Infinite time

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