Infinite time

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