(May 12, 2016 at 1:58 pm)LadyForCamus Wrote:(May 12, 2016 at 12:45 pm)SteveII Wrote: Defeater for P1: infinite regression of past causes is logically absurd.
But, but! You can't prove that the actual universe isn't an infinite regress, so therefore my premise is true and you have to agree with me!
Sound familiar?
No, not at all familiar. Sure you can prove that an infinite regress is absurd. I posted about Hilbert's Hotel awhile back. Here it is again:
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.