(February 14, 2018 at 11:52 am)Grandizer Wrote:(February 14, 2018 at 11:25 am)SteveII Wrote: Hilbert's Hotel:
Imagine a hotel with a finite number of rooms. All the rooms are full and a new guest walks in and wants a room. The desk clerk says no rooms are available.
Now imagine a hotel that has an infinite number of rooms. All the rooms are filled up so an infinite number of guests. A new guest walks up and wants a room. All the clerk has to to do is to move the guest in room #1 to room #2 and the guest from #2 to #3 and so on so your new guest can have a room #1. You can do this infinite number of times to a hotel that was already full.
Now imagine instead the clerk moves the guest from #1 to #2 and from #2 to #4 and from #3 to #6 (each being moved to a room number twice the original). All the odd number rooms become vacant. You can add an infinite number of new guests to a hotel that was full and end up with it half empty.
How many people would be in the hotel if the guest in #1 checked out?
If everyone in odd number rooms checks out, how many checked out? How many are left?
Now what if all the guest above room number 3 check out. How many checked out? How many are left?
So from the above we get:
infinity + infinity = infinity
infinity + infinity = infinity/2
infinity - 1 = infinity
infinity / 2 = infinity
infinity - infinity = 3
Conclusion: the idea of an actual infinite is logically absurd.
infinity is not a number, lol.
The set of all positive integers is still the same size as the set of all even positive integers.
Also, what's 0/0? Or 6/0?
Is 0 logically absurd as well?
Leave Cantorian set mathematics to those who are qualified to work with it.
NOT SO FAST. You are not proposing Catorian set mathematics. You are proposing there are real infinities in the real word and Hilbert's hotel shows you what happens when you start talking about infinities in the real world--you get absurdities.
Quote:
(February 14, 2018 at 11:50 am)SteveII Wrote: Two things. First, he said that if the universe is finite in time and space, all of our calculations work.
He also said it's still a problem nevertheless.
Yes, a problem because the math/physics that are showing promise also don't indicate a past eternal universe--and so then begs for an explanation. He clearly does not say there is a problem with the math/physics that infinities would solve. The universe not being past eternal brings up metaphysical question he does not like--a problem for an atheist.
Quote:Quote:Second, he said that our best hope for an explanation is an infinite (in time and space) universe. He did not say that is what the theory is. He has no idea what that is but he realizes the consequences that if the universe is not eternal, an explanation is required for it. In other places he has called the universe a brute fact. By definition, if you consider something a brute fact, you have no explanation.
I thought the argument we're trying to make here is that it is a logical possibility. What theory did you want exactly?
Admitting the universe is a brute fact is the same as admitting you have no explanation. An explanation would be that it is possible that an infinite series of causes is logically possible. In other words, if your explanation is that a series of infinite past causes is possible, you are NOT saying the universe is a brute fact--you have an answer!
The problem is no one is saying that. The smartest atheists admit the universe is a brute fact.