Category Archives: Scientific Method

Saving Energy Conservation

There’s an interesting conversation on Energy Conservation going on under my post about how The Universe can’t `Just Exist’. I wrote a reply in that thread which I’ve decided to turn into a main post.

Saving Energy Conservation:
What would Physicists do if an Experiment showed that Energy Conservation is False?

Just because current experiments seem to show that energy is conserved, doesn’t mean a future experiment might not violate energy conservation.

However, what this would actually look like in practice, would be a complicated dialectic involving both experiment and theory.

So suppose for example we do an experiment and it looks like under such-and-such conditions, a box of electrons seemed to get new kinetic energy seemingly coming out of nowhere. Then I think scientists would probably go through something like the following stages (not entirely unlike the silly pop-psych notion of “Stages of Grief”)

1. The first thing physicists would do is suspect that there is some sort of experimental measurment error. In other words, reject the experimental result on the basis of well-established theory, and try to look for a reason why the mistake was made. Either because of a measurement error, or because of leakage from some established type of energy (like thermal leakage or external electric fields or something).

[This is like the “Denial” stage of grief, but unlike when somebody dies, most of the time when a scientific experiment discovers something really weird, denial is the right first reaction! Maybe there might be a bit of “Anger” too if the experimentalists are crackpots or making a slipshod mistake, and refuse to accept correction.]

2. If scientists conclude the effect is real, then they would try to find a new physical theory which explains the effect. Most conservatively, by adding a new type of particle or interaction. Importantly, we would normally try to redefine energy in such a way that it is still conserved in the new theory, even if we have to add a new term to the formula for energy.

[I guess this is the “Bargaining” stage of grief, but again if this is successful there is no need to go onto the next stages…]

3. If, after repeated efforts, it appears that there is NO reasonable or natural way to modify our physics theories (and associated definitions) in such a way that there is a conserved energy, then this would rise to the level of a crisis in physics [“Depression”], and people would start looking for more radical solutions to the problem.

4. But if it was discovered that there ARE simple ways to explain the data, by using theoretical models which DON’T have any interesting or useful concept of energy conservation; then (and only then) would we conclude that Energy Conservation is false. [“Acceptance”]

In other words, the first instinct of physicists would be to try to save the paradigm of the theory of Energy Conservation, and there are lots of different ways that this can be done—including questioning the experiment, postulating new physics, and subtle redefinitions of what we mean by “energy”. This might lead one to think that physicists have an absolute a priori commitment to energy conservation. But I don’t think that’s true. I think the paradigm of Energy Conservation is like a piece of toffee, where you can stretch it a lot, but if you stretch it too much it will break. In other words, there exists the potential for future experiments to drive sufficiently radical changes of our theories, that the concept of energy is no longer applicable (except in whatever approximations are needed for the old paradigm to hold).

As I said before, one can certainly write down differential equations which do not satisfy a conservation law, for any quantity that resembles an energy. (A simple example would be if the laws of Nature turn out to be explicitly time dependent. In that case Noether’s proof of energy conservation would not apply, and energy could be created or destroyed!

[As I mentioned previously, to some extent energy conservation is already problematic already in general relativistic cosmology, as I’ve discussed before here and here.]

Theology: Less Speculative than Quantum Gravity

32 Replies

A reader, Martin B, asked me a question in response to my review of Krauss’ talk on “A Universe from Nothing”. I had written:

“Atheists such as Krauss scorn theology as being completely non-empirical. They claim it is not based on evidence of any sort. I find it extremely ironic when this sort of atheist thinks that speculative quantum gravity ideas are just the right thing to further bolster their atheism. Suppose you think that Science is better than Religion because it is based on evidence, and suppose you also want to refute Religion by using Science. Here’s a little hint: consistency would suggest using a branch of Science that actually has some experimental data!”

Martin asks:

But isn’t there empirical data that suggests “speculative quantum gravity” is real? It’s not taken out of the blue, is it?

Anyway, the problem I have with religion/faith is that it’s so arbitrary. Depending on who you ask there are all kinds of idea of what’s “true” when it comes to theology. May I ask what it is that makes you think Christianity stands out and is more believable than other religions and faiths on this planet?

It is common for atheists to assert that religion is based entirely on speculation, and that therefore there is “no evidence” for it. Now I don’t agree that religion is based primarily on speculation, but I also don’t agree that speculation counts as “no evidence”. Let me explain.

Speculation, in the particular sense we are considering, is defined by various dictionaries as follows:

“the forming of a theory or conjecture without firm evidence” (Google)
“ideas or guesses about something that is not known” (Miriam-Webster)
“reasoning based on inconclusive evidence; conjecture or supposition” (American Heritage)

In other words, speculation is essentially what you do when you don’t know something for sure, so you sit around without guidance and try to figure out what makes the most sense.

Now sometimes when we sit around and think about things, we find a really good reason to think that something is in fact the case. For example, we might find a rigorous mathematical argument. In that case, we would talk about having a “proof” instead of mere speculation.

More controversially, many philosophers have also believed themselves to have deduced certain propositions by thinking about them carefully. The track record for this is not very good, since philosophers can’t agree on which things are in fact provable in this way, and some of them have claimed to prove things which later turned out to be false (e.g. Kant thought that Euclidean geometry and Newtonian mechanics were necessary truths!). However, it is plausible that at least some philosophical arguments are strong enough to be considered “proofs”. (Even if you are a skeptic about the ability to deduce most truths about the world by philosophical reflection, you probably came to that conclusion by thinking about it philosophically, so there’s no escape.) Also, Logic and Probability Theory are sometimes considered branches of Philosophy, and these seem to be on fairly solid footing for most purposes (at least if we ignore the puzzles raised by quantum mechanics).

Be that as it may, normally our experience is that, at least about most subjects, “armchair reasoning” is not very likely to lead people to the truth, unless it is supplemented by some source of data which is based on empirical evidence. Two particular fields of study which do involve large quantities of empirical data, are History and Science. The former is based on testimonies, documents, and artifacts left behind by those who lived in the past, while the latter is based on repeatable observations carefully scrutinized by the scientific method.

I would judge that normally the strength of evidence we obtain from the fields I’ve mentioned is as follows:

$$\text{Math & Logic > Science > History > Most Philosophy}$$

However, this is just a general expectation based on averages; specific cases might turn out differently. As I said before, some philosophical arguments are very strong (e.g. if you don’t believe the philosophical arguments that we can learn things about the external world based on observation, you can’t have any grounds for believing in Science either.) Math proofs are supposed to be completely certain, but if they are thousands of lines long it is easy for errors to sneak in.

And, in cases where historians or scientists don’t have enough strong enough evidence to prove the truth about something they care about, they too will resort to weaker evidence, including (educated) speculation. Just because an argument is made by people who work in a History or Science Department, doesn’t necessarily make it non-speculative. You have to look at what (if any) actually supports the statement!

Now, it is clear that educated speculation is right more often than chance would predict. It has often happened that scientists have brilliantly guessed in advance correct theories of Nature, based on partial or incomplete evidence. This is the sort of thing theorists get Nobel prizes for. (If they were guessing based on chance, you’d expect they’d never get it right, since the space of logically possible ideas is huge.) On the other hand, it also often happens that the brilliant conjectures turn out to be completely false. So reasonable forms of speculation do involve a kind of evidence. It’s just not a very strong kind of evidence. How strong it is, depends on just how many leaps of conjecture one takes, beyond what is already known.

Therefore, we should not conflate “speculative” with “no evidence”.

II.

So when you say:

But isn’t there empirical data that suggests “speculative quantum gravity” is real? It’s not taken out of the blue, is it?

I entirely agree with you. Quantum gravity isn’t an idea which just comes out of the blue with no evidence whatsoever. If I thought that were true, I wouldn’t work on it professionally!

We know that Quantum Mechanics is a good description of the world of atoms and other small stuff. We know that General Relativity is a good description of situations in which gravitational fields and/or the speed of light are important. It stands to reason that there must be some mathematical model which embraces both sets of ideas into one, mathematically consistent description. Since the physical world exists, there must be some description of it in situations where both quantum and gravitational effects are important. (I suppose conceivably the description might not involve math and equations, but if not that would be a total surprise in light of previous experience with new models of physics. Normally math is the best language for describing Nature in a precise way.)

So the mere fact that there is such a thing as quantum gravity is not particularly speculative. But most of our specific ideas about quantum gravity are highly speculative. Some reasons for this:

Dimensional analysis suggests that in order to see actual effects from quantum gravity, we’d have to look at distance scales equal to the planck length, which is about $10^{-35}$ meters (details here if you want the math.). For comparison the Bohr radius (the approximate size of atoms) is about $5 \times 10^{-11}$, and the smallest distance scale we’ve ever been able to probe with the Large Hadron Collider is about $(\hbar c) / (14\,TeV) = 8.8 \times 10^{-20}\,\text{m}$. So quantum gravity is smaller compared to the tiniest thing we can measure, then atoms are to us! So in the absence of some really clever and dramatic experiment, it will be a really long time (if ever), before we have any direct experimental evidence of quantum gravity effects.
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One could also try to look at what happened in the very, very early universe, but once again this puts quantum gravity earlier than anything we have good evidence for, with the possible exception of inflation (there is decent evidence for inflation, although it is not confirmed for sure; also we don’t know whether it happened at the same time scale as quantum gravity or not.)
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The attempt to combine quantum mechanics with gravity leads to severe conceptual difficulties, making it difficult to say what we even mean by a quantum spacetime. In addition there are seeming paradoxes which nobody knows how to resolve.
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Our current best candidate for a theory of quantum gravity, string theory, is understood well only when the strings are weakly interacting (or when it is dual to certain other theories which don’t involve gravity.) In truly quantum gravitational situations, even if we assume string theory is right, we’re still in the dark about how to formulate it precisely, let alone calculating what it says. Also string theory, although it has certain very beautiful aspects, is a very complicated construction which includes many elements (supersymmetry, extra dimensions, GUTs, etc.) that have not been confirmed experimentally as separate ideas, let alone as a combined package.
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The next most popular candidate, loop quantum gravity, space at the Planck scale is described by a network labelled by numbers, but there is no agreement on how to describe time evolution, nor is is clear whether a continuous-seeming spacetime emerges as we zoom out to larger distance scales.

So the situation is desperate, but for that reason also exciting!

Now the particular idea which Krauss was using, the Hartle-Hawking “no boundary wavefunction of the universe”, has in some ways even less evidential support than string theory itself (it certainly doesn’t seem to logically follow from string theory, though it might or might not be combined with it). It’s just a particularly beautiful proposal for the state of the universe. The best that can be said for it is that it is specific, simple, and elegantly relates the laws of physics to the initial conditions. The worst that can be said about it, is that it may be mathematically ill-defined, and probably contradicts observational data (such as the fact that the universe contains any stuff at all).

So I think I was justified in saying that:

The crucial physics here is totally speculative! It was entirely based on speculative ideas about quantum gravity which anyone working in the field would admit are not proven.

But when I say totally speculative, I don’t mean there’s no support at all! I just mean really really weak evidence. I’m not trying to bash Hartle or Hawking here, who I’m sure would agree with my assessment. Quantum gravity is hard! We’re doing the best we can.

(Commenter St. Scott Church said something similar here.)

But I think it’s crazy, if an atheist thinks religion is based entirely on silly speculations, to turn to this as their paradigmatic example of something which is supported by strong evidence. I’ve also criticized Quentin Smith (a better philosopher than Krauss) for the same offense.

III.

Now let’s talk about religion.

On this blog, I’ve discussed before certain philosophical arguments for Theism, which I think are pretty good, so far as armchair reasoning goes. But I don’t think that the strongest evidence for religion comes from this source, and indeed I had a huge long disclaimer at the beginning of that series in which I said so.

What these philosophical arguments point to, in my opinion, is something like Ethical Monotheism, which is sort of the lowest common denominator shared by traditions as diverse as Judaism, Platonism/Stoicism, Christianity, Islam, Sikhism, Baha’i, certain sects of Hinduism, and Deism. (So believing in Christianity does not require that you think everything about other religions is false and misguided.)

But it’s clearly impossible to prove something like Christianity from purely abstract philosophical arguments, since it involves a lot of particular doctrines about Jesus (particularly the Trinity and Incarnation etc.) which are much too specific and weird to derive by philosophical plausibility arguments. (Is this similar to what you mean by saying religion / faith is “arbitrary”?)

Instead, I would say that the primary reason for believing in Christianity comes from History—although some elements of philosophical reasoning and personal religious experience come into it as well. I said above that History was based on collecting testimonies and documents from past eras. And this is what the New Testament is.

The primary event on which the Christian faith is based on is the Crucifixion and Resurrection of Jesus. (Followed by his Ascension into heaven, and the giving of the Holy Spirit at Pentecost in order to start the Church.) These events were observed by normal human beings like us, using their ordinary sense data. Those people are no longer alive, but they left behind documents, collected in the New Testament, which describe the teachings and miracles of Jesus Christ and his Apostles (those who were the eyewitnesses to his Resurrection, listed by St. Paul about 20-25 years after the event here, although he omits the women who first went to the empty tomb and were the first to see Jesus, as described in the Four Gospels.)

Now whatever the New Testament is, it is not philosophical speculation. (I will get to other religions in just a moment.) Various of its documents clearly claim to be the records of people who literally saw supernatural events with their own eyes. It could be lies, or some sort of mistake, or perhaps legends which grew up later (although I find all of these theories implausible for various reasons, in part because of the large number of claimed eyewitnesses and in part because the claims arose so early and clearly in the development of the religion). What it certainly is not is a bunch of philosophers, theologians, and mystics sitting around meditating on the nature of the universe and trying to figure out what makes sense to them.

As I have argued before, type of evidence in question (muliple written claimed testimonies) is considered by historians to be strong evidence whenever it supports non-supernatural events, for example the Assassination of Julius Caesar. (Indeed, ancient history would be basically impossible without it.) The quality of the historical documentation compares quite favorably to that supporting similar events at around that time and place. So unless we have a strong prejudice against the supernatural—or have some other specific reason to disbelieve it—we should believe it.

(And, incidentally, you should not have a strong prejudice against the Supernatural, among other reasons because of the abundant documentation of miracles which have occurred in more modern times.)

I argued above that History is, in general, more reliable than Philosophy. For this reason, I would argue that the accounts of the Resurrection of Jesus are more evidentially important than things like e.g. philosophical arguments for Materialism / Naturalism, arguments about how a good God could allow evil in the world, and so on. Those things are speculation, this is data.

Of course, once you accept the Christian data-points, recorded in the New Testament, you still have to do some philosophical/theological analysis to figure out exactly how to explain the extraordinary event. I’m not claiming that e.g. the doctrine of the Trinity was directly observed by human beings. Instead people had to work through the facts (e.g. Jesus claims to be divine in some way and this is backed up by his ability to do miracles; but he also prays to God as the Father, and accepts the Jewish teaching that there is only one God; then he promises to send the Holy Spirit to live in the hearts of those who follow him, who also seems to carry the authority and power of God) and when they worked everything out they had the doctrine of the Trinity. Using the language of Science, this is a theory rather than a fact, but it is a good theory because it is the simplest explanation of the facts in question. (Of course atheists and members of other religions will generally deny that the facts were as the New Testament claims, but that is a completely different question than whether the reported facts support the theory. Just as, if there is controversy over whether a scientist falsified his data, this is a separate question from whether the data, if true, supports the theory.)

I don’t want to give the impression that Christianity is only about stuff that’s happened in the past: Christians also believe that the Holy Spirit is present in believers, in order to guide us into the truth and to form in us the kind of loving character that Jesus had. Some Christians have also had few dramatic communications from God or other mystical experiences, but this is quite secondary compared to learning to live life together as a holy community of people. Once you come to believe it is true, then faith is indeed necessary to continue along the path even when nothing much seems to be happening.

Religion is about the encounter of the soul with God. It seems clear that most people don’t come to faith by robotically analyzing the evidence (or to disbelief, for that matter). But I still think people should carefully consider the evidence when deciding whether to believe. It is important to check that one is not being deceived by something false.

IV.

May I ask what it is that makes you think Christianity stands out and is more believable than other religions and faiths on this planet?

Gladly. When analyzing a religion for truth, I would ask questions such as these (none of these criteria are necessarily intended to be definitive when taken in isolation):

Has the religion persuaded a significant fraction of the world population, outside a single ethnic group, to believe in it?
How does the religion relate to previous and subsequent religions?
Did the religious founder claim his message came from supernatural revelation, or is it only the reflections of some wise philosopher who didn’t claim to have divine sanction for their teaching?
Are the primary texts describing some sort of mythological pre-history, or are they set in historical times?
Related, does it sound like fiction, or does it sound like history?
How long was it between the time when the supposed supernatural events took place, and when they were first written down (in a document that has had copies of it preserved). Is it early enough to suggest the text is based on testimony rather than later legends?
What are the odds that the purported supernatural events could have occurred for non-supernatural reasons?
Did the main witnesses benefit materially from their testimony, or did they suffer for it?
Is there significant evidence of fraud among the originators of the religion?
What is the general moral character of the religious teaching?
Do people who are serious about this religion generally feel that they are put into an actual relationship with the divine?

In a future blog post, I will try to provide my own personal answers for how well various religions satisfy these criteria, and why I think Christianity is the most convincing case of divine revelation that has occurred. However, I’ve included these questions separately from my answers, in order to encourage you to think about them on your own.

Sometimes I meet people with a sort of learned epistemic helplessness, just in the area of religion. The attitude is: well, group A claims this miracle, and group B claims this divine revelation, and I am completely at a loss and unable to even begin to say which claim is more plausible! Therefore I won’t accept any of them.

Yet when it comes to less important matters in their everyday life, they are perfectly able to use their brain to decide what is credible and what is not. If you really want to know what is true, I’m convinced you are able.

Look, and maybe you’ll find. Ask, and you might just get it. Keep on knocking at that door, without giving up, and—if there’s anyone on the other side—surely it will be opened to you.

Physics culture and theistic cosmology models

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A reader asks this question, testing the boundaries between physics culture and religious belief:

How hostile do you think a learning institution would be to someone in their Physics department looking at the Horizon problem via the Universe being an Ex Nihilo creation of God, where matter was purposefully set in place and then a God-caused spacetime expansion? (As opposed to the thought experiment of assuming a singularity and a “Theistic or Non-Theistic Big-Bang” requiring another speculation (inflation) to explain one of the shortcomings of the theory.)
— Dean C

Dean,

Most physicists aren’t actually militant atheists, but all of us (whatever our views on religion) have been exposed to numerous “crackpots” who think that they have found major flaws in conventional physics and have a completely new and revolutionary way of doing things. I discussed this pathology here and here. At least 99.99% of time, outsiders making such grandiose claims are totally wrong (or “not even wrong”, because their ideas aren’t precise enough to be testable), and so we filter out pretty automatically anything which pattern-matches onto typical crackpot-seeming claims and behaviors.

But this is not to say that simply criticizing inflation, all by itself, would get you lumped into the “crackpot” category. Even among respectable mainstream physicists, inflation isn’t completely uncontroversial. While most of us believe it is true, this hasn’t been established with total certainty.

A lot of the original arguments for inflation (e.g. the flatness and horizon problems) are a little bit philosophical in nature, and it’s understandable if you don’t find them completely convincing. But it’s not just generic arguments like that. Inflation also makes some very specific predictions about the state of the universe after inflation ends, and these predictions seem to match very closely to what we actually observe (as the graph in that article shows). There are respectable researchers (such as Neil Turok and Paul Steinhardt) who have philosophical objections to inflation (not based on religion) and are working on alternatives which may predict the same features in the microwave background. But they are able to do that only because they fully understand the mathematics of inflation and the observational tests that it passes.

If somebody said something like “For philosophical reasons I am skeptical of inflation, and therefore I am interested in exploring alternatives to inflation such as X, Y,” and if this person understood the mathematics of inflation (so they weren’t just criticizing something they didn’t know well enough), and if X and Y were mathematically-precise models with equations (such that even somebody who didn’t believe in God could manipulate the equations and work out the predictions of the model), and if there was some hope that in the future, that model could be confirmed by empirical observations, then if all of these conditions are met, I think at most places this would be regarded as acceptable though eccentric. Even if the “philosophical reasons” included some religious considerations.

It would be even better if this person had the ability to “suspend their disbelief” by sometimes having useful conversations with other people that presupposed the truth of inflation, without bringing up their reasons for skepticism every single time. (Because that would make them a more useful colleague, and its scientifically it’s an important skill to be able to work out the consequences of hypotheses even if you aren’t convinced by them yet, as a way of keeping a open mind and understanding the relationship between ideas.) Such a person would be capable of interfacing with other scientists who don’t share his conviction.

(Which is not to say you could actually obtain a research job simply by working on X, Y, since there also need to be a sufficiently large number of other people who think work on X, Y is valuable enough to pay somebody money to do it. In practice, people who work on long-shot alternatives to standard physics also need to work on more conventional topics, in addition, to be viable. There are limited resources and funding in science, and not everyone can be supported. But not getting a job is quite different from being excommunicated as a heretic!)

On the other hand, if X and Y can’t be understood without reference to a Creator, and have phrases like “and then God miraculously caused this to happen” in them, or if the model doesn’t lead to any mathematically precise predictions that could in principle be tested by future experiments, then this would not be anything like Science as it is traditionally practiced, and it would be dismissed off-hand by almost all scientists as a scientific theory.

And rightly so, because it would, at the very least, involve an enormous paradigm shift in what it even means to practice the scientific method, and justifying such a change would require overwhelmingly convincing evidence. Of course, as a Christian I believe that miracles have happened in history, and that the universe was created by God. But in the field of Cosmology as practiced in Physics departments, the job is to mathematically model the universe using a set of natural processes described by equations.

It’s hard to see how “matter was purposefully set in place and then a God-caused spacetime expansion” could, all by itself, be a mathematically predictive theory. Because if the matter was just spontaneously created, there are almost an infinite number of configurations it could have appeared in. Without some physical process or principles to limit it, it could have been anything! And a “God-caused spacetime expansion” must either be described by a set of specific equations like that of Einstein’s (in which case, an atheist could also use those same equations, while denying the existence of God) or else it means we (not having access to God’s “hidden counsels”) simply can’t predict exactly how the size of the early universe changed with time. But then how do you get any quantitative predictions for what you see when you point your telescope into the sky?

But if all you mean is that, in the ordinary course of doing science, scientists should not a priori rule out mathematically well-defined hypotheses (such as the fine-tuning of the constants of nature in a way that happens to permit life, or a net nonzero number of baryons coming out of an initial singularity), simply because those hypotheses seem “unnatural” in the absence of an intelligent creator, then I agree with this. Nor, obviously, should a theist rule out the possibility that God might have created our universe using inflation (I don’t see why not). Such scientific hypotheses should stand or fall on their own individual merits, as the case may be. It’s okay (and indeed essential) to be guided by our own individual sense of parsimony, but we shouldn’t be so biased that we rule out sensible models which explain the facts better.

(Incidentally, if inflation did happen, then the hypothesis that the universe just “started off” with more matter than antimatter can’t work. Even if there were more baryons than antibaryons coming out of the initial singularity, the universe expanded so rapidly during inflation that the initial baryons would have been diluted to homeopathic proportions. For this reason, physicists generally prefer models of baryogenesis, in which the baryons are created by some specific physical process some time after inflation ends.)

Construct your own Cosmological Argument

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First read this piece by St. Feser:
So you think you understand the Cosmological Argument?
about the traditional structure of Cosmological Arguments, rebutting several popular misconceptions.

Now take the following argument scheme, making suitable choices as needed:

(Major Premise) Every [thing/event] with property X needs a [cause/explanation/reason] outside of itself to [cause/explain/be the reason of it]
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(Minor Premise) There is at least one [thing/event] with property X.
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(Inductive Principle) You have a choice…
A. argue that an infinite regress of [causes/explanations/reasons] for the X’s is unreasonable, OR
B. argue that such an infinite causal chain would itself have property X, OR
C. argue that the entire set of X’s taken together (which might, depending on X, include the entire physical universe we know and love) has property X.
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(Conclusion) Tracing back the [causes/explanations/reasons] back to their ultimate origin, we find that there is [one/at least one] thing which does not have property X, which, taken [singly/together], [causes/explains/gives the reason for] all the things which do have property X.
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(Atheist Baiting) Add the famous words: “And this all men call God”. Works best if ~X is a traditional divine attribute, or even better if you can collect several such ~X’s and can argue that they all refer to one and the same Exalted Being!

For example, in the debate, St. Craig’s kalam argument used “comes into existence” as X, and then used a lumping strategy (3C) to talk about the universe as a whole and ask whether it had a cause. This form of the Cosmological Argument ended up being strongly dependent on what the Science of the Big Bang actually shows, but most forms don’t really depend that strongly on Science.

Other traditional X’s include “changing with time”, “contingent” (something that might or might not exist), “composite”, and some other possibilities mentioned in the link above. The idea is that there are some features of objects which make us seek out causes for them, for example if an object is composed of several disparate objects, we naturally want to know what brought them together. Depending on what you pick for X, the Cosmological Argument may be more or less plausible.

You will also want to consider what type of causal concept you want to include in your argument. A key question is how we know there is such a thing as causation? If it is primarily for empirical reasons, then presumably we know about it through some type of inductive* argument from experience, in which case we could wonder how applicable it will be in unusual situations. On the other hand, if it is primarily motivated by reason, through analyzing what types of explanations would make sense of the universe, it may be less dependent on observation. Or perhaps the truth is somewhere in the middle.

[* Footnote: I somewhat regret using the term “inductive” here, given my previous usage of “Inductive Premise” to label premise 3. In both cases one is moving from specific applications to more general applications, but for premise 3 I had in mind something closer to mathematical induction, a step which (given the right background premises) is logically necessary, whereas in the paragraph directly above, I am referring to something more like scientific induction, where if you observe something happening enough times you guess that maybe it always happens that way.]

Another thing to figure out is what types of entities are connected by cause-effect relationships. Does a cause have to determine the effect with certainty, or is it sufficient if it in some way produces it? For example, if we want to argue that all contingent things were caused by something which is necessary, this is a contradiction in terms unless a necessary thing can produce contingent things, i.e. if causes don’t have to be deterministic. A related question: when we talk about causes, are we primarily talking about beings causing things to happen (a.k.a. agent-causation), or states of affairs causing things to happen (a.k.a. event-causation), or both?

Regarding step (5), note that excessively glib atheist baiting obscures the fact that nearly everyone should accept some type of Cosmological Argument, even if they don’t necessarily take it to a Theistic conclusion! If you are going to talk about causes/explanations/reasons AT ALL (and I really don’t see how to avoid this) then you really need an account concerning the domain to which the concept is applicable. And then it is an interesting fact, that either you must accept infinite or circular chains of [causation/explanation/reasons] or you end up going outside the domain to something else which is different.

This type of reasoning should be interesting, even if you are an atheist. The trouble is, if people only encounter Cosmological Arguments in the context of Theism, then Atheists adopt an argumentative approach where they just feel the need to poke a few holes in the arguments and then retreat to where they were before. This doesn’t do justice to the fact that there are numerous X’s for which the argument’s premises are at least plausible, even for people who don’t start out committed to any particular religious doctrine.

For example, Carroll himself gives an account of the scope of causation when he says:

Why should we expect that there are causes or explanations or a reason why in the universe in which we live? It’s because the physical world inside of which we’re embedded has two important features. There are unbreakable patterns, laws of physics—things don’t just happen, they obey the laws—and there is an arrow of time stretching from the past to the future. The entropy was lower in the past and increases towards the future. Therefore, when you find some event or state of affairs B today, we can very often trace it back in time to one or a couple of possible predecessor events that we therefore call the cause of that, which leads to B according to the laws of physics. But crucially, both of these features of the universe that allow us to speak the language of causes and effects are completely absent when we talk about the universe as a whole. We don’t think that our universe is part of a bigger ensemble that obeys laws. Even if it’s part of the multiverse, the multiverse is not part of a bigger ensemble that obeys laws. Therefore, nothing gives us the right to demand some kind of external cause.

There seem to be some question-begging moves in this paragraph, but leave that aside. My point is that Carroll gives a positive account of when he thinks makes the notion of [cause/explanations] make sense. He endorses a version of (1) whereby the concept of causation makes sense if (a) there are laws of nature, understood as unbreakable regularities, and (b) there is a thermodynamical arrow of time whereby entropy increases, making a distinction between the past and the future. (Since causes normally precede effects, but the laws of physics don’t strongly distinguish between the two directions of time except through thermodynamics, it seems clear that the arrow of time has to play some role in distinguishing causes from effects in physics.)

He also allows (2) that this concept—though not fundamental in his opinion—nevertheless makes sense for certain particular cases.

Then for (3) he allows us to lump together the universe taken as a whole, but claims that this whole does not meet his criterion (1). He thus comes to an object—the whole universe, apparently—for which, in his view, it wouldn’t make sense for it to have a cause (4), although he does not identify it with God (5). Thus his reasoning has an implicit atheist version of the Cosmological Argument behind it. Though one can certainly question whether the metaphysical assumptions behind this claim are right.

But it’s just possible you came here hoping, not to construct your own Cosmological Argument, nor to deconstruct Carroll’s, but instead to find out what I think about it, something which you may think I have postponed saying for quite long enough. Well, it just so happens that I’ve written a 16,000 word essay on the Cosmological Argument and related topics, and will be posting it in installments over the course of the next few weeks.

Explanation needed

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I’ve been discussing Sean Carroll’s claim that:

The demand for more than a complete and consistent model that fits the data is a relic of a pre-scientific view of the world. My claim is that if you had a perfect cosmological model that accounted for the data you would go home and declare yourself having been victorious.

In my last post, Models and Metaphysics, I tried to argue that there are substantive philosophical questions about causality which Carroll is dismissing unduly as pre-scientific.

But in this post, I thought I’d give a concrete example of a situation where we would not declare victory and go home, even with a complete and consistent model of the universe. While at some point fairly soon I’d like to give my own take on the Cosmological Argument, my counterexample in this post isn’t going to depend on any seriously heavy-duty metaphysics. Instead I’d like to try to focus on something fairly quantitative and precise, something “rational almost to the verge of rationalism“, in short, an argument that even someone steeped in scientism could love.

Let’s imagine that in the future, we come up with a seeming Theory of Everything™ which explains almost everything about the world. Every single physical phenomenon which has ever been observed has now been explained by a simple equation. Let us stipulate that the initial state of the universe is itself determined by these equations, leading to a cosmology consistent with what we observe. If you like, we can also pretend that no supernatural events have ever been verified, and that (after the Great Riot of 2438 C.E., when all the metaphysicians and philosophers were confined to the tops of their Ivory Towers and forbidden to communicate with the ordinary citizens outside) we have all agreed not to inquire to closely into the question of why certain physical states of the brain correspond to conscious experiences. It is indeed a great triumph for the Scientific Method.

There’s one catch. The remaining (non-meta)physicists tell us that there is one universal constant of nature in the theory, designated by a capital alpha $A$, whose numerical value needs to be fixed before any predictions can be made. This constant is dimensionless, meaning that all the units cancel out, so that it isn’t measured in meters per gram, or joule-seconds, or anything like that, but is just a real number. For example, it might be the ratio of two things with the same units. Because this constant $A$ is dimensionless, it’s numerical value is independent of the choice of units used to measure this parameter.

(In real life there are currently about 26 or so dimensionless constants in the Standard Model plus General Relativity—not counting inflation or dark matter—the most famous of these constants being the fine structure constant, which is approximately $1/137.036\ldots$.)

Since the equations work equally well no matter what the value of $A$ is, we have no choice but to do experiments to see what its value is. Let us suppose (rather unrealistically) that the scientists have measured this parameter to 800 decimal places, and that—lo and behold!—the answer is exactly$$A = \frac{2\pi}{7}.$$No one knows why, that’s just the way things are.

(Note: this situation is different from the usual Fine-Tuning Argument, because I am not supposing that there is any reason why life requires the constant to take on this precise value.)

I submit to you that, notwithstanding the fact that this TOE™ gives a complete description of everything in the universe, we ought not to declare victory and go home. Because it is plain as day that this number $2\pi / 7$ requires some sort of explanation which has not yet been given. In other words, we don’t just demand that our models completely explain the data. We also demand that they be complete in the sense of providing explanations for anything which seems to require an explanation.

True, $2\pi / 7$ is not an extremely complicated number; in most computer languages one can write a fairly short computer program that spits out this number. But I didn’t become a physicist in order to compress my sense-data into as few bits of information as possible; WinZip does a better job of data compression than I ever could. I became a physicist in order to understand how and why the world works the way that it does.

So I wouldn’t be completely satisfied with this TOE™ as it stands, even though it would be a big improvement on our current best theories of physics. Instead I would start asking naïve questions like:

“Why is there a $2\pi$ in the formula for $A$, given that we all know that $2\pi$ is the ratio between a circle’s circumference and its radius? Where do circles come into it?”

and

“What’s so special about $7$? Is this just a random whole number that was pulled out of a hat?!? Why is the denominator even an integer at all? What is $7$—a sufficiently awkward prime that it seldom comes up in physics formulae—doing in the most fundamental equation of the universe?”

Now I don’t know whether all of these mutterings about sevenths of circles would get me shoved up a Tower or not. But I am convinced that this question would be meaningful, that it must have an answer, and that any red-blooded human being with basic curiosity about the world should hope to find the answer.

Or, to speak in Bayesian terms, nearly all of my prior probability would be placed on there is an explanation for this odd fact that I don’t know yet, and nearly none on this is just an inexplicable basic fact about the universe which has no explanation at all. I’m not sure how to convey this intuition to you if you don’t already share it. But it seems to me that basic inexplicable facts about the universe shouldn’t fall into patterns which seem to indicate the existence of a deeper layer of reality, unless there actually is a deeper layer of reality behind the shadows we see on the cave wall…

“What’s that? Yes officer, I was just headed for that Tower over there right now! Please don’t let me trouble you any further. No, I just stepped out for a moment. Yes. Look I’m heading back right now. See?”

Of course, just because I would think that there must be an explanation, doesn’t mean that we would ever find out what that explanation is. Life can be a bummer that way:

All this I have proved by wisdom.
I said, “I will be wise”;
But it was far from me.
As for that which is far off and exceedingly deep,
Who can find it out?
(Ecclesiastes 7:23-24)

I would be potentially open to any explanation involving either “natural” or “supernatural” elements, so long as it in fact explained the parameter.

Of course, if the explanation involved more ad hoc elements than the thing being explained, then that would raise questions about whether it was really the best or simplest explanation. And even if I thought of a good explanation, I might wonder if there were some other equally good explanation. Or conversely, I might not be able to think of any good explanation at all. So at the end of the day I might have to be an agnostic about what type of explanation should be considered.

But that wouldn’t change the fact that I’d think there’d be one.

Undivided Looking

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