# Did the Universe Begin? V: The Ordinary Second Law

The next piece of evidence we will consider for the beginning of the universe is the Second Law of Thermodynamics.  I sometimes call this the "Ordinary Second Law" to distinguish it from the "Generalized Second Law" which involves black holes (or other types of causal horizons).

The Second Law of Thermodynamics is a rather special law of nature because it distinguishes the past from the future.  It says that a quantity called the "entropy" always increases as time passes.  I've already written some articles explaining (1) what the entropy is (hint: it does not measure the amount of evil), (2) why it increases, and (3) how it has an interesting generalization to situations involving black holes (the "Generalized Second Law" mentioned earlier in this series).  Rather than repeat myself, I will link to these articles here:

If you're back from reading those—or if you're willing to take my word for it that there's a number called the "entropy" which has to increase as time goes on—then let's start by using it to make an argument that there had to be a Beginning.  Then we can see if there are any loopholes that can be used to evade the argument.

At each time $t$ the entropy $S(t)$ takes some particular numerical value.  As you go back in time, the Second Law says that $S$ gets smaller and smaller, until eventually it reaches its minimum value.  (Because of the way entropy is defined, it normally can't be a negative number, so the smallest it can get is 0.)

Now, either (a) there was a beginning of time, or (b) the entropy remained more or less at the same value for an infinite amount of time prior to some particular moment; let's call this $t_\mathrm{early}$ since it would have to be at least 13.8 billion years ago (since we know the entropy has been increasing since then).  But in that case, the universe would have had to be really boring for the first "half" of eternity $t < t_\mathrm{early}$, since interesting processes tend to produce entropy.  It's unclear what mechanism would cause the universe to suddenly become interesting.  Since scenario (b) seems implausible (though not necessarily impossible), we conclude that probably (a) is right, and there was a first moment of time.

Now, how might we evade this conclusion?  Here's three possible ways, although the first one doesn't really work, and the second one seems to run into some problems as well...

1. Thermal Fluctuations.  One way might be to take advantage of the fact that the Second Law is not an exact law of Nature.  Because it is statistical in Nature, the entropy can decrease, it's just very unlikely for it to decrease by large amounts.  But if you keep a system at maximum entropy for an very very long amount of time, eventually there will be thermal "fluctuations" in which the entropy gets down to arbitrarily small amounts.

So could our universe be a thermal fluctuation?  No, because a thermal fluctuation is unlikely to produce a whole cosmology filled with low entropy galaxies.  It would be much more likely for the fluctuation to produce the minimum amount of matter necessary to support a (briefly existing) intelligent life form (this is called a Boltzmann brain, by the way).  Since fluctuations are totally random, every possible matter configuration (with a given energy) would be equally likely, whereas elementary sanity says that this is not the case.

2. Shell Games with Infinity.  Another possible loophole is that actually none of this is well-defined because space is infinite and so $S = +\infty$.  Entropy could be produced both to the past and the future, but it wouldn't matter since the total amount is always infinity.

This loophole is used (e.g.) in the ekpyrotic scenario, a rather wild alternative to inflation in which there are membranes living in a 5th dimension which periodically collide with each other, causing Big Bounces (supposedly—this was really just a guess about what might happen).  The bounces are supposed to happen on a cyclic basis, so that the model is eternal in both time directions.  From the perspective of the 4 ordinary spacetime dimensions, the universe is infinite and expanding on average, which makes it so that the entropy "thins out" and prevents the universe from dying of heat death when its entropy reaches a maximum value.  Hence the BGV theorem tells us that the spacetime would have a beginning for most geodesics, even though some of them go back in time infinitely.

(Also, If the BICEP2 measurement of primordial gravity waves is right, that's also inconsistent with the ekpyrotic scenario.  Although there's some doubt now about whether BICEP2 properly screened for alternative sources of CMB polarization due to intervening dust.  Anyway the ekpyrotic scenario is just an example, not necessarily the only model like this.)

3. Arrow of Time Reversal.  This exploits the fact that we don't know the real reason why the Second Law is true in the first place.

Here is a paradox: the fundamental Laws of Physics are (more or less) symmetric between the past and future.  That is, if you replace $t \to -t$ in the equations, everything stays the same, more or less (*).  Yet, in the actual universe the past and future are quite different because of the Second Law, which says that the entropy is increasing.  And yet, the Second Law is regarded not as a fundamental law of Nature, but merely an effective statistical measure of what is most likely to happen given the fundamental laws of Nature?  So what gives?—How can you get a time asymmetric Law to pop out of time symmetric Laws.

The best people can tell is that the universe just started in a low entropy state.  It's a matter of the "initial conditions", not the Laws of Physics themselves.  (Although later we will discuss the Hartle-Hawking proposal, which blurs the boundaries between "initial conditions" and "Laws of Nature".)

Since we don't really understand why the universe began in a low entropy state, we are free to build (equally perplexing) models in which the entropy of the universe is small somewhere in the middle of time, rather than at the beginning.  If we assume the entropy was small at some time (let's make an arbitrary coordinate choice and call it $t = 0$), and then evolve that low-entropy state in both time directions, we typically find that the entropy will increase in either time direction.  Thus, for times $t < 0$, we find that $S(t)$ is a decreasing function of $t$.  We then say that the thermodynamic arrow of time is reversed.

This occurs in the Aguirre-Gratton model, in which the entropy decreases during a period of contraction, and then when the universe reaches its smallest size, there is a "bounce" instead of a singularity, after which the universe expands and entropy increases.  This model is symmetric under $t \to -t$.  Any people living in that time would (un)die and then shrink than be (un)born, but it would all seem just the same to them, because they'd also remember things backwards in time!

Sean Carroll and Jennifer Chen have also suggested a model like that, which involves many baby universes being created from an original inflating mother universe, whose arrow of time reverses.  (**)

During the debate, Craig focused most of his fire on the Carroll-Chen model, although Carroll modestly wanted to talk about the Aguirre-Gratton model instead:

So, I want to draw attention not to my model but to the model of Anthony Aguirre and Steven Gratton because this is perfectly well defined. This is a bouncing cosmology that is infinite in time, it goes from minus infinity to infinity, it has classical description everywhere. There is no possible sense in which this universe comes into existence at some moment in time. I would really like Dr. Craig to explain to us why this universe is not okay.

When Carroll says that there is "no possible sense in which this universe comes into existence at some moment of time", I think he is neglecting to consider that the thermodynamic arrow of time itself defines a notion of past and future.  There is a very real sense in which, in the Aguirre-Gratton or Carroll-Chen models, the time $t = 0$ is a beginning of time (due to being the lowest entropy state), and that as one travels away from $t = 0$ to either positive or negative values of $t$, one is travelling to the future in the sense that actually matters to us living and breathing creatures.  As I said in the concluding section of my own paper:

This kind of bounce evades both the singularity and thermodynamic arrow constraints, but still has in some sense a thermodynamic ‘beginning’ in time at the moment of lowest entropy [$t_0$]. That is, both the past and the future would be explained in terms of the low entropy state at $t_0$, while the state at $t_0$ would itself have no explanation in terms of anything to the future or the past. (Thus the moment $t_0$ would seem to raise the same sorts of philosophical questions that any other sort of beginning in time would.)

The Aguirre-Gratton model has no beginning in a geometrical sense, but it still has a beginning in a thermodynamic sense of unexplained "initial conditions".  Thus, I stand by my comments that an Aguirre-Gratton bounce raises the same sorts of questions as a more traditional "beginning" would.

Indeed, one could argue that the low entropy conditions of Aguirre-Gratton would be even more mysterious than in the traditional Big Bang model with a singularity.  In the latter case, there's a mysterious low entropy state, but it emerges from a singularity, and we don't know what laws of physics might exist at that singularity which cause the low entropy condition to emerge.  To some extent the mysteries cancel and make each other less mysterious, since it's not surprising that unknown causes should have unknown effects.

Whereas, if the low entropy condition occurs at a bounce, and the laws of physics there are by stipulation perfectly normal and comprehensible—and even so there is an additional low-entropy condition there, without any explanation in terms of anything else in the universe, either before or after it—then to me that suggests a need to find some sort of philosophical explanation for this strange phenomenon.

This would include potential Cosmological Arguments for the existence of God, although such arguments obviously have philosophical premises as well as physics premises.  This is made abundantly clear by the fact that Carroll doesn't accept the Cosmological Argument even on the assumption that there was a first moment of time.  One wonders therefore why he spent so much time trying to rebut Craig's claims that the universe probably did have a beginning, if it doesn't actually matter in the end.  (For purposes of the debate about God, I mean.  Obviously the cosmological origin of time is a fascinating question, which merits discussion even apart from any theological considerations!  Speaking as a physicist myself, I can certainly sympathize with Carroll getting sidetracked by interesting physics questions, as I've been doing myself throughout this series.)

Endnotes:

(*) Except for some tiny effects associated with the weak force which may not be relevant here, and even these are invariant under CPT, the combination of time reversal $t \to -t$ (T), a spatial reflection $x \to -x$ which switches left and right (P), and switching matter & antimatter (C).  Since the phrasing of the Second Law doesn't care about the distinction between matter/antimatter or left/right, one still has the question: why is the CPT-asymmetric Second Law true?

(**) For some reason in their paper Carroll and Chen wanted to have space be infinitely large even at $t = 0$, which runs into potential issues with the Penrose singularity theorem.  I wrote a paper with Alex Vilenkin slightly extending the classical singularity theorem in this context.  We showed that even if black holes form, the resulting singularities (inside the black holes) are not enough to satisfy the singularity theorem.  You need more of a "cosmological" singularity which is extended through space.  A bounce is not possible unless any observer that escapes to infinity is at least "completely surrounded" by an event horizon, beyond which there are singularities.

I am a Lecturer in Theoretical Physics at the University of Cambridge. Before that, I read Great Books at St. John's College (Santa Fe), got my physics Ph.D. from U Maryland, and did my postdocs at UC Santa Barbara, the Institute for Advanced Study in Princeton, and Stanford. The views expressed on this blog are my own, and should not be attributed to any of these fine institutions.
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### 26 Responses to Did the Universe Begin? V: The Ordinary Second Law

1. g says:

This is made abundantly clear by the fact that Carroll doesn't accept the Cosmological Argument even on the assumption that there was a first moment of time. One wonders therefore why he spent so much time trying to rebut Craig's claims that the universe probably did have a beginning, if it doesn't actually matter in the end.

If someone makes an argument of the form "A and B, so C" and you consider both A and B incorrect, then either of them individually "doesn't actually matter at the end" -- but you can't use that as a reason for not arguing against either of them. And then, if you are aware that any given argument (however strong) will be unconvincing to some people, why not argue against both? It seems to me that that's what Carroll was doing.Also: given that Carroll's target was not "cosmological arguments" generally but Craig's favourite "kalam cosmological argument" specifically, and that does at least appear to depend on a "geometrical" rather than merely a "thermodynamic" arrow of time, it seems clear enough why Carroll regarded Aguirre-Gratton as a better counterexample than Carroll-Chen: neither of them has the kind of beginning Craig claims the universe must have had, but it's clearer-cut for Aguirre-Gratton than for Carroll-Chen.

2. Aron Wall says:

Hi g,
Sure, but I guess maybe I don't care too much about the debate as a debate, considered as a tool to persuade people by whatever means possible, even by ways one doesn't personally agree with. I'd rather get to the heart of which assumptions are actually important, according to Carroll, or to Craig, or to me. (I don't think Carroll has an extremely strong commitment to the view that the universe had no first moment of time---he would admit that this is quite possible---while he does have a strong commitment to the view that in either case one shouldn't deduce the existence of God.)

In light of that, I would eventually like to eventually place the debate in the context of cosmological arguments more generally, not just kalam. (Personally, I think the strongest cosmological arguments do not depend on whether the universe had a beginning, which is why---as I hinted in my last sentence---someone might well wonder about my current crop of posts the exact same thing I wondered about Carroll! Since I admitted to doing the exact same thing, I didn't really intend this as a harsh criticism of Carroll, just a guide to focus people in the direction of what I think are the more important aspects of the debate.)

Regarding whether the kalam argument requires a geometrical or thermodynamical beginning, surely one could phrase it in either way? That is, one could either cash it out as:

1. The Universe had a first moment of time in a geometrical sense,
2. Anything that began to exist in a geometrical sense was caused,
Therefore, 3. The Universe has a cause.

or one could argue:

1. The Universe had a first moment of time in a thermodynamic sense,
2. Anything that began to exist in a thermodynamic sense was caused,
Therefore, 3. The Universe has a cause.

These arguments can be made equally valid, so the question is whether the premises are true. I'm curious whether (and if so, why) you find it so obvious that the first #2 is superior to the second #2 (leaving aside any criticisms which would apply to both arguments, and just making a differential comparison.)

If the premise is based on intuitive notions of cause and effect, it seems to me you could make a claim that our notions of what counts as a cause vs. an effect are rooted more deeply in the Second Law than in anything purely geometrical. With geometry alone, the past is the same as the future, and there is no distinction between cause and effect! So it seems to me that, to the extent that we can justify our notions of causation in terms of physics at all, we should say that if thermodynamic arrow of time is reversed, effects (geometrically) precede their causes. But then the lowest entropy slice of the AG model wouldn't be caused either by the moment just before, or by the moment just after. It would be causeless, unless it has a cause which is outside of the usual timestream. Since the AG model is time-symmetric, this is the only way to assign causation which makes any sense to me.

If you're just trying to go with what Craig claims about the kalam argument, I think that in the spot where he quotes me in his first speech, Criag is implicitly endorsing the second form of the kalam argument. Carroll doesn't accept this change, as he says quite explictly here:

Most importantly, he talks about the fact that if the universe is eternal and you have a Second Law of Thermodynamics then there must have been a moment in the middle when the entropy was lowest, and he calls this a thermodynamic beginning and he quotes another paper. That’s fine except it’s an equivocation on the word beginning. A thermodynamic beginning is not a beginning---it happens in the middle. It’s a moment in the history of the universe from which entropy is higher in one direction of time and the other direction of time. There is no room in such a conception for God to have brought the universe into existence at any one moment.

To his last statement about "no room" I of course strongly disagree, especially since I wouldn't think of God's act of creation as referring to one specific "moment" in the first place---I would say that God is the Creator of all the moments of the Universe. (Although, even on a more "mechanical" view of creation where God creates one moment which in turn produces the rest, I don't see why that moment couldn't be in the middle.)

Regarding Carroll's statement that Craig is equivocating, I think that my numbered arguments above show that this is based on a misunderstanding of what Craig is doing. Craig may be changing the argument, but the new argument is equally valid, and Carroll didn't present any actual argument that the second #2 is worse than the first #2 (although he did perhaps present some criticisms which might apply to either).

3. g says:

I agree that the two forms of the kalam cosmological argument can be made equally strong, but only because I think both are hopeless. But a "merely thermodynamic" beginning seems in some sense like a much less fundamental thing, and therefore (even) less credible as a basis for saying there must be some kind of external cause. I'm aware that this is kinda handwavy, but since I am unable to see any credibility in any version of the KCA it's about the best I can do.

(It seems to me that the only remotely like a justification for the axiom "whatever begins to exist has a cause" comes from a sort of intuitive picture where first X isn't there, and then *bang!* suddenly X is there, and it's natural to ask "why?". Of course this sort of beginning is very different indeed from either a "geometric" or a "thermodynamic" beginning, and is rather the wrong sort of thing to be imagining when thinking about the beginning of the universe. I can't help entertaining the -- admittedly uncharitable -- suspicion that whoever first thought of the argument began with the simpler "everything has a cause; so the universe has a cause, et hoc dicimus Deum, QED" and then tried to patch it up on noticing that this would also require God to have a cause. Or, to put it differently, I uncharitably suspect that the real reason why advocates of the KCA accept its first premise is simply that that premise forms a part of the KCA! At any rate, I find myself wholly unconvinced by every actual justification I have seen offered for it.)

I share your preference for mutual truth-seeking over adversarial debate -- but given that Carroll and Craig were in fact engaged in something approximating an adversarial debate, I still find it odd to say "one wonders" why Carroll chose to explain more than one error he considers to be present in Craig's argument.

4. Roy Carvalho says:

One can argue that the Second Law is incomplete. Entropy always increases, if you draw a box around the process, such as "The egg fell off the table." Voila, entropy. But how did the egg get on the table? It took four billion years of evolution to make that egg. And if you just left it alone, it would become a chicken.
There is a tremendous anti-entropy at work. The presence of the egg tells you that.
Anti-entropy (perhaps negative entropy is better term) is driving evolution. Statistically, evolution from dust into chickens, is a trillion times impossible.
Anti-entropy can be modeled by fractal math. The Mandelbrot Set gives you more and more texture the more you let it run. Now look at the surface of the Eath. A barren rock, eroding, eaten by entropy, according the Second Law? No, a branching paradise of greater and greater complexity. The living ecosystem eats entropy as well as energy. Alive systems look like fractals. Branching trees, leaf structure, vasculaur structure, nerve systems.
What is the source? God? I won't argue for or against God. But look at the math. Non-alive systems are doomed by thermodynamics, in other words, statistics. But alive systems are quite simply not doomed. Alive systems eat energy, eat entropy, and evolve.
What does it mean to evolve? It means to continue, in other words, retain Identity, but to change over time.
Mandelbrot Sets are generated by the process z = z2 + c. This means z keeps changing its value. It sounds like cheating. How can z keep changing, yet stay z? Because it's not an equation, it's a process. We know it is a real process because we see fractals forming all around us, formed by living systems.
Is there something quantum in nature that can proceed as z = z2 + c? Yes, the carbon atom. Add carbon to carbon, and what do you get? Carbon. Now just add water. Carbon and hydrogen and oxygen. Yes, it's a miracle that it is so stable, and so good at processing energy, that it can evolve. But evolve it did.
We have a bridge from quantum to classical, carbon chains. Put a bunch of helium in space, and you get helium. Put a bunch of carbon in space, add energy and water, and you get organic compounds. In space!
You may call it anthropic, but I would disagree. The fractal process is at work. It works with carbon atoms, uniquely, at the base. It works because carbon binds to carbon and is stable. Eventually carbon chains absorb both energy and entropy. Apparently, this process can run away. It did, here on Earth.
I would venture to say that the Second Law is exactly balanced by the Anti-Second Law, universally. If that be not the case, the Earth must be unique. That is also possible.

5. Alex says:

Thanks for all these fascinating explanations ! I just have one comment : the fact you can change "t" to "-t" without changing the form of equations of motion doesn't mean the concerned motion is actually reversible. Most of dynamical systems (classical or quantum ones), especially those composed by a lot of particules, are chaotic and "loose" any information about their past after their Lyapounov time (the latter could be really short, think about a molecule in gas even at standard temperature an pressure). The common reversible and then integrable dynamical system is more and idealization (pendulum,...) than a real example of "how it works in nature". Hence, most of the time, you cannot go back in time, even with the familiar Newton's equations. Obviously, it doesn't solve the fascinating "initial value of entropy" issue, but it could suggest that laws of nature are reversible, and they're not.

6. i like pizza says:

Hey Aron,

I have a few questions about the Aguirre-Gratton model. First you'll have to forgive me for my ignorance on the topic. I know next to nothing about physics, so even dumbed down explanations can go over my head.

I'm visualizing the Aguirre-Gratton model as an hourglass on its side with the vertical plane measuring entropy and the horizontal plane measuring time. At the left of the hourglass is negative infinity; at the center is t=0, when entropy is at its lowest; and at the right is infinity. If that's not a proper way to visualize it, please let me know.

(1) Time isn't "actively" moving in both directions, correct? In other words, time isn't currently moving towards negative infinity (which it hasn't yet reached) on the left of the hourglass in the same way that it's moving towards infinity on the right. Rather, time is only moving from left to right (using the hourglass visualization). Is that correct?

(2) If that's right, and time is moving from negative infinity to infinity, I don't quite get what you mean when you say it has a "thermodynamic beginning". If negative infinity came before it, and positive infinity comes after it, how is it a "beginning" and not the middle? As you said, this is a model: "in which the entropy of the universe is small somewhere in the middle of time ..."

If it's because that's when entropy was at its lowest, wouldn't that just be the beginning of increasing entropy, not the beginning of the universe?

I read an explanation by James Sinclair, which seems to address this question (http://www.reasonablefaith.org/current-cosmology-and-the-beginning-of-the-universe). I'm not really sure I understand his explanation, but he seems to say that because the universe at t0 universe's past, meaning that the t>0 universe would have 'begun' to exist.

I'm not sure I got that right, though; and even if I did, it still makes my brain melt trying to understand.

(3) Does the universe under this model bounce an infinite number of times or just once? It seems just once, but I wanted to confirms this.

(4) As we move forward in time (or backwards in time when t<0) entropy increases. Is there a point at which max entropy is reached, or does it continue to increase to infinity?

(5) Does this model have a singularity (t=0) at which point the laws of physics are unknown to us? I take it that's not the case, based on your comment that "if the low entropy condition occurs at a bounce, and the laws of physics there are by stipulation perfectly normal and comprehensible ..." Is that correct?

7. i like pizza says:

bah...the comments feature thinks the less-than and greater-than signs are html tags, and is omitting everything in between. sorry for the spam (feel free to delete the previous comment), but let me try rephrasing without those symbols:

"I'm not really sure I understand his explanation, but he seems to say that because the left hourglass universe has a reversed arrow of time, it wouldn't be a part of the right hourglass universe's past, meaning that the right hourglass universe would have 'begun' to exist."

8. Aron Wall says:

Dear i-like-pizza,

1) I don't think the concept of time "actively" moving has any meaning. Once we plot time on an axis as if it were a spatial direction, the spacetime universe just IS. It doesn't flow. the only way it could "flow" is if there were some sort of "meta-time" in which time exists and could change, like in fiction about time travellers going back in time and changing things. I admit that in our conscious perceptions, it seems to us as if time flows, but I think this is the result of how our perceptions and memories are structured, and not an objective fact about time.
In the AG model, the past and future are treated symmetrically on the mathematical level. Any observers who lived in the past contracting region would feel like time was "flowing" in the opposite direction (towards $t = -\infty$), and I don't think it corresponds to an objective fact about the universe...

(St. Craig would disagree with me about this, by the way. Analytic philosophers would say that he endorses the "A-theory" of time, while I endorse the "B-theory" of time.)

2. To the extent that there is an objective distinction between the past and future, I believe it is due to the Second Law of Thermodynamics. As a result of the Second Law, events in the future have explanations in terms of past events, but not vice versa. As a result, in the AG model, the middle slice at $t = 0$ would in this thermodynamic sense be the cause or explanation of all the other moments of time, but not vice versa. This is one sense in which it would be like a "beginning" of the universe. The philosophers can then go argue about whether this is the right type of beginning to run something like the kalam argument (if any).

3. The AG model just bounces once.

4. I think this is a point which is confusing even to many experts, for the following reason. At late times, the universe seems to approach something like de Sitter space. We know there is an entropy associated with de Sitter space, but it is controversial what the entropy represents, this being related to deep quantum gravity questions. I would say it is the maximum entropy associated with one causal patch of de Sitter space (i.e. the region accessible to a single observer, inside of their horizon), and that there is no maximum entropy if you consider all of the patches. My preferred terminology for expressing this is that the universe has a maximum generalized entropy but no maximum ordinary entropy. Not all physicists are as careful to make this distinction, so I think they end up being confused.

5. It is correct that there is no singularity at the bounce of an AG model. However, there could still be black holes formed to the future of the bounce (and white holes formed in time-reverse to the past). These would have singularities inside of them. So there are singularities, but not at $t = 0$.

9. Aron Wall says:

Alex,
I think we have to be careful what we mean by reversible. If you know about a chaotic system only to some finite precision, then it's true you can't predict what it used to be like far in the past. But you also can't predict its behavior an equal time to the future! So as far as that is concerned, the past and future are the same. Distinctions between them in the laws of physics are implicitly based on the Second Law.

On the other hand, if you know the system to infinite precision, then you can predict what it will do at arbitrarily long times in either direction. So classically, we can still talk about the laws of physics as being perfectly predictive, even though practically speaking there are limits. Of course, in a quantum system there are limits on the precision due to the uncertainty principle.

Roy,
There is no contradiction between the Second Law and the evolution of complex life forms. The Second Law only says that the total entropy of a closed system can't decrease. But the Earth is not a closed system: it receives low-entropy radiation from the sun, and emits high-entropy radiation into space. The entropy of an individual life form can decrease, because it doesn't just eat energy and entropy, it also emits them, by a variety of processes which I feel no need to describe in detail. On balance, the entropy of the universe goes up. But the entropy of an individual entity can decrease, so long as the entropy goes somewhere else.

10. Aron Wall says:

g,
If you mean that you yourself are unconvinced by the argument, fine. But if by "hopeless" you mean that no reasonable person could find it persuasive, I think that's excessive. Certainly the major premise (my #2) holds for all of the objects of our everyday experience. Carroll (and you) argue that the beginning of the universe is different in some relevant respects (namely, there not being any moment of time before). That's true, but I'm not sure it drains the premise of all intuitive plausibility. Someone might still think that an entity which has a first moment of existence is not a suitable candidate to be the most fundamental entity in existence. Although I think the best versions of the Cosmological Argument don't need to invoke time explicitly in this way.

Since you admit your attribution of the "Everything has a cause" argument to the Theists is uncharitable, I'm not sure there's much left for me to say about that, besides to link to this polemic against some similar attributions. One can throw about accusations of bad faith all day long: for example, a theist could accuse atheists of denying premise #2 simply because they don't want to believe in God. That sort of conversational move isn't usually very productive unless one can back it up with solid evidence.

Empirically, I think it can be shown that there exist at least some people who accept the major premise of kalam, but not because they want to believe in God! At least some atheists seem to prefer models of the universe in which time goes infinitely to the past. I think this is probably because they implicitly accept something like the major premise of kalam, and since they don't believe in a transcendental cause of the universe, they deny the minor premise (my #1). You are free to disagree with these folks' intuition, but they certainly don't have it because they want to prove Theism by any means necessary!

11. g says:

I don't think there's anything so hopeless that no reasonable person finds it persuasive. So that isn't what I mean by "hopeless". (So what exactly do I mean? Something like this: I not only am unconvinced by it, but am unable to find any version of it that I think anyone can believe without on that particular point failing badly to be reasonable. Of course an otherwise very reasonable and intelligent person can have blind spots, and these blind spots seem particularly common (on all sides) in the general vicinity of religious questions. So, e.g., it is beyond question that William Lane Craig is an extremely intelligent and widely read chap, but -- at least so far as I can tell from what I have seen and heard of his arguments on this point, which is by no means everything he's said and written -- I think that in defending the kalam cosmological argument he is thinking really badly, much worse than he is capable of at his best.

Perhaps it's true that "whatever begins to exist has a cause" when we consider only "the objects of our everyday existence", but: (1) so far as I can tell none of those objects ever "begins to exist" in anything much like the way the universe may have done; (2) if generalizing from those objects one could equally, and more simply, say "everything has a cause" (this is one reason for my uncharitable speculations); (3) there are any number of other ways in which one could restrict the scope of the generalization while still covering "the objects of our everyday existence", such as these: "whatever is made of atoms has a cause", "whatever is strictly contained in the universe has a cause", "whatever ceases to exist has a cause"; (4) I actually am not at all convinced that the principle holds even for everyday objects, though it depends on exactly how one defines the fuzzy term "cause" (incidentally I agree with Carroll that the notion of "cause" doesn't really belong in any attempt to think maximally clearly), because I think in many cases what one actually has is a cloud of causal antecedents that there's no particular reason for regarding as a thing in their own right -- but maybe one can say "whatever begins to exist has causal antecedents" and try to drive through some version of the KCA.

My admittedly uncharitable speculation is not that advocates of the KCA are arguing in bad faith; to whatever extent it's correct, the relevant mental gymnastics are going on below the surface. I agree that there's not much one can say in response to such uncharitable speculations; I suppose I was just (1) thinking aloud, (2) vaguely hoping that you or some other reader might know of some genuinely good (or, failing that, at least somewhat credible) reason for holding that "whatever begins to exist has a cause" with enough confidence for the KCA to say anything useful (supposing arguendo that the rest of the argument is any good), and that speculating about bad reasons for holding it might motivate someone to propose better ones :-), and (3) indirectly suggesting that any reader who finds that premise credible might want to consider whether their reasons -- whatever they are -- for believing it are also reasons for believing "everything has a cause".

I have read Feser's polemic, but I don't think it's quite fair and, more to the point, it isn't relevant to what I'm saying -- because I am not claiming or insinuating that any serious philosopher put forward a first-cause argument that says "everything has a cause, so the universe has a cause, et hoc dicimus Deum". I am suggesting that perhaps the thought of such an argument is what underlies the more sophisticated but (it seems to me) consistently terribly broken cosmological arguments serious philosophers actually put forward. Maybe there's a better explanation; I hope so, I suppose.

Your last paragraph might be right, but I remark that it consists of pretty much exactly the same sort of not-very-charitable suspicion of people's motives for belief that you objected to when I put forth such a suspicion, the only difference being that I said in so many words "of course the following is really uncharitable, but I can't help suspecting that ..." whereas you simply said "I think this is probably because ...".

12. Aron Wall says:

g,
Of course I recognized that there was a difference between what you were doing, and what Feser's targets are doing. But I still thought it was sufficiently relevant to be worth linking to.

I'm not going to leap in and defend the major premise of the kalam argument as compelling, partly because I agree with you that it isn't completely so, and partly because the kalam argument isn't my preferred approach to cosmological reasoning in the first place. But I don't think it's so terrible as to justify you calling it "thinking really badly" and "terribly broken". If Craig's claim was that the argument provides deductive certainty, because it is based on premises which no thinking person could possibly disbelieve, you would be quite right that he's failed to meet that standard. But I wouldn't think he claims to meet that standard, and indeed very few philosophical arguments possibly could meet such a standard. If the syllogism is valid and the premises have some intuitive appeal, then it does some amount of work as an argument. It's clear that there is some sufficient condition which allows us to infer the existence of something "cause"-like, and while you present some alternatives to Craig's assumption, it's not like you've shown that your proposed alternatives are any better (why should "being made of atoms" make any difference?), and some of them might even be strong enough to ground other types of cosmological arguments. (For comparison, "terribly broken" would be a much more apt description of the Ontological Argument, something which can't possibly get off the ground because of an inherent logical flaw.)

Your last paragraph might be right, but I remark that it consists of pretty much exactly the same sort of not-very-charitable suspicion of people's motives for belief that you objected to when I put forth such a suspicion, the only difference being that I said in so many words "of course the following is really uncharitable, but I can't help suspecting that ..." whereas you simply said "I think this is probably because ...".

On the contrary, my last paragraph was perfectly charitable. It is in fact the exact opposite of what you were doing. You took something presented as a valid argument, and read between the lines to say that people were secretly being motivated by a transparently ridiculous different argument. I, on the other hand, took certain atheists' preference for an eternal universe, and read between the lines to find a valid syllogism. I have no idea why you think this was uncharitable, especially considering that I didn't criticize the resulting syllogism in any way. I didn't say it was because they secretly hope that there is no God, or that they have no reasons for their atheism, only that disbelief in God is one of their background assumptions for purposes of deciding which cosmological model seems most reasonable. I don't see why anyone should be offended by the presupposition that they are engaging in valid reasoning beneath the surface.

13. g says:

I wasn't (of course) merely observing that the KCA isn't a watertight logical argument; I agree that those are basically nonexistent outside pure mathematics.

I don't agree that it's clear that there's some sufficient condition that allows us to infer the existence of something cause-like -- except for sufficient conditions so strong, and notions of cause-like-ness so weak, that this is no help at all to anyone wanting to argue for theism. It seems to me that the notion of "cause" is no more than a convenient approximation, and plays no fundamental part in any sufficiently detailed account of how the world works. Further -- and importantly, though it may sound like a quibble -- things don't have causes, events do. This is relevant, of course, because while it's hard to deny that there's such a thing as the universe (though I think Bertrand Russell did, at least at one point), it's eminently reasonable to deny that there's known to be any such event as its beginning. (Even if it has an earliest instant in one of the available senses.)

Anyway, although that's an important point it's a secondary one. My main objection to this argument in terms of "cause" is that the notion of "cause" simply isn't robust enough to do this sort of work. Talk of things causing one another is like talk of the sun rising. It's traditional, it's clear enough roughly what you mean when you do it, etc.; but cosmological arguments in terms of cause all sound to me a bit like this: "We all know that the sun rises; but to where does it rise? We can see that it doesn't rise in the physical world, so its rising must be in a spiritual world, therefore materialism is wrong". Taking something more literally than it deserves, broadening its scope, and drawing untirely unwarranted conclusions.

I will readily agree that the ontological argument is even more terribly broken than the KCA.

I will also readily agree that your last paragraph was not uncharitable, if you will show me three examples of notable atheists saying that they believe the universe has no beginning because the alternative is theism, which they reject on other grounds. It doesn't seem to me that this is an argument many atheists would make, and I don't think attributing it to them is charitable. (And if I learned that someone, notionally a scientist, believed in an eternal universe mostly because that made atheism easier for him, then I would stop regarding his belief in an eternal universe as any evidence for one, and I would become substantially more skeptical of any other scientific-looking claims he put forward on the basis of informed intuition. Wouldn't you? Really?)

14. Aron Wall says:

g writes:

Further -- and importantly, though it may sound like a quibble -- things don't have causes, events do.

That seems to me like a rather disputable philosophical view. It's certainly not obviously true to me. The statement "babies have causes" seems like a perfectly reasonable assertion to me. I'm not sure what is gained by rephrasing it as "the act of a baby coming into existence has causes".

I get your point that causation may be, in part, a folk concept which doesn't enter directly into our best physical theories, but I feel that that this point of view can be taken to extremes. It's clear, at the very least, that some things have explanations in terms of other things. It's also clear that some entities have the power to produce other entities. I don't think that any possible advance in Science could make those common-sense statements untrue, indeed the very possibility of doing Science requires that at least some concepts along these lines make sense. One can certainly have legitimate arguments about which things are such as to require explanations. But that some things have them is clear.

I will also readily agree that your last paragraph was not uncharitable, if you will show me three examples of notable atheists saying that they believe the universe has no beginning because the alternative is theism, which they reject on other grounds.

So two notable atheists saying it wouldn't be enough for you to take back your accusation?

Sorry, I really don't like your tone here. If I said something earlier to offend you I'm sorry. But your doubling (tripling?) down on your attack here is unjustified, and my spleen is not robust enough to allow me to continue this conversation, if this is how things are going to go.

The definition of charity, in this context, is interpreting other people's arguments so that they are saying something reasonable and valid. That's what I was doing. You might think I was mistaken in my interpretation of their thinking, but that doesn't change the fact that I was trying to interpret their position to be a reasonable one, and wasn't motivated by any type of desire to show them up as silly.

Thus your challenge---in addition to sounding too much like a homework problem (I already have a research job I get paid for, you know!)---and likely to lead to irrelevant disputes about the meaning of "notable"---and probably impossible since I was asserting that they were "implicitly" using an assumption similar to that of the major premise of kalam, not that they explcitly stated it in so many words---is unrelated to your original accusation of uncharity. The relevant question is whether I was motivated by a desire to show these atheists up as silly and wrong by reconstructing their position into an absurd form. I wasn't.

I don't think it's that surprising that people's scientific intuitions are affected by their background beliefs (mine certainly are) and I don't think it's an insult to point it out. Your image of an atheist who believes in an eternal universe "mostly because that made atheism easier for him" is completely not my point and is your statement rather than mine. I was simply imagining some scientist who---maybe without even thinking about God in this context (which he might regard as a non-possibility because of the Argument from Evil or because Theism is "unscientific" or "unfalsifiable" or whatever, the reason why is not relevant!)---thinks that it would be weird if the universe just began without antecedent causes out of a singularity, and therefore prefers a model where time is infinite (with some approporiate degree of tentativeness).

I'm pretty sure that such people exist, but no I'm not going to spend a week of my time searching for three of them who made statements along these lines in public in order to "win" this argument. I'd rather you just apologize to me for being wrong about my motivations.

15. g says:

On things and causes: I'm not really sure what to say other than that to me it seems perfectly obvious that causation is fundamentally a relationship between events rather than between things. Let's consider some arguable counterexample -- say, a baby as per your suggestion (with the obvious disclaimer that for quite good reasons it's unusual to apply the word "thing" to a baby). And let's take the cause that I'm guessing you mostly had in mind, namely some act of copulation between the baby's biological parents. So, when we say that thisact of copulation caused that baby, what are we actually saying? It seems to me that the nearest thing to a fundamental truth here is that copulation led to insemination led to fertilization led to implantation led to ... to birth; saying that the copulation caused the baby is merely a useful shorthand. The point of all this is that we really shouldn't expect convenient shorthands to generalize very far, and the generalization being sought here is a bit one indeed.

Speaking of which, I don't think it's "taking [it] to extremes" to suggest that something that's "in part a folk concept which doesn't enter directly into our best physical theories" can't be relied on to generalize from everyday experience to the very origin of the universe. So I think even someone less skeptical than I am about the notion of cause in general should be very hesitant to go from "some things around us have causes" to "the universe itself has a cause" or (should the someone in question be persuaded by the foregoing paragraph) to "the beginning of the universe has a cause".

I will take your word for it that in your last paragraph a few comments back you really were trying to find an explanation for others' behaviour that makes it reasonable and logical. But I remain entirely unable to see how what you wrote really is such an explanation, and I'd like to explain why in the hope that that'll make it clearer why I responded with incredulity.

So, let us consider a hypothetical atheist; call her Alice. What we know about Alice is that (1) she is an atheist, (2) she finds it more credible that time extends infinitely backward than that it has a beginning, and (3) she doesn't have a detailed physics-based justification for that belief.

Now, at this point I'm not sure which of two explanations you're offering for Alice's position. I'll describe first the one I took from your original comments, and then what I think your latest comment says. I may have misunderstood on either occasion or both. In each case, you're offering to explain #2 in the light of #3 (whose negation would make further explanation of #2 unnecessary) and of #1 (which informs your choice of explanation).

What I originally thought you were proposing: (a) on some level Alice believes (for reasons left unexplained) that "whatever begins to exist has a cause", (b) on some level Alice further believes that if the universe has a cause then that would have to be something rather like God, and (c) on some level Alice reasons: If the universe has a beginning then it has a cause which would have to be God-like; but there isn't anything God-like; therefore the universe probably doesn't have a beginning.

Your latest comment seems to propose (at least as one possibility) something rather different, but I don't understand it. Namely: (a) on some level Alice believes that "whatever begins to exist has a cause", (b) the possibility of a God-like cause never even arises, and (c) on some level Alice reasons: If the universe has a beginning then it has a cause; but it probably has no cause so it probably has no beginning.

What I don't understand about that second option is what problem Alice is supposed to have with non-God-like causes. Are you assuming that there can't be any, or that they couldn't properly be considered causes of the universe as opposed to events within a universe bigger than we currently conceive, or what?

So, anyway, in either case what you say you're doing here is finding a justification for Alice's #2 which is a valid syllogism, and hence giving a charitable explanation for her beliefs or preferences about cosmology.

But it seems to me that what you've actually done is something Alice would be less pleased about than that: you've given a justification for #2 in terms of a valid syllogism plus two other premises still awaiting justification, namely the ones in (a) and (b). Your explanation in no way reduces the amount Alice is seen to believe without logical justification.

(Or, in the case of the second version of your proposal, an invalid syllogism -- because of the gap surrounding the possibility of non-God-like causes -- plus one other premise still awaiting justification, namely the one in (a). That doesn't seem any better.)

Further, premises (a) and (b) seem to me to be ones Alice might well be very unwilling to endorse. I haven't conducted a survey of cosmologically-minded atheists or anything, so this is just guesswork, but my guess is that both (a) and (b) are less widely believed among such people than the original #2.

If Alice's situation as I've described it is what you were referring to, then -- while I will gladly take your word for it that you intended what you wrote to be a charitable interpretation of her beliefs and attitudes -- I have to say that the Alice in my imagination would be the exact opposite of flattered to have her preference for a past-eternal universe explained in such terms. There should be a word for something charitably intended but counterproductive; I suspect that sincerely intended attempts to interpret others charitably frequently have that outcome, and I think it may be what's happened here. (Whether it is or not, I know it's happened to me with the signs reversed: I have tried to interpret someone as making the most reasonable argument I can get from what they've written, but their idea of what's reasonable turns out to be different from mine and they don't feel charitably dealt with at all.)

My own explanation of Alice's position, pending more insight from Alice herself, would simply be: it seems that she has an intuitive preference for a past-eternal universe; I wonder why?. It would not be wholly unsatisfactory to have no idea why she has that preference, but I don't see how it's any worse than having no idea why she believes that whatever begins to exist has a cause or that any cause of the universe must be God-like.

I'm sorry if you felt like I was setting you homework. I just thought that if you said "Empirically, I think it can be shown that ..." then you ought to be willing to offer some actual empirical showing! Of course I know that you have other calls on your time that pay better than arguing with some random guy on the Internet; so, for that matter, do I.

And, for the avoidance of doubt, I did not intend to accuse you of being motivated by a desire to show those atheists up as silly and wrong. (I should perhaps say, given that you thought I did, that so far as I can tell my aspersions on the authors of first-cause-type arguments are also not motivated by a desire to show those people up as silly and wrong. Though, as it happens, I think that in their capacity as authors of first-cause arguments some of them are being silly and wrong.) I merely thought that your proposal did in fact represent the atheists in question as silly and wrong. (I still think it does, even if it looks to you as it's representing them as reasonable and logical.)

16. Aron Wall says:

Dear g,

Thanks for your comment. I appreciate the rapproachement.

I ran across a quote by the English idealist F.H. Bradley the other day: "Metaphysics is the finding of bad reasons for what we believe upon instinct; but to find these reasons is no less an instinct". I hope the situation is not quite so bad as that, but it's certainly true that a lot comes down to intuitions.

It's true that if Alice tries to justify her belief with a syllogism, she's replacing one unjustified premise with two. But I don't think just counting the number of unjustified premises is the right way to measure the reasonableness of her belief. At least the version of Alice who makes a syllogism has something to say to justify her intuition, even if it's in terms of assumptions not everyone would accept. I'm having a hard time seeing it as more justifiable to not provide any reasons for her belief.

I guess I was imagining that Alice might think that each moment of time (or the events within that moment, however you want to phrase things) needs to have a physical cause, in terms of prior events, but that all of time taken as a whole doesn't necessarily need one. This viewpoint (inspired perhaps by the type of determinism in classical Newtonian physics) would seem to require an infinite past.

If Alice instead decided that it was OK for the universe to begin so long as it had some external atemporal cause, then (as in other versions of the Cosmological Argument), there is of course the question of whether such a cause of the entire physical universe would necessarily count as "God" in anything like the traditional religious sense. I didn't mean to dismiss this as a logical possibility for atheists, but an atheist like Alice who believes the universe had an infinite past obviously must not find such an account plausible for whatever reason.

I think it would be best to put this conversation on hold for the time being. The main reason is that I think I may end up having to do some research anyway concerning what atheists have in fact thought (historically, before the acceptance of the Big Bang Model) about the eternity of the universe, and that should probably go into some kind of main post rather than in the comments section here. As you reiterate, to the extent that we are talking about real people, it is an empirical question why they claim to believe what they believe.

So I think it would be more productive to drop this topic for the time being and take it up again later, although I don't want to prevent you from responding to this comment if you feel it is necessary to do so.

17. Andrew says:

Dear Aron, Thanks so much for your very informative analysis of the Craig-Carroll debate. I am wondering if you have read my published work which defends the causal premise 'everything that begins to exist has a cause'?:

18. Mactoul says:

"As you go back in time, the Second Law says that S gets smaller and smaller, until eventually it reaches its minimum value. "

1) Entropy is defined for systems, closed or in contact with the environment. So, isn't it an extrapolation to talk about the entropy of the whole universe?
The second law holds for systems but how do we know it holds for the universe as well?

2) Given that, the universe contains entities apart from physical entities that obey the laws of physics, viz. living bodies, that may not obey the second law, how do we justify the extrapolation of the concept of "entropy" and the second law to the entire universe?

19. Aron Wall says:

Andrew Loke,
[who is not the same as any of the other Andrews commenting on other threads...]

Thanks for the link. I'll take a look.

Mactoul,
1) Entropy can be defined for any system which has a certain probability to be in some set of possible states. I agree that it is an extrapolation to think that these concepts may apply to the entire universe, but extrapolating concepts to the whole universe is kind of the whole point of cosmology! To my mind, the most obvious thing which might go wrong is that the total entropy might be infinite...

2) I don't agree with your premise that the laws of physics don't apply in living bodies. It seems fairly obvious that quite a lot of laws of physics (e.g. $F = ma$ where F is determined by the standard set of electromagnetic, gravitational etc. forces in physics) and chemsistry DO apply inside living tissues. If the laws of physics don't apply to our bodies, then why do we need all this physical machinary of neurons and nerves and muscles and bones (and proteins and enzymes etc.)? How come chemists can use the standard laws of chemistry to predict what a drug will do inside of the body? How come scientists have never observed violations of the law of conservation of energy inside of our bodies? How come we have to eat in order to survive; why don't our bodies just magically generate as much energy as we need using vital forces?

So if there are any exceptions to the usual laws of physics inside of living bodies, they must be very subtle! As I said, I don't actually believe there are such exceptions in normal human life, but let's suppose for the sake of argument that you're right and there are.

I think the concept of "entropy" would still be applicable because I think you could still count the number of possible states of the system, or at least the physical aspects of the system. However, whether or not this entropy actually increases with time would depend on your hypothesis about what happens instead of the usual laws of nature. The 2nd law follows rather generally from the assumptions that (i) you can use the laws of nature in both time directions to predict both the past and the future, (ii) the universe started in a low entropy state, and (iii) the dynamics of some systems are sufficiently complicated that it can irretrevably scramble information. But if you think that (i) is violated inside of living creatures than the 2nd law might not hold.

Let me pause to note the odd implications of this point of view. It would imply that (in principle) you could build a perpetual motion machine that would convert heat to useful work, so long as one of the components of the machine is a living creature! (Like in those Rube Goldberg cartoons...)

But, it could be that this would be impossible in practice. If any living creature only has the power to decrease the entropy by a few bits per second through e.g. voluntary choices (see Maxwell's demon), but meanwhile its normal metabolism (which presumably obeys standard laws of chemistry, yes?) increases the entropy by something proportional to Avagadro's number, then the second effect would totally swamp the first!

It's an interesting thought experiment, but unless it's actually experimentally shown that organisms are capable of decreasing entropy, I don't see why I should believe it.

20. Mactoul says:

It is not that organisms are capable of decreasing entropy but it may not be straightforward to define entropy for the organisms. In the non-reductionist scheme, the fundamental entity that the organism is composed of is the organism itself.
"Atoms must be said to exist virtually rather than actually in the substance of which it is a part"

The term "virtually" is used here in the sense of philosophy and not in physics. The organism is a substance. The standard ways to compute entropy all depend upon reductionist atomistic picture.

It is true that F=ma works for organisms. But F=ma fails to capture the entirety of an organism, even in principle. Organisms act for themselves. This elementary fact, obvious even to any toddler, is beyond the capability or confines of any physics or chemistry.

21. i like pizza says:

It's been a long time since this discussion but I have a few follow up questions:

(1) First I wanted to see if I correctly understand the difference between the A-theory and B-theory of time. Is the following an accurate explanation. If we were able to step outside of time and view it from a sort of 'metatime':

Under the A-theory of time, the past would no longer exist, and the future would not have yet come into existence.

Under the the B-theory of time, the past, present and future would all exist simultaneously.

(2) Under a B-theory of time, do we move through time like we move through space? In other words, if I traveled 20 years back in time, which of the following would be the case:

(2a) I would see my younger self. And if so, does that mean there's a 'version' of ourselves at each moment of time during which we're alive?

(2b) I would see different people and events, since I already traveled through that part of time (and now there are different people and events at that moment)?

(2c) Something different?

(3) Is time and space continuous or made up of a series of very small units (like planck units)? In other words:

(3a) Do we travel through time and space continuously?

(3b) Do we jump from one region of space and moment to the next, like frames in a film?

(3c) Something different?

Apologies if some of these questions don't make sense; I may be basing them on faulty assumptions.

22. Boltzmann says:

What if one argued that according to Poincaré recurrence theorem , a universe which will reach thermal equilibrium can repeat itself again?

23. Aron Wall says:

Boltzmann,
It is generally accepted that Poincaré recurrances aren't a good explanation of the low entropy of our current universe, because a fluctuation that produces just a human brain would be much more likely than one that produces the whole Solar System, and one that produces just the whole Solar System is much more likely than one that produces an entire galaxy, and so on. So on this theory, there doesn't seem to be any good reason why we should observe a huge low entropy universe surrounding us.

It's not totally clear if the Poincaré recurrence theorem applies to cosmology anyway... for this we probably need to consider the Generalized Second Law.

24. Turtles Galore says:

What do you think about the suggestion by Sinclair and Craig that in the Aguirre Gratton model, neither universe in either direction is the past of the other and so you're still forced into a beginning of the universe?

25. Aron Wall says:

Turtles Galore,
I've made a similar suggestion in my quantum singularities paper.

It seems to me that the thermodynamic arrow of time is the relevant one if one is asking which time slices of the universe are explained by other time slices. In a model where the arrow of time reverses during a Big Bounce, both branches of the cosmology are explained by the middle, and neither is explained by the other. The state of the universe at the moment of lowest entropy---at the exact moment where the arrow of time reverses---is not explained by either time direction, but must logically either (1) have no explanation, or (2) be explained by something outside the timeline altogether.

(Note however that some people have proposed bouncing models of cosmology where the arrow of time does not reverse at the Bounce, in which case this particular comment wouldn't apply.)