Infinite time

I will be arguing that time had a beginning, that it is impossible for time to have gone back infinitely. Good luck.

My argument is, if time is infinite, we could not possibly arrive to the present.

If a series of past infinite events is infinite, then an infinite number of events would have to elapse before the present moment could arrive. But it is impossible for an infinite number of events to elapse. Therefore, if the series of past events is infinite, the present moment could not arrive. But the present moment has arrived. Therefore, the series of past events cannot be infinite [1].

Given the additional premiss that whatever begins to exist must have a cause, one concludes to the uncaused first cause of the temporal series of events.

There are so many paradoxes on infinite numbers. The problem is, things that deal with the physical do not often get along well with the infinite numbers. An example of this is Hilbert's paradox of the Grand Hotel [2]. It is a mathematical concept that is logically impossible. Likewise, infinite time is a mathematical concept that is logically impossible.

[1] Julian Wolfe and infinite time; William L. Craig
[2] http://en.wikipedia.org...'s_paradox_of_the_Grand_Hotel

Thanks to Con for providing an opportunity to debate such an interesting topic. This should be fun!

In this debate I will simply be arguing that it's possible (in a metaphysical sense) that the past be eternal or infinite. Since Con is arguing that time being infinite is impossible all I need to do is argue the that is not an impossible state of affairs; I shall not be arguing that it is actually the case that the past is eternal or infinite. That may or may not be the case (although I suspect that it's not the case).

To make things clearer Con is arguing against the possibility of an actual infinity [1] in two different ways. He has two considerations for this:

1) The impossibility of traversing an actual infinite number of past temporal events. This means, in short, that if an infinite amount of events had passed before the present there could always be one more event that could be added to the collection of past events thus we could never reach the present which is an infinitely distant point (and always will be infinitely distant). Since, obviously, there is a present moment there can be no infinite series of past events.

An analogy can be helpful: imagine someone who's task it is to count down to zero from an infinite amount negative numbers - it seems obvious they will never reach zero because they were will be one more negative number they can count before they reach zero.

2) He argues against the concept of an actual infinity by appealing to Hilbert's Hotel which is a hotel with infinitely many rooms and infinitely many guests. The absurdities come in when we are asked to consider the state of affairs where the hotel has no empty rooms for new guests yet new guests can be accommodated just by the simple task of the hotel managers putting the old guests in different rooms so they can free up rooms for the new guests. And this can happen an infinite number of times and account for an infinite number of new guests. The implications seem obviously absurd so therefore we should reject the concept of an actual infinity of anything.

I don't think these considerations are successful.

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Against 1)
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I think Con here is relying on an implicit assumption that makes this state of affairs seem obviously absurd here that I need not hold to. Once this is made clear the situation doesn't seem impossible. It seems impossible if one assumes that starting from a first event - an infinitely distant point in the past, a beginning - that one could never reach infinity (the present) because there is always one more event that can occur before the present occurs. But, if I reject this assumption and instead assume a beginningless past - i.e. no first event - then in reaching the "present" (infinity) one has already had an infinite number of events elapse because that was always the case at every point in time. To repeat: it'd always be the case that an infinite series of past events has elapsed if one assumes that there is no beginning point in time. The only reason 1) seems impossible is if you implicitly assume a beginning point. I conclude that it is possible for there to be a series of past events that are infinite.

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Against 2)
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I accept that the implications of Hilbert's hotel make it absurd and (metaphysically) impossible but reasoning from that analogy to the conclusion that this is a problem with all kinds of actual infinities is problematic because there are several disanalogous points here. [2] For one, the problems that Hilbert's hotel generates come from it's conjunction of several concepts with the concept of an actual infinity. Not from the actual concept of actual infinity itself. In the hotel all of the occupants and rooms exist together at the same time. Furthermore, all of the occupants and rooms are capable of being shifted around and moved into new rooms, or new rooms being built, etc. The shifting around of the occupants and all of these elements being present all the same time is what generates these absurdities. If all the occupants weren't present in the hotel at the same time there wouldn't be an issue at all because it'd just be a constant merry-go-round of guests and occupied and non-occupied rooms would alternately be filled and unfilled. If the occupants weren't capable of being shifted around to new or old rooms then the absurdities wouldn't follow. But notice that a series of past events is not analogous to Hilbert's hotel precisely because past events aren't possible to move around nor are they all present at the same time. So the absurdities that Hilbert's hotel generates are not a problem at all of the concept of a series of infinite past events.

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Sources
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[1] http://en.wikipedia.org...
[2] http://www.colorado.edu...

1) "It seems impossible if one assumes that starting from a first event - an infinitely distant point in the past, a beginning - that one could never reach infinity (the present) because there is always one more event that can occur before the present occurs." Alright lets look at this from a different angle. We shall use Pros counting analogy. How long would it take for someone to count from 1 to infinity? It would take forever, the counting would never end. Now let's reverse it. How long would it take for someone to count down from infinity to 1? It would take the same amount of time, i.e. forever. You see, it would take an infinite number of events forever to occur before the present. In other words an infinite number of events would never end and we would not reach the present. This is does not rely on whether or not there was a beginning event and is mathematically and logically impossible.

2) Hilbert's Hotel is not my main argument and was not necessarily meant to disprove infinite time. It is merely an example of infinities in the physical universe. The hotel can never be full. But infinite and infinite should be the same amount. The hotel should be full then with infinite guests, but it isn't. This is more of case to show the universe is finite. There are other paradoxes such as an infinite stack of books. Taking books out of the stack will do weird things.

What does finite time mean? (given that you don't disprove it)
a.It means that time needs a cause, as well as the rest of the universe. Only God could cause time, and time exists, therefore God exists.
b. Since God exists outside of time, he does not need a cause. Often people will claim that God needs a cause. But if God is infinite, not a physical being, and not constrained by time (in fact he created time) then this would not be the case.

Thanks to Mr. Carrol for his response but I fear it's inadequate to support his stated resolution and here's why:

1) Con here seems to miss my point. Con presupposes the very thing that I said is what I need not assume in order to defend the possibility of an infinite past. As I said in the first round if one assumes that there is no beginning in the past then at every moment in time an infinity of past temporal events has passed. Notice what this does - it makes the "problem" of traversing an actual infinite series of past events to reach the present quite tractable because since there was no beginning and at every point in time temporal infinity has past if you pick event in the past and try to go from that point to the present it only takes a finite amount of events to get there. Not infinite. There is no issue here. Con actually seems to make the same mistake in his own counting analogy. He confuses "counting all the numbers until you reach 1" with "counting an infinite amount of numbers until you reach 1". You do not have to count all numbers in order to reach 1 ("the present"/an actual infinite) because at every time if you are counting down from infinity to 1 () then you have counted an infinite amount of numbers. You just haven't counted all the numbers. There is a crucial distinction.

In any case, I think Con is grossly mistaken if he thinks that the concept of an infinite past is mathematically and logically impossible. For one, mathematicians work with infinity all the time. [1] It's hard to think that most mathematicians don't know enough about their field to know that infinity is "mathematically impossible". Second, there doesn't seem to be any logical contradiction in asserting that it's possible that the past be infinite. If there is Con has not shown it.

2) I actually granted that Hilbert's Hotel showed the problem with actual infinities instantiated by physical objects but as I noted in the last round this feature of Hilbert's Hotel cannot be generalized to a problem with all actual infinities - including an actual infinity of a series of pasts event. I showed this to be the case when I explicated how it's some features of the hotel like occupants and rooms being able to be shifted around and them existing together paired with an actual infinite that generates the absurdities. As I also noted last round these features are lacking when talking a series of infinite past events - you can't shift them around and they aren't present at the same time since temporal events happen in succession. There is not threat posed here by the hotel to a defender of the possibility of an infinite past.

Con seems to acknowledge that my point is correct when he says, "Hilbert's Hotel is not my main argument and was not necessarily meant to disprove infinite time. It is merely an example of infinities in the physical universe". But he seems to contradict himself a couple of sentences later when he says, "This is more of case to show the universe is finite". Which is it? How can it be true that the hotel illustration was not meant to disprove infinite time but it also shows that the universe is finite. If he means something like "spatially finite" (as in the universe can't have infinite space) then there's no issue per se, but, then, what does that have to do with the resolution? We are talking about a temporally infinite series of past events.

Con also mentions a library but I see no need to refute it because it is not developed. It stands as a bare assertion as of right now.

I won't be addressing his "what does finite time mean?" because he has not adequately supported his resolution. I will mention, however, the illicit shifting of the burden of proof I see here with his comment "(given that you don't disprove it)". It's not my job to disprove finite time. It's my job to prove it's possible that there exists infinite time. If anyone must do the disproving here it's Con as he has argued that "...time had a beginning, that it is impossible for time to have gone back infinitely." (Emphasis mine.)

Good luck.

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Sources
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(1) http://en.wikipedia.org...

Firstly, your sentences are very long, so please use more punctuation lest my mind explodes. Secondly, you put up better arguments then I've ever heard from any atheist. I'm not sure if that's a good thing or a bad thing. Anyway let's get back to the subject.

1) I did miss your point that "at every moment in time an infinity of past temporal events has passed" but still, I think this is impossible. My point is that a moment would never occur if an infinity of past temporal events occurred before it because an infinity of past temporal events cannot end. You're argument assumes that they can.
Then you go back into the number counting and you confuse me greatly. "You do not have to count all numbers in order to reach 1 ("the present"/an actual infinite) because at every time if you are counting down from infinity to 1 () then you have counted an infinite amount of numbers. You just haven't counted all the numbers." Wait, so were infinite numbers counted or not? Infinite numbers cannot already be counted or else the numbers would still be in the process of being counted. You are claiming that infinite time has already been traversed, but that is impossible.

My apologies for saying that the concept of infinite time is mathematically impossible as I am not a mathematician and cannot claim this. However, I still contest that it is logically impossible.

2) I agree with your points on Hilberts Hotel. It doesn't make much sense to the argument. When I said, "It is merely an example of infinities in the physical universe," I meant that infinities in the physical universe are impossible. I will not back this statement up because I am not intelligent enough to apply this to the entire universe. The stack of books analogy I heard from a friend, and since I cannot remember it, forget about it.

My apologies on the last paragraph. You do not have to address the statement, and I did not mean to shift the burden of proof. That was more of a typo than anything.

Thanks, Con, for the debate. It's been fun.

1) Con is wrong that my argument assumes that it is possible that an infinity of past temporal events in a strict sense. All I argued was that it is possible that the past is beginningless and by implication this shows that an infinity of past temporal events being traversed is possible. I have argued for this and Con has failed to provide reasons to doubt my arguments and his arguments in support of the resolution have been found wanting.

Con as stated he is confused by the idea of counting infinite numbers because if the infinite counter had counted an infinite amount of numbers he would have always be counting and would never reach 1 when counting down from infinity. There are a lot of problems with line of thinking but the obvious one is that there are infinite sets of different sizes or cardinalities. For example, if I counted down from infinity to 2,000,000 I have counted an infinite amount of numbers. Similarly, if I counted down from infinity to 1 I have also counted an infinite amount of numbers but obviously the first set I counted is not the same size as the second set of numbers but they are both infinite. I need not count all the numbers on the number line * to count an infinite amount of numbers. And that's the whole point. At every point counting down I'm counting an infinite amount of numbers and have thus traversed an actual infinite amount of numbers. This ties in nicely with my point about an actual infinite series of past events. I maintain that it's possible that the past was beginningless and thus at every point an infinite amount of past events had already occurred. Therefore and actual infinite has already been traversed in my scenario. There is nothing impossible (in the logical or metaphysical sense) about this state of affairs.

*Where n represents infinity.

Con still contests that the notion is logically impossible but, unfortunately, has done nothing to illustrate this except vaguely gesture in an indeterminate direction towards his argument. The burden of proof was on him to show that the concept is impossible.

2) Con has conceded my main points.

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