Gaps at the Dinner Table

by Aron Wall Posted on May 17, 2014

Speaking of the God of the Gaps™, I was myself accused of believing it just the other day.  I was at dinner with Raphael Bousso, Eva Silverstein, Ori Ganor, and some other physicists, and they were discussing fine-tuning and questions involving the precise way in the Multiverse is supposed to explain it.

Well, eventually I got tired of remaining in the closet, and I asserted: "Given that I believe in God for other reasons, I think it's most likely that God chose the Laws of Nature to be conducive to life".  Well, this got everyone pretty worked up (in a friendly way) and Raphael tried to apply that ominous phrase: the God of the Gaps™.

Well, it isn't.  In my comment, it was completely manifest that I did not believe in a God whose sole purpose was to fill the fine-tuning "gap".  I believe in God primarily for other (good, evidence-driven) reasons.   Once you already believe in God, it is seems totally natural (supernatural?) that he should pick laws of Nature which support life.  Theism isn't an ad hoc hypothesis invented solely to fix the problem of fine-tuning.   Whereas the Multiverse is, so I guess I should have made a counter-accusation regarding the Multiverse-of-the-Gaps!

Or perhaps it should be called Naturalism-of-the-Gaps, that touching faith that Naturalism can explain away the apparent meaning and purpose of the Universe (something which is perfectly obvious to many ordinary people, who haven't been trained out of this intuition by a Naturalist worldview masquerading as "Science").

Of course, for all I know God did create gazillions of other universes besides ours, and this is the explanation for the fine-tuning of our universe.  But I'm certainly not required to believe that the laws of physics are ultimately due to blind processes which don't care about us.  Without that premise, a fine-tuned universe just doesn't seem like as big of a problem.  Hence there is no need to fill the gap with elaborate new physics.

(But don't worry, if I think of a wonderful physical explanation with experimental consequences, I'll still be perfectly happy to publish it and collect my Nobel prize... just because I am open to supernatural explanations, does not mean my mind is closed to natural ones.)

The other thing the dinner conversation made clear is that some physicists get seriously nervous about the fact that God can't be described by equations, and is therefore (in their eyes) ill-defined.  I'll have something to say about this later, in response to Sean Carroll's debate comments.  For now I'll just say that it seemed rather insular to me—there are only a small number of people who are capable of using equations to describe the world, yet everybody else manages somehow.  As they say, if all you have is a hammer, everything starts to look like a nail.  It is our job as physicists to describe the world as completely as we can using equations, but it does not follow that there are no other ways of gaining knowledge about the world.

Perhaps I should have asked whether any of them had ever had a mystical experience.

On the other hand, somebody else (I think it was Ori) pointed out that Monotheism is the ultimate example of a unification hypothesis—explaining diverse things in Nature based on the operation of a single principle.  The elegance of Monotheism seemed to have some appeal to him.

It's a funny thing.   These days, the Multiverse is taken seriously by theoretical physicists, yet God isn't.  (Although the more old-fashioned types attack both concepts as equally unscientific.)  And yet, there is at least some observational evidence for the existence of God (in the way of claimed miracles and visions and so on).  On the other hand, there is no observational evidence for the existence of the Multiverse.

Apart from fine-tuning itself, the best that can be said about the Multiverse is that certain types of speculative new physics (such as string theory) might also predict multiple universes with different laws of physics (depending on certain other factors).  But it's not like there's any actual experimental evidence for other universes, or for any specific theory which predicts them.  It's almost as if people care more about whether an idea has the flavor of Science (or science-fiction) than if there is any actual evidence for it.  The most important aspect of Science is always observational support!

(It's important for people like me who study quantum gravity to remind ourselves of this point from time to time.  It's always especially ironic when people in my field dismiss concepts for lack of observational evidence, since there isn't much in the way of quantum gravity experiments.  10^{-35} meters is just way too tiny to see!)

Posted in Theological Method | 29 Comments

God of the Gaps

by Aron Wall Posted on May 12, 2014

Then there is the phrase "The God of the Gaps"™.  In any long discussion on "Science and Religion", this phrase must eventually be deployed by one or the other party, either by the skeptic (with a triumphal tone as of one finally deploying his most powerful weapon) or else by the articulate and educated defender of a modern faith, showing his sophisticated ability to rise above primitive superstitions: "But that's the God of the Gaps™!" they say in response to a proposed act of the Deity, "We can't possibly believe in that!"

In the debate between Carroll and St. Craig, both participants had their obligatory five seconds of hate towards this idea.  Craig:

This is not to make some sort of naïve claim that contemporary cosmology proves the existence of God. There is no God-of-the-gaps reasoning here. Rather I’m saying that contemporary cosmology provides significant evidence in support of premises in philosophical arguments for conclusions having theological significance.

Carroll:

It is certainly a true issue that we don’t know why the early universe had a low entropy and entropy has ever been increasing. That’s a good challenge for cosmology. To imagine the cosmologist cannot answer that question without somehow invoking God is a classic god-of-the-gaps move. I know that Dr. Craig says that is not what he’s doing but then he does it.

It is difficult to fight against a slogan delivered so frequently and with such conviction, especially when for some perverse reason educated and intelligent people on both sides insist on attacking the same strawman.  But it is worth pointing out, that if the detractors of an idea could be defeat it simply by labeling it with a silly-sounding alliterative phrase, we wouldn't be able to believe in the “Big Bang” theory either.

As Carroll quotes the philosopher David Lewis as saying:

I do not know how to refute an incredulous stare.

These references to the God of the Gaps™ often function as a similar incredulous stare, not any kind of actual argument.  (Mind you, the incredulous stares Lewis got were because of his belief in modal realism, i.e. every single logically possible world is equally real.  Perhaps those incredulous stares just meant that ideas which flagrantly violate common sense should be assigned a tiny prior probability?)

Anyway, if the God of the Gaps™ is a fallacy, it's a very strange one.  It is not any one of the standard textbook logical fallacies, and it is only ever brought up in theological contexts.   On the surface, it sounds awfully like claiming that inference to the best explanation is a fallacy.  Let me pull out some home truths here, and make the following bold statement:

Any time we ever believe in anything rationally, we do so because there is some kind of "gap" in our understanding of how the universe works, which is filled by postulating the existence of that thing.

In other words, all valid arguments that something exists are based on Of-the-Gaps type reasoning.  This is just how reasoning (scientific or otherwise) works.

This is not to say, of course, that all gaps are best filled by postulating specific divine intervention.  Of course not.  Admittedly, Monotheists do believe the following:

All phenomena which occur in Nature do so because God sustains the world in being, thus (at least indirectly) causing everything.

But this hardly implies that all phenomena make equally good evidence for God's existence.

To the best of my knowledge, no Christian apologist has ever made the following argument: 1) Science cannot explain high temperature superconductivity [a puzzling phenomenon in condensed matter physics], 2) therefore an intelligent designer must have caused it, 3) therefore God exists.  The reason is that it is obvious in this case that there should exist in principle an ordinary scientific explanation for this phenomenon.  Superconductors involve complicated, messy physics and there is no particularly good reason to be surprised that we don't understand them fully yet.

(When an Intelligent Design theorist such as St. Behe argues that: 1) there exist phenomena in Nature such as bacterial flagellum which could not plausibly have evolved naturally because they have irreducible complexity, 2) therefore they must have been created by an intelligent designer, he is not committing any type of logical fallacy, let alone God of the Gaps™.  The problem with his argument is that biologists have shown that his premise (1) is false, but it's a perfectly good type of argument, if its premises were really true.)

In other cases, such as the seeming low-entropy beginning of the Universe, or the fine-tuning of the constants of Nature to permit life, or why certain forms of life have conscious experiences, or why murder is wrong, or for that matter why there is a material Universe at all, it is at the very least not completely obvious that there will exist a natural explanation of the usual scientific type.  There is a reason that theistic philosophers (not being totally stupid) latch onto these types of "big" or "fundamental" questions rather than questions about superconductivity.

It's actually the exact same reason why many atheistic philosophers will deny that these are meaningful questions to which one has a right to expect an answer.  (Carroll does this in the debate, regarding the question of why the Universe came into existence.  Assuming for the sake of argument that it did, he argues that this is not the sort of thing one needs an explanation for.)  One could imagine a hypothetical physics which is in one sense a complete system of equations, and yet fails to answer some or all of these questions.  In that case the Naturalist will (because of his conviction that Science is the only ultimate path to truth) deny that the questions are meaningful, while any person who feels unable to swallow this will have for themselves an argument for the existence of God.

Other, more optimistic Naturalists may hold to the belief that "Science will one day explain that".  Since data about what Science will do in the future is sadly unobtainable, this type typically appeals to one of those historical just-so stories I mentioned in my previous post.  To rephrase it once more (note that I do not accuse Carroll of making the following argument in all particulars; as I said I am using the debate as a springboard to talk about larger issues):

"Our superstitious ancestors thought that nearly all natural phenomena—the rising of the sun, the growth of the crops, etc. were attributable to numerous supernatural beings. Science has discredited nearly all of these ideas, but of course Science is not yet complete. The modern day defenders of religious traditions, therefore, although their original motivation for belief is gone, cling to these holes in our understanding as keeping a place for the divine activity. If only evolution or Big Bang cosmology or something leaves a place for God's activity, these religious types argue, then we have some role for Religion. But as Science continues to discover more and more, the gaps get smaller and smaller, and eventually these claims will disappear as well. To cling to this sort of Religion is worthless."

This type of reasoning (which is quite common, although I phrase it in my own words) tends to glide imperceptibly from popular pagan polytheists (who thought there was a divinity for every major or minor phenomenon) to the Hebrew monotheists (who resisted this trend as superstitious and wrong).

It was perfectly obvious to any pagan philosopher or early Christian that Nature proceeds according to orderly laws, and natural processes. Modern Science can take credit for unifying the description of many phenomena into common mathematical frameworks, but to act as though the existence of order in Nature is a modern discovery is simply absurd. It is true that this fact is in considerable tension with certain forms of Animism or Nature Polytheism. But certainly almost any astute monotheist living in the last two thousand years, is going to admit that God causes most things to happen, not through whim but through the operation of certain natural processes, which can be understood to some extent by human reason.

In this sense, Naturalism and Monotheism have a shared (and highly successful) common heritage.  Both of them imply that the material world is not to be understood as divine, and that therefore it is fair game for impersonal study and observation.  To act as though the fruits of this shared common presupposition is some type of falsification of one of these two positions is completely unfair.

So then, everyone should stop using this phrase, God of the Gaps™.  In addition to being confusing and condescending, and not really a logical fallacy, it almost always indicates the presence of a strawman opponent.  Very few religious people believe that God exists only to fill gaps in our understanding of Science.  Let's argue against the real positions on the table.

Posted in Reviews, Theological Method | 15 Comments

Thoughts on the Carroll-Craig Debate

by Aron Wall Posted on May 10, 2014

Recently, Sean Carroll (cosmologist and atheist, whom I have met a couple times at physics events) and St. William Lane Craig (philosopher and Christian apologist) had a debate about this topic:

"God and Cosmology: The Existence of God in Light of Contemporary Cosmology."

Transcript,  Video,  Carroll's post-debate reflections, Craig's: One Two Three

(Warning: when the debate transcript says something like 10500, it really means 10^{500}.  Apparently whoever (or whatever) transcribed it doesn't understand scientific notation.)

Several readers have asked me to comment on this debate, and I plan to write more than one post doing so.

Let me just say first that I am not particularly interested in the question of who "won" this debate (between two people whom I both respect).  The existence of God does not, of course, depend on any particular person's ability to effectively argue for (or against) him.  I'd rather just make some opportunistic comments based on what the participants said.  What limited comments I have about the debate as a debate I will try to confine to this post.

William Lane Craig is a skilled debater who has done his best to keep abreast of Modern Cosmology.  This is commendable, but it was inevitable that his depth of knowledge in Cosmology was not as great as Carroll, who works on this subject professionally.  And often it showed.  That is why Craig had to rely mainly on a lot of quotes from famous physicists such as Alex Vilenkin—and sometimes this backfired, as in the case of Alan Guth, who apparently believes that the universe is eternal.

Since the topic was limited to Cosmology, Craig was unable to bring in any other types of evidence for the existence of God, besides those related to the Cosmological or Fine-Tuning Arguments.  In other debates, Craig has focused more on the evidence for miracles (such as the Resurrection of Jesus), which personally for me is much stronger evidence for the existence of God than anything coming from Cosmology.  For me, if Modern Cosmology is sufficient to get people to even wonder, "Is there maybe somebody who did that?" that's enough to start with—so long as it makes them curious enough to start exploring other lines of evidence, based on History or personal experience.

In other words, it's not necessary for Cosmology by itself to get people to a belief in God.   What matters is the cumulative case from Cosmology plus everything else.  If there are puzzling things such as fine-tuning which might be explained by God, and might have a different explanation (e.g. the multiverse), to me the most natural response seems to be to keep an open mind about all possible explanations.  But that would imply, that at least the existence of God is not absurdly unlikely (so far as Cosmology is concerned).  And if a person gets that far, then when they examine historical evidence or religious experiences, at least they won't do so with a giant presupposition in favor of Naturalism that requires them to explain away practically anything.

Assuming they are rationally consistent, that is.  Most people, if you try to argue for some proposition X that they don't want to believe in, will ask only whether the argument is so compelling as to force them to believe in it.  If not—if they can think of any possible way to defeat or evade the argument—they will act as though the argument has no force at all.  They are like the fearsome Barghest of legend, a monstrous black dog which can only be killed with a single blow.  If you do not strike hard enough to kill, then all of the damage is transferred from it to you.  (At least, that's how it works in Pendragon, the Arthurian Roleplaying System.)  With such people, if they can find any clever loophole in your argument—even if it involves totally speculative new physics—the next day they will say that the argument was refuted and provides no evidence for X at all.  This makes it impossible to make a cumulative case argument.

Anyways, I thought Craig did a pretty good job of sticking to the restricted topic of Cosmology.  Carroll somewhat less so, when he said:

If theism were really true there’s no reason for God to be hard to find. He should be perfectly obvious whereas in naturalism you might expect people to believe in God but the evidence to be thin on the ground. Under theism you’d expect that religious beliefs should be universal. There’s no reason for God to give special messages to this or that primitive tribe thousands of years ago. Why not give it to anyone? Whereas under naturalism you’d expect different religious beliefs inconsistent with each other to grow up under different local conditions. Under theism you’d expect religious doctrines to last a long time in a stable way. Under naturalism you’d expect them to adapt to social conditions. Under theism you’d expect the moral teachings of religion to be transcendent, progressive, sexism is wrong, slavery is wrong. Under naturalism you’d expect they reflect, once again, local mores, sometimes good rules, sometimes not so good. You’d expect the sacred texts, under theism, to give us interesting information. Tell us about the germ theory of disease. Tell us to wash our hands before we have dinner. Under naturalism you’d expect the sacred texts to be a mishmash—some really good parts, some poetic parts, and some boring parts and mythological parts.

[As an aside, there's something a bit funny here.  Carroll thinks that God should have provided us with some scientific information in the Bible.  The most useful scientific fact he can think of is the importance of good hygiene.  And it is a fact that the most famously boring book of the Bible, the book of Leviticus, is chalk full of hygiene rules about cleanliness (embedded among other religious rituals).  Fairly decent rules too, given the 2nd millennium BC context.  No germ theory of disease, I admit.  But highly practical nonetheless.  Now, I'm not a religious fundamentalist who thinks that the Bible is a Science textbook.  Nor am I an antireligious fundamentalist who thinks it ought to have been a Science textbook.  But I do think it is ironic that the particular thing Carroll demands is, in some sense, present in the least-loved book of the Bible!  Carroll continues:]

Under theism you’d expect biological forms to be designed, under naturalism they would derive from the twists and turns of evolutionary history. Under theism, minds should be independent of bodies.  Under naturalism, your personality should change if you’re injured, tired, or you haven’t had your cup of coffee yet.

[Huh?  Theism is the belief that God exists.  It does not commit one to any particular view about the soul's relationship to the body.  The fact that our personalities are encoded in our brains is logically independent to the question of whether God exists.  Particular religious traditions might have particular views about the soul, but that's not what we're talking about here.]

Under theism, you’d expect that maybe you can explain the problem of evil – God wants us to have free will. But there shouldn’t be random suffering in the universe. Life should be essentially just. At the end of the day with theism you basically expect the universe to be perfect. Under naturalism, it should be kind of a mess—this is very strong empirical evidence.

This, however, strayed from the parameters of the debate topic.  Whatever the merits of the Argument from Evil, it cannot be said that Evil is a discovery of Science.   It has nothing to do with Cosmology.  It is not a discovery of contemporary physics that there is random suffering, and that the universe isn't fair.  (What would a scientific theory of "Justice" even look like?)  Granted, the Argument from Evil is relevant to the cumulative case concerning God's existence (some of my own thoughts about that are here.)  But then Craig would also be entitled to throw in historical data about Jesus and anything else that might be relevant to the inquiry.

Naturally Craig called him on it:

He is very concerned to show that God’s existence is improbable relative to certain non-cosmological data. For example, the problem of evil, our insignificant size, and so forth. The very fact that these are non-cosmological data shows that they are not relevant in tonight’s debate. I have addressed things like the problem of evil extensively, for example, in Philosophical Foundations for a Christian Worldview.  So the debate tonight is not over the probability of theism versus naturalism. That would require us to assess all sorts of non-cosmological data. Rather, the question is: is God’s existence more probable given the data of contemporary cosmology than it would have been without it? And I think it certainly is.

Craig, being a skilled debater, makes sure to frame the debate question to be one which is comparatively easy to show.  According to Craig's framing, he only needs to show that Theism is more plausible given e.g. our current understanding of the Big Bang Model, compared to if we didn't know these facts.  This is a fairly modest ambition.  It certainly seems more likely now that the universe has a beginning than it would have seemed to a materialist living 500 years ago.  So if the beginning of the universe is a relevant datum for the existence of God, then cosmology provides some positive evidence.   (On the other hand, if it isn't relevant, why are we even discussing whether there was a beginning?)

At times, Carroll even seems to assume that if Craig doesn't believe in Theism for scientific reasons, his views can't be based on evidence at all:

There are very few people in the modern world who become religious, to come to believe in God, because it provides the best cosmology or because it provides the best physics or biology, or psychology, or anything like that. And that includes Dr. Craig. There’s a famous quote by him that says, “The real reason, the primary reason, for believing in Christianity isn’t cosmological arguments.”

[I was unable to track this quote down, but having some knowledge of Craig's views in other contexts, I highly doubt that Craig was referring to some inarticulate leap of faith not grounded in any good evidence at all.  I imagine—especially since he referred to Christianity—that he was thinking about some type of historical evidence that has to do with, say, Jesus or something.  Maybe something related to the fact that he did lots of miracles, and rose from the dead, and was seen by many eyewitnesses, who themselves did several miracles, leaving a band of committed followers to this day, who sometimes do miracles in his name, including naturalistically inexplicable healings with solid medical documentation—have I made my point yet?]

I’m not mentioning this as a criticism; it is simply an observation of fact. There are other reasons to be a theist other than cosmology, and I think that is true. I think that makes sense. Most people who become religious do so for other reasons—because it gives them a sense of community, a sense of connection with the transcendent, it provides meaning or fellowship in their lives.

These subjective warm fuzzy feelings are nice and all, but it is scientism to think that they are the only thing left after we remove stuff like Cosmology.  For example, History is also an evidence-driven field, and it has plenty of data supporting things like miracles.  Carroll made a joke about taking into account new evidence if the roof were to fall on his head, but perhaps if Carroll does some historical investigation, there might be more subtle ways for God to make a point.

The problem is that the basis of religion in the modern Western world is theism, belief in the existence of God. I’ve tried to make the case that science undermines theism pretty devastatingly. Five hundred years ago it would have made perfect sense to be a theist. I would have been a theist five hundred years ago. By two hundred years ago science had progressed to the point where it was no longer the best theory. By a hundred years ago after Darwin it was a rout. And by these days with modern cosmology there’s no longer any reason to take that as your fundamental worldview.

I always find it interesting, that when you poke a person who makes grand claims about the philosophical implications of Science, sooner or later they end up telling one of these historical just-so stories about how things used to be completely different before Science came along.

You know the drill.  Once upon a time, people used to use God to explain everything, and then one or two things got explained by Science, and then some more things got explained by Science, and now there are only two or three gaps in our knowledge, which stubborn religious people cling to in order to justify Theism, but we all know (by linear interpolation, I guess) that Science will eventually explain these things too, which is just as good as if it already had done so.  (This is closely related to the infamous "God-of-the-Gaps"™ strawman, about which I will have more to say later.)

In order to tell this story properly, Carroll needs to insist that he would have been a pious religious person 500 years ago.  But I'm not at all sure this is true.  He didn't really present any arguments for Theism based on the Science of 500 years ago, let alone one which is refuted by our present day understanding.  All he did was say why he doesn't believe in Craig's arguments (which, whether you believe them or not, are based on Modern Science, and couldn't even have been made 100 years ago, let alone 500).   All that stuff about random suffering, and multiple religions, and weird stuff in the Bible, and that the universe is really big while Earth is really small, and that tiredness and drugs and physiological secretions influence the mind, was just as evident to smart people 500 years ago as it is now.

No matter how much lecturing you hear about how Science works because we can always correct our theories with new data, they seldom bother to check these supposedly historical narratives with any actual data.  When you do, you usually find the story is far more complicated.

In the paragraph quoted above, the only actual Scientific revolution mentioned is that due to Darwin.  The rest is left suspiciously vague (for example, I'm not sure from the description what exactly is supposed to have happened 200 years ago, that made Theism "no longer the best theory").

In fact, for the most part it's pretty unclear what the implications of scientific theories are for or against Theism.  Take for example Maxwell's equations.  One could try to argue that: 1) lots of stuff is described by equations, 2) Maxwell's equations mean that one more thing is described by equations, 3) therefore probably everything is described by equations, 4) God is not an equation, therefore 5) God does not exist, but this seems like a rather weak argument from induction, not something that "undermines theism pretty devastatingly".  It's not like anyone in the 1500's was saying that magnetism couldn't be understood except as a special miracle of God, and then St. Maxwell showed they were all wrong.

There's a reason, therefore, why people fixate on Darwin.  Darwin's theory of Evolution really did remove one possible argument for the existence of God: namely that an act of special creation was necessary to explain the existence of each individual species, and its close adaptation to its environment.

Of course, the removal of a particular argument for God's existence isn't the same as disproving Theism.   In particular, this argument for the existence of God was not by any means the historically most important one.  In fact, you only really see people shortly before Darwin (like St. William Paley) making this argument.   In medieval times, people used to think that life-forms like flies would spontaneously generate in rotting meat.  Obviously, they wouldn't have thought much of Paley's view that each species needed to be created individually by God.  It was only with the increase of scientific understanding that this "gap" in our understanding was noticed.  Thus, to say that filling this gap refutes the ideas of the medievals (who didn't even know there was a gap here to be filled) is absurd.

What history actually shows, is not a monotonic replacement of Theology by Science, but a complicated back-and-forth process where new Science produces some new arguments for Theism (Paley, fine-tuning...), discredits others (Paley, the need for a Prime Mover rotating the outer heavenly sphere...), and so on.  But that's too complicated to reduce to a tidy, one-sided historical meta-narrative, so lots of people just make up a story about Science and Religion being enemies, and stuff everything into that mold.

All of this was just picking around the edges.  In the next post, I will talk more about the so-called God-of-the-Gaps™-fallacy, which both Carroll and Craig pay their obligatory disrespects to.  Then I'll try to get to the actual substantive questions about whether the universe had a beginning, according to Modern Science.  And whether that has any theological implications.  And fine-tuning.  And about Carroll's arguments that Theism is ill-defined and false.   Things that relate to the actual substance of the Carroll-Craig debate.  That sounds like a plan.

Posted in Reviews | 42 Comments

A Question about the Multiverse

by Aron Wall Posted on May 6, 2014

Another question from St. Paul, the reader from New Zealand:

I hope that you are well and that you are having fun with your work. I see that you posted our email exchange on your blog, it was a great answer and much appreciated.

I actually have another question I would like to ask, (although I realise that you may well be planning on writing about it already) but as always I completely understand if you don't have the time!

I've been reading about the recent detection of gravitational waves and how they confirm the theory of inflation. What I have found interesting is that there have been quite a few articles reporting that most models of inflation imply the existence of a multiverse, with quotes from Alan Guth, etc. I realise that the term "multiverse" can be used for several quite different situations, but they seem to be referring to one with variation of the laws of physics, meaning the anthropic principle can be invoked.

I was wondering what you make of this new discovery and what your take on the idea of the multiverse is? I have always felt that the fine-tuning argument was a helpful pointer to God, so I am curious about the implications of confirming inflation (although the existence of multiple universes certainly doesn't rule Him out).

Thank you for your time,
Paul

A quick explanation concerning "fine-tuning" and the "multiverse".   Fine-tuning refers to the observation that the fundamental constants of Nature seem to take special values which appear to be necessary to the existence of life.   The fine-tuning argument is a theistic argument which claims that this is good evidence for the existence of God.

One common atheistic retort is to say that maybe there are lots and lots of universes—with different laws of physics in each universe—and that any observers would therefore have to live in the universes which permit life.  This idea is a called the multiverse.

This may sound like crazy science fiction thinking, but I actually think it is the most plausible naturalistic response, given what we now know about physics.  Although there is no really good reason to believe in the multiverse, it seems much more plausible then any of the attempts to construct physical mechanisms to account for this fine-tuning.

However, it is not really clear to me that the multiverse is the sort of thing that ought to count as an explanation for fine-tuning.  In some moods it seems to me like cheating.  Science normally works by postulating theories to fit the observed data, not by postulating (new and unobservable) data to make the theories we have seem less weird.

In fact, there are in fact some serious controversies as to how to properly do Bayesian reasoning in the context of a multiverse.  Pretty much all viewpoints lead to some horrendous paradoxes.  Since the proper way to do probabilistic reasoning in this context is unclear, it is also unclear to what extent the multiverse would be an explanation for fine-tuning.  But this is a complicated question I don't have time to go into right now.

Instead, Paul asks the different question of to what extent the multiverse is supported by real, actual Science.  In particular, the very recent results from last March about inflation.  For those of you who have been living under a rock, there was a recently announced experimental result in cosmology.  The BICEP2 experiment claims to have seen the gravitational waves resulting from inflation, a very early period in our universe's history where the size of the universe expanded at an extremely quick, exponential pace.

[Update: the BICEP2 results have since been discredited.]

I wrote to Paul roughly as follows:

Most models of inflation predict "eternal inflation", meaning not that there wasn't a beginning, but that in some regions of the universe, inflation continues forever towards the future.

In order to have a multiverse of the sort that might be conceivably relevant to fine-tuning, you need to meet two criteria: (a) a mechanism for producing gazillions of different universes (at least 10^{150} without supersymmetry, or 10^{60} with supersymmetry), and (b) in these different universes, there are an equally large number of different effective parameters describing the low energy physics in each of the universes.

Eternal inflation is conducive to (a) insofar as it would result in widely separated regions which can never causally communicate with each other even at the speed of light.  But it does not by itself do anything to meet condition (b).  The best argument for (b) is probably string theory, which seems to have gazillions of different types of metastable vacua, but there is currently no successful experimental predictions for string theory.  (String theory does seem to imply the existence of gravity, but that's more of a retrodiction, and isn't unique to string theory...)

Posted in Physics | 39 Comments

Reasonable Unfalsifiable Beliefs

by Aron Wall Posted on April 2, 2014

In a previous post, I argued that falsifiability is not the be-all and end-all of Science.   There are valid scientific beliefs that are not falsifiable.

However, there is something to the idea that beliefs should be falsifiable.  One way to make this precise is to use Bayes' Theorem.  This is a rule which says how to update your probabilities when you get some new evidence E.  It says that your belief in some idea X should be proportional to your prior probability (how strongly you believed in before the evidence), times the likelihood of having measured the new evidence given X.   (You also have to divide by the probability of having measured the new evidence, but this is the same no matter what X is, so it doesn't affect the ratio of odds between two competing hypotheses X and Y.  It's just needed to get the probabilities to add up to 1).  As an equation:

P(X|E) = P(X) P(E|X) / P(E).

We won't actually plug any numbers into this equation in this post.  Instead, I'll just point out a general property which this equation has.  Suppose you are about to perform an experiment.  On average, you expect that your probability is going to be the same after the experiment as before.

For example, suppose you believe there is a 1/50 chance that there exists a hypothetical Bozo particle (I just made that up right now).  And suppose you perform an experiment which has a 50% chance of detecting the Bozo if it exists.  Just for simplicity in this example let's suppose there are no false positives: if you happen to see the Bozo, it leaves a trail in your particle detector which can't be faked.

There are two possible outcomes: you see the Bozo or you don't.  In order to see the Bozo, it needs to (a) exist and (b) deign to appear, so you have a 1% chance of seeing it.  In that case, the probability that the Bozo increases to 1.

On the other hand, you have a .99 chance of not seeing the Bozo.  In that case, your probabilty ratio goes from 49:1 to 98:1 since the Bozo exists possibilities just got halved.  This corresponds to a 1/99 probability that the Bozo exists.

On average, your final probability is (.01 \times 1) + (.99 \times 1/99) = .02.  Miraculously, this is exactly the same as the intitial probability 1/50 of the Bozo existing! Or maybe it isn't so much of a miracle after all.  On reflection, it's pretty obvious that this had to happen.  If you could somehow know in advance that performing an experiment would tend to increase (or decrease) your belief in the Bozo, that would mean you that just knowing that the experiment has been done (without looking at the result) should increase or decrease your probability.  That would be weird.  So really, it had to be the same.

We call this property of probabilities Reflection, because it says that if you imagine yourself reflecting on a future experiment and thinking about the possible outcomes, your probabilities shouldn't change as a result.

Now Reflection has an interesting consquence.  Since on average your probabilities remain the same, if an experiment has some chance of increasing your confidence in some hypothesis X, it must necessarily also have some chance of decreasing your confidence in X.  And vice versa.  They have to be in perfect balance.

This means, you can show that it is impossible for an observation to confirm a hypothesis, unless it also had some chance of disconfirming it.  VERY ROUGHLY SPEAKING, we could translate this as saying that you can't consider a theory to be confirmed unless it could have been falsified by the data (but wasn't).

Even so, there are a number of important caveats.  In some situations in which we can and should believe things which are, in various senses, unfalsifiable.  This occurs either because (a) The Reflection principle doesn't rule them out, or (b) the Reflection principle has an exception and doesn't apply.  Here are all the important caveats I can think of:

  1. It could be that the probability of a proposition X is already high (or even certain) before doing any experiments at all.  In other words, we know some things to be true a priori.  For example, logical or mathematical results (such as 2+2 = 4) can be proven with certainty without using experiments.  Similarly, some philosophical beliefs (e.g. our belief that regularities in Nature suggest a similar underlying cause) are probably things that we need to believe a priori before doing any experiments at all.
    .
    Propositions like these need not be falsifiable.  This does not conflict with Reflection, because that only applies when you need to increase the probability that something is true using new evidence.  But these propositions start out with high probability.
    .
  2. It could be that a proposition has no reasonable chance of being falsified by any future experiment, because all the relevant data has already been collected, and it is unlikely that we will get much more relevant data.  Some historical propositions might fall into this category, since History involves unrepeatable events.  Such propositions would be prospectively unfalsifiable, but it would still be true that they could have been falsified.  This is sufficient for them to have been confirmed with high probability.
    .
  3. Suppose that we call a proposition verified if its probability is raised to nearly 1, and falsified if its probability is lowered to nearly 0.  Then it can sometimes happen that a hypothesis can be verifiable but not falsifiable.  The Bozo experiment above is actually an example of this.  There is no outcome of the experiment which totally rules out the Bozo, but there is an outcome which verifies it with certainty (*).
    .
    This doesn't contradict Reflection.  The reason is that Reflection tells us that you can't verify a hypothesis without some chance of lowering its probability.  But it doesn't say that the probability has to be lowered all the way to 0.  In the Bozo case, we balanced a small chance of a large probability increase against a large chance of a smaller probability decrease.
    .
    The Ring Hypothesis was another example of this effect.  We have verified the existence of a planet with a ring.  Had we looked at our solar system and not seen a planet with a ring, this would indeed have made the Ring Hypothesis less likely.  But not necessarily very much less likely.  Certainly not enough to consider the Ring Hypothesis falsified.
    .
  4. Suppose that, if X were false, you wouldn't exist.  Then merely by knowing that you exist, you know that X is true.  But X is unfalsifiable, because if it were false you wouldn't be around to know it.
    .
    For example, no living creature could ever falsify the hypothesis that the universe permits life.  Even though it didn't have to be true.  Nor could you (in this life) ever know that you just lost a game of Russian Roulette.
    .
    This type of situation is an exception to the Reflection principle.  The arguments for Reflection assume that you exist both before and after the experiment.  (You can also construct counterexamples to Reflection involving amnesia, or other such funny business.)

To conclude, these are four types of reasonable beliefs which cannot be falsified.  It is a separate question to what extent these types of exceptions tend to come up in "Science" as an academic enterprise (as opposed to other fields).  But I don't see any good reason why these exceptions can't pop up in Science.

(*) Footnote: Some fictitious person (let's call her Georgina) might say that the Bozo is still falsifiable since nothing stops us from doing the experiment over and over again, until the Bozo is either detected or made extremely improbable.  Hence, Georgina would argue, the Bozo IS falsifiable.

My answer to Georgina is that it actually depends on the situation.  Maybe the Bozo experiment can only be done once.  Maybe (since I'm making this story up, I can say whatever I want) the Bozo can only be detected coming from a particular type of Supernova, and it will be millions of years before the next one.  More realistically, maybe the Bozo is detected using its imprint on the Cosmic Microwave Background, and the phenomenon of Cosmic Variance means that you can't repeat the experiment (since there is only one observable universe, and you can't ask for a new universe).  More realistically still, maybe the experiment costs 100 billion dollars and Congress can't be persuaded to fund it more than once.

Georgina might not like the last example very much, since she might say that all she cares about is that the Bozo is in principle falsifiable.  Perhaps as a holdover from logical positivism, the Georginas of this world often talk as though this makes some kind of profound metaphysical difference.  But it's not clear to me why we should care about falsifiability in principle.  The only thing that really helps us is falsifiability in fact.

If a critical experiment testing the Bozo will not be performed until next year, for purposes of deciding what to believe now, we should behave in exactly the same way as if the experiment could never be done.  Experiments can't matter until we do them.

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