's binaries through and "install" the game to the HD, but who am I to judge their programming analysts.

It would be cool because my ps3 is agonizing and I was considering buy another one anyways..

Same as if ms announced real backward compatibility for the 360 on the xb1... I'd be very surprised!

for those who don't get it yet, most 360 games won't work on the xb1, why even bother?