Some questions - would you want to anti-alias at 1920 x 1024, and wouldn't the physical pixels on the HDTV screen prevent anti-aliasing having any effect over blurring the image? Anti-aliasing surely only works when you have screen pixel resolution more than the displayed pixel resolution.
Final question - why should games at 1080p be any different from TV at 1080p? If we see jaggies in games at this resolution, will we see jaggies in TV programs/video at this resolution?
This final question needs to be answered for you to understand the former. On a fixed resolution display like an LCD screen, each pixel is a discrete entity, a little square of light. When you render a picture, if the difference between some pixels and other is large enough, you'll notice a distinct stepping or aliasing. Games suffer from this because every pixel on the screen is a single sample from the game. You take a point in the game (a pixel from the screen), determine what colour it should be, and put that on the display.
In a TV picture, a pixel isn't one sample but lots and lots. Consider the case of inside a car, with back window borders and a bright outside. Rendered in a game, one pixel will be near black and the other near white, depending on whether in that pixel is frame or window. In a TV picture, each pixel contains varying amount of frame and window. You might have a pixel that is halfed filled with frame, half filled with window. The colour for that pixel is than an average, halfway between dark and light. The pixel has
more information than just one sample. It's this average of more than one point that creates 'antialiasing'. Adding more samples when you render a game produces more inbetween values, which decreases the contrast between adjacent pixels and decrease aliasing.
As for 1080p not having aliasing, that's a matter of pixel size. If you had 1080p resolution in a 4" display at arms length, you woudln't need AA as you couldn't notice the individual pixels. If you had a 1080p display that was 87" across, each pixel would be a millimetre in size, and depending on the distance you sit from the screen, that may be noticeable. Genreally speaking, we're not, and likely won't be for decades, at a point where pixel resolution is fine enough to remove the need for AA. Jaggies will always be present, because as resolution increases, so does display size. A 14" 1080p display would look pretty jaggie free at a comfortable viewing distance, but doesn't exist and probably never will.
