Infinity is weird. Take the sequence of natural numbers (1, 2, 3, etc.). Half of them are odd and half of them are even, right? Well sure, as long as you’re working with a finite sequence. You can count from one to any number you like, and it will remain true. But it’s also true you can multiply all those numbers by two and you’ll get a sequence of even numbers that’s just as long. That will also be true no matter how high you count, so it’s perfectly correct to say that in the infinite sequence of natural numbers, there are just as many even numbers as there are numbers. There really is no ratio between them. You can do something similar with the set of all positive and negative integers. If you arrange them as 0, 1, -1, 2, -2, and so on, you can write the natural numbers 1, 2, 3, 4, 5, etc. beneath them, and there will be a natural number for every integer. You’ll never run out no matter how long you go. So again, in the infinite set of integers, there are just as many positive (or negative) numbers as there are numbers.
It gets even weirder if you look at the set of rational numbers (numbers that can be expressed in the form of simple fractions: 1/2, 1/3, etc.). Obviously, there are infinitely many of these between any two of the natural numbers, right? Well, it turns out you can construct a sequence of the rational numbers such that all of them will be included exactly once, and it is therefore also possible to write a natural number beneath every number in that sequence. On any finite interval on a number line, there are infinitely more rational numbers than there are integers, but on an infinite number line, there are the same number, and thus there’s no ratio between them either.
When I think about these kinds of things very long, I can understand why Aristotle rejected the possibility of an actual infinity. It only gets more convoluted when you read about Georg Cantor proving that the irrational numbers can’t be ordered into a countable sequence and the implications that discovery had on mathematics. I’ve read a lot about set theory, but I only understand a tiny sliver of it.
I knew going into this chapter that I was going to disagree with Aristotle’s belief in an eternal universe, and I do, but I’ve found I don’t disagree quite as strongly with his arguments as I was expecting to. It does seem impossible that there could be a first moment of time or a first movement in time, and I agree it would be absurd to believe that time and motion could begin naturally. But then, arguing that universes can just start up on their own wouldn’t be a very good way of trying to prove our particular brand of theism, would it? The whole point of the cosmological argument is that a thing that definitely did happen absolutely can’t happen naturally.
Astronomers now find they have painted themselves into a corner because they have proven, by their own methods, that the world began abruptly in an act of creation to which you can trace the seeds of every star, every planet, every living thing in this cosmos and on the earth. And they have found that all this happened as a product of forces they cannot hope to discover. That there are what I or anyone would call supernatural forces at work is now, I think, a scientifically proven fact. —Robert Jastrow, Christianity Today, August 6, 1982
I’m assuming that the imperishability of motion is part of the overall argument for the unmovable mover. I guess my question is: would a challenge of change being eternal cause the whole argument to fall apart? Or can the core argument stand without it ?
Ha. I had no idea that the multiverse idea can trace it back that far.
Related to it, I find it interesting that the only solution at this time that agnostics/atheists offer to the fine-tuning argument is this. To me that only emphasizes how strong that fine-tuning argument is.
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