The Central Problem for Cosmological Arguments


In this post I hope to sketch out the problem of actual infinities as is often utilized in the Kalam cosmological argument, the response that I am unable to respond to, and the basic question whose answer would settle the issue for me but I am unable to answer.

First, a quick note on mathematical symbols to clear things up for those who are not familiar with mathematical notation or the notation I sometimes made up because I did not know the proper way to express my idea. The main symbol I am going to use is the hebrew letter aleph (ℵ), which has come to represent an actual infinity in set theory. This is used instead of the more commonly known lemniscate (∞), which represents only a potential infinity or something without bound that would not be considered to include an infinite number of things. Also, I use the subscript 0 with the aleph to represent a certain kind of actual infinity, in this case it will usually be some subset of the natural numbers. This is only to be more specific as there are many larger infinite sets, a fact that is not relevant to my argument here. Moreover, I will use superscripts with aleph to specify the exact numbers included in the infinite set that the aleph stands for. This is only to make things clearer. I am not sure if that is proper notation. Hopefully the rest is pretty straightforward.

Understanding Infinities

At first, arithmetic with transfinite cardinals seems fairly straightforward. It is simplest to imagine, the set of all natural numbers, as the infinite set under consideration. Cardinality is simply the property of any set that identifies the number of members in that set and is usually indicated by normal numbers used as cardinals. If I say I have 2 hands, then I could also say the set containing my hands has a cardinality of 2. This is different from ordinal numbers that indicate rank or position such as 1st, 2nd, and 3rd or nominal numbers that simply label something such as when we label athletes with numbers on their jerseys. One easy to understand property is that adding a new member to a set with infinite cardinality does nothing to change its cardinality. So taking the set of all natural numbers and giving it another 1 as a member does not make it any greater of an infinity.

      (Eq. 1)

In fact, adding an infinite number of members to the set does not affect the sets cardinality. So the union of the set of all natural numbers to the set of all natural numbers would produce a set with the same cardinality as the set of all natural numbers.

      (Eq. 2)

So addition does not lead to anything logically problematic, though it obviously is strange and difficult to grasp intuitively. However, this is not seen as a problem that prevents an actual infinity from being metaphysically inconceivable.

Actual Infinities and the Kalam Cosmological Argument

The problem for actual infinities steps in when one thinks of inverse operations such as subtraction. Again, things start out simple if you consider removing a single member of an infinite set because you are still left with an infinite set as would be expected by the rules of infinite set theory.

      (Eq. 3)

The source of controversy crops up when one considers removing an infinite number of members from an infinite set because it can result in a set with any cardinality between 0 and infinity.

      (Eq. 4)

This is exactly what apologists like William Lane Craig are trying to illustrate when they use examples like Hilbert’s Hotel. If this more formal take on it doesn’t make sense then I would recommend listening to William Lane Craig describe the problem using Hilbert’s Hotel. Anyway, one can illustrate this problem by thinking of removing all the odd numbers from the set of natural numbers, leaving one with an infinite set, namely, all the even numbers.

      (Eq. 5)

On the other hand, by removing all numbers greater than 3 from the set of all natural numbers, one is left with a set containing 3 members and therefore having a cardinality of three.

      (Eq. 6)

This could be repeated with different sets to achieve a set with any cardinality one wants. The problem then is that subtraction seems to be ill-defined and leads to the unacceptable and possibly illogical conclusion that removing an identical number of members from the same set can lead to different answers.

      (Eq. 7)

The proponent of the Kalam cosmological argument is going to argue that this proves the metaphysical impossibility of an actual infinite. This is because mathematicians can simply restrict inverse operations by fiat to prevent these illogical conclusions from following and then move forward in developing further theories. However, in the real world, nothing would prevent things from being removed from a set (though there are some persuasive arguments against this) and therefore such a fiat could not be imposed to prevent the illogical conclusions as is done in mathematics. Given the logical absurdity that could arise if an actual infinity existed in reality, it must be the case that actual infinites are metaphysically absurd and therefore do not exist in any possible world.  From here the Kalam argument attempts to show that the past cannot be actually infinite, that space cannot be actually infinite, that an actually infinite number of universes cannot exist, and so on.

 Objecting to the Kalam

The main objection I hear to this and the objection against which I cannot respond is that by simply taking into account the exact makeup of the infinite sets, than the metaphysical absurdities do not result. By keeping in mind that we are removing the infinite-set-of-all-even-numbers from the infinite-set-of-all-natural-numbers, it will always be the case that the result is the infinite-set-of-all-odd-numbers. It is only in ignoring the exact make-up of the infinite sets that absurdities result in performing inverse operations.

The issue that this all seems to boil down to is the relationship of different infinite sets of equal cardinality. The proponent (and possibly the objector) of the Kalam argument assumes that such sets are equal.

      (Eq. 8)

The controversial assumption is then whether this equality implies the ability to substitute sets of equally infinite cardinality for one another in an equation. If such substitution is allowed than the contradiction can be made undeniably explicit.

      (Eq. 9)

However, if the objector denies that equality between sets implies the possibility of substitution, then the logical problem is avoided and inverse operations become metaphysically possible.

So the most general way of stating the issue that is at the root of this whole argument, but that I am unable to know the answer to is this: can two infinite sets with equal cardinality be considered equal to each other such that substitution between equations is possible regardless of the exact makeup of either infinite set?

      (Eq. 10)

Implications for Cosmological Arguments

In my opinion, this is what the entire Kalam Cosmological Argument rests on. I don’t think anyone can seriously object to the first premise when it is properly stated, though I acknowledge that some people try. However, premise 2 and the conclusion that God must be the cause of the universe rest on this claim. For if actual infinities are not metaphysically impossible, the atheist can simply accept that fullness of the Kalam’s 3 premises and still maintain their atheism.

Atheists simply have to hold to the following: The universe, taken to be our current spacetime reality or any larger spacetime reality of which it is a part, has a cause. However we do not know that this cause must be personal. Instead we claim that minimally it is some type of mechanistic generator, that is constantly in a state of causal sufficiency for creating various kinds of universes and has therefore created an infinite number of them. We don’t know what this timeless and spaceless cause is and we may never know but it consistently explains everything we currently know about the universe without adding on the additional property of it being a person. We could even tack on that it is necessary in response to the Leibnizian cosmological argument. So God would work as an explanation as well but that would be ruled out by Ockham’s razor because the necessary mechanistic universe generator is the same in every respect to coherently explaining the existence, contingency, and fine-tuning of the universe but does so in a simpler way by not unnecessarily ascribing personhood to the cause.


Actual infinities seem to be one of the few core issues of contention in apologetic concerns surrounding cosmology. Unless it is shown that actual infinities are metaphysically absurd in some substantial way that is more than just being non-intuitive, atheists would seem to have no problem accepting the soundness of cosmological arguments. I have attempted to show that giving good reasons for the metaphysical absurdity of infinity boils down to whether or not inverse operations can be defined for infinite sets. This issue requires a mathematical background beyond what I currently have and so I would not presume that this a knock down objection in any sense. However, I hope this brings attention to what my research as an undergraduate philosopher and physicist has indicated as one of the (if not the) central issues for cosmological arguments in Christian apologetics.

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  1. Profile photo of Roland Elliott

    Roland Elliott - October 14, 2013, 10:33 am

    I think there’s some confusion about the supposed problem of actual infinities. The “objection” says that if we subtract sets and not cardinalitites then there’s no problem. Well of course, but the whole point is that there *is* a problem when dealing with cardinalitites. Subtraction of cardinalitites is different from subtraction of sets. This is the reason subtraction isn’t allowed in transfinite arithmetic (which deals with cardinaities) but subtraction of sets has never been a problem.

    When we are talking about cardinalitites we’re talking about “quantities”, but when we’re talking about sets we’re talking about “collections”. Big difference. So, for example, {1,2,3} – {2,3} =/= {4,5,6} – {5,6} but |{1,2,3}| – |{2,3}| = |{4,5,6}| – |{5,6}| (where |A| is the cardinality of the set A).

    So I think the objection is wrongheaded. I also disinclined to agree that the kalam argument rests entirely on the impossibility of actual infinities. I don’t even like the argument for the finitude of the past based on the impossibility of actual infinities anyway! The concerns in this “objection” do nothing to stop the argument from the impossibility of forming the infinite via successive additions, the grim reaper argument, and scientific evidence for the finitude of the past.

    • Profile photo of Alex Armstrong VI

      Alex Armstrong VI - October 15, 2013, 1:28 am

      First off, thank you for the reply Roland. I think you have highlighted an important distinction I neglected to make. However, I think I can still show that it does not make clear the problem with actual infinities such that it can be applied in the Kalam. Also, assuming actual infinities are not metaphysically absurd, I think my necessary mechanistic universe generator can deal with all the other arguments you brought up. However, let me make that claim more clear.

      Let me begin with why I think this is the central issue for the Kalam. I put forth my necessary mechanistic universe generator as possible cause of our universe that is atheist friendly. If we ignore the problem that it implies the existence of an actually infinite number of universes than I do no think any other flaws can be pointed out with it. The impossibility of forming an infinite collection via successive addition only applies to dimensions displaying dynamic behavior (i.e. the dimension of time). So even assuming that it is impossible to successively form an actual infinity, that only means our time-like universe cannot extend infinitely into the past. However, the universe generator was posited to be spaceless and timeless so it does not create the infinite multiverse one by one in some alternative time-like dimension but instead creates them all “in an instant” we could say. Our universe is one of the many, each having its own time dimension. At that point it falls on the anthropic principle to explain why we experience ourselves to live at this current time step of our universe.
      A similar fate seems to befall the grim reaper paradox and even any conceivable scientific evidence. As for the grim reaper paradox, it tends to follow similar time-dependent reasoning and can only show that time cannot extend infinitely into the past. However, it is usually not used as an argument to show that space cannot be infinite or that and infinite number of universes could not exist. The scientific evidence for a beginning of the universe again seems to show that any dimensional reality involving certain characteristics, usually on-average expansion as time progresses, must be finite in some crucial sense. The scientific evidence rules out a narrow range of responses from the atheist, namely positing some eternal or beginningless spacetime reality that is continuous with the spacetime we currently observe. However, given that my mechanistic universe generator is spaceless, timeless, and discontinuous with our observed universe, it seems like scientific evidence can say little about its plausibility. So the bulk of the argument is going to fall back on the philosophical evidence.

      In short, what I am trying to say is that the crucial point for the Kalam or other cosmological arguments is to refute atheism to some degree or at least make it more implausible than theism. However, I think such is not possible unless it can be shown that actual infinities are metaphysically absurd. As unscientific as my universe generator is, it still serves as the theoretical explanation that needs to be ruled out before one can claim the cause must be personal.

      Your distinction between quantities and collections was valuable but it seems like it only requires me to reword my original concern. Can |{1,3,5,…}| be considered equal to |{4,5,6,…}| such that it can be substituted into Eq.5 to make |{1,2,3,…}| – |{4,5,6,…}| =/= |{2,4,6,…}|. This way, the problem of actual infinities is made explicit. Atheists I talk to are either going to deny that the equality implies the ability to substitute or now it seems like they could claim that subtraction is only possible with sets and not with quantities. In either case their seems to me no way of demonstrating metaphysical absurdity. Almost all the examples of infinity dealt with in cosmology models, particularly my universe generator, are infinite collections and not infinities quantities. Examples like Hilbert’s Hotel or the Infinite Library seem to work with subtraction of collections from one another and not quantities. Therefore, if you affirm that actual infinities are permissible only as sets but not as quantities (e.g. infinite temperature or density at the big bang singularity), I think atheist are left with nothing to fear about the Kalam.

      So in conclusion, demonstrating the metaphysical absurdity of actual infinities, which I still think is the only possible way of showing that the universe has a cause and that cause is a person, remains a complicated demonstration that I feel I have yet to come across.

      The two sources that have caused me to wrestle with these doubts are given below: – This is a youtube video objecting to the philosophical concerns raise in the Kalam Cosmological Argument – this is a paper that really goes into the details that I have been trying my best to do here. It deals with nearly all the examples of actual infinities being a problem and attempts to dismantle them. The author tries to conclude that there is no basis upon which a division can be made between mathematics and metaphysics such that actual infinites could be considered “metaphysically absurd” in any meaningful way.

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    Roland Elliott - October 15, 2013, 8:04 am

    Wow, long reply. I must ask, have you read much of Craig’s defences of the Kalam argument? I would really recommend reading the various questions and answers he’s given over at, and also the paper he and Sinclair wrote in the Blackwell Companion to Natural Theology. I think it’d clear up a lot of issues here, and I’m not particularly interested in giving a systematic defence of the argument here.

    But, I don’t see why I can’t say something by way of clarification in the mean time. The Kalam argument can be stated like this:

    1. Whatever begins to exist has a cause.
    2. The universe began to exist.
    3. Therefore, the universe has a cause.
    4. If the universe has a cause, then an uncaused, personal Creator of the universe exists, who sans the universe is beginningless, changeless, immaterial, timeless, spaceless, and enormously powerful.
    5. Therefore, an uncaused, personal Creator of the universe exists, who sans the universe is beginningless, changeless, immaterial, timeless, spaceless, and enormously powerful.

    So, a few comments:
    a. The arguments from the impossibility of actual infinities and forming the infinite from successive addition, the grim reaper paradox, and the scientific evidence are *not* arguments for (4). They are arguments for (2), and as far as I can see, you agree that they establish that. If we attack these arguments, we’re are attempting to undermine the warrant we have for beleiving in (2), not (4). Any suggestion otherwise is a misunderstanding of the dialectical situation the defender and detractor of this argument find themselves in.

    b. As far as I can see, your “necessary mechanistic generator” (NMG) response assumes that (1) and (2) (and therefore (3) as well) are correct. The detractor of the argument agrees that the universe has a cause, but denies that this cause *must* be personal. And if we end at (3), that’s exactly right, the first cause *could* be impersonal. It is a strange kind of atheism, however, that accepts a transcendent cause of the universe. I wouldn’t call that atheism, but perhaps that’s just me. Now the defender of the argument is welcome to leave it there. After all, he has now established a first cause that for all we know could be personal, and he can use this as part of a cumulative case for [Christian] theism. Of course, the defender could also give an argument for (4), which we’ll discuss in point (d).

    c. It seems to me that when talking about your NMG you’ve conflated the kalam argument with the fine tuning argument. I see no reason why the “atheist” couldn’t simply say that the first cause is impersonal and caused only this universe. Why should the detractor have to gratuitously postulate an infinity of causally disconnected universes? Thus, even if infinities really are absurd, I see no reason why the detractor can’t take this course (in fact, until recently, this was the very reason I denied (4)).

    d. Craig has offered three arguments in defence of (4), two of which I like. The first is deductive, stemming from the principle of determination. It makes us of the fact that the first cause is changeless so long as there is no first event (since two of the arguments or (2) imply a beginning of metric time, caused by the first cause). It could be formulated like this:

    4.1. There was a first event, caused by a changeless and beginningless being.
    4.2. The first event was either the effect of state-state causation, event-event causation, or agent-event causation.
    4.3. It was not the effect of state-state causation or event-event causation.
    4.4. Therefore, it was the effect of agent-event causation.

    (4.1) follows from the fact that the first cause caused metric time. (4.2) is a list of putative causal relations, and I don’t think I’ve left anything out. (4.3) follows because the first event was an *event* and not a state, and it was the *first* event, and therefore not an effect of a prior event.

    The next argument Craig gives is inference to the best explanation: the only things we know of that are timeless, spaceless, and immaterial are unembodied minds and abstract objects. But abstract objects are causally inert, so they can’t be the first cause. This leaves us with an unembodied mind. Now, this isn’t a deductive argument, but then again neither is most of science (at least, physics and evolutionary biology are not), so that shouldn’t deter us too much. You might think (as I did) that one can just insert the NMG here, but this doesn’t work, because it’s not actually a candidate explanation, for you haven’t told us *what* this explanation is, all you’ve told us are some properties of it. Consider this quote from Craig: “…it is not legitimate to offer as an explanation a hypothesis which simply repeats the data to be explained—for example, explaining that opium induces sleep because it has “dormitive powers.” Saying that the cause of the universe is an uncaused,…, indeterministic, impersonal being is like that. It is not to offer an explanation at all. Therefore, it could never be the better explanation. Similarly, it is no good appealing to unknown entities. That just is to admit that one has no explanation, no alternative hypothesis to offer. It would be like saying that fossils are not best explained as the vestiges of organisms that once lived on Earth but were instead the effect of some mysterious, unknown fossil-forming power in the rocks. Again, that could never count as the best explanation.”

    e. Okay, this response is getting a little too large for my liking, so I’ll end with a reponse about collections and quantities. To be clear, the problem with Hibert’s Hotel does *not* revolve around collections, but quantities. No-one denies that if we remove every second person from their room on the one hand, and if we remove every person who has a room number greater than 4 on the other, that we’ll arrive at different collections. What’s important is that the *quantities* that we removed are the same, but the quantity we arrived at was different: we remove *the same amount of people* and arrived at different answers.

    As for your reworded concern: the point is that subtraction of actual infinities is meaningless, but subtraction of quantities in real life is not. Let A = {1,2,3,…}, B = {4,5,6,…} and C = {2,4,6,…}. Now, clearly |A|=|B|=|C|=alpeh_0. But what is aleph_0 – alpeh_0? If we consider the quantity |A-B| we get 3. But the quantity |A-C| is alpeh_0! In fact, depending on our choice of B, we can get any natural number as the answer (actually, any rational number, but whatever). The lack of unique answer (which is unlike the finite case) is the reason that we don’t allow subtraction in transfinite arithmetic, for it is not well-defined. However, while imposing such a rule is fine in our mathematical systems, we can’t simply impose such rules in reality. As such, it seems that actually existing actual infinities are absurd.

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    Alex Armstrong VI - October 16, 2013, 10:59 pm

    Once again I appreciate your response and you continue to make helpful comments that are moving this discussion forward. I don’t mind the long replies and I hope you feel the same way. As to your opening question, I have definitely read William Lane Craig and I appreciate your recommendation because he has been very helpful for my own thinking on this issue. This past summer I decided to look a lot more deeply into the Kalam argument and try to defend it against some of the better objectors I could find online. I read through Dr. Craig’s defense of the Kalam in Reasonable Faith, Philosophical Foundations of a Christian Worldview, and The Blackwell Companion to Natural Theology as well as his discussions of philosophy of time in his book Time and Eternity and some excerpts from his writings on tensed and tenseless theories of time. I feel like I understood his works so hopefully I can clarify any areas where it seems like I am missing an important point. Anyway, let me get into responding to your comment.

    I understand that your five premise formulation of the Kalam is probably the fullest statement of the Kalam but it is rarely formally stated by Dr. Craig or others though mostly for rhetorical purposes. Regardless, when I refer to the Kalam, I typically have meant it only in its usual 3 premise from while simply recognizing the later two premises as being important imports into the overall argument in Christian apologetics.

    Point a) Your point is well taken and I hope I can clarify my point so it doesn’t appear that that is what I was implying. I was talking about those arguments and their relevance to premise two. My issue comes down to what premise two means by “the universe” and what those other arguments show about “the universe” as premise two means it. If the universe simply means our current spacetime reality and anything topologically continuous with it than I think the premise two is much less scandalous. However, if it means any mechanistic impersonal reality or reality captured by the 11 or so dimensions that people currently posit as the basis for physical reality, then I think the claim is more of a threat to atheism. Being short because this ties into your other points, I think this is important because the threat of the argument seems to be its ability to rule out that there is not some non-theistic cause. This is instead of saying that God is just the most plausible explanation, a move which drives us into tons of other discussions about the possibility of disembodied minds, the truth of a tensed view of time, etc.

    Point b) You are right that NMG assumes 1-3 are correct. My point with it was to hopefully show that someone can accept 1-3 without feeling threatened that theistic explanations are made any more plausible as explanations than if we assumed the universe was eternal. The cause must be transcendent in the sense that it is not exactly like our current spacetime universe but it doesn’t have to mean different in kind, which would be a threat to atheism. The cause of our spacetime universe could be something very similar to it (i.e. involving similar dimensional structure and even operating according to similar laws) but be transcendent only in the sense that it is not topologically continuous with our universe. Maybe our intuitions just differ but hopefully this makes it clearer why I think establishing that our particular universe has a cause does not have to lead to an atheist losing sleep (which I guess is what I want it to do or something like that).

    Part c) My goal is not to attack the fine-tuning argument though I do think the NMG would have implications for that argument that I pointed out but will avoid elaborating on. There are a couple reasons why I think one couldn’t postulate an MG that only created one universe and it actually ties into one of the arguments Craig gives for why he thinks the cause of the universe has to be personal and not mechanistic. In short, if your mechanistic cause only creates one universe and then stops you have some kind of fundamental change that implies the cause is in time and also contingent because it existed contingently in a state of causal sufficiency to create the universe as evidenced by the fact that it is no longer in that state or doesn’t exist at all. This cause is then subject to various critiques about why it didn’t create the universe at a earlier or later time as well as Leibnizian concerns of why it exists at all. The NMG exists necessarily in a state of constant state causal sufficiency and so even after creating a particular spacetime universe, it has not changed and therefore must create another universe. Furthermore, since it is timeless it creates an actually infinite number of universes in a sense “instantaneously”. In the Blackwell Companion, Craig asks, “how can all the causal conditions sufficient for the production of the effect be changelessly existent and yet the effect not also be existent along with the cause?”(Blackwell 193) Now Craig is trying to argue that the any mechanistic “state-causes” would have to create a universe coeternal with itself but I think this objection only applies to your universe generator because it involves some time-like dimension. Now the NMG would fail if actual infinities are metaphysically absurd hence my feeling that the question is central to the Kalam.

    Part d) You raised some good points here and I like how you applied them to my questions and concerns. Defending premise 4, particularly the claim that the cause is personal, is in my opinion what makes this a theistic argument and not just stating the obvious for anyone who believes the standard model of big bang cosmology and premise 1. I might at this point better state the intention of my whole blog post as showing how defending that part of premise 4 is where the metaphysical absurdity of actual infinities is a central point. Let me move on to the specific arguments you put forth though.
    I think 4.3 is not obvious and the NMG is my attempt to give more concreteness to why I think state-event causation is possible if one allows that an actually infinite number of things exist. This applies to the Kalam in the case that the state is a necessary one, which it must be if it is to be a competing explanation for the cause of the rest of reality.
    Your next argument, namely that the NMG cannot be considered an explanation, is in my opinion the best response and the one which I think is the best avenue to pursue alongside trying to show the metaphysical absurdity of an actual infinity. I will unfortunately not say much else here mainly because I would need to do more thinking as to the how an atheist might respond and then how that could then be responded to as well. Basically, it doesn’t seem obvious to me that it works because one could challenge your understanding of what something takes to be an explanation, the degree to which a disembodied mind counts as a good explanation, and also the degree to which we could imbibe the NMG as a more substantive explanation. Towards that last possibility, if we are allowed to defend unembodied minds as a possibility because of extrapolations from our experience of embodied minds, maybe the atheist could extrapolate from our experience of mechanistic causation in spacetime to mechanistic explanation outside of spacetime. For me these all deserve more looking into and I believe William Lane Craig among others deal with these but I will have to give it a deeper look. Point is, I think this objection needs to be fleshed out much more than either of us should do in these blog comments.

    point e) Your continued specification is helpful but I still think I can make a response. From what you said, I think I can clarify best what I am trying to say as this: the atheists I am talking to are saying we cannot seperate quantity and collections when applying infinity to reality. In all the examples demonstrating the metaphysical absurdity of actual infinities, they deal with infinite quantities “taken from” (sorry but I cant think of a better word) infinite collections. True infinite quantities that are not infinite collections would be something like actually infinite temperature or an actually infinite volume. These infinities are quantities without having an infinite number of parts. But now we have lost the ability to create paradoxes because it doesn’t make sense to talk about removing every odd degree from the temperature to be left with all the even degrees. Temperature is not a set of 1K, 2K, 3K, and so on. The same goes for space. Infinite collections like infinite numbers of people, balls, books, orbits, etc. can be used to create Hilbert’s Hotel like paradoxes because we can talk meaningfully about numbering them off and removing various collections from an infinite collection. It is only after this has been done, in a logical sense, that we ask for the magnitudes of those sets to show that absurdities result. The atheists I have tried responding to are arguing that when collections are involved, one can’t neglect what collection is in a sense “behind” the magnitude involved in the subtraction. In a sense it might be saying that the magnitude of a collection is not a physically meaningful claim, only the magnitude of scalar values. So when dealing with metaphysical infinities, one is either dealing with infinite collections or infinite quantities, and arithmetic with infinities in reality must take this difference into account.

    Overall let me just say, that I am fascinated by this argument and have not lost hope that it is a valuable tool for the christian apologist. I am just interested in defending it against the best objections I hear and this whole post is my attempt to flesh out what seems to me to be the biggest and best objections to the Kalam. Your responses Roland have been very helpful and I hope my persistence in asking for clarification and better responses makes it seem like we are progressing towards a better understanding of the ins and outs of this argument.

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    Roland Elliott - October 17, 2013, 1:34 pm

    I’m glad you’ve read all of those things. Although I’d suggest also reading the Q&As on his website. I must confess I don’t really like long comments, because they’re fatiguing to read and follow and usually raise too many topics for the discussion to be of any help. As such, I’ll just give brief responses to some of the points and give more detailed responses to the ones I think more pertinent.

    a. By universe, Craig means the maximal aggregate of space and time. If we feel the need to gratuitously postulate a multiverse, then that is included. The scientific evidence suggest that the universe, and inflationary multiverses (ie. our best multiverse theories) had a beginning. The philosophical arguments conclude that any metric time must have a beginning, including the time of a multiverse, or anything. This includes 11-dimensional theories (which, by the way, are not the standard contemporary physical theories. We’re still quite happy with our 3 spatial dimensions and 1 temporal dimension. String theory is still very much non-mainstream).

    b. The cause must transcend time at least and probably space, and if we accept reasons for (4), must be personal. This is not a comfortable position for an atheist. Curiously, you said that you aren’t concerned with (4) and (5), yet any discussion of “theistic” explanations or “God” is discussion about (4) and irrelevant to (1), (2), and (3).

    c. The postulation of an infinity of universes does nothing to stop the comment by Craig you quoted. There the relevant problem is not the number of universes created, but the fact that the first cause must be changeless and beginningless (by the way, this is the first argument I gave in (d), I just like my way of wording it). The same problem could be posed to you: why is your infinity of universes not co-eternal with the first cause in a beginningless and changeless state? Merely increasing the number of the supposed universes does nothing to reduce the mystery.

    d. I’m sorry, but state-event causation seems completely incoherent. An event is a “happening” and a state is a “circumstance”. Now a “circumstance actualising” might cause an event, but this is event-event causation. (4.3) is unimpeachable. What you’re actually denying is (4.2), but you’ve given us no coherent interpretation of “state-event causation” and until you do such an objection is without substance.

    I think the problem with the NMG is that you haven’t actually told us what it is, for at the moment it’s just a collection of properties. The unembodied mind case we haven’t just said “oh well, it’s a personal cause”. We have experience of minds (or at least they are coherent ideas, and probably defensible in their own right) as personal immaterial things, and we’re offering a legitimate candidate. The NMG, however, is not a candidate, it’s just a list of properties. But *what* impersonal non-deterministic cause are you suggesting we take? You haven’t given one.

    You could imagine a dialogue: “I think the cause is personal”
    “What personal immaterial things do you know of that might fit the bill?”
    “An unembodied mind works”

    On the other hand: “I think the cause is impersonal”
    “What impersonal immaterial things do you know of that might fit the bill?”

    e. I’m not really sure we need to separate quantities from collections completely (after all, quantities are of collections), but I deny that they are so intrinsically linked as your objection requires. For example, I can meaningfully ask what 6-2 is without reference to a specific collection. These are quantities that could apply to any collection, and in each collection, if I take 2 of the things from the 6 I will always get 4 things, no matter which 2 things I removed. So we can give meaning to the subtraction. Sure, I can take different pairs and get different collections, but the quantities always agree and make sense.

    In the infinite case, there is no meaningful answer to the question of what aleph_0 – aleph_0 is. And the absurdity arises because I can take away two collections of *exactly the same quantity* but arrive at different results. It is no answer to say, “yes but you removed different collections”, for that just misses the points. While we are definitely working with collections, the important thing is that the collections we remove are of the same quantity but at the end of the day we arrive at contradictory results.

    Think about the case where I told you that I removed 2 items from 6 in two different ways and got 4 items the one time and 3 the other. It would certainly not solve anything by saying “Oh yes, but you removed two different pairs from the 6 items”. That is completely irrelevant to the problem at hand.

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    Alex Armstrong VI - October 17, 2013, 4:21 pm

    I can understand your concerns regarding long comments and so I will do what I can to keep this brief.

    a) I think we both agree that all arguments for premise 2, excluding the metaphysical absurdity of an actual infinite, require that the universe have a time dimension and also one that is treated in a tensed sense. My only point here will be that this seems to be what drives people to pursue universe models that either don’t involve a tensed time dimension or a time dimension at all either to describe our universe or the cause of our universe. However, the argument against actual infinities would seem to me to refute all models that don’t involve an agent-event creation. We seem to disagree here but I at least hope I am clear that that is what my point with this blog post and various comments have been.

    b) I agree that the debate comes down to premise 4 as far as christian apologetics is concerned, especially if one considers “the universe” in premise 2 to be as you defined it in part (a). I don’t think this concern for premise 4 contradicts anything else I have said.

    c) If the NMG is timeless than it think it avoids Craig’s objection because one can’t ask why our universe wasn’t created earlier or later. Similarly we can’t ask why our universe is not coeternal because eternality in a timeless sense is different from eternality in a temporal sense. I tried to show why your universe generator would have to be temporal while mine would not be.

    d) I agree that this will come down to the possibility of defending either state-event causation or maybe showing that the NMG involves some other kind of causation. I think we can agree to leave it at that until someone is actually willing to defend it.
    As before, I am in most agreement with your objection that the NMG needs to be more substantially stated. Ill leave that defense of the NMG for someone more seriously objecting to the argument. I will say that if the NMG illustrates one belief of the objectors I come across, it is that they would rather assume we have yet to discover some meaningful candidate for the NMR than postulate God as a cause. This could either be a disagreement in intuitions or a shift to the question of one’s theory of explanation and whether God is ever a viable explanation. Im obviously inclined to think he is but can’t say I could defend that belief against intelligent objectors.

    e) I understand you distinction between collection and quantity. Im trying to shift the discussion more towards the relationship of those distinctions in math to their distinction in reality. In general, how does the math represent reality and what effect does that have on doing arithmetic purely theoretically or doing it as a representation of actual things happening. I recommend checking out that second link i posted in my first comment if you want a more detailed discussion of this topic. I will leave it at that though. Maybe in a later post I can try to focus on this issue more specifically and try to be more clear.

    As always, I really do appreciate your comments and have benefitted a lot from what has been said.

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    Roland Elliott - October 18, 2013, 12:34 pm

    Alex I appreciate the briefness of your responses, I was much more able to focus on them, so thank you 🙂

    a. I’m actually of the impression that, contrary to Craig’s constant claims, the Kalam argument is not dependent upon a tensed theory of time, but I won’t go into that here.

    b. Don’t see much disagreement here 🙂 My point of (4) wasn’t claiming you were contradicting yourself, it was just that you said, “Regardless, when I refer to the Kalam, I typically have meant it only in its usual 3 premise”, but all your concerns about the personhood and/or further identity of the cause (so, like everything regarding the NMG) are to do with (4).

    c. Craig’s point has nothing to do with the question of why the cause didn’t create the universe earlier. He has explained that he finds such a question meaningless, because we’re talking about the beginning of metric time, and terms like “earlier” are without meaning in this context. I think your comment about the co-eternal question is the same problem I’ve had in the past, and I’ve come to realise it’s predicated on a misunderstanding. What Craig is really asking there is why the effect is not also in the beginningless and changeless state if the conditions for its existence have always been satisfied. This is actually just what my argument in (4.1)-(4.4) is about, although I have phrased it in what I find more helpful terms. It applies to whatever supposed effect was caused, whether it be a single universe or a plethora of universes.

    d. With regard to the inference to the best explanation argument, it seems to me that the atheist cannot consistently refuse to give a candidate. You see, it’s not the case that he’s saying the unembodied mind isn’t the best explanation because he can think of a better one. All he’s doing is denying the unembodied mind (for reasons I can only attribute to stubborn denial) and saying that something impersonal must have done it. You see, this isn’t a better explanation because it’s not even a candidate. This isn’t really advocating a new theory of explanation or anything, either. If all we knew was that the cause is either personal or not but had no putative candidate for either option, then it would be ok. But now we have a candidate for the personal case, and if we know of no candidate for the impersonal one (which we don’t), then it seems the personal option is better at the moment (if for any reason, that it’s less ad hoc). This conclusion isn’t as conclusive as the deductive arguments, I admit, but that’s the nature of the game when it comes to inference to the best explanation :/

    e. Hmmm… I must admit I’m not too sure what you’re saying here. I mean, I’ve explained that transfinite subtraction is meaningless (both in maths and reality). As such, it is banned in maths. But if it these quantities were possible in reality there’s nothing stopping subtraction. But this is clearly an absurd conclusion.

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    Alex Armstrong VI - October 19, 2013, 2:52 pm

    I appreciate the brief response as well. I think at this point we can leave aside points (a) and (b) but let me try to continue with the remaining points.

    c. It seems that any timeless cause, whether God or the NMG, creates the universe at what will be considered t=0 within that universe. It seems impossible that it could be otherwise. So unless you are objecting to the very concept of a temporal universe arising out of a timeless cause, then I don’t believe i’m understanding you fully. As for its similarities to your previous argument (4.1)-(4.4), I think its going to come back to the question of state-event causation.

    d. This is going a little far afield from my original post but its interesting so let me try to be more specific. Here are some the objections I hear for why God can’t be an explanation unless he is shown to be the only possible explanation (in a broad sense) . I’ve called it a different theory of explanation because it is in line with Hume’s approach to showing that even if God was the cause it would never be justified to posit him as an explanation. Im aware of the critiques of Hume but I think there are still attempts to establish the same result that are worth our attention. Here are two of them that I have heard from objectors online: (1) God is not a possible explanation because he can never be ruled out as a cause until another satisfactory explanation is achieved. In other words, God is always the best explanation if he is allowed and we should find ourselves pushed to just become Berkeleyan idealists. Claiming God is unfalsifiable might be the right word but that also might be importing too much extra connotations. In a similar sense, (2) God is the cause of everything either directly or indirectly (in the sense of Aquinas) but unless we have shown it impossible that God could have done something by indirect intervention, what else besides ignorance of an indirect intervention makes us conclude that God did something through direct miraculous intervention?

    e. I don’t think you have shown that but to keep things brief here, I will end this issue here and try to pick it up more explicitly in a sequel post. Again, I will recommend you check out this article ( if you want to see a more detailed treatment of this issue that I am only trying to summarize and extend on.

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    Roland Elliott - October 21, 2013, 2:09 pm

    c. Consider, for example, a ball sitting on a cushion from eternity. This is an example of state-state causation, because the ball will be causing an impression in the cushion. This will be a changeless and beginningless state. The ball did not bring about the effect as a new event, however, because the sufficient conditions for the effect had been present from eternity in a changeless and beginningless state. The same is true for your NMG. I grant that once the first cause effects a change via an event, it will be time t=0, but that’s not relevant to question at hand (which, I agree, comes back to the coherency of state-event causation (or lack thereof)). The question is if the conditions met for the universe’s/multiverse’s existence have been present from eternity past why the effect is not changeless and beginningless like the cause? If a coherent interpretation of “state-event” causation could be given that doesn’t collapse into either state-state or event-event causation, then this problem for the NMG would be solved. But it seems to me that no such interpretation can be given.

    d. Two valid options for the detractor are for him to (i) bring forward a candidate that better explains the phenomenon at hand or (ii) to show that the “unembodied mind” candidate given by the proponent is unacceptable as an explanation. Now, you (or the “atheists” you paraphrase) are going for the second of these two strategies, and this is perfectly legitimate. As for the proposed problems, (1) I see no reason why we should be pushed to Berkeleyan idealism, that just doesn’t follow at all. If I understand the statement, “God is not a possible explanation because he can never be ruled out as a cause until another satisfactory explanation is achieved” correctly, it is patently wrong. It is true for *any* instance of inference to the best explanation (like evolution, big bang cosmology, quantum mechanic, and every other major breakthrough in modern science) that the best explanation cannot be ruled out until a better explanation is given. This does nothing to detract from the quality of the explanation. In the case at hand, there is only one putative explanation, and until such time as another is suggested, it will remain the best. But there is nothing in the argument that assumes that an unembodied must *always* be the best explanation. And it is simply false that it is unfalsifiable: there are incoherence arguments, and arguments against the existence of God. (2) seems completely irrelevant to the argument at hand, and I can’t see how it could be stated without presupposing the existence of God anyway.

    e. I showed in a few comments ago. I’ll repost it here: “subtraction of actual infinities is meaningless, but subtraction of quantities in real life is not. Let A = {1,2,3,…}, B = {4,5,6,…} and C = {2,4,6,…}. Now, clearly |A|=|B|=|C|=alpeh_0. But what is aleph_0 – alpeh_0? If we consider the quantity |A-B| we get 3. But the quantity |A-C| is alpeh_0! In fact, depending on our choice of B, we can get any natural number as the answer (actually, any rational number, but whatever). The lack of unique answer (which is unlike the finite case) is the reason that we don’t allow subtraction in transfinite arithmetic, for it is not well-defined. However, while imposing such a rule is fine in our mathematical systems, we can’t simply impose such rules in reality. As such, it seems that actually existing actual infinities are absurd.”

    And I continued later by saying, “In the infinite case, there is no meaningful answer to the question of what aleph_0 – aleph_0 is. And the absurdity arises because I can take away two collections of *exactly the same quantity* but arrive at different results. It is no answer to say, “yes but you removed different collections”, for that just misses the points. While we are definitely working with collections, the important thing is that the collections we remove are of the same quantity but at the end of the day we arrive at contradictory results.”

    You were concerned about discussing these things in reality as opposed to just maths. But that’s exactly what I’ve been doing: pointing out that in reality you can’t willy-nilly impose restrictions on quantities like you can in maths.

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    Alex Armstrong VI - October 22, 2013, 10:21 am

    c) It seems then that a lot of this rests on the the plausibility of state-event causation. I’m completely agree that a beginningless state can only give rise to a state that is itself also beginningless. I don’t think a beginningless event makes sense so I probably wouldn’t say the same applies in event-event causation but that still seems to fit very well in your argument for agent-event causation. I don’t claim to have a robust defense of state-event causation but since its turning out to be a crucial point for the argument let me offer some food for thought. The best example in physics I can think of for state event causation would be atomic emission. An electron is in an excited state and then that eventually leads to the event of the electron “falling” to a lower energy state in turn emitting a photon. No one seems to think that there is any efficient cause involved in this process but the excited energy state is clearly the material cause and few would dispute that it is a state whereas the “falling” to the lower state is an event as is the emission of the photon. I think similar reasoning could be applied to virtual particle creation in a quantum vacuum, atomic decay, and other quantum events that arise spontaneously out of quantum states without efficient causes.

    d) I can agree that my objection (ill just claim it for myself at this point) is taking route (ii). However, the way you have characterized inference to the best explanation (IBE) is problematic for me because it gives up any threshold before which we could claim to not have an adequate explanation. I take it as intuition that it is unreasonable to consider each instance of lightening the direct miraculous cause of God regardless of whether we understand why lightening occurs. Your understanding of IBE implies that pre-scientific cultures would be justified in concluding God is directly causing every lightening bolt until a better alternative is available. This is where Berkelyen idealism comes in because almost every naturalistic explanation or theory has some anomalous phenomena it is still looking (and might always be looking) to explain that could in principle be explained as a reoccurring miraculous intervention of God. If we just take Berkeley’s approach and explain everything as a direct act of God, then all anomalous phenomena go away. Basically, I don’t see how your understanding of IBE allows us to conclude that no explanation currently works, a feature that I think is necessary to prevent falling into Berkeley’s idealism.
    As for God being falsifiable, you only showed that his existence is falsifiable, which obviously implies he can’t be an explanation, but I think it needs to be possible to show that he should not be considered an explanation for some specific phenomena even if he is a coherent concept. This is getting into where I was saying that falsifiable is probably not the best word because I don’t mean it in such a broad sense as Popper meant it. Hopefully I was able to clarify what I meant.
    Furthermore, (2) was meant to show how a Christian could see the Kalam as a bad argument for God’s existence because it doesn’t show why we must posit his miraculous intervention as opposed to merely our ignorance of his indirect intervention. Going back to the lightening example, Christians can admit the possibility that God directly causes lightening but pre-scientific cultures had no reason besides ignorance of God’s indirect intervention to claim they knew God directly causes lightening as opposed to indirectly through some means currently unknown. That we currently have a satisfying, though not perfect account of lightening, does not change how reasonable it is for us to posit God as the direct cause. So Christian’s might say that the Kalam argument doesn’t demonstrate God’s miraculous intervention to be the best explanation until it rules out the possibility of him doing it through indirect intervention. I sometimes find myself leaning in this direction though I like the Kalam argument too much to just give it up before I really understand its ins and outs.

    e) I didn’t intend my last comment to imply that I had forgotten what you had said. I understand what you are saying (at least I think so) but I am just not convinced that it demonstrates your conclusion. To keep things brief, I am putting off presenting my reasons for thinking so for a sequel post.

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    Roland Elliott - October 22, 2013, 11:37 am

    Wow, these comments are really getting interesting 🙂 (sorry to detract from your original post, however)

    c. It’s difficult to know where to begin here (not because I think you have grievous misunderstandings or anything, but because there are so many interlinked topics involved). Perhaps I should start by explicating what I mean by the words “state” and “event” (I haven’t thought especially hard about these accounts, so they could probably be developed further, but I think they’re sufficiently developed for the discussions here): by “state” or “circumstance” I mean a collection of substances exemplifying properties. By “event” I mean a change from one state to another.

    In principle, I think we’re ony considering efficient causation. You see, material causation is between *things*, not events or states. Of the four different causes of Aristotle, only efficient causation deals with events or states (formal deals with essences, final with ends, and material with things). If there is no efficient cause for an effect, then it is causeless in the sense we’re restricting ourselves here.

    That said, I don’t actually think the examples you gave are examples of state-event causation. In the electron case, it is the absorbing or emitting of a photon (event) that causes the electron to change energy levels (event).

    I’ve always been fascinated when people mention virtual particles. In our case, this would be a potential example of an event not having an efficient cause, not of it being an instance of state-event causation. However, I see no reason to think that virtual particles coming in and out of existence in a quantum vacuum (for example) are causeless. After all, these events happen according to the laws of nature (nomically), and minimally whatever grounds these laws (be it the essential dispositions of natural objects, or an external law-enforcer) will therefore be the cause of these events. But this will inevitably be an example of event-event causation. In some cases, we needn’t even have to go the grounds of natural laws. For example, why are the fluctuations in the quantum vacuum (events) be the cause of the virtual particle coming into existence?

    So none of these, I think, are examples of state-event causation.

    d. Your point here is a good one, and I’m inclined to agree that a better form of IBE is one that requires a certain level of explanatory power before some putative explanation can be deemed the best, even if it is the only one. However, I think it is the burden of the detractor to give us a reason for thinking that the proffered candidate is not valid. After all, we routinely accept libertarian explanations in other circumstances, and I see no reason why it should be different here. For a positive case of the explanatory power of libertarian decisions specifically in science, there are papers by Meyer, Moreland, and Plantinga which I suppose we could read 🙂 I can try dig them up if you’re interested. (By the way, I think there might be a typing mistake in your sentence, “you only showed that his existence is falsifiable, which obviously implies he can’t be an explanation”, for merely being falsifiable doesn’t mean something is false, which you know :))

    I’m not sure I understand your concerns in (2). In the argument, we aren’t too concerned with *how* God caused the universe, merely *that* he did. Once we’ve established that a personal first cause exists, then we can ask questions of how he might of caused things. In any case, the Kalam argument doesn’t say either way, and so I see no reason why a Christian should think it bad (we can’t expect a single argument to carry the whole burden). Since we’re doing IBE, it seems to be ad hoc to postulate additional and unecessary entities through which God would work indirectly in order to cause the universe. Does that respond to your concern?

    e. Fair enough 🙂

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    Alex Armstrong VI - October 23, 2013, 9:15 am

    Im enjoying the side quests so no worries about getting off from the original post. My hope is to clarify these side issues because either they turn out to be a lot more important than I originally gave them credit for or they are important issues to clarify before launching into the issue of actual infinities.

    c) I find your restricting causation to efficient causation problematic because if you apply it to the first premise of the Kalam than I think our best physics has falsified it. I think its not that debatable that all effects have efficient causes, material causes, or both but it is wrong to say that all effects have both. Most of the best objections to the Kalam try to show that the universe arose without efficient causation but only material causation, thereby not violating the metaphysical intuition that something cannot come from nothing, which is the basis for premise one.
    My appeal to atomic emission was not about the connection between emission (event) and changing energy states (event) but between both of those events and the original excited energy state (state). Physics considers it an indeterministic (i.e. lacking efficient causation) event that a photon is emitted (event) from an excited energy state (state). This seems to me to be not only a good example of an effect with only a material cause but also of state-event causation.
    The virtual particles example is a bit more complicated and I dont understand the mathematics behind calculating vacuum energy fluctuations as well as I do tunneling of electrons out of the potential energy wells created by the atom. The main point is that both are typically considered indeterministic events which to me always implies that there are no conditions considered sufficient to guarantee the event (i.e. no efficient causation) only what is necessary (e.g. an excited energy state or quantum vacuum fluctuations). The mathematics and physics of any indeterministic system lacks any sort of event that necessitates a following indeterministic effect. The best we can do is give probabilities. So your understanding of the laws describing vacuums is probably incorrect because if it was than we would have a deterministic understanding of the production of virtual particles, which we don’t. I thinks its best to focus on the emission example because its the most easy to understand example of an indeterministic system.

    d) I think you are defending your position with an equally controversial piece of evidence. Not only is the freewill debate just as if not more controversial but many christians are going to be compatibilists and therefore not find this appeal compelling evidence. Now I myself am a libertarian but I think there are ways one can show that arguments for the mind are different than arguments for God. I wont bring those up here to keep things brief and because I think my first point is a more serious objection.
    It seems best to just drop (2) because its mainly an issue of misunderstanding between us and it only seeks to illustrate the same point as (1), namely that God’s miraculous intervention cannot be appealed to as the best explanation but must be shown to be the only valid explanation. The only exception would be if some threshold criterion can be given for when it is better to consider God or an unembodied mind’s direct interaction as an explanation for some physical phenomena than to just claim that we don’t understand the phenomena.

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    Alex Armstrong VI - October 23, 2013, 9:23 am

    two revisions:
    1) I talked about understanding the tunneling of electrons but that has to do with something completely different. I meant to say that I better understand the mathematics behind the emission of photons, changing energy levels, and the probabilities describing those events arising out of an excited energy state.
    2) I said “your understanding of the laws describing vacuums is probably incorrect because if it was than…” but i meant to say “if it was correct, then…”

    Hope that clarifies things

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    Roland Elliott - October 25, 2013, 6:53 am

    Hey Alex 🙂

    c. I think I should start off by noting that an event happening indeterministically does not mean there was no efficient cause. We can all appreciate the plausibility of libertarian agents causing outcomes (which is indeterministic) even if we aren’t libertarians ourselves, or there’s the statistical causation, like the following: “A standard counterexample… is the syphilis-paresis case…. We can explain why a person has paresis in terms of the earlier having of latent untreated syphilis, even though latent untreated syphilis leads to paresis only in a minority of cases.” I’ve often heard people say smoking causes cancer, too, which would be another example of this. Consider another example: I pull the trigger of a gun which has a 50% chance of firing each time the trigger is pulled. In the cases where it *does* fire, it will be my pulling of the trigger that caused it.

    In the case of natural phenomenon, Humeanism is almost definitely wrong (for it prevents natural laws from being explanatory), and so there must be something that grounds the laws of nature. This thing would then indeterministically cause the natural happenings, and the regularity of this causation is how we ground the regularity of the laws. This “lawmaker” would be another example of indeterministic efficient causation.

    So, I don’t think that citing inderterminisitic natural phenomenon does anything to raise problems. Also, events are changes between states, and so wherever there is an event (electron emitting photon and transitioning to lower level) there will also be a state (electron being in higher energy state). This doesn’t mean its an example of state-event causation however, because here it is an event that is causing the other event, and therefore changing the state.

    Now, I’m inclined to think that the universe cannot have a material cause, for if it is the total aggregate of all space and time, it seems that there simply cannot be any logically prior material from which it can be formed. But lets imagine that there *was* material logically prior to the universe, in this changeless beginningless state we’ve been considering. We still haven’t answered the question of what caused the universe, because any such cause needs to cause time too, and so effect change in a changeless state. In other words, we have not evaded the need for an efficient cause. Furthermore, every objection I’ve heard that tries to show the universe causing itself, or something along those lines, has been offering an efficient causation, not a material one. Usually, people will (hopelessly) cite natural laws, and the assumption is that whatever grounds these laws will be an efficient cause of the universe.

    d. I suppose I don’t need to invoke *libertarian* explanation, since I can point to *agential* explanation, which is sufficient to make my point. Again, there has been no reason given for thinking that agential explanation is insufficient in this case, and therefore no reason to think that an unembodied mind is sufficiently explanatory. And since no alternative candidate has been given, it follows that the work of an extremely powerful unembodied mind *is* the only valid explanation. The detractor either needs to give us a better candidate, or show us that this candidate is invalid, neither of which he has done.

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    Roland Elliott - October 25, 2013, 6:54 am

    Oh, by the way, the quote was from here:

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    Todd - October 25, 2013, 1:29 pm

    Is the first premise, “Whatever begins to exist has a cause,” meant to be inductively grounded or metaphysically necessary?

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    Roland Elliott - October 25, 2013, 3:22 pm

    It is both. You might not think that necessary truths can be evidenced a posteriori, but consider what Craig says, “Lessing reflects the thinking of Leibniz, Kant, and others of his day that necessary truths, whether these were analytic or synthetic, were known a priori, that is, not on the basis of experience. But one of the insights of Saul Kripke in our day is that there are also necessary truths which are known a posteriori, for example, that Gold has the atomic number 79. This is not a truth that we could know by reason alone, but having once become familiar with the element gold, we can see that an element which had a different atomic number than 79, no matter how much it resembled gold, just is not gold.”

    (

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    Todd - October 29, 2013, 12:02 pm

    The problem I have with “Whatever begins to exist has a cause,” is that we don’t seem to have any inductive base for it. The familiar examples that we have of things beginning to exist are recombinations and modifications of things that already exist. Since the cosmological argument isn’t about God creating the natural order out of something else, these aren’t relevant. In that case, the first premise looks like it should be “Whatever begins to exist ex nihilo has a cause.” But we have no inductive warrant for that claim, since it looks like a one-off–a singularity, as we now like to call it.

    That leaves it as metaphysically necessary, and presumably only knowable a priori. At that point I tend to go all Kantian and say that the best we can do is a kind of transcendental deduction, but we can’t get to it by direct demonstration.

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    Roland Elliott - October 29, 2013, 5:26 pm

    I’m not sure I understand. You grant that in everyday experience we see that things begin to exist have causes, yes? Your concern seems to be that when we see a table begin to exist, it involves both an efficient and material cause, is that correct? It seems to me that this nonetheless is evidence for the more general claim that things don’t begin to exist without a cause (be it material or efficient or both), and as such is evidence for the first premise. The first premise is more general than the one you suggest, and I see no reason why we should have to restrict it. While our uniform experience of causation might not be conclusive evidence for its more general claim, it is still confirmatory of it.

    Besides, there’s another sort of inductive evidence (which I personally prefer): if things can pop into existence from nothing (contrary to the first premise), then it is inexplicable why anything and everything doesn’t just pop into existence all the time. You can’t say that it’s a property of the things that they don’t pop into existence from nothing, for logically prior to something existing it has no properties. This concern is also independent upon the types of causes we experience in everyday life, and includes beginning to exist ex nihilo.

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    Todd - October 30, 2013, 1:54 pm

    I think I prefer your alternative construal of the case for the first premise.

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    Roland Elliott - October 30, 2013, 3:07 pm

    Fair enough. That makes two of us then 😛

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    Alex Armstrong VI - October 30, 2013, 5:44 pm

    My apologies for the waiting time. Let me jump right back in.
    c) I agree that I unnecessarily restricted the meaning of indeterminism but I simply must qualify that I was talking about purely material situations that are indeterministic as you seemed to recognize. Your understanding of statistical causation neglects that a distinction can be made between systems that are deterministic and we simply use statistics for the sake of approximation or because we lack a non-statistical theory. For example, what one gets when rolling a dice is not truly indeterministic because if one understood all the physical properties and laws involved after the dice leaves someone’s hand, theoretically (i.e. in the classical world) we could calculate the rest. We only use statistics because we lack the ability to be so precise. The same reasoning applies to your examples of syphilis-paresis, smoking, and even the gun depending on how you construe that example. I am idealizing a bit because the world is not so neatly divided between the microscopic world of quantum mechanics and the macroscopic world of classical mechanics but the idealization helps make the important distinction clear.
    If your gun example is to be like photon emission from an excited atom, you would have to say that when you pull the trigger, the gun is in a ready-to-fire state. A probability defines when the gun will fire but theoretically the gun could wait centuries before it finally fires. Why it fires 5 seconds after you pull the trigger as opposed 5 years is an in principle unexplainable event if it is truly indeterministic. You may have been a key part in the causal chain but you only explain why the gun went into the ready-to-fire state and not why it fired 5 second after you pulled the trigger instead of 5 years. This to me implies that there is no efficient cause for the event of the bullet firing though there is an efficient cause for the ready-to-fire state.
    Im not sure what your point about Humeanism and laws is. I don’t believe I am giving up on there being any grounds for laws. It seems like I need to better understand your idea of indeterministic causation and why we can posit something as the efficient cause of an event where time elapses between the efficient cause creating the “sufficient” state and the event actually occurring (e.g. the gun example). Ill wait to hear more from you on that before talking about how the NMG could be a cause of the universe.

    d) I might be able to simplify my point to this. If agential explanation is allowed, particularly of the theistic sort, it cannot be limited. I have trouble explaining why God’s miraculous intervention is not a better explanation for gravity than general relativity or any scientific theory. Every scientific theory has various features of reality it cannot explain. It may be completely unfruitful for future research but for the Berkeleyen idealist, nothing is left unexplained and so it seems better on all fronts compared to our current scientific attempts if our goal is to explain things. Unless some criterion can be given for how to know when not to use agential explanation, I find it difficult employing it at all.

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    Roland Elliott - November 9, 2013, 10:04 am

    I hope I remember everything 😛 I’ll post about (c) first.

    c) Alex, if I remember correctly, you cited a bunch of indeterministic phenomenon in nature and said that this implies that they have no efficient cause. I gave examples of indeterministic situations that are caused. You complain that the examples I gave were not indeterministic, or rather that the statistics in those cases don’t model the system but our knowledge of the system. Surely I could say the same about your quantum mechanics cases? After all, there are certainly deterministic interpretations of quantum mechanics out there. I see no reason for thinking that relevant processes required in the syphilis-paresis and smoking cases (more so the former) are deterministic (especially if the fundamental laws are indeterministic). That, in spite of this, we are still comfortable saying that these are cases of causation surely undercuts your claim.

    What about the libertarian cases? I don’t think it’s sufficient for you to restrict to *material* cases, for here we are concerned about efficient causation in general. If libertarian causes are coherent examples (as many people think they are), then that is sufficient to show that efficient causation needn’t be deterministic.

    What about the gun case? You seem to assume some specific working of the gun, which isn’t what I had in mind. We don’t need the gun to be constructable in this world for the thought experiment (about the nature of causation) to work. What if the gun were set up (by some ingenious method) such that on pulling the trigger there is (ontically) a 50% chance of the bullet being shot? I would also challenge your concern about me being merely part of the causal chain, for the same could be said about any macroscopic event, surely? Yet we regularly call certain things causes (like, consider the case where I pull the trigger of a deterministic gun. Here I merely start a series of events that lead to the bullet being launched too).

    Now, those are my examples. And even if they don’t work, I think you need to give some reason for thinking that causation being indeterministic means there’s no efficient cause.

    My point about Humeanism is that unless one is a Humean, one *has* to account for the laws of nature (whether they be deterministic or not) by some sort of more fundamental thing. This thing, then, would be their cause. Say we go the Aristotelian route, where the laws of nature are grounded in the essential dispositions or tendencies of the natural objects themselves. In this case, the objects would be the efficient causes (for example, the quantum vacuum would be both the efficient and material cause of the virtual particles). If we are convinced that quantum events are non-deerministic, indeterminisitic efficient causation follows as a consequence.

    I wanted to say one additional thing, perculiar to the issue at hand. I think we have non-arbitrary motivation for asking for an efficient cause here. Say the detractor said that they’ve given a material cause of the universe, and denies that they need to give an efficient one. They still couldn’t answer the question of how a temporal universe came from a changeless state. To illustrate this, perhaps they say that the material is eternal, or that it into existence from some other process. Neither of these answer how we got a changing universe. The question of efficient cause of a changing universe from a changeless state is inevitable, I think.

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    Roland Elliott - November 24, 2013, 1:34 pm

    d) If we’re talking about the existence of God as broadly understood in the Christian tradition, then I agree that God can be invoked to answer most questions, but the answer will not always be appropriate.

    Take, for example, the case where I let go of an apple and it falls to the ground. I ask you, “why did the apple fall?” You can answer me with some will of God answer or something along those lines, but chances are that’s not the sense in which I was asking the question. In that case I was asking about natural laws and so a more appropriate answer would be to explain the idea of gravity (perhaps discussing the equivalence principle from general relativity and/or the bending of spacetime if I were sufficiently interested).

    This isn’t particular to theistic explanations either (as you note). If the kettle was boiling and I asked why, you could answer by telling me you put it on earlier, or by saying, “the heat of the flame is being conducted via the copper bottom of the kettle to the water, increasing the kinetic energy of the water molecules, such that they vibrate so violently that they break the surface tension of the water and are thrown off in the form of steam” (taken from the KCA article in the Blackwell Companion to Natural Theology). Depending on the sense in which I asked the question, only one of these answers will be appropriate.

    One more example: imagine, again, we go the Aristotelian route in grounding the lawness natural laws. Go back to the question of the apple falling. Here you could answer my question by explaining that the particles in the apple (or even the apple itself depending on the scale at which you’re talking) have the disposition to do such and such which has the consequence of the apple falling. Again, whether this answer is adequate will depend on the sense in which the question is asked.

    The reason God can be used in so many explanations is because, per the Leibnizian-style cosmological arguments, he makes for a good ultimate explanation. So, depending on how far back we want to go, we can probably trace an explanation back to him. This doesn’t mean, however, that theistic explanations are always appropriate to the question at hand.

    Now, when it comes to the case at hand, we aren’t really restricting ourselves to a specific class of explanations. We’re simply asking what sort of being the first cause could be. That the first cause is an unembodied mind best explains the data at hand.

    I thought this blog post by Alexander Pruss was also interesting when thinking about the strength agential explanations:

    So, in summary, allowing agential (theistic) explanations isn’t really as limiting as you suspect, for we need to take into account of the sense in which we need explanation. While agential explanations aren’t always the best, in this case it seems sufficient (since we’ve been given no reason for thinking the “unembodied mind” explanation is insufficient) and we have no competing candidates.

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    Alex Armstrong VI - December 2, 2013, 10:04 pm

    Unfortunately I currently do not have a response to give but I felt I must say a brief comment about the lack of my comments. I might not be able to get back to commenting on this for at least a couple more weeks but hopefully Ill make the time after Christmas to write a thoughtful response to the thoughtful comments. On a related note, I plan on doing some research during this upcoming year on the principle of parsimony and its role in science, particularly in relation to theistic/agential explanations. I look forward to how this will enlighten me on the interesting issues we have raised here.

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    Alex Armstrong VI - January 7, 2014, 4:44 pm

    Ok. My apologies for the long break and I hope that we have not lost the opportunity to keep thinking about these interesting issues. Let me jump right in:

    c) You are right that there are potential deterministic interpretations of quantum mechanics (e.g. pilot-wave theories), but I find merely acknowledging this to be insufficient as a response. In objecting to the kalam, it only seems necessary to show that material causation without efficient causation is coherent. I am arguing that such a notion is coherent if we believe indeterministic theories of quantum mechanics are coherent as well. All this response shows is that another interpretation exists but not that the indeterministic ones are problematic, which the defender of the Kalam needs to do.
    We seem to have a continued confusion about what we mean by causation. I agree with what you are saying if we blend the variety of ways we colloquially use the word “cause.” I think its important to distinguish between cause as (1) the event (or state) that is in direct logical, spatial, and/or temporal contact with the event it causes (I am going to ignore entanglement and similar counter examples for the issue at hand) and (2) the event that is most relevant or significant to a given inquiry into a causal chain leading to some event. You seem to conflate these two understandings. In firing the gun, you may be cause(2) for the detective who wants to know who murdered someone but you are certainly not cause(1) because as you said you only started off a series of events. Your definition needs to be refined or else it leads to the absurd conclusion that I am the cause of nearly everything. The cliche butterfly effect of chaos theory highlights how your firing the bullet plays at least some role in the unfolding of all history after that point. All our actions are part of the vast chain of events causing many things to happen so its important to keep these two notions of causation distinct when arguing about what is cause(1) of the universe.
    All this to say that the cause(1) of events that are ontologically indeterministic, such as photon emission, seem to consist only of a material cause and no efficient causes. There may be deterministic interpretation of this but there are also coherent indeterministic interpretations. So far you have provided cases of events that are typically considered ontologically deterministic (e.g. rolling dice, probability guns, etc..) though we may treat them as epistemically indeterministic by using statistics instead of a set of deterministic equations. You construed the gun example so that it is ontologically indeterministic showing that indeterministic event-event causation is possible. However, at that point your analogy is just not analogous to photon emission, which still seems best described as stave-event causation because of the temporal separation between the emission and any preceding event. I think this provides grounds for responding to the points about Humeanism (which i would not consider myself to be) and a temporal universe arising from a changeless state but I will keep things short here and let you bring those points back up if you find them important objections still.

    d) If you are making the distinction between natural and teleological explanation (or whatever you want to call the distinction) then I think the question remains as to whether God or an agent can be used as the natural explanation of something in the physical world. I think the issue of teleological explanation is not relevant to the discussion here because we are asking if we can posit God as the natural explanation (or whatever you want to call it) of the origin of the universe. If one wants to know why the kettle is boiling in the natural sense, one can explain it as resulting from various laws of nature or take the Berkeleyan approach of saying that there are no laws and it is merely the arbitrary will of God that makes the kettle appear to us in such a way. There is no objection to the Berkeleyan approach that I am aware of that doesn’t amount to simply rejecting it as unacceptable because in explaining everything it explains nothing. It values explanatory power over all other goals of an explanation. I could hold that God’s will is the teleological explanation of the universe even though the natural explanation is the NMG. However, the kalam argument is trying to show that God’s will and action are the teleological and natural explanations. It is this move that I have trouble restraining because once God is allowed as a natural explanation at all, why not explain the boiling kettle or falling apple with God instead of thermodynamics or gravity. The article by Pruss seems to me to address the question of competing agential explanations or competing physical explanations but does not delve into competing agential and physical explanations as I am discussing here. Unless Pruss more specifically laid out some principle or criterion for comparing agential and physical explanations, I still struggle to see how it is possible.

    Summarizing my overall argument at this point to keep things clear, I think that unless an actual infinity can be shown to be metaphysically absurd, then one cannot eliminate the NMG as an alternative explanation to God as the cause(1) of the universe, leaving God as the only possible cause(1). Because we lack a way of preferring God as a natural explanation for some phenomena without preferring Berkeleyan idealism where God is the natural explanation of everything, it is better to remain agnostic about the specific candidate for the NMG but continue looking for one given that there are at least no sustainable objections to the concept. You have made various objection to this claim to which I have tried responding but I include this to keep us on the same page because it has been a while.

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    Roland Elliott - January 15, 2014, 10:14 am

    c) I was trying to retrace everything, and I think this is where we stand: I noted that state-event causation is incoherent and you attempted to show that state-event causation happens by pointing to indeterministic quantum events. If it occurs in reality, then it must be coherent.

    I’m slightly confused by what you’re saying here though. You seem to be equating material causation and state-event causation, but these are quite different. It seems to me that something like “M is the material cause of E if and only if E is materially constituted from M”. State-event causation is a putative example of efficient causation (that is, somehow, the state is the efficient cause of the event). It seems to me that if your reasoning is not to be question-begging, you need to abandon the quest for finding an example of state-event causation (it’s question begging, because in order for your interpretation of quantum events to be examples of state-event causation, you first need state-event causation to be coherent) and rather claim that quantum mechanics shows us that some effects occur without efficient causes. So, the argument would go something like:

    1. Quantum events are indeterministic
    2. Indeterministic effects cannot have efficient causes
    3. Therefore, some effects do not have efficient causes

    Since I’m personally inclined towards the consistent histories interpretation of quantum mechanics, which is indeterministic, I won’t deny (1). I don’t think, however, that you’ve managed to show (2).

    You pointed to state transition of a electron. It seems (from my cursory reading on the topic) that electrons change state through absorption or emission of photons. This is event-event causation. Perhaps you’ll push the question back a step and ask why the electron emitted the photon in the first place. I’m not too clued up on the physics of this all, so perhaps there is a nice physical answer to this (like about it’s environment constantly being in flux and these changes causing the relevant behaviour, which is again event-event causation), but metaphysically, if we’re Aristotleans we’d say that the electron’s emission was effected by its acting on its natural dispositions. Again, event-event causation. If we’re “Externalists”, in which case we ground the natural laws in the causal activity of a non-natural being, then it is in virtue of this causal activity that the electron acts as it does. This is again event-event causation. This is the point I was trying to make about non-Humeanism: naturally occuring phenonmena, whether they be indeterministic or deterministic, will inevitably have efficient causes, which derive from our grounding of natural laws (which we need if we’re non-Humean).

    There’s also the quantum vacuum and virtual particles. But this is clearly a case of event-event causation: physically, the fluctuations in the vacuum cause the particles to exist, and metaphysically, the vacuum acting on its natural dispositions brings the particles into existence.

    I’m not sure if we want to consider state-event causation (since I think I correctly summarised your argument above, and it doesn’t involve state-event causation), but to give an example of its incoherence: imagine a man was sitting down, and then stood up. What was the cause of his standing up? I doesn’t make any sense to say that it was the state of him sitting down. It would have to be something like an change in his environment (like an explosion), or a change in him (like a decision). At best the state of him sitting down causes the state of there being an impression in the chair. But this is state-state causation.

    You introduced the distinction between “direct causes” (cause(1)) and “indirect causes via a causal chain” (cause(2)). That’s fine, but I’m not sure it really helps (also, indirect causation doesn’t mean I cause everything, for there being free agents and multiple causal chains prevents this): if I start a causal chain, the end of which is an indeterministic effect, then surely it follows that there was a case of indeterministic efficient causation in the chain itself?

    Finally, I don’t think you’ve adequately responded to my concern about the material cause being insufficient in the case at hand. Assume, for the sake of argument, that I agreed with (3) in the argument above. Then I wondered how a changing universe could be produced from a changeless state. Positing that the material of the universe existed in the changeless state doesn’t help at all, for now all we know is where the material came from. We’re still at a loss to explain how we have a changing universe that arose from a changeless moment. It seems the only adequate answer needs to be in terms of an efficient cause of the universe, and this inevitably leads to agent-event causation. We can see again how state-event causation doesn’t make sense here: it doesn’t answer the question “what caused the first event?” to say something like “the universe was in a state of changelessness”. If someone gave an answer like that, I’d assume they’ve misuderstood the question.

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    Roland Elliott - January 15, 2014, 10:14 am

    That was quite long. I can’t respond to (d) at the moment, but when I do, I’ll make it shorter.

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    Roland Elliott - January 15, 2014, 10:31 am

    Actually, it turns out I’ve got a bit more time than I thought, so here comes by comments on (d)

    d) Hmmm… I’m not sure I was getting at teleological vs. non-teleological explanations there. Of my examples, only one happened to be teleological. My point was that even though God is an ultimate explanation, that doesn’t mean he’s the appropriate answer for every “why?” question. Again, imagine the question is “why do apples fall?” We can answer this by citing the law of gravity, or by citing their natural disposition to do so, or by citing God’s creating them with such dispositions and concurring with their bringing these effects about. Not all of these are equally appropriate given the sense in which the question was asked.

    Or again, the kettle. Why is the kettle boiling? Well, we could cite the physical laws are involved in a kettle boiling (like in my earlier quote from the Blackwell companion), or we could explain that I put the kettle on earlier. Again, it might be that only one of these answers is adequate.

    Now in our case, if positing agents is not in principle invalid, then I see no reason why positing an unembodied mind (the only candidate we know of that fits our data) isn’t valid. We’ve posited this being as an explanation for a phenomenon, and we know of only one type that this being could be. How is it not fair to infer that this being is indeed that type until such time as we have alternative candidates?

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    Alex Armstrong VI - January 17, 2014, 5:44 pm

    c) In terms of my argument for state-event causation, I am not trying to use electron transitions as evidence as much as I was hoping it would be an illuminating example of what state-event causation would look like. We agree that using an example as evidence would be question-begging. My main point, which you pick up on in the later paragraphs, is that the main conceptual objection against state-event causation is that it involves no efficient cause but I have been trying to show that this is not a problem because efficient causes are not involved in acceptable understandings of indeterministic causation. So your statement of my argument most adequately addresses my point here. Your responses are good objections as well. Your attempt to explain physically how electron transition could be event-event causation is speculative and I would be interested to see you find an article that postulates an explanation for transitions because as far as I am aware the scientific community considers them spontaneous and lacking and physical mechanism that produces them. Your metaphysical objection is the strongest objection and at this point I will admit my lack of sufficient awareness on the literature of the metaphysics of causality. So I will merely accept that objection for now until I can more adequately prepare a response.
    I agree with your points about virtual particles and the man standing up but then I don’t find those analogous to the electron transitions where there are no fluctuations or environmental disturbances we are aware of that would cause the transition. As for the the cause distinction, if my construal of indeterministic effects in taken as true in electron transition than I don’t see how you could be considered even a cause(2). Consider the case of you loading a gun and then someone coming along and firing it. You are clearly not the efficient cause of the gun firing because the person who came along and fired it is. However, what happens in the electron transition case is analogous to you loading the gun and then the gun firing on it own hours later. You check and nothing about the gun changed. There is no measurable disturbance in the gun that shows it to have misfired or something happened. Its as if the bullet just freely willed to go flying out of the gun with no discernable external explanation for its decision to move. We hold the bullet to be impersonal so it isn’t an instance of agent causation. You being the one who loaded the gun seems irrelevant to our wondering if there is an efficient cause to the gun going off. Again your metaphysical concerns seem most relevant here depending on if we can consider something about the bullet’s nature or the influence of “laws of nature” to be the efficient cause. However, I am not convinced that is a satisfying response but will need to look more into the Humean alternative because as I said before I have generally found such a view unfavorable.
    As for your last paragraph, I still think that construing the material cause of the universe as being in a constant state of sufficiency such that it is never not generating a universe allows for there to be sense of nothing changing in so far as the NMG is concerned. Change occurs only in so far as universes are being created but nothing about the NMG is changing. There may be no efficient cause that we can point to but at least it avoids the absurdity of creation out of nothing.

    I will get to you points for (d) in a later comment

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