 This regress of events is very similar to the regress of natural numbers. In each case we start from the claim that there is a thing of a certain kind (a number or an event), and we have a principle that tells us that for each thing of that kind, there is another thing of that very kind that bears a certain relation to the previous one (it is its successor, or it is its preceding cause). We then have supplementary principles that rule out the other thing of that kind being any of the things on our list so far, thus forcing us to introduce a new thing of that kind, thus inviting the application of the principles to this new thing, and so on ad infinitum. But while the regress and resulting infinity of natural numbers is arguably unobjectionable, the regress of events seems problematic, because we have good empirical reasons to deny that there are infinitely many events, each preceded by another. For either that infinite sequence of events takes place in a finite amount of time or an infinite one. We have good empirical reason to rule out the latter option, since we have good empirical reason to think that there has only been a finite amount of past time: that time started a finite time ago with the Big Bang. And we have good empirical reason to rule out the former option, since the only way of fitting an infinite series of events, each preceded by another, into a finite stretch of time is by having the time between them become arbitrarily small. So for example, \(A_2\) might be a minute before \(A_1\), and \(A_3\) half a minute before \(A_2\), and \(A_4\) a quarter of a minute before \(A_3\), etc. If the time between events \(A_n\) and \(A_{n + 1}\) is always half the time between events \(A_{n - 1}\) and \(A_n\), we can fit infinitely many events into a two minute time-period. But this requires the time between events to become arbitrarily small, and there is some reason to think that time is quantized, such that there is a minimum length of time during which a change can occur, thus providing a lower limit on the amount of time that can separate two temporally distant events. (See Nolan 2008b for relevant discussion and further references.)