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Review of Sinnott-Armstrong's Morality Without God
Mark C. Murphy (Georgetown University) reviews the book for NDPR, here.
Rounding Up Posts: Moreland, the Kalam Argument, and a Beginningless Past
Here is a list of posts critiquing J.P. Moreland's four main arguments against the traversabilty of a beginningless past in Scaling the Secular City:
Part One
Part Two
Part Three
Part Four
Part One
Part Two
Part Three
Part Four
Moreland, the Kalam Argument, and a Beginningless Past, Part 4
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.
Moreland, the Kalam Argument, and a Beginningless Past, Part 3
Moreland offers an Aristotelian solution to one of Zeno's paradoxes as the basis of an argument against a beginningless past. Moreland sets up Zeno's Dichotomy paradox as follows:
"...Consider a runner who begins at some point A and who wishes to reach the midpoint between A and B. But before he can reach this midpoint, he must reach the midpoint of the midpoint. In order to move from any point to any other point, a runner must traverse an infinite number of points and this is impossible. Thus, [concludes Zeno] motion is an illusion."[1]
Moreland then argues that a structurally identical paradox applies to the hypothesis of a beginningless universe: he argues that if the past were beginningless, then the prospects of traversing all the events of the past to reach the present moment would be like those of Zeno's runner on the assumption that his task involved the traversal of an actual infinite: one couldn't even begin such a task, much less finish it.[2]
So Moreland thinks Zeno's Dichotomy paradox and his paradox for a beginningless past are structurally similar. His next step is to argue for a solution to the former, and then reason that, by analogy, the solution to the latter is thus similar. Thus, he argues that the most plausible solution to Zeno's Dichotomy paradox is to distinguish between an actual and a potential infinite, and to assert that the racer's task only involves the traversal of a potential infinite. And since all spatial distances that are merely potentially infinite are traversable in principle, the racer can traverse the whole track.[3] Similarly, the set of temporal distances in the universe's past is potentially infinite only, and thus finite. But that solution entails that the universe had a beginning. Therefore, thinks Moreland, the finitude of the past is justified.
What to make of this argument? One sort of worry about it is that it's not clear that the two paradoxes are sufficiently relevantly similar to justify Moreland's conclusion that their solutions are similar. For the runner's traversing task has a beginning or starting point; not so for a beginningless past. And the worry is that the feature that generates the problem in Zeno's Dichotomy parodox -- i.e., that the runner must start a task that has no starting point -- doesn't necessarily apply to a beginningless past. In other words, if the requirement of a start is merely a feature of Zeno's thought experiment, and not an essential property of traversals in general, then the grounds for thinking Zeno's runner's task is impossible do not provide grounds for thinking that traversing a beginningless past is impossible.
Now of course one might reply that it is an essential property of all traversals that they have a starting point. But the problem is that that's the very issue in dispute. For it's part of the very concept of a beginningless past that it involves traversing an infinite without a starting point. Therefore, whether or not such traversals are impossible, one cannot just assert the impossibility of a traversal that lacks a starting point without begging the question against the antecedently unconvinced.
By this time I'm no doubt belaboring the point, but here's a slightly more developed variation on the same worry: Roughly, the problem with the runner's task in Zeno's Dichotomy paradox is generated by the following inconsistent set of propositions.
1. The racetrack consists in a particular infinite open interval of spatial distances (IOISD).
2. The runner can traverse IOISD from the direction of the open "end".
3. The runner must start his traversal of IOISD if he is to engage in it at all.
4. All Infinite open intervals lack a first member from the direction of the open "end".
5. All intervals that can be traversed by starting have a first member.
For given propositions (1) and (3)-(5), Zeno's runner is required to start the traversal if he is to engage in it at all. But given that there is no starting point or beginning to the open "end" of the interval, it follows that the runner can never finish his traversal, on the grounds that he can never begin. He will thus forever remain "outside" of, or "external" to, the segment represented by the negative integers. And if that's right, then (2) is false, i.e., the runner cannot traverse IOISD from the open "end".
Now, at first glance, Moreland's paradox about a beginningless past looks sufficiently similar in structure to warrant a similar solution:
1'. The past consists in a particular infinite open interval of temporal distances (IOITD).
2'. IOITD can be traversed from the direction of the open "end"
3'. The traversal of IOITD must have a start if the traversal is to occur at all.
4. All infinite open intervals lack a first member from the direction of the open "end".
5. All intervals that can be traversed by starting have a first member.
However, at second glance, there are reasons for doubting that the runner's predicament in Zeno's Dichotomy paradox is sufficiently analogous to the case of traversing a beginningless past. For the reason why we're supposed to accept (3) in the former paradox -- i.e., that the runner's task must have a starting point -- is that Zeno stipulated that it have one. Now Moreland may be right that all traversals require a starting point. However, when it comes to the basis for accepting the parallel (3') in the latter paradox, something on the order of a mere stipulative ban on traversals without starting points is not going to cut it for those antecedently unconvinced of a finite past; they need a reason to think that it belongs to the very nature of a traversal that it has a starting point. But as we've seen, Moreland has so far failed to offer such a reason. Pending such a reason, then, traversals without beginnings remain epistemic possibilities for the unconvinced.
I conclude, then, that Moreland's use of Zeno's Dichotomy paradox fails to justify the claim that the past is necessarily finite.
===================
[1] Scaling the Secular City, p. 30.
[2] Ibid.
[3] Ibid.
"...Consider a runner who begins at some point A and who wishes to reach the midpoint between A and B. But before he can reach this midpoint, he must reach the midpoint of the midpoint. In order to move from any point to any other point, a runner must traverse an infinite number of points and this is impossible. Thus, [concludes Zeno] motion is an illusion."[1]
Moreland then argues that a structurally identical paradox applies to the hypothesis of a beginningless universe: he argues that if the past were beginningless, then the prospects of traversing all the events of the past to reach the present moment would be like those of Zeno's runner on the assumption that his task involved the traversal of an actual infinite: one couldn't even begin such a task, much less finish it.[2]
So Moreland thinks Zeno's Dichotomy paradox and his paradox for a beginningless past are structurally similar. His next step is to argue for a solution to the former, and then reason that, by analogy, the solution to the latter is thus similar. Thus, he argues that the most plausible solution to Zeno's Dichotomy paradox is to distinguish between an actual and a potential infinite, and to assert that the racer's task only involves the traversal of a potential infinite. And since all spatial distances that are merely potentially infinite are traversable in principle, the racer can traverse the whole track.[3] Similarly, the set of temporal distances in the universe's past is potentially infinite only, and thus finite. But that solution entails that the universe had a beginning. Therefore, thinks Moreland, the finitude of the past is justified.
What to make of this argument? One sort of worry about it is that it's not clear that the two paradoxes are sufficiently relevantly similar to justify Moreland's conclusion that their solutions are similar. For the runner's traversing task has a beginning or starting point; not so for a beginningless past. And the worry is that the feature that generates the problem in Zeno's Dichotomy parodox -- i.e., that the runner must start a task that has no starting point -- doesn't necessarily apply to a beginningless past. In other words, if the requirement of a start is merely a feature of Zeno's thought experiment, and not an essential property of traversals in general, then the grounds for thinking Zeno's runner's task is impossible do not provide grounds for thinking that traversing a beginningless past is impossible.
Now of course one might reply that it is an essential property of all traversals that they have a starting point. But the problem is that that's the very issue in dispute. For it's part of the very concept of a beginningless past that it involves traversing an infinite without a starting point. Therefore, whether or not such traversals are impossible, one cannot just assert the impossibility of a traversal that lacks a starting point without begging the question against the antecedently unconvinced.
By this time I'm no doubt belaboring the point, but here's a slightly more developed variation on the same worry: Roughly, the problem with the runner's task in Zeno's Dichotomy paradox is generated by the following inconsistent set of propositions.
1. The racetrack consists in a particular infinite open interval of spatial distances (IOISD).
2. The runner can traverse IOISD from the direction of the open "end".
3. The runner must start his traversal of IOISD if he is to engage in it at all.
4. All Infinite open intervals lack a first member from the direction of the open "end".
5. All intervals that can be traversed by starting have a first member.
For given propositions (1) and (3)-(5), Zeno's runner is required to start the traversal if he is to engage in it at all. But given that there is no starting point or beginning to the open "end" of the interval, it follows that the runner can never finish his traversal, on the grounds that he can never begin. He will thus forever remain "outside" of, or "external" to, the segment represented by the negative integers. And if that's right, then (2) is false, i.e., the runner cannot traverse IOISD from the open "end".
Now, at first glance, Moreland's paradox about a beginningless past looks sufficiently similar in structure to warrant a similar solution:
1'. The past consists in a particular infinite open interval of temporal distances (IOITD).
2'. IOITD can be traversed from the direction of the open "end"
3'. The traversal of IOITD must have a start if the traversal is to occur at all.
4. All infinite open intervals lack a first member from the direction of the open "end".
5. All intervals that can be traversed by starting have a first member.
However, at second glance, there are reasons for doubting that the runner's predicament in Zeno's Dichotomy paradox is sufficiently analogous to the case of traversing a beginningless past. For the reason why we're supposed to accept (3) in the former paradox -- i.e., that the runner's task must have a starting point -- is that Zeno stipulated that it have one. Now Moreland may be right that all traversals require a starting point. However, when it comes to the basis for accepting the parallel (3') in the latter paradox, something on the order of a mere stipulative ban on traversals without starting points is not going to cut it for those antecedently unconvinced of a finite past; they need a reason to think that it belongs to the very nature of a traversal that it has a starting point. But as we've seen, Moreland has so far failed to offer such a reason. Pending such a reason, then, traversals without beginnings remain epistemic possibilities for the unconvinced.
I conclude, then, that Moreland's use of Zeno's Dichotomy paradox fails to justify the claim that the past is necessarily finite.
===================
[1] Scaling the Secular City, p. 30.
[2] Ibid.
[3] Ibid.
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