Is True Uniqueness Possible in an Infinite Universe?

[Alestair]

Because space and time are infinite, doesn’t that make it impossible for anything to be truly unique. I propose there are an infinite number of this planet right now in this universe. The distance between each planet is probably unconceivable. Also there is an infinite number of this planet in the past and in the future. Not only is there an infinite number of Earth's exactly the same as this one, there are also an infinite number of this planet with slight differences and infinite number with extreme differences. This possibility is opened up because time and space are infinite. Nothing can ever be unique.

 

[Gregg]

I think there are a lot of assumptions you have made which aren't necessarily true, like that space and time are infinite in ways which imply that our local configuration is repeated indefinitely in both.

 

[Integral]

So given what the OP said, how could you tell the difference between an infinite or a closed universe. If I set out traveling in some direction, in a closed universe I would, after some time, return to my starting place. But how can I differentiate between that or arriving at one of the duplicate planets in an infinite universe?

 

[CRGreathouse]

I see a number of assumptions in your post:
1. Space is infinite
2. Time is infinite
3. (1) and (2) imply that nothing is unique
4. There are infinitely many Earths (Earth = "exactly the same as this" planet)
5. The distance between the objects in (4) is "unconceivable".
6. (4) was and will be true (that is, together with (4), there are at least three points in time in which the generalization of (4) is true)
7. There are infinitely many near-Earths (near-Earth = "this planet with slight differences")
8. There are infinitely many foos (foo = this planet with "extreme differences")
9. Nothing is unique

I grant that, given (1), (2), and (3) your point (9) holds. But it's not obvious to me that any of (1)-(9) hold. Care to justify?

 

[matheinste]

Because space and time are infinite, doesn’t that make it impossible for anything to be truly unique. I propose there are an infinite number of this planet right now in this universe. The distance between each planet is probably unconceivable. Also there is an infinite number of this planet in the past and in the future. Not only is there an infinite number of Earth's exactly the same as this one, there are also an infinite number of this planet with slight differences and infinite number with extreme differences. This possibility is opened up because time and space are infinite. Nothing can ever be unique.

If we assume that space is infinite in spatial extension and time, an assumption not generally held to be true, I assume your assertion applies such a universe contains an infinite amount of matter or particles. Assume that is true. If we have an infinite number of configurations of this matter can we assume that among this infinite number of configuratiuons that all configurations will happen even once. Juggling with infinities is beyond me but the correct manipulations need care and are rarely intuitive.

Matheinste.