I've always been somewhat skeptical of the Kalam argument. But recently I've had a change of sentiment: I now think the argument is defensible--at least to someone with my background beliefs about time and causation. Previously, there were three obstacles to my confidence in the argument: (1) seeing how to justify the finitude of the past; (2) seeing how to justify the inference from the finitude of the past to the universe's having a genuine beginning to its existence; and (3) seeing why a cause of our universe should be a personal agent. (Others may face different obstacles.) Those obstacles have recently been removed for me. What follows is an autobiography explaining my shift in thinking.
The Finitude of the Past
Arguments against an actual infinity do not hold weight for me because I find it extraordinarily implausible that (i) propositions do not exist or that (ii) propositions exist, but there is only a finite number of propositions. I also have reasons to think that extended simples are impossible, and their impossibility coupled with the possibility of shaped objects entails the possibility of an actual infinite of concrete entities (because every top half of a shaped thing would itself have a top half, ad infinitum) So, I modus tollens the arguments against an actual infinite...
Arguments from physics hold some weight, but things get murky when it comes to events in the plank era, and there is always the question of whether our universe might have been caused by an event in a beginningless super-universe. It does seem to me simpler not to posit a super-universe whose contents can somehow produce matter ex nihilo, but an atheist can argue that this complexity is offset by the save in complexity from not having to posit a god. (I might argue back that the concept of a maximal being is theoretically simpler than any concept of a super-universe; a skeptic might counter-reply by pointing out that a maximal being introduces a new kind of thing; I might reply back by asking what is meant by "kind"; and so on.)
Arguments against the possibility of completing an actual infinite sequence of events have some intuitive appeal. But for me, the intuition is subtle, and there is always the question of whether I'm being misled by subconsciously conflating the scenario of completing an infinite task after starting it, on the one hand, and the scenario of completing an infinite task without starting it, on the other.
But recently, I've become convinced that an infinite series of past events is impossible after thinking hard about Alex Pruss's argument from the grim reapers (see his entry here and further developments here ). Thus, I now consider this obstacle removed (for me).
From a finite past to a beginning
A bigger obstacle for me has been the inference from a finite past to a beginning of our universe. The worry here is that God is supposed to have existed for a finite duration of time (on Craig's view anyway) yet lack a beginning. Why can't the universe be like that? Craig answers that it's because the universe never had a timeless state, whereas God has. I've had an idiosyncratic difficulty with this answer by virtue of my belief that there is no such thing as a timeless mode of existence (better: my lack of belief in the intelligibility of 'timeless existence'). Plus, if there can be timeless states, then why couldn't the universe itself have sprung from a timeless state? Why think state-event causation is impossible?
Staring out a car window, blurred trees and grass before me, a light-bulb flashed in my mind. I had been wrong--foolishly wrong--to think that something could exist for a finite amount of time, have no prior non-temporal state of existence, and yet not have begun to exist. If a pen cap has existed for a finite duration of time (and has no non-temporal state), then that pen cap just obviously had a beginning--no matter whether other things happened to exist earlier than it or not. Somehow that just seems as obvious as can be to me now. (If it isn't to you, I can only recommend thinking hard about what it means for something to have existed for a finite duration of time, perhaps while looking out a car window.) This means that unless the universe is preceded by a non-temporal state, it had a beginning. I don't think the universe was preceded by a non-temporal sate (because it's essentially changing, I think), so I think the universe had a beginning.
However, suppose the universe was preceded by a non-temporal state. And suppose state-event causation is possible: a non-temporal universe can become temporal. Assume that's what in fact happened, and call the event of its happening E. E is the transition from the universe's being non-temporal to its being temporal. As such, it is intrinsically temporal. Since its duration is finite, E--like every event--had a beginning (to its existing or to its obtaining, depending on one's view of events). I'll argue in the next section that E must either record an uncaused, free will choice or be caused by a series of events initiated by a free will choice. So, this isn't a way out for the naturalist (if I'm right below).
Ok, but if the universe had a beginning, what about God? If the only way to avoid having a beginning is to have a timeless state (assuming a finite past), what about my complaint that timeless existence is unintelligible? Well, I thought of a way to define 'x is timeless' that is consistent with my views about time (in particular my view that necessarily, whatever exists is present).
'x is timeless' =def 'x exists, and there is no t, such that t is a time,' where
't is a time' =def 'there is an x, such that t is earlier than x, or t is later than x' ('earlier than' and 'later than' may be treated as primitives.)
I'm not out of the woods yet because I said that x exists and that whatever exists is present. How can something be present yet not exist at a time? Answer: by being included (its existence entailed) by the maximal proposition that is tenselessly true. In other words, analyze away tense the Tom Crisp way (see his Presentism and The Grounding Objection). The result is that a thing can be present without being in a state of becoming or change (perhaps the type of state that "irreducible tense" is supposed to pick out by those who think tense is irreducible). Times enter the picture when there is change, because as soon as there is a changing thing, there is, of necessity, a future and thus maximal propositions (times) related by earlier than and later than relations. But prior to change, there is no time in the sense defined above. All of this seems to me coherent and intelligible. Thus, I no longer have an obstacle to saying that the universe began to exist but God did not.
From a first event to a personal cause
I considered this to be the biggest obstacle. Why should a cause have to be a person just by virtue of having a timeless state? (I've sympathetic to Morriston's published worries.) Nevertheless, I've come to find the following argument for personhood plausible:
(1) Every event has a cause.
(2) There was a first event E [by a grim reaper argument]
(3) Therefore, E had a cause.
(4) Circular causal chains are impossible.
(5) Therefore, the cause of E was not an event [because E was the first event].
(6) If the cause of E was not an event, then it was the action of a personal agent (what else?).
(7) Therefore, E was caused by the action of a personal agent.
If someone complains that actions are themselves events, then I suggest dropping (6) and modifying (1) to
(1*): Every event that isn't the freely chosen action of a personal agent has a cause.
(Note: it is consistent with the argument that every freely chosen action has an explanation.)
I personally find each of these premises plausible (or supportable), independently of any beliefs I might have stemming from the conclusion. Therefore, I now think the kalam argument constitutes a good argument. At least that's how things seem to me. Others, as I've suggested, may have different obstacles to contend with.
Josh:
Here's an argument for "From finite past to a beginning." It seems as obvious as anything can be that anything that had a first moment of existence--a time at which it existed but prior to which it did not exist--had a beginning at that first moment of existence. But if the Grim Reaper argument works, it establishes the impossibility of a backwards infinity of times, from which it follows that each thing that exists in time and does not exist timelessly has a first moment of existence. (Proof: For a reductio, suppose x exists in time and does not exist timelessly and has no first moment of existence. Then if it exists at t(0), it has a previous moment of existence in time, say t(-1), and then a previous, say t(-2), and so on, contrary to the conclusion from the GR paradox.)
Here are some worries about your definition of tenseless existence, though.
Objection 1: You need some serious modifications of Crisp's view. For on Crisp's view, a time is any maximal consistent proposition. Let t0 be the present time--this is the maximal consistent proposition that is true. Either t0 does or does not include the claim that God exists. If it does include the claim that God exists, then God exists at t0, which seems contrary to his tenseless existence, unless you want to say he exists both tenselessly and in time (in which case the second objection below will have to be used). If it does not include the claim that God exists, then the maximality of t0 implies that t0 is not compatible with the existence of God. But then you have the consequence that something not compatible with the existence of God is true, from which it follows that God does not exist.
Objection 2: Maybe the suggestion is that in addition to God's existing at the present time, God also exists tenselessly, because he exists at a tenseless quasi-time (a maximal proposition that is not a time, because it has not before or after). But if one counts as existing tenselessly if one exists at a tenseless quasi-time, then any possible tenseless being is actual. For any possible tenselessly existing being exists at a tenseless quasi-time. But do we really want to be committed to the view that there could not be a tenselessly existing being other than God, and so by definition of tenseless existence?
Objection 3: Suppose I exist at only one time, t0. This does not make me timeless, tenseless or anything like that. Rather, it makes me maximally fleeting and ephemeral. Suppose, further, that everything else that is temporal also exists at t0. That does nothing to make my existence be any the less fleeting--it's entirely an extrinsic fact. Add, further, that t0 is a last time--a time after which there is no time. This does nothing to make my existence be less fleeting. Add, finally, that t0 is a first time--a time before which there is no time. This does nothing to make my existence be less fleeting. But after we do all this, then t0 is what I've called a "tenseless quasi-time": it is a maximal proposition that has no before or after. If we like, we can even add two more posits that seem not to affect things: there couldn't be an earlier or a later time.
Alex,
Thanks, those are important worries. Let's see if I can make some clarifications.
Objection 1: I say: always, all things exist "tenselessly" in the sense that one can grasp the fact that they exist without grasping a time (cf. Crisp 2007). The property of existing tenselessly neither entails nor precludes the property of changing. Now consider the maximal prop t0 that was true prior to the existence of any change. t0 is a time because it is earlier than all other times. However, necessarily, if t0 is true, then t0 is not earlier than anything and so is not a time. t0 is not earlier than anything because it doesn't record any changing things, and only change entails a future... Is this making any sense?
So, yes, t0 includes the claim that God exists. When t0 was true, t0 didn't count as a time because there was no future. But then by virtue of God's creative choice, change entered reality and along with it the flow of time (that is, a certain set of maximal props became related by earlier than/later than relations).
Objection 2: The suggestion is not that he has both timeless existence and temporal existence. It's that he had timeless existence but now exists at a time. I see no problem with saying something was timeless, because I see no problem with saying WAS, [t0 IS not a time].
Objection 3: I need to think more about this. My initial reaction is to simply suggest that if I exist at only one time, then I'm maximally fleeting only if reality contains change (because fleeting connotes change), but if there is no change--no future or past--then I'm not fleeting. But I wish to think more about smallest units of change and the implications of existing at a single time...
I take it that you are denying the principle:
1. If at t1: t0 is earlier than t1, then at t0: t0 is earlier than t1.
Isn't that really weird? How could facts about sequence change?
Moreover, isn't there going to be a problem with God's omniscience or even deliberation at t0?
Presumably, at t0, God is deliberating, no? After all, the argument requires that God as he is at t0 is the cause that gets everything else going. But what is he deliberating about? Presumably about what sort of a world there is to be when there is time. But I am not sure you have any coherent way of making sense of this deliberation. He can't, for instance, be deliberating about what is to happen at t1, because the contents of t1 are an essential property of t1.
I think the only answer is something like this. Say that a "fiber" is a maximal collection of times linearly ordered by earlier-than. Now, from our temporal point of view, we can identify one of the fibers as actual--the actual fiber is the one that contains the present time, i.e., the time that is true. At t0, God is presumably deliberating over which fiber is to be actual (where "is to be" should not be taken to be a concealed future tense). But if so, then we cannot any longer define a fiber as actual in terms of its containing a true time. For: at t0, either t0 is a member of no fiber, or it is a member of exactly one fiber, or it is a member of every fiber. In the first and last case, the deliberation makes no sense. So, suppose that at t0, t0 is a member of exactly one fiber. But then by the definition of the fiber, it is true at t0 that t0 is temporally connected with everything else in the fiber. But if at t0, t0 is not temporally connected with any other time, it follows that the fiber must consist of the singleton { t0 }. And since t0 does not, on the view on the table, contain information about what things "will" happen, it does not seem right to say that what God is deliberating about is t0.
Interesting paradox in the title:
"I was wrong about the Kalam argument (maybe I still am)."
Is that like the following:
"I was wrong about X, but I don't fully believe I was wrong about X (because perhaps I was wrong to believe I was wrong about X)."
Or maybe Josh is unparadoxically worried that he is wrong in a different way? For instance, maybe he's worried about the coherence with presentism of the conclusion of the argument? :-)
It's more that I realize that being wrong about something once gives me reason to be cautious--maybe I'm wrong about being wrong, though I don't believe I am. :)
Alex,
Yes, I am committed to denying (1) that
1. If at t1: t0 is earlier than t1, then at t0: t0 is earlier than t1.
That's a consequence of t0 entailing that there be no times. I don't know if that's weird. What might be weird is if facts about sequence could change even after there is a sequence (though that may be what an open theist would say).
I don't see a problem with omniscience. What true proposition would God fail to know?
As for deliberation, I'm not sure I understand what you mean by "maximal" collection of times. Is the actual fiber at t0 maximal? I think of it this way. Let a "fiber" be a proposition that specifies the temporal relations between whatever times there are. At t0, there are no temporal relations between any times, so no fiber is true. God deliberates over which fiber is to be true. (Or more accurately, he deliberates over which universe to make, where the making of that universe entails that a certain fiber, or part of it, is true.) The actual fiber is simply the true one. Does that make sense?
To Pruss:
Yeah, but where's the fun in that? ;)
We coulda had a new paradox: Rasmussen's!
Since I'm not convinced by the Grim Reaper argument (I actually think Hawthorne's solution is correct), I'm not sure if I can endorse the impossibility of past causes. But there's another argument that I find in Aquinas that gets the same result in terms of the cosmological argument that I do think is sound. It isn't so much against the infinite past or against the inference from a finite past to a beginning but against an infinite succession of causes with no ultimate ground for the whole series.
If A is caused by an earlier cause B, and B is caused by an earlier cause C, then merely appealing to B does not fully explain A, because it doesn't yet provide the explanation for B. We need C for that. But we then need a cause for C. No matter how far back we go, we will still need further causes, or we still won't have explained A fully. Does it help to appeal to an infinite succession of causes, then?
Aquinas says no, as I read some of his arguments. Unless we have a first cause that is itself fully explained, we never have a complete explanation for A. Even if we simply take the whole series of causes as the explanation, it's not enough, because we haven't explained why that series exists rather than a different series of causes or none at all.
A simpler way to put it is that a series of contingent things, even if it's infinite in extent, does not explain why there are any contingent things, because the sum total of all contingent things is contingent and needs something external to itself to explain why there are any contingent things at all. This is one of the things Aquinas means when he says an infinite series of past causes isn't going to do it.
I don't have much patience with the idea that something can first be timeless and then (which implies temporal succession) be temporal. Craig says he's aware of this problem, but his language describing his view makes me suspect he isn't. The only way I can conceive of the view in any way that's metaphysically possible is that there is a timeless aspect of God in a point-dimension just like the atemporalist holds but that God is also fully in time in another respect. The before/after language Craig uses is thus completely misleading as to what the view must be for it to work.
If that's right, then I don't know how it helps to say that the universe is both in the eternal atemporal moment and in time. That wouldn't explain how its first temporal moment came to occur, would it? If the universe is contingent, you'll still need an explanation of what explains why this contingent thing occurs. If it's necessary, then nothing is contingent unless something other than its existence is contingent but somehow also caused by the necessary universe. I'm not sure what that might be. The personhood account does do much better, since it can be the person's contingent choice to create (which I think can be a simpler argument than what you present, since it doesn't need to assume a finite past).
Jeremy, it sounds like you like a version of the argument from contingency. My own sense is that the arg from contingency is 3 times more powerful than the kalam (at least to me), and for a long time I didn't see any way of defending the kalam without recourse to a principle of explanation that could be used in a cleaner, easier, more plausible argument from contingency (one which doesn't even require a finite past). But my recent thinking is that the kalam might be defensible without having to make recourse to principles that would allow the easier arg from contingency go through.
Josh: I admire your intellectual integrity in the way you now profess to accept (however waffling-like) the Kalam Cosmological Argument. You explain this important shift in your thinking about the KCA in three stages. The first pertains to The finitude of the past. After due reflection you have concluded that “Alex Pruss’s argument from the grim reapers … Thus, [you] now consider this obstacle removed.” But I am afraid that your conclusion here has been improvidently made.
In the first place, Alex’s argument from the grim reapers http://prosblogion.ektopos.com/archives/2009/10/from-grim-reape.html) involves a scenario in which “we have a contradiction; [Fred] both was and was not killed.” Alex acknowledges “that there are many sets of timings for GRs that do not give rise to a paradox. It is only with certain sets of timings that paradox arises. So there is no problem with GRs per se.” (AP, October 4, 2009 11:11 AM.) The particular scenario-generated contradiction does not, in my opinion, warrant the conclusion that “there cannot be a backwards infinite sequence of events.” It does warrant the conclusion, however, that the scenario-generated contradiction is a metaphysically impossible state-of-affairs—even for an omnipotent God.
It is important to notice that the relevant period of question began at 11:00 am, when Fred is alive, and ends at 11:02 am, when “Fred is certainly dead.” Within that time frame there are infinitely many times after 11:00 am at which infinitely many GRs are respectively set to go off in a staggered way. The scenario therefore involves a scheduled backwards infinite sequence of events within a closed temporal interval. It thus involves an infinite yet to elapse or be traversed—quite unlike a traversed or elapsed infinite temporal series of moments or events as to which there never was a moment when there was an infinite yet to elapse or be traversed. So taking the most charitable interpretation of the GR scenario all that we are warranted in concluding is that a backwards infinite sequence of events within a closed temporal interval is metaphysically impossible. And this conclusion is fully in accord with my own view. It is also my view that a backward infinite sequence of events of finite duration with an open first temporal interval is metaphysically impossible.
Alex stated that “[t]he Kalaam argument needs the premise that there couln’t be a backwards infinite sequence of events.” But this is woefully not accurate. What the KCA needs is a premise that there cannot be any infinite temporal series, whether or not of infinite duration. So Alex’s GR argument fails to establish that any backwards infinite sequence of events of infinite duration is metaphysically impossible.
Josh, you also discuss matters under the rubric, From a finite past to a beginning. Assuming arguendo that any infinite temporal series of infinite duration is metaphysically impossible, your salient point for my purposes is your assertion that you “don’t think the universe was preceded by a non-temporal [state] (because it’s essentially changing …” I am quite willing to agree that this universe is essentially changing. I think, however, you are jumping the gun in concluding that this universe, if indeed it began to exist, could not have been preceded by another material universe that was not essentially changing prior to the event constituting the beginning of this universe. Quite obviously the proto-universe in question would have to be radically different with respect to its components and structure. (I think it would be more plausible to say that this pre-universe was characterized by a non-changing state until the time of the beginning of our universe, rather than to say it was characterized by a non-temporal state.) It seems to me that it is per se somewhat less antecedently improbable that the supposed beginning of this natural universe was caused by a natural event involving a proto-universe that had previously been in a non-changing state than that the beginning was caused by an event involving a supernatural being that was changeless before that event. Since I believe that the temporal series of moments or events constituting or including the history of this universe is an infinite series of infinite duration, were I to believe that this universe began to exist and that this beginning was supernaturally caused I would then believe that the supernatural agent was an essentially temporal and changing being sans creation.
Last you discuss matters under the rubric, From a first event to a personal cause. Your argument concludes with the proposition that the first event E was caused by the action of a personal agent, the action not itself being an event. Like you (until your recent change of mind) I have many worries about the creation of this universe with an absolute beginning of time by a supernatural agent who sans creation is atemporal or at least changeless. Since the otherwise implausible conclusion that the Creator is essentially atemporal and/or changeless personal being sans creation is driven, as it were, by the premise that any infinite temporal series is metaphysically impossible it seems to me we should on that account alone be very cautious before concluding that the KCA is sound.
Josh:
"God deliberates over which fiber is to be true."
But what does that mean? At t0, God knows that only one fiber is true--the one that contains only t0, since at t0 there is no future. If God knows that there is no future, how can he deliberate over what if any future there will be?
The eternalist has a similar problem. God is at the actual world w0, and knows that he is at w0. How, then, can he be deliberating whether to actualize w0 or to actualize some other world w1, given that he knows that w0 is what is actual? The eternalist has this answer: "That God is at w0, and that God knows he is at w0, are explanatorily posterior to his deliberation." But I do not think you can make this move. For that God is at t0 is not explanatorily posterior to his deliberation.
Arnold,
Thanks for that. It seems to me that the possibility of a GR scenario is plausibly inferred from the possibility of an infinity of past events given certain general recombination principles. See e.g. http://prosblogion.ektopos.com/archives/2009/10/two-more-argume.html#comment-107275.
Alex,
Hmmm... Is the problem with deliberation, or is it with the thought that there could be no future at t0 but then after t0, there is a future?
Let's see if this clarifies anything:
at t0, it is true that there are no times. For example, the proposition P that Earth exists stands in no temporal relation to t0, at t0. Now there is a fiber F that includes the proposition that P is later than t0. F is false at t0. But at t0, it is possible that F is later than t0. (Note: that isn't to say that it is possible that at t0, F is later than t0.) If at t0, it is possible that F is later than t0, then couldn't God at t0 deliberate over whether or not to decree F? If so, then we've isolated your concern to this sort of proposition: at t0, it is possible that F is later than t0. Yes?
I am not sure the possibility issue is all there is. Not everything that is possible can be deliberated over. It is possible that the world came to an end yesterday, but this cannot be deliberated about, either by me or by a God who is in time.
Let's try this tack. Consider a paradigm case of human deliberation. I am deliberating (contrary to fact, because in actuality my quizzes are randomly set by my looking around for an inscription of a number in my vicinity and seeing if it is divisible by three) whether to have a quiz tomorrow. So, now at t0, there is a proposition, p, that is the object of my deliberation: that there will be a quiz tomorrow (or at t1).
Observe three features which seem important:
A1. I do not know with certainty that ~p
A2. p is about a future time
A3. I do not know with certainty that there will be no future time
Now, in your case, we have:
B1. At t0, God knows with certainty that t0 is actually true, and hence God knows that ~p
B2. At t0, p is not about a future time
B3. At t0, God knows with certainty that there will be no future time.
So, there seems to be a rather radical disanalogy between the two cases. It would be as if I knew with certainty that that I will not eat lunch, and I was deliberating whether to each lunch, or I knew with certainty that there will be no tomorrow, and I was deliberating where to go to lunch tomorrow.
Now, I think it may be possible for God to know that ~p and yet to deliberate over p. In fact, anybody with standard views about omniscience--whether taking God to be in or out of time--has to say this. But in that case, we have to either say that God brackets his knowledge while deliberating or that his deliberation is explanatorily prior to (though coeternal or simultaneous with) the knowledge. The explanatory priority does not, I think, apply, because God's being at t0 is not explanatorily posterior to God's decision, say, to make horses.
So maybe God at t0 brackets his knowledge that there is no future. But that's weird, isn't it? Surely the knowledge that there is no future is highly relevant to deliberation!
(6) If the cause of E was not an event, then it was the action of a personal agent (what else?).
Wasn't "The personal agent chose to create" an event?
You would have to argue that this event was caused by the agent's desires - but what caused the causing?
Alex,
Thanks for thinking through that. This is really tricky. Let's see if this helps:
Let P be the proposition that there will be an earth. At t0, P is false and God knows it. Your worry, if I'm understanding it (and I may not quite be), is that it's hard to see how God could deliberate over P if God knows that P is false. But I say that although P is false, P could be true and could be made to be true. Thus, God deliberates over whether or not to decree that P is true, though during the state of deliberation, P is false. The key is that P can change from being false to being true. This sort of situation is unique to t0, so it's hard to make analogies. For example, if I believe that some event won't happen, then I also believe that there's nothing I can do to make it the case that the event will happen. But at t0, things are importantly different: at t0, God believes that it's false that there will be an earth, yet according to my hypothesis, God believes that there's something he can do to make it the case that there will be an earth.
Mathis,
Good question. My sense is that free agent causal acts are themselves uncaused. If such acts count as events (I'm not sure they do), then those are the only kinds of events that are uncaused because those are the only kinds of events that couldn't be caused.
Josh:
But it's also true at t0 that God knows that he doesn't do the thing that would be needed to make P be true.
Josh: In your terse reply posted November 9 to my comment of November 7 the only thing you write is that “it seems to [you] that the possibility of a [Grim Reaper] scenario is plausibly inferred from the possibility of an infinite of past events given general recombination principles. See e.g., http://prosblogion.ektopos.com/archives/2009/10/two-more-argume.html #comment-107275" [October 20, 2009, 12:03 pm]. I imprudently failed to address the content of the comment just referred to because it had appeared to me to endorse the erroneous notion that an infinite sequence of events yet to elapse or be traverse is metaphysically possible—a notion also presupposed by the GR and RGR scenarios as respectively presented by Alex Pruss in his post “From Grim Reaper to Kalaam” (http://prosblogian.ektopos.com/archives/2009/10/from-grim-reape.html) and in his “Two more arguments against the infinite past” {http://prosplogian.ektopos.com/archives/20009/10/two-more-argume.html); a notion which I had addressed in my November 7 comment. But I now think I had better explicitly address your comment of November 9 lest it be rashly thought that I am in dialectical retreat.
In your October 20 comment (comment 107275) you include “Axiom 6: “If there can be an infinity of past events, then there can be an infinite series in which each event results in the existence of a GR.” Given this and the other axioms, you conclude with: “Theorem: If there can be an infinity of past events, then there can be a paradoxical GR scenario.” In my opinion the theorem provides an insufficient basis upon which to conclude that any infinite series of past events is impossible. What the premises of your argument warrant is the conclusion that a particular infinite series of past events each event resulting in the existence of a GR, together with the axioms stated in your system, makes possible a paradoxical GR scenario. Hence it does not follow from the premises of your argument that the temporal series constituting or including the history of this physical universe cannot be infinitely many and of infinite duration since no GR exists or has existed in this our universe.
Alex presents his randomized GR scenario in his comment of October 12 (Two more arguments) in which he concludes that a contradiction obtains as to whether Fred is alive at every time after noon, said “contradiction now ensu[ing] from the supposition that there are infinitely many RGRs.” More specifically his argument includes “the following premises: 9. Possibly there exists an RGR. 10. If possibly there exists an RGR and there were infinitely many past events, the possibly there exist infinitely many RGRs. And from infinitely many RGRs we get 7 and 8, which are contradictory.”
Jeremy Price, in his comment of October 16, astutely protests that these arguments [by Josh and Alex] do not show why an infinite past is impossible since they “seem to [Jeremy] have the following form:
1. An infinite past does not rule out X.
2. X is impossible.
3. Therefore, an infinite past is impossible.”
Alex, in his reply of October 17, corrects Jeremy, stating:
“I think the logical form of these arguments is this:
1. If an infinite past is possibly, then by a plausible rearrangement principle, P is possible.
2. But P is not possible.
3. Therefore, an infinite past is not possible.”
Alas! It seems to me that Alex did not accurately present the true logical form of the arguments in question. The true logical form is:
1. If an infinite series of past events pertaining to infinitely many RGRs [or GRs], then by [a] plausible rearrangement principle[s] then the RGR [or GR] paradox is possible.
2. But the RGR [or GR] paradox is not possible.
3. Therefore, an infinite series of past events pertaining to infinitely many RGRs [or GRs] is impossible (—assuming the truth of the plausible rearrangement principle[s]).
But, again, just because an infinite series of past events pertaining to infinitely many RGRs [or GRs] is impossible, it does not follow that the temporal series of events constituting or including the history of our universe is metaphysically impossible since this history does not include any GR or RGR. But even were the temporal series in question to somehow include GRs or RGRs, the infinite temporal series pertaining to them in the Gedankenexperimente by you and Alex involve rearrangement or modal continuity principles that make possible RGR or GR paradoxes.
So, my rightfully esteemed friend, I respectively submit that you are still wrong about the Kalam argument concerning the issue of the finitude of the past concerning this our universe.
Arnold,
You wrote: In my opinion the theorem provides an insufficient basis upon which to conclude that any infinite series of past events is impossible."
I'm not sure I follow. The antecedent of the theorem is perfectly general: if there can be an infinity of past events, then there can be a GR scenario. Since the consequence is false, so is the antecedent (if the theorem is true). Perhaps what's going on here is that you reject one or more of the axioms. You mentioned axiom 6: “If there can be an infinity of past events, then there can be an infinite series in which each event results in the existence of a GR." Do you reject that?
Josh,
In your reply you refer to your axiom 6: "If there can be an infinity of past events, then there can be an infinite series in which each event results in the existence of a GR." You ask whether I reject that. Well, I go along with it for the sake of argument for our purposes if the possibility you have in mind is metaphysical rather than just broadly logical possibility. So, fine, let us assume that there can be an infinite series in which each event results in the existence of a GR. On the other hand, if there can be an infinity of past events then there can also be an infinite series in which no event results in the existence of a GR. The point I am trying to make is that there also can possibly be other infinite series as to which it is false that any event results in the existence of a GR. So the possibility of a GR paradox can only obtain with respect to those infinite series which are such that they involve the creation of GRs. The notion of omnipotence behooves the theist to believe that every broadly logically possible world of concrete entities (consistent with the truth of theism) is defeasibly a metaphysically possible world. For me it is strange that the construction of possible world scenarios involving infinite series with events generating GRs, together with the possibility of GR paradoxes, leads a theist to deprive the omnipotent God of the awesome power to create essentially changing universes that are beginningless and of infinite duration. But speaking as a philosophical naturalist, I am more than disposed to favor the neo-essentialism as advocated by, for example, Brian Ellis. So, in any event, I think that it is metaphysically impossible for there to be an infinite series in which any event results in the existence of a GR or RGR.
Arnold,
Thanks for pressing me on this, though I confess that I'm not sure what exactly you are objecting to (if not axiom 6). Do you think that the theorem doesn't follow from my axioms? I do grant that if there can be an infinity of past events, then there can be series that don't result in the existence of GR. But that's consistent with my axioms and with the theorem that follows from them. What isn't consistent with the theorem is that there can be an infinitity of past events (assuming a GR scenario is impossible). So I'm not following your objection, which I apologize for. :)
Josh: What we are exploring is your conclusion vis a vis the KCA in your initial post that a infinite series of past events is impossible. What I have been urging is that your argument's premises, and I have axiom 6 particularly in mind, and your theorem do not warrant the conclusion that any infinite series of past events is impossible--certainly not those in which no past event results in a GR or RGR. Now I'm happy to note that you agree that "I do grant that if there can be an infinity of past events, then there can be a series that don't result in the existence of GR." So I conclude that you now consider the obstacle (i.e., the impossibility of an infinite series of past events) to your acceptance of the KCA to have been rolled back.
Josh: Thanks so much for your persistence and patience in pressing me concerning my perplexing proposition claiming that your theorem does not provide a sufficient basis upon which to conclude that any infinite series of past events, even one in which no event results in a GR, is impossible. So, sheepishly and shamefully, I must explicitly acknowledge that given your theorem (i.e., “If there can be an infinity of past events, then there can be a paradoxical GR scenario”) and that a paradoxical GR scenario is impossible, then it indeed follows that an infinity of past events is impossible. But I do not easily give up.
In the first place, I take heed of your comment of November 9 in which you wrote; “It seems to me that the possibility of a GR scenario is plausibly inferred from the possibility of an infinity of past events given certain general recombination principles.” And, in the second place, I take heed of your statement in your comment of November 13; “I do grant that if there can be an infinity of past events, then there can be a series that don’t result in the existence of GR.”
Although I should like to register my inability to accept axioms 1-5 and 7 (your general recombination principles) as necessarily true (i.e., true in all possible worlds), I do not want to fight the problem. And so I should like to criticize your argument assuming arguendo the truth of all your axioms 1-5 and 7. I shall also assume arguendo your axiom 6 (“If there can be an infinity of past events, then there can be an infinite series of events in which each event results in the existence of a GR”). Since axiom 6 states what purports to be a contingent truth, it is also a contingent truth that if there can be an infinity of past events, then there can be an infinite series of events in which no event results in the existence of a GR. Thus, in my opinion, your axioms are incomplete and must therefore be augmented.
So, in addition to your axiom 6 I should like to add the following:
Axiom 6*: If there can be an infinity of past events, then there can be an infinite series of events in no event results in the existence of a GR.
From the axioms 1-6, 6* and 7, I draw the following:
Theorem 1: If there can be an infinity of past events in which each event results in the existence of a GR, then there can be a paradoxical GR scenario.
Theorem 2: If there can be an infinity of past events in which no event results in the existence of a GR, then there cannot be a paradoxical GR scenario.
Since a paradoxical GR scenario is impossible, it follows that there cannot be an infinity of past events in which each event results in the existence of a GR. This leaves open the question whether there can be an infinity of past events in which no event results in the existence of a GR.
I rest my case (for the time being).