If you don't compare two side by side, then you'll never notice. The problem is that sharpness isn't determined by the resolution, that's a myth. How many people would pick a 1080 OLED over a 4k LCD?
Another problem is the size of the screen, which we guaranteed know that OP is already losing a ton of detail on the screen, even though technically and on paper it's there. Just like looking at our arms, moving closer unveils more detail. After you factor in visual acuity and viewing distance, then we would be able to answer the question which you are trying to answer @Pat Flynn.
With that said, just like a 720p screen from across the room, compared to a 1080 across the room, they'll appear identical, provided the specs are identical as well. We know that OP is using a laptop, so the screen is very small...
Esaelias187 :
can you downscale the graphics to 1080p and play like its a 1080p monitor without blurriness?
The answer is no. As soon as you lose 1:1 mapping, you will lose fine detail. Just like a 3% overscan affects the entire image, regardless if the screen and source is 1080. There is no getting around this. The only solution to this problem would be to play in a forced aspect ratio, meaning OP would have to only use 1/4th his screen when playing games.
So in order to view his game(s) properly, he would have to move closer to the screen. So, it's pointless, and should therefore buy a true 1080 screen that's bigger, and sit further away. Sitting that close to a 4k screen would increase the frequency of which you feel eye strain, and would make it overall a bad and uncomfortable experience.