Minecraft will not spawn any pigs in this area. It fits the required dimensions on the Minecraft Wiki.
"A monster spawner is only active when a player is within 16 blocks of it. While the block is active, it will spawn mobs within an 8x3x8 block area (8×8 wide and 3 high), centered on the corner of the spawner block with the lower x and z coordinates. Mobs can spawn anywhere in this range that is suitable, even if the immediate vicinity of the spawner block itself is not suitable."
Our area fits these dimensions exactly, why wont pigs spawn?
Picture of area:
Best Answer
The conditions shown in your screenshot should be able to spawn pigs, assuming it's a pig spawner. I did a rough recreation of your setup in my world.
Even in the dark, pigs were spawning, and within seconds of placing the spawner, so it's not as if you aren't waiting long enough. (Yes, the pigs also spawned when I surrounded the spawner with Glowstone). Because of this, I have a feeling that the spawner in your image isn't actually a pig spawner; it's likely a zombie spawner, or some other hostile mob. This is especially likely if you found the spawner and it wasn't manually placed by anyone, since there wouldn't be any natural pig spawners around.
Like Kevin Reid said, you could test this by making the room dark and seeing if any hostile mobs spawn. If you have admin privileges (and don't feel like this is cheating in some sort of way), you could use
/give 52 1to give yourself an actual pig spawner, place it in the room, and see if that one spawns pigs, just to verify if this is an odd SMP glitch that is only happening for you.