This is something I came up with a long time ago, but I haven't been able to find, so I'll write it again.
In my arguments for the existence of God based on time, space, and material, I suggest that an spatially infinite universe has many bad implications . However, the implications are far too many to place in that post so I will enumerate them here.
No matter what goals you may have in life, an infinite universe makes them futile. (this assumes a non-deterministic philosophy, that people have choices)
In a spatially infinite universe, assuming that matter exists in some of it (space around us isn't totally empty), then there are civilizations and earths out there that are exactly like ours - exactly - down to every last particle. This is what happens when you work with non-mathematical things. Also, there are an infinite number of them. There are also earths that are slightly worse and slightly better than us.
Moral Excellence
There is someone out there with your name and your parents, house, children, job, and money that has made better choices, not hurt as many people, and deserves to live more than you do. There are also worse people. There is no such thing as perfection, accomplishing your goal. Someone exactly like you has already done better.
Advancement of Moral Civilization
Civilizations exist that began with our exact situation and are more moral than us, have not enslaved their populations, didn't have any wars, didn't mistreat women, and many other things. Eventually, assuming that civilizations continue to expand without dying out, that civilization will find ours and consume us. They may treat us well but all our efforts at advancement will have been for nothing, for we will be swept along by them. Likewise we may sweep along other lesser civilizations, but no matter how many we conquer, we will also be conquered.
Advancement of Science
Like morality, plenty of other places out there know way more than we do about science and will eventually find us and make all of our research irrelevant. We should sit here and do nothing.
Pleasure
If your main goal is to eat, drink, and be merry, you're missing out. You want to get as much happiness out of life as possible? There are an infinite number of people in your circumstances who have derived more pleasure out of life, sought pleasure with greater clarity and success, and had less negative side effects. Actually, there are people in your situation who have never felt pain, anger, sadness, loneliness, etc.
Being Content
Some may say that all of this is irrelevant. I'm content with what I have. I don't care about how successful other people are. Yes, sure. But other people are doing exactly what you're doing, pursuing contentment with their circumstances, with much greater success. They have completely eliminated annoyance at other people, greed for other peoples stuff, anger at their own situation, etc.
Anything Else: General Principle of Measurement
Whatever you have set out to do, or not to do, other people have been more successful. So successful in fact, that the little advancements you make are negligible in comparison to how far ahead they are, and the speed at which they are advancing.
Basically, if the universe is spatially infinite, all goals are meaningless. This actually applies to a time-infinite universe too. There has, at some point in time, been a person just like you doing what you're doing just now, who goes on to live such better life than you will, no matter what your strategy is, that it makes you look irrelevant in comparison.
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