Moreland offers one more argument against beginningless traversals -- one he says was suggested to him by Dallas Willard (his mentor at USC). After a brief discussion of the nature of causal sequences, and how any given event depends on the actualization of every event in the causal sequence that led up to it, he expresses the argument as follows:

"...the present moment has as its ultimate chain of causal antecedents the entire history of the cosmos. If any past event has not already been actualized, then the present moment could not have occurred. This means that the past is actual and contains a specifiable, determinate number of events. This chain of events must have had a first member. Without a first member, there could be no second, third, or nth member in the chain where the nth member is the present event. But an infinite succession of past events would not have a determinate number of members nor would it have a first member. So if the past is actually infinite, the present moment could not have been caused; that is, it could not have come to be."[1]

In short, Moreland argues that the actualization of the present moment entails the finitude of the past. For the actuality of the present moment entails that its entire causal history has been actualized, since that is the causal chain upon which it depends. But the actuality of such a chain requires that it have a determinate, specifiable number of events, and that it have a first event. But if the past were infinite, it would meet neither condition. Therefore, the past is finite, and had a beginning or first event.

It will help to evaluate this argument if we express it a bit more formally:

1. The present moment M is actual.

2. If M is actual, then all the members of the set S of events that constitute M's causal chain have been actualized.

3. Therefore, all the members of S have been actualized. (from 1 and 2)

4. If all the members of S have been actualized, then S is constituted by a specifiable, determinate number of events, and S has a first member.

5. Therefore, S is constituted by a specifiable, determinate number of events, and S has a first member. (from 3 and 4)

6. If the past were beginningless, then S would not be comprised by a determinate number events and S would not have a first member.

7. Therefore, the past is not beginningless (from 5 and 6)

What to make of this argument?

Well, it's valid; so if the premises are true, then the conclusion follows of necessity. Furthermore: (3) follows from (1) and (2), (5) follows from (3) and (4), (7) follows from (5) and (6), and (1) and (2) look to be impeccable. That leaves us with (4) and (6). Why should we accept them?

For my purposes, I'll focus on (4). For I will argue that (4) is without sufficient justification, which is enough to undermine the force of the argument.

On to an evaluation of premise (4), then. Now (4) is a conditional statement, and its consequent has two conjuncts. We can thus split the conditional into two, viz.,

4a. If all the members of S have been actualized, then S is constituted by a specifiable, determinate number of events.

and

4b. If all the members of S have been actualized, then S has a first member.

Start with (4a). To evaluate the conditional, we'll need to know what Moreland means by a "specifiable, determinate number of events". A natural interpretation of the language is that it is meant to denote a number of events that can be specified by some natural number n. This reading is further supported by his use of such language in his discussion of actual infinites a few pages back, on p. 20. For there, he says that "a finite set has a definite number of elements which can be specified by counting the number of members in the set and assigning the appropriate number to that set. Thus, our set A had n=2 elements, and B had n=5." (italics mine) This interpretation is further confirmed by his use of the language in an argument we considered in a previous post -- the one on p. 29. In his argument there against the possibility of counting to infinity, he writes that at any point in such a count, one "can always specify the number he is currently counting. Furthermore, he can always add one more to what he has counted and thereby increase the series by one. Such a series can increase forever without limit, but will always be finite." (italics mine)

Thus, prima facie, it appears that by "specifiable, determinate number of events", Moreland at least means a finite number of events. But if so, then conditional (4a) asserts that the actualization of the causal sequence responsible for the present moment requires that the sequence be finite. But since that's the very point in dispute, Moreland can't just assert without argument that (4a) is true without begging the question against those antecedently convinced of the conclusion.

However, while Moreland doesn't explicitly offer an argument for (4a), he does offer a reason in support of (4b), and that rationale can be used to support (4a) as well. What about (4b), then? Well, that conditional asserts that the actuality of the present moment requires that its causal chain have a first member. But why think that? Recall Moreland's reason from the passage above: it's because "Without a first member, there could be no second, third, or nth member in the chain where the nth member is the present event." We can thus express Moreland's rationale as follows:

1. If the causal series S that led to the present moment lacks a first member, then S lacks a second, third, etc. member.

2. Therefore, S has a first member.

Unfortunately, (2) doesn't follow from (1). To get (2), we must add another premise:

1. If the causal series S that led to the present moment lacks a first member, then S lacks a second, third, etc. member.

1.1 S has a second, third, etc. member.

2. Therefore, S has a first member.

(2) then follows from (1) and (1.1) by Modus Tollens. Unfortunately, one cannot assert without argument that (1.1) is true without without begging the question against those who are antecedently unconvinced of the finitude of the past. For if the past is beginningless, then it has no second, third, etc. member, any more than the series ...-3, -2, 1 has a second, third, etc. member.

I'll belabor the point a bit more. Consider two epistemically possible causal sequences, represented by the following two series of numbers:

A: 1, 2, 3, ....

B: ...-3, -2, -1

Now it's of course true that any causal sequence of the sort that contains second, third, etc. events -- i.e., any sequence like A -- requires a first event. But of course, a beginningless causal sequence -- i.e., a sequence like B -- is precisely the sort that lacks second, third, etc. events. For a beginningless causal sequence is, by definition, a sequence that lacks a beginning, or first, event. Now of course, for all I've said, it could turn out that such an epistemically possible sequence like B is in fact metaphysically impossible. But the problem is that the metaphysical possibility of a causal sequence that lacks a first event -- i.e., the metaphysical possibility of a B-type causal sequence -- is the very issue in dispute here, and so Moreland can't just assume without argument that it's impossible without begging the question against the antecedently unconvinced. Unfortunately, though, that's precisely what Moreland seems to have done here.

===========================

[1] Moreland, Scaling the Secular City, pp. 28-29.

[2] in Moreland and Kai Neilsen's Does God Exist? The Great Debate (Thomas Nelson Publishers, 1990), pp. 197-217. That's where it is in my copy, anyway. The book has since been re-published with Prometheus Press.

[3] Ibid., pp. 203-204.

"...the present moment has as its ultimate chain of causal antecedents the entire history of the cosmos. If any past event has not already been actualized, then the present moment could not have occurred. This means that the past is actual and contains a specifiable, determinate number of events. This chain of events must have had a first member. Without a first member, there could be no second, third, or nth member in the chain where the nth member is the present event. But an infinite succession of past events would not have a determinate number of members nor would it have a first member. So if the past is actually infinite, the present moment could not have been caused; that is, it could not have come to be."[1]

In short, Moreland argues that the actualization of the present moment entails the finitude of the past. For the actuality of the present moment entails that its entire causal history has been actualized, since that is the causal chain upon which it depends. But the actuality of such a chain requires that it have a determinate, specifiable number of events, and that it have a first event. But if the past were infinite, it would meet neither condition. Therefore, the past is finite, and had a beginning or first event.

It will help to evaluate this argument if we express it a bit more formally:

1. The present moment M is actual.

2. If M is actual, then all the members of the set S of events that constitute M's causal chain have been actualized.

3. Therefore, all the members of S have been actualized. (from 1 and 2)

4. If all the members of S have been actualized, then S is constituted by a specifiable, determinate number of events, and S has a first member.

5. Therefore, S is constituted by a specifiable, determinate number of events, and S has a first member. (from 3 and 4)

6. If the past were beginningless, then S would not be comprised by a determinate number events and S would not have a first member.

7. Therefore, the past is not beginningless (from 5 and 6)

What to make of this argument?

Well, it's valid; so if the premises are true, then the conclusion follows of necessity. Furthermore: (3) follows from (1) and (2), (5) follows from (3) and (4), (7) follows from (5) and (6), and (1) and (2) look to be impeccable. That leaves us with (4) and (6). Why should we accept them?

For my purposes, I'll focus on (4). For I will argue that (4) is without sufficient justification, which is enough to undermine the force of the argument.

On to an evaluation of premise (4), then. Now (4) is a conditional statement, and its consequent has two conjuncts. We can thus split the conditional into two, viz.,

4a. If all the members of S have been actualized, then S is constituted by a specifiable, determinate number of events.

and

4b. If all the members of S have been actualized, then S has a first member.

Start with (4a). To evaluate the conditional, we'll need to know what Moreland means by a "specifiable, determinate number of events". A natural interpretation of the language is that it is meant to denote a number of events that can be specified by some natural number n. This reading is further supported by his use of such language in his discussion of actual infinites a few pages back, on p. 20. For there, he says that "a finite set has a definite number of elements which can be specified by counting the number of members in the set and assigning the appropriate number to that set. Thus, our set A had n=2 elements, and B had n=5." (italics mine) This interpretation is further confirmed by his use of the language in an argument we considered in a previous post -- the one on p. 29. In his argument there against the possibility of counting to infinity, he writes that at any point in such a count, one "can always specify the number he is currently counting. Furthermore, he can always add one more to what he has counted and thereby increase the series by one. Such a series can increase forever without limit, but will always be finite." (italics mine)

Thus, prima facie, it appears that by "specifiable, determinate number of events", Moreland at least means a finite number of events. But if so, then conditional (4a) asserts that the actualization of the causal sequence responsible for the present moment requires that the sequence be finite. But since that's the very point in dispute, Moreland can't just assert without argument that (4a) is true without begging the question against those antecedently convinced of the conclusion.

However, while Moreland doesn't explicitly offer an argument for (4a), he does offer a reason in support of (4b), and that rationale can be used to support (4a) as well. What about (4b), then? Well, that conditional asserts that the actuality of the present moment requires that its causal chain have a first member. But why think that? Recall Moreland's reason from the passage above: it's because "Without a first member, there could be no second, third, or nth member in the chain where the nth member is the present event." We can thus express Moreland's rationale as follows:

1. If the causal series S that led to the present moment lacks a first member, then S lacks a second, third, etc. member.

2. Therefore, S has a first member.

Unfortunately, (2) doesn't follow from (1). To get (2), we must add another premise:

1. If the causal series S that led to the present moment lacks a first member, then S lacks a second, third, etc. member.

1.1 S has a second, third, etc. member.

2. Therefore, S has a first member.

(2) then follows from (1) and (1.1) by Modus Tollens. Unfortunately, one cannot assert without argument that (1.1) is true without without begging the question against those who are antecedently unconvinced of the finitude of the past. For if the past is beginningless, then it has no second, third, etc. member, any more than the series ...-3, -2, 1 has a second, third, etc. member.

I'll belabor the point a bit more. Consider two epistemically possible causal sequences, represented by the following two series of numbers:

A: 1, 2, 3, ....

B: ...-3, -2, -1

Now it's of course true that any causal sequence of the sort that contains second, third, etc. events -- i.e., any sequence like A -- requires a first event. But of course, a beginningless causal sequence -- i.e., a sequence like B -- is precisely the sort that lacks second, third, etc. events. For a beginningless causal sequence is, by definition, a sequence that lacks a beginning, or first, event. Now of course, for all I've said, it could turn out that such an epistemically possible sequence like B is in fact metaphysically impossible. But the problem is that the metaphysical possibility of a causal sequence that lacks a first event -- i.e., the metaphysical possibility of a B-type causal sequence -- is the very issue in dispute here, and so Moreland can't just assume without argument that it's impossible without begging the question against the antecedently unconvinced. Unfortunately, though, that's precisely what Moreland seems to have done here.

===========================

[1] Moreland, Scaling the Secular City, pp. 28-29.

[2] in Moreland and Kai Neilsen's Does God Exist? The Great Debate (Thomas Nelson Publishers, 1990), pp. 197-217. That's where it is in my copy, anyway. The book has since been re-published with Prometheus Press.

[3] Ibid., pp. 203-204.

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