Simply put, Olbers’ thought was that if the universe were infinite with stars distributed equally throughout, then such stars would provide an infinite amount of light to shine upon any point in space. Even if dust inhibited some of the light, the sky would be brilliant at all times.
But the sky is dark.
How can that be? How can the universe have an infinite amount of light and yet offer its inhabitants a dark sky?
Ordinarily, the word paradox refers to a pair of statements that seem to contradict, but, upon closer examination, turn out to be unexpectedly compatible. In the case of Olbers’ Paradox, however, something different is going on. Some people are seeing a contradiction and concluding that the universe must not be infinite. Others are so committed to an infinite and eternal universe that they persist in calling it a paradox and trying to find a way that it can work.
History of Olber’s Paradox
Olbers’ paper on this subject dates only from 1823, but though he got his name on the idea, it seems to pre-date him by a good 200 years or more. Thomas Digges, who was the first to discuss Copernicus in English, and whose life falls between the death of Copernicus and the very early teaching career of Galileo, talked about the problem of so much light.
Shortly afterwards, in 1610, Kepler talked about it, and concluded that the universe must be finite.
The first detailed presentation was given by Lord Kelvin in 1901, and he proposed to resolve it by considering that the distance to some of the stars was so great that their light had not reached us. One wonders how such a state of affairs could arise, given that the light has an infinite amount of time for its travels, but of course the lives of individual stars are not infinite, so perhaps the universe proposed by Boltzmann was the right approach for maintaining the idea of a paradox.
A material totality
Still, this takes us back to the question of a genuine material totality.
- Material objects can be counted.
- An infinite universe with an even distribution of stars must have an infinite number of stars, which cannot, therefore, be counted.
- Therefore: there can be no such no such universe.
Boltzmann’s proposal, so far as I read it, did not necessarily present an infinite universe, just one so large that its parts did not interact. I wonder what he thought kept the parts apart?
But Kelvin was really going for infinity, and the reason for this was pantheistic at heart. Remember that if the universe is so segmented that its parts do not interact, then there is nothing scientific to say about any part except our own. Even the assertion that those other parts exist is not scientific. Why would you say it? Only because you find an infinite universe comfortable or because you are uncomfortable with the metaphysical implications of a finite universe. There’s less room for accident.
A matter of philosophy
Still, even if you have unworthy reasons for believing the material universe is infinite, unworthy reasons do not, by themselves, make a proposition wrong. False premises do not make a false conclusion; they make a conclusion with uncertain truth value.
So Jaki goes farther.
He states, as a point of philosophy, that countability is part of being material, and that there cannot be a collective material entity that does not have a countable totality. In other words, he is proposing a philosophical proof for the existence of a finite material totality.
At least this is how I understand his writing.
Note that since we are a part of the universe, it is not really like other scientific or astronomical objects. You can study all stars without taking human life into account – or all leaves or all bugs or all atoms. But the universe includes us, and its nature must be understood to include the fact of our presence.