Let's assume the universe is not expanding but is infinite. At some point in time stars started lighting up. Maybe they even all lit up at once, long time ago. But some stars are so far away that the light from them has not yet reached us.
Even though there are an infinite number of stars we can only see the light from a subset of them because the light from the rest of them has not reached us yet.
So I think the simple resolution of the paradox is that the speed of light is not infinite. No?
What I also never understood was what about matter that is not lit up? There could be many more unlit heavenly bodies than stars, which would block the light from the stars.
Yes, a spatially infinite universe, with no expansion, but finite time since the stars all turned on, doesn't have this paradox. I think people didn't like this answer because it needs a beginning of time (or at least, of time with stars).
Having expansion just-about implies there must be such a time. Because if you run it backwards, eventually the stars will all be touching each other, and clearly can't then behave exactly like stars do -- something else must have been going on.
Our modern answer does have such a time, and expansion. And the answer for why no stars shine before some time is that they took a while to condense into dense clumps from the initially quite smooth hot gas. What you see in the gaps between them is precisely this hot gas, at the moment it first became transparent to light, this is the microwave background radiation.
In their scenario of infinite time, matter which isn't lit up doesn't help. It would, like your eyeball, get the light of the stars from all directions, and would soon equilibrate to the same temperature as these surfaces.
> It would, like your eyeball, get the light of the stars from all directions, and would soon equilibrate to the same temperature
I see, that may be the crux of the paradox.
But if we assume that stars were born at some time then dark planets could be too. And if stars became to existence at some time it is not too crazy to think that new stars might be continually become into existence and planet too so new planets would get created continually to block the light.
If there's a time at which the stars are born, then there's no paradox. Non-star things can stay cold for the same reason comets stay cold in our universe: they can radiate heat in almost all directions (into the black sky) and receive heat from only a few (like the sun on a brief swingpast, still only < 1% of the sky).
But if the stars have been there forever, the comet is effectively in an oven of uniform temperature. The equilibrium state at which it radiates heat as fast as it gets it has the comet's surface the same temperature as the rest of the oven. So it glows.
