Yes. While measurements differ, research (and observation, and logic) all indicate there is a point where our eyes cannot see anything smaller, and this defines the limit of the minimum necessary Pixels Per Inch (PPI) at which we cannot see the individual pixels comprising the image.
1920x1080 is actually quite low-density, even on a 5 inch phone screen. The average eye can easily see individual pixels at this resolution, as this is only about 440ppi.
Personally, I've used a "Quad HD" phone, the LG G3, which had a 5.5 inch screen packing 1440 x 2560 pixels (4 times 720, hence "quad") with a density of 538ppi, and while it was beautifully sharp, I could still see individual pixels with my unaided eye.
Research suggests that beginning around 800ppi is where the eye can no longer detect individual pixels, with some studies indicating the number is closer to 2000ppi. Personally, I'd say the real number is closer to that lower number.
A slightly funny fact regarding all this is that Apple's vaunted "Retina" displays, which were supposed to be so very sharp (they are quite beautiful, but they aren't what they claim to be) are about 220-260ppi, a very low number compared with other high-end mobile device displays.