Here's another argument Moreland offers for the finitude of the past in Scaling the Secular City:
"...suppose a person were to think backward through the series of events in the past...Now he will either come to a beginning or he will not. If he comes to a beginning, then the universe obviously had a beginning. But if he never could, even in principle, reach a first moment, then this means that it would be impossible to start with the present and run backward through all the events in the history of the cosmos...But since events really move in the other direction, this is equivalent to admitting that if there was no beginning, the past could have never been exhaustively traversed to reach the present. Counting to infinity through the series 1, 2, 3, ... involves the same number of steps as does counting down from infinity to zero through the series -5, -4, -3, -2, -1, 0. In fact this second series may be even more difficult to traverse than the first. Apart from the fact that both series have the same number of members to be traversed, the second series cannot even get started. This is because it has no first member!" (p. 29)
Stripped down to its essentials, we can express the core of the argument as follows:
1. If the past is beginningless, then it’s impossible in principle to traverse from the present all the way through the past.
2. If it’s impossible in principle to traverse something in one direction, then it’s impossible in principle to traverse it in the other direction.
3. Therefore, if the past is beginningless, then it’s impossible in principle to traverse the past all the way to the present. (from 1 and 2)
4. But it’s not impossible in principle to traverse the past all the way to the present (after all, here we are!).
5. Therefore, that past is not beginningless. (from 3 and 4)
What to make of this argument? Well, it's formally valid; so if the premises are true, then the conclusion follows of necessity. Furthermore, I grant (1), at least for the sake of argument. Also, (3) follows from (1) and (2), and (4) is undeniable. That leaves us with (2). Why are we supposed to accept it?
One might think that (2) has a lot going for it, since all finite sequences are such that if one direction can be traversed in principle (at least mentally -- leave aside worries about actual traversals into the past), then so can the other direction (again, at least mentally).
However, one might worry that although this is so for finite temporal sequences, it's not obviously so for infinite temporal sequences. After all, there clearly are a number of differences between finite and infinite traversals. and pending further investigation, how can we be sure that no such difference makes a difference? Perhaps, then, we need a little more help before we're able to confidently accept (2).
Thankfully, Moreland doesn't leave us guessing as to his own reasons for accepting (2). For recall that he offered two such reasons. First, he argued that admitting that it's impossible in principle to start with the present and mentally traverse the whole past "is equivalent to admitting that if there was no beginning, the past could have never been exhaustively traversed to reach the present", on the grounds that "Counting to infinity through the series 1, 2, 3, ... involves the same number of steps as does counting down from infinity to zero through the series -5, -4, -3, -2, -1, 0."
What to make of his first argument for (2)? Now Moreland is clearly correct to say that there are the same number of steps in each direction of a beginingless history. However, it isn't clear that sameness in number of steps entails sameness in difficulty of traversal. In fact (and quite unlike finite traversals), there are several asymmetries in direction of traversal that seem relevant to difficulty or ease of traversal in a beginningless past:
(i) Going forward, there is an endpoint to reach; not so going backward.
One might believe that no infinite spatial or temporal distance is crossable on the grounds that it's self-evident that one cannot reach the end of that which has no end. Suppose we grant this. Still, this point only applies to the case of starting at the present and mentally traversing through a beginningless past; it doesn't apply to the crucial case here of a traversal from a beginningless past to the present. For the latter has an endpoint, viz., the current moment. Therefore, whether or not the intuition about the impossibility of reaching the end of that which has no end is correct, it doesn't support Moreland's premise (2).
(ii) Going forward, you don’t have to begin at some point; not so going backward. One might believe that no infinite is crossable on the basis of Moreland's argument discussed in the previous post, viz., that if one begins an infinite count from 0 or 1 to infinity, one will at every point be counting a finite number n, in which case the set that corresponds to n at that point cannot be put into a 1-1 correspondence with any of its proper subsets. Suppose we grant this. Still, this point only applies to the case of starting at the present and mentally traversing through a beginningless past; it doesn't apply to the case of a traversal from a beginningless past to the present moment. For the latter has no starting point. Therefore, unless and until Moreland (or anyone else) can come up with an argument that it's necessary for all traversals to have a beginning (a claim that Moreland repeatedly asserts without argument), Moreland's line of reasoning here is unsupported.
(iii) Going forward, some infinite traversal or other is completed at each point; not so going backward. This point is related to the last. One might believe that no infinite is crossable on the basis of Moreland's argument, discussed in the previous post, that if one tries to count to infinity by beginning at some point -- say, with the number 1 or 0 -- then one will never get over the hurdle of going from having counted a finite set to having counted an infinite set. Grant that this is true. But while this would then apply to the task of starting with the present moment and mentally traversing all the events of a beginningless past, it doesn't apply to the task of never starting -- but always counting -- from a beginningless past and then stopping with the present moment. For there is no such hurdle with such a task. For before every point in a beginningless past, some infinite set of events or other has already been traversed -- one is always on the other side of the hurdle, so to speak. Now as we have seen, Moreland thinks that traversals lacking a starting point are impossible; that is, he thinks that all traversals require a starting point. However, that is the very point at issue in the debate about the possibility of a beginningless past. For part of what it means to say that a beginningless past is possible is to say that a traversal without a beginning is possible. Therefore, Moreland can't just assume without argument that all traversals require a starting point without begging the question. I conclude, then, that Moreland's point here cannot serve as the basis for premise (2) of his argument.
Prima facie, then, there seems to be good reason to think that Moreland is wrong about this: direction of traversal does seem to make a difference with respect to difficulty of traversal. Or, more weakly: Given these asymmetries, at the very least we must say that Moreland owes us an explanation as to why they have no bearing on ease or difficulty of traversing a beginningless past. Pending such an explanation, it appears that Moreland's first argument for (2) is undercut.
What about his second reason? Here's the relevant part of the passage above: "In fact this second series [i.e., counting down the negative integers and ending at 0] may be even more difficult to traverse than the first [i.e., starting with 0 or 1 and then counting through all the natural numbers]. Apart from the fact that both series have the same number of members to be traversed, the second series cannot even get started. This is because it has no first member!"
What to make of this second argument for (2)? Well, we've already seen what is wrong with it in the previous post, so here I'll just summarize that discussion: of course a beginningless traversal could never "get started", but no one is claiming that it could. Rather, by the very nature of the case, a beginningless series has no beginning point from which it “got started”; if such a past is possible -- which is the very issue under dispute -- then it’s always been going, in the sense that prior to every event, there is another event that caused it. Furthermore, while it’s true that in traversing such a series you never get to a point in which a "first" infinite is traversed, this is only because some infinite temporal segment or other is already crossed at every point in a beginningless past. We also saw in a previous post that one is guilty of an illicit quantifier shift if from this one reasons that such a past would absurdly contain an infinite segment that was not formed by successive addition.
It looks, then, that Moreland's case for the crucial premise (2) is undercut. Thus, whether or not the past is finite, the arguments we've discussed from Moreland fail to give us a good reason for thinking so.
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