Olber's Paradox

Olber's paradox pertains to the logical ramifications of how the sky would appear at night--depending on whether there is a disparity between perception and the natural world beyond it, as I will address--if the universe had no beginning, had no spatial boundaries and thus is not expanding, and is populated by an infinite sea of stars.  Infinite in age (in other words, past-eternal), infinite in scope, and infinite in its number of stars (for it stretches on in all directions and is inhabited by celestial bodies, or else the physical universe would not be infinite in scope/size, leaving some metaphysical space empty), which would have had an infinite amount of time to come into being, this sort of universe was recognized as being contrary to what one sees when one gazes into the dark, star-spotted skies at night.

If there is an infinite array of stars in a universe extending endlessly in all directions, there would not be distinct darkness marking the night sky that is illuminated only at scattered points by stars. The night sky would be far brighter and more densely lit than what appears to us on Earth.  This would require that there is a sufficient number of stars to crowd the night sky in an unbroken, uniform light, which itself would mean that all starlight aimed towards the planet is visible regardless of distance.  Not even the fact that light takes time to travel distances would account for what is seen above us because there would have been an infinite amount of time that has elapsed, which is already an utter logical impossibility in itself independent of empirical evidence.  On the level of epistemological limitations and sensory perceptions, Olber's paradox, however, could still not logically prove that the universe is not metaphysically infinite in the aforementioned ways (that is impossible for non-empirical reasons).

There could be more stars that I cannot see although they exist, for instance, whether for some more practical, scientific reasons like these particular celestial bodies being obscured by some unknown laws of nature, or because of a more metaphysically explicit disconnect between my mental and sensory experiences and the external world of matter, such as if a grand eldritch being is manipulating my sensory experiences.  Also, there might not be stars at all, as unlikely as it seems; visually perceiving something, whether a building up close or a star in the cosmic distance, epistemologically proves nothing beyond that one's visual perceptions exist.  The correspondence of those perceptions to a material universe outside of the mind and its senses is entirely up in the air.  Thus, Olber's paradox only shows that if we are seeing the universe as it is, the universe would have to at least be finite in its boundaries (size), finite in its age, or dynamic instead of static with regard to expansion, because there is not starlight at every point in the night sky.

It is nevertheless true that the cosmos can be proven to have had and only to be capable of having a beginning, and this is due to logic instead of probabilistic scientific methodology.  The logical impossibility of an infinite number of past moments or causal events within those moments is absolutely certain since it is a logical necessity.  Whether it is units of time or a chain of causal events, an infinite amount leading up to this moment or whatever events are happening right now would mean that the present could never be reached.  An infinite amount of time or occurrences could never fully elapse in order for this moment and the events transpiring during it to arrive.  Thus, whether time and the universe have been around for a moment or billions or trillions of years, they cannot have always existed.

As a logical necessity, all of this is true by default and any scientific truths must be consistent with it to even be possible.  All the same, Olber's paradox does entail that scientific observations from the standpoint of Earth, if they reflect reality beyond our perceptions and not just our subjective experiences, disqualify a universe of eternal age, boundless spatial distance, and thus one that is not expanding (because it is already inhabiting infinite space).  It is only as a response to a very particular philosophical error refuted by pure reason or scientific assumptions that do not match the sensory evidence that one would ever need to bother with looking to the night sky and thinking about how stars, visible light, and the age or size of the universe would relate to the cosmos not being eternal, infinite, or static.