God of the Gaps

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.


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 | 5 Comments

Thoughts on the Carroll-Craig Debate

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."

TranscriptVideoCarroll'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 | 14 Comments

A Question about the Multiverse

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,

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.

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 | Leave a comment

Reasonable Unfalsifiable Beliefs

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.

Posted in Scientific Method | 5 Comments

When God kills the Innocent

A Christian reader named Paul writes to me from New Zealand with the following common question.  With permission, I am posting his question and my answer on my blog.

St. Paul writes:

A few months ago I discovered your blog via the Biologos website. It has been a real encouragement for me to read your articles and I can honestly say that I enjoyed everything that I've read.

Anyway, a Church friend and I have been meeting up every few weeks to have discussions about tricky issues in Christianity and something that has come up (and was always bound to...) is the depictions of God in the Old Testament. In the Old Testament, God is often depicted as acting violently and sometimes in ways that can seem barbaric. For example, God gives instructions for the Israelites to kill people. Likewise, an atheist friend of mine was shocked when I referred to God as "just" because he had just read about the exodus and the plagues.

The issue for me is not that God doesn't have a right to judge/ punish guilty people (for example the Canaanites), but the fact that innocent people are also involved in some of these situations. For example children and babies. In some verses they seem to be explicitly mentioned (i.e. 1 Samuel 15:3). I realise this is only a single example, but there are one or two other examples that are quite easy to find.

The most common response of Christians seems to be that God created all of us and therefore He can do whatever He wants. I agree that God is sovereign, but these actions seem inconsistent with the nature of God revealed clearly in Jesus.

I have some ideas about what to make of it all, but I thought that I would ask you what you make of these sorts of verses? I realise that you must be very busy (and you don't know me!) so please don't feel obligated to reply! However, if you have the time and the inclination I would really appreciate it.

My reply was as follows (some slight editing):

This is a tricky problem in theology, isn't it!  But it isn't just an Old Testament vs. New Testament thing.  The following verses are all God speaking in the Old Testament:

  1. "I, the Lord your God, am a jealous God, punishing the children for the sin of the parents to the third and fourth generation of those who hate me, but showing love to a thousand generations of those who love me and keep my commandments." (Ex. 20:5-6)
  2. "My angel will go ahead of you and bring you into the land of the Amorites, Hittites, Perizzites, Canaanites, Hivites and Jebusites, and I will wipe them out." [including the children, as other parts of Scripture make clear] (Ex. 23:23)
  3. "Fathers are not to be put to death for their children or children for their fathers; each person will be put to death for his own sin.  Do not deny justice to a foreigner or fatherless child, and do not take a widow's garment as security.  Remember that you were a slave in Egypt, and the Lord your God redeemed you from there. Therefore I am commanding you to do this." (Deut. 24:16-18)
  4. "Yet you ask, 'Why does the son not share the guilt of his father?' Since the son has done what is just and right and has been careful to keep all my decrees, he will surely live. The one who sins is the one who will die. The son will not share the guilt of the father, nor will the father share the guilt of the son. The righteousness of the righteous will be credited to them, and the wickedness of the wicked will be charged against them." (Ezekiel 18:19-20)

The tension lies within the pages of Hebrew Scripture itself.  We have to understand in what sense all of these Scriptures can be true.

Let me start by demolishing the idea that "God created all of us and therefore He can do whatever He wants."  If this were true, there would be no meaning in saying that God is just and righteous in how he treats us.  It wouldn't allow us to predict anything whatsoever about what he would do.  Yet St. Abraham—our father in faith—pleads for Sodom and Gommorah by asking: "Far be it from you to do such a thing--to kill the righteous with the wicked, treating the righteous and the wicked alike. Far be it from you! Will not the Judge of all the earth do right?" (Gen. 18:25).  God does not respond by saying "Whatever I do is just by definition".  Rather, he grants Abraham's requests, and goes beyond them to ensure that, in this case, the innocent are not punished alongside the guilty.  The fact that God is just implies that there are some things which he won't do, because they are unfair.

On the other hand, God IS the ruler of the universe.  This gives him authority to make decisions which ordinary human beings are not allowed to make.  Just like an earthly Governor or Judge has authority to do some things which ordinary citizens don't have the right to do, God has the authority to do anything, i.e. any type of act.  For example, everything belongs to God, so when he takes things from us it is not stealing, but doing what he likes with his own property.  Similarly, if God kills people it is not murder.

(This does not, I think contradict the point of the previous paragraph.  The scope of authority is different from how one uses that authority.  God has the authority to do anything, precisely because, since he is perfectly good, he never abuses this authority, but only does what is just and right.)

Note that, as the ruler of the universe God actually kills everyone.  All people are mortal, some of them die young, and God is responsible for this state of affairs.  Sometimes he does it miraculously in order to make a special point, but more often it he causes it to happen naturally.  Before I ask whether I can trust a God who killed the Caananite children, I first need to ask whether I can trust a God who will kill ME.  As Christians, we trust that God is using death as a tool in order to turn us into the people he wants us to become.  Partly, we trust him because he came to Earth and died for us, so he isn't asking us to suffer anything which he hasn't gone through himself.

God's motivations for killing people are not the same as that of a human murderer.  Most of the time, people kill other people out of hatred, because they want something bad to happen to them, or because they don't care about them.  But God swears to us that this is not why he does it. "As surely as I live, declares the Sovereign Lord, I take no pleasure in the death of the wicked, but rather that they turn from their ways and live" (Ezekiel 33:11)

Also God is unchangable.  If you or I killed somebody, we would become more violent and hateful people who would be more likely to kill someone else.  Whereas God's character, being eternal, cannot be corrupted.  Paradoxically, this means that a perfectly good being is more likely than a good human to do bad things in order to produce good consequences.

And God is omniscient, so he knows when a group of people have become so wicked that it would be bad for them, and for their children, and for the rest of the world, if they remain alive to keep sinning.  For example, the Canaanites sacrificed their children as part of their religion, and if God hadn't put an end to them, we might still be doing that today.  It may seem ironic that God also ordered that their innocent children be killed, but remember that they would not have remained innocent if they had been able to come to maturity.  Instead they went to Heaven, which might not have been possible if they had been corrupted by the religion of their parents.

This brings us back to the group justice vs. individual justice question.  Ultimately, I believe God is committed to bring justice and vindication to every innocent person, including those who were victims of bad circumstances.  On the other hand, God has also set up the world in such a way that our good or bad actions can have an effect on other people: if we sin against others, they are harmed, and can be tempted either to hate or to imitate us.  This is especially true in the case of our parents, who bring us into being and choose what enviornment we will come to maturity in.  Because of this strong moral influence, it is inevitable that to some extent our moral and cultural condition is inherited from others.  Alcoholic parents often have alcoholic children.  We may resist this influence and become different people than our parents, but there is a correlation which cannot be entirely removed.

As a result, in his role as Judge of the Earth, Guardian of Human Culture and Supervisor of the Gene Pool, God must necessarily engage in some amount of group justice as well as individual justice, because that is the nature of how humans propagate ourselves (and our ideas).  He does not, however, delegate this authority to us.  The Israelite judicial system was based strictly on individual desert (although even there, indirect punishment of others is inevitable: see the story in 2 Samuel 14:6-7 for an example).  The Israelites were also commanded to exterminate certain people groups, but had no authority to decide which ones—God provided them with a specific and limited list.

In the end, God will provide us all with individual justice.  But I think that once everything is revealed, our moral interdependence will prove to have been a means of grace.  If no innocent people ever suffered punishment for guilty people, then Christ could not have saved us, and we would be dead in our sins.  If we ourselves struggle, if sins have been transmitted to us by others, or if the punishment of others has ruined our lives as well, then what?  I think that by forgiving our forbears, and by seeking God's help for our problems, we become imitators of Jesus, as St. Peter says:

For you were called to this,
because Christ also suffered for you,
leaving you an example,
so that you should follow in His steps.
He did not commit sin,
and no deceit was found in His mouth;
when He was reviled,
He did not revile in return;
when He was suffering,
He did not threaten
but entrusted Himself to the One who judges justly.
He Himself bore our sins
in His body on the tree,
so that, having died to sins,
we might live for righteousness;
you have been healed by His wounds.
For you were like sheep going astray,
but you have now returned
to the Shepherd and Guardian of your souls. (1 Peter 2:21-25)

If Christ—the Innocent One—suffered for the sins of others and brought about the redemption of the world, then all of us who in lighter measure bear the sin of others, will also recieve through Christ this redemption.  From the the infants killed by St. Joshua for the sins of the guilty Canaanites, to the infants killed by Herod in place of the innocent Christ-child, everyone who has a share in the sufferings of Christ will also rise with him in eternal glory.  This is both a justice and a mercy beyond our comprehension.

Posted in Theology | 3 Comments

My take on Loop Quantum Gravity

A friend of mine from St. John's College, who was recently accepted to a physics doctoral program at Penn State, asked me what my opinion of Loop Quantum Gravity is.  I replied be email, and then I decided, why not tell the world!

Now, Loop Quantum Gravity is the main rival to String Theory as an attempt to quantize gravity, although it only commands about a tenth of the resources that String Theory does.  The people who work on it tend to have more of a General Relativity background than a Particle Physics background, and this tends to influence what types of problems they are trying to solve.

Warning: Unlike my other physics posts, I have made no attempt to make my commentary here accessible to non-physics people.  (Yes, that means every other time I wrote a physics post and nobody understood it, I was the one to blame for not making it accessible enough!)

Einstein's theory of general relativity is background free, meaning that it does not start with any absolute background space or time, but instead allows the spacetime geometry to be dynamically constructed from the evolution of the metric.  A theory of quantum gravity ought to be similar---it ought to be expressed in a way which doesn't depend on the prior specification of any spacetime metric.  I think this is really important, but no one really knows how to do this.  There are many ideas, but they all have various difficulties.

In principle, I think the idea of LQG---to build spacetime out of a discrete, quantum structure---is a very elegant and moving idea.  (I first got interested in quantum gravity by reading the online writings of John Baez, who used to work on LQG.)  Also, the LQG people have a very beautiful quantization of space at one time, in terms of spin networks.  Essentially, by doing a step-by-step quantization of GR at one time (minus the dynamics), making only a few arbitrary choices, they were able to obtain spin networks.  I'm sure you [i.e. the friend I was writing to---AW] know what these are, but let me assure you that they are beautiful and have some deep connections to geometrical ideas.

The next step in the construction of LQG is to decide what the dynamics are.  Technically, this is done either (A) by choosing a "Hamiltonian constraint" in parallel with the Hamiltonian formulation of GR, or (B) in the spin-foam formalism, by postulating some sort of sum over histories assigning an action to each spin foam.  It is here which we encounter the major problem: There is no agreement over how to implement the dynamics!  There are many ideas, but no consensus on what to do.  Implementing dynamics seems to involve some arbitrary choices.  Some of the proposed solutions seem to me obviously wrong (e.g. see Smolin's criticism of Thiemann's Hamiltonian constraint: arXiv:gr-qc/9609034).  There is also a serious danger that by choosing the wrong dynamics, one breaks the diffeomorphism invariance of the theory.  In the Hamiltonian approach this manifests itself in so-called "anomalies in the constraint algebra", while in the spin foam approach it is unclear whether the inner product obtained from the sum over histories really has the necessary gauge invariance.  I summarized these problems in passing, with citations, in the
Introduction to this article of mine: arxiv:1201.2489.

Thus---even leaving aside the critical hard problem of whether and how a continuum spacetime can emerge from a discrete description (a problem aggravated by the fact that it is difficult to see how any discrete model of spacetime besides causal sets could possibly preserve Lorentz invariance, see arXiv:gr-qc/0605006)---I would say that LQG really doesn't exist yet as a well-defined theory.  Unless you consider dynamics to be an unimportant part of a theory.  And finding sensible dynamics is a really hard problem, perhaps impossible.

Yet, despite the lack of dynamics, there's no end of papers where people do specific applications, like count black hole entropy, or even attempt to do quantum cosmology (basically by truncating the theory to a finite number of degrees of freedom, and then quantizing those degrees of freedom in a way which is "loopy" in spirit).  But all of these things are totally provisional until one can embed them in an actual theory with dynamics.   People used to be really interested in solving these hard problems, but I feel like a lot of them have now given up and are seeking more limited goals.  This is a shame, since I think progress can only come by facing the hard issues head on.  And maybe by showing some flexibility in how the theory is formulated.

Once one has the dynamics, again one can say nothing about the real world until one has identified the correct vacuum state.  An arbitrarily constructed "weave" state that happens to look like some Riemannian geometry doesn't cut it.  You have to figure out how to identify the right vacuum state---the one with lowest energy (once you figure out how to define that!).  Many deep questions here!  I think most people in LQG are asking all the wrong questions.

One can put too much emphasis on quantizing gravity---really that's backwards, we need the classical theory to emerge from the quantum theory, not vice versa.  When people calculate discrete area and volume spectra for spin network edges and vertices, they've got things backwards.  These are just some operators at the Planck scale.  The really interesting question is not, how much "area" is associated with each spin, but how many of each type of spin crosses a given area of the vacuum state (if such a thing even exists).

I despise the ignorant bigotry which most string theorists show towards LQG, even though LQG barely exists as a theory.  Their contempt is undeserved.  The LQG people are trying to do something genuinely harder---to reconstruct spacetime from first principles.  We don't know how to formulate string theory except by means of strings propagating in some background spacetime, or via dualities like AdS/CFT.  Since the theory has gravitons, with a diffeomorphism gauge symmetry, it's clear to me there has to be some background free formulation of string theory, but no one has any idea what this would look like.  And most string theorists don't even understand why it is important.

Personally (and unexpectedly for me) I've found that as someone who studies black hole theormodynamics, I can interface better with string theorists than with LQG people---the ones who are really interested in fundamental concepts, like Don Marolf and others at UCSB, for example---even though I don't really consider myself a string theorist.  This may be a bit of a conceit at this point, since I've now written multiple papers on AdS/CFT.  My heart is more strongly devoted to the types of ideas LQG people explore, but my mind
recognizes that they really haven't made all that much progress.

Posted in Physics | 3 Comments

Yet More Random Stuff

I've been staying home sick with some horrible cough for about 3 weeks now.  One would think that this would be quite conducive to blogging, but when I'm running a fever I find it hard to concentrate enough to produce mental output.  (Mental input, like books and movies, is fine).

Fortuantely—either because of taking antibiotics, or for some other reason—I'm beginning to feel much better, so here's a post, consisting of links which I've found interesting since the last time I did links:

  • Of This and Other Worlds blogs on the Problem of Susan in the Narnia books.  The Superversive adds some interesting personal testimony.
  • A New York Times article on computer software that supposedly grades essays.  Anyone who thinks that computer programs can substitute for human graders is completely misinformed about the point of essays.  Which is always to communicate some sort of meaning through organized thought.  This is something that no computer can do, prior to the development of some actual AI overlords.  The best it could possibly do is check for pretentious vocabulary, correct bad grammar (badly) and enforce meaningless and stupid rules about how many paragraphs there must be.   No machine could possibly check for the presence of an interesting thesis supported by coherent argument based on plausible evidence.  There are probably some things you could measure which are corollated with being a good writer, but even this will cease once students learn how to flatter the machine.
    The sad thing is that there are probably human teachers who grade this superficially.  Although, even they could probably tell if the sentences didn't actually fit together in any way (besides beginning with words like "Moreover").
    Out of curiosity, I just went and checked the webpage of the discern program to see what their alogorithm was.  It's machine learning based on sample essays which are already graded.  Oh my.  That means neither the student nor the classroom instructor will even know what criterion the machine is using.
  • What St. Lewis (in his capacity as a literary scholar) thought of the Puritans.
  • You've probably heard how the first man in space, Soviet cosmonaut Yuri Gagarin, said that didn't enocunter God there.  As if God were literally located in the sky.  Well, it turns out, the whole story was a Soviet lie; St. Yuri was an Orthodox Christian.  More details here.
  • A haunting article, by and about a woman who acts the part of a sick patient for medical students.  This is one of the best written narratives I've read in quite some time.
  • An interesting (and to me inspiring) letter from missionary St. Anthony Norris Groves (1795-1853) to crankish schismatic (St?) John Nelson Darby (1800-1882) on the topic of Christian unity.
    Darby was one of the first people to teach that Christians would be raptured into heaven 7 years prior to the Second Coming of Christ, a belief almost completely unheard of prior to Darby.  This is part of a detailed scheme called Dispensationalism, popular in American Fundamentalist circles, which is based on that idea that apparent contradictions in the Bible should be resolved by assigning different texts to one of seven different covenants or "dispensations" in which God treats people differently.  This way of thinking leads them to construct an elaborate timeline of End Times events (a suprise Rapture, followed by 7 years of Tribulation, followed by the Second Coming, followed by 1000 years of The Milennium [this one at least has a  foundation in a literal reading of the Book of Revelation], and then finally the Final Judgement).  Oddly enough, people think that this elaborate scheme comes from reading the Bible literally as a fundamentalist should, even though no one who read the Bible without influence from Darby would ever come to this elaborate scheme on their own.
    More relevantly to this letter, Darby went on to found a small denomination of his own which excommunicated nearly everybody else.
  • St. Maxime is a Stylite monk with a much better way to isolate himself from the World.  Make sure to click through the slide show.
  • An article about my grand-advisor (i.e. the Ph.D. advisor of Ted Jacobson, my advisor) Cécile DeWitt-Morette.
  • An article on the simplicity of God (hint: it doesn't mean that he is easy to understand).  Consider me firmly in the "classical theism" camp.  I consider the idea that God is just a person like us, but pure spirit and infinitely powerful etc., to be idolatrous.  True, we humans are the image of God.  The converse is not true: God is not to be conceived as being in our image.
  • The New York magazine interviews St. Antonin Scalia.  There was an interesting moment where Scalia brings up that he believes in the Devil.  The interviewer acts a bit incredulous, and asks:

Isn’t it terribly frightening to believe in the Devil?
You’re looking at me as though I’m weird. My God! Are you so out of touch with most of America, most of which believes in the Devil? I mean, Jesus Christ believed in the Devil! It’s in the Gospels! You travel in circles that are so, so removed from mainstream America that you are appalled that anybody would believe in the Devil! Most of mankind has believed in the Devil, for all of history. Many more intelligent people than you or me have believed in the Devil.

Posted in Links | 3 Comments

Must Science be Falsifiable?

There's a common notion floating around, due to Karl Popper, that scientific theories are characterized by the fact that they are falsifiable.  The idea is that it is never possible to verify a scientific theory (i.e. the sun always comes up) because one day it might not happen.  But it is possible that the sun might not come up some day, and then the theory is falsified.  It must then be rejected, and replaced with something more complicated.

Now, let me confess right away that I have not gotten this idea by reading any of Popper's writings.  It is an idea which has been popularized in the scientific community.  You see, everyone knows what Popper said without having read any of it ourselves.  It could be that if I actually read Popper's books, my idea of what he said would be falsified.  So let me confine myself in this post to discussing Popperism as commonly understood.

If a theory is unfalsifiable (that is, if no experiment you could possibly perform would rule it out, then according to Popperism it is not a scientific theory.  Among those who subscribe to Scientism, this is usually assumed to be A BAD THING™.  (The way some people talk, if a theory is unfalsifiable, that means it is false!)

People often characterize bogus pseudoscientific ideas as unfalsifiable, because of the tendency of people who believe in them not to subject them to rigorous scrutiny.  But this is clearly an oversimplification.  True, there is such a thing as mystical Woo-Woo from which no definable predictions can be made, either because the ideas are not precise enough or because they don't relate to any actually observable phenomena.  But many psuedoscientific ideas, such as homeopathy, reflexology, or astrology, can be tested experimentally, it's just that the people who believe in them don't like the results when people do!)  I've heard people refer to Young Earth Creationism (YEC) as unfalsifiable.  I think their reasoning must be the following:

1. YEC is unscientific and wrong.

2. I've been taught that when ideas are unscientific, the reason is because they are unfalsifiable.

3. Therefore, YEC is unfalsifiable.

In fact, though, the real problem with YEC is that it IS falsifiable, and in fact has been falsified many time over. If the universe were created about 6,000 years ago and we have to get all of the layers of fossils and rock from a single planet-wide Flood about 4,500 years ago, then there are a gazillion problems with observation.  It contradicts the results of almost every branch of science which tells us anything about the past.  (Adding bizarre extra ideas, like God created the earth with fossils in it in order to trick us into believing in evolution, may make YEC unfalsifiable, but it might be better to characterize this as pigheaded refusal to accept reasonable falsification.)

[Fun fact: if you interpret all of the genealogies in Genesis as being literal, with no gaps—which of course I don't—then it follows that when Abraham was born, all of his patrilineal ancestors were still alive, back to the tenth generation (Noah)!  (This is using the Masoretic Hebrew text that omits Cainan, who is included in the Septuagint Genesis and Luke.)]

All right, digression over.

Clearly there is something right about the idea that theories ought to be falsifiable, yet not confirmable with certainty.  Major scientific theories usually deal with generalities: they make predictions for a large (perhaps infinite) number of different situations.  Normally, it is not possible to verify them in all respects, because even if it works well in many cases, it could always be an approximation to something else.

On the other hand, I think there are some scientific ideas which are verifiable but not falsifiable.  Here's an example:

Ring Hypothesis: Somewhere in this universe or another, there exists a planet with a ring around it.

I submit to you that: 1) our observation of Saturn verifies the Ring Hypothesis, 2) when scientists verify a proposition by looking through a scientific instrument, that counts as Science, and 3) no possible observation could have falsified the Ring Hypothesis.  (Even restricting to the Milky Way, eliminating planets with rings would be a tall order, impossible with current technology.)  Therefore, there are scientific propositions which are verifiable but not falsifiable.

On the other hand, even if an experiment "falsifies" a theory, it could be that the experiment rather than the theory is wrong. As Einstein once said "Never accept an experiment until it is confirmed by theory".  This witticism may seem to turn science on its head, but nevertheless it has a bit of truth to it.  A while back, there was an experimental observation which seemed to suggest that neutrinos travel faster than light.  Soon there were many papers on the arxiv trying to explain the anomaly.  But it turned out, not surprisingly, that there was an error in the measuring devices.  Usually, when a well-tested theory is in conflict with an experiment, and the anomaly has no particularly good theoretical explanation, it is the experiment which is wrong.  Not always, but usually.

What this means is that we need a more flexible set of ideas in order to discuss falsification and verification.  In particular, we ought to accept that falsification and verification can come in degrees—observations can make an idea more or less probable, without reducing the probability to exactly 0 or 1.  The accumulation of enough experimental data against a theory should make you reject it, but it may be able to withstand one or two anomalous measurements.

The quick answer is that one ought to use Bayes' Theorem instead.  This is a general rule for updating beliefs, taking into account both our prior expectations and observation.  This goes not just for Science, but also for everything else.  The only thing that makes Science special is that, due to a number of special circumstances, the process of testing through observation is particularly easy to do.

Even though falsification is not the best way to think about Science, it still works pretty well in many cases.  In a later post, I hope to explain the connection between Bayes' Theorem and falsification.  Usually we should expect good theories of the universe to be falsifiable, but in certain situations they don't have to be.  Bayes' Theorem can be used to understand both the general rule, and why there are exceptions.

Posted in Scientific Method | 12 Comments