Category Archives: Scientific Method

Models and Metaphysics

In my previous posts about the Carroll-Craig debate, I’ve been skirting around the edges of an important claim by Carroll which summarizes the main reason he doesn’t buy the Cosmological Argument. That’s because I was focusing on the question of whether the universe had a beginning. Now I want to grapple with his more philosophical claim.

Carroll says this:

So, I think I can make these points basically by following Dr. Craig’s organization starting with the kalam cosmological argument, and unlike what he said I should be doing I want to challenge the first of the premises: If the universe began to exist it has a transcendent cause. The problem with this premise is that it is false. There’s almost no explanation or justification given for this premise in Dr. Craig’s presentation. But there’s a bigger problem with it, which is that it is not even false. The real problem is that these are not the right vocabulary words to be using when we discuss fundamental physics and cosmology. This kind of Aristotelian analysis of causation was cutting edge stuff 2,500 years ago. Today we know better. Our metaphysics must follow our physics. That’s what the word metaphysics means.

[Well, many scholars think that Aristotle’s book on causation/God was called Metaphysics because it was the book immediately following his Physics in the traditional order of the canon. But perhaps Carroll knows this and is simply introducing his thesis in a joking way…]

And in modern physics, you open a quantum field theory textbook or a general relativity textbook, you will not find the words “transcendent cause” anywhere. What you find are differential equations.

[Of course, because QFT and GR concern the interactions between various material entities (excitations of fields). Their interactions (i.e. their causal relationships) are indeed described by differential equations. And therefore the subject matter does not concern transcendental or ultimate causes, any more than economics or psychology textbooks discuss the weak force. What he really ought to say to make his argument, is that the term “cause” does not appear in many modern physics textbooks (apart from the use to mean “logically implies”) due to its lack of usefulness in specifying the precise form of the laws of physics.

It is, however, a separate question whether concepts of causation are implicit in the fact that some particular differential equation holds. It does not seem outrageous to state that the state of the fields at a given point are caused by the state of the fields just beforehand in the past lightcone; indeed this concept is called causality in contemporary physics. This concept may indeed be different in some ways from traditional philosophical ideas of causality, but it is not sheerly different, and there is room for argument about the precise relationship between these ideas of causation. Carroll continues:]

This reflects the fact that the way physics is known to work these days is in terms of patterns, unbreakable rules, laws of nature. Given the world at one point in time we will tell you what happens next. There is no need for any extra metaphysical baggage, like transcendent causes, on top of that. It’s precisely the wrong way to think about how the fundamental reality works. The question you should be asking is, “What is the best model of the universe that science can come up with?” By a model I mean a formal mathematical system that purports to match on to what we observe. So if you want to know whether something is possible in cosmology or physics you ask, “Can I build a model?” Can I build a model where the universe had a beginning but did not have a cause? The answer is yes. It’s been done. Thirty years ago, very famously, Stephen Hawking and Jim Hartle presented the no-boundary quantum cosmology model.

[See here for my discussion of the claim that the Hartle-Hawking model leaves no room for a Creator.]

The point about this model is not that it’s the right model, I don’t think that we’re anywhere near the right model yet. The point is that it’s completely self-contained. It is an entire history of the universe that does not rely on anything outside. It just is like that. The demand for more than a complete and consistent model that fits the data is a relic of a pre-scientific view of the world. My claim is that if you had a perfect cosmological model that accounted for the data you would go home and declare yourself having been victorious.

Carroll seems to be saying that the ability to construct a mathematically precise and consistent model of the universe is the only important criterion for the fundamental laws of physics, aside from fitting the data. Presumably he would add something about simplicity if we were considering two rival models which both accounted for the same data, but I think he doesn’t mention that since his primary concern is saying what counts as a possible model according to the contemporary set of informal procedures that cosmologists use, rather than asking how we decide between models once we have them.

This is probably the most important claim that Carroll made during the debate. I appreciate the fact that he was able to state his view in such a clear and accessible way. Now, there is one important point in which I agree with Carroll, and one important way in which I disagree.

I agree that Modern Science has involved some shifts in how we think about causation in the physical universe. This shift, which occurred sometime around the beginning of the 20th century (give or take a couple hundred years) involved a move away from mechanistic notions of causation, towards more abstract mathematical models. As a characteristic example, in the 19th century it was presumed that light waves couldn’t exist unless they were supported by a medium, called the luminiferous aether. When Einstein developed special relativity, he showed that no such aether was necessary. If you can write down a satisfactory equation for the way the electromagnetic field propagates, there’s no need to ask questions like “In what medium does it propagate?” (Of course, this philosophical point could have been made in the time of St. Maxwell as well, but it wouldn’t have been as compelling then, since before Einstein’s theory of relativity an aether was needed to preserve the principle of relativity).

Another example concerns normal forces of the sort that prevent two solid bodies from occupying the same space. A premodern physicist would have said that solid bodies have a property of solidity or massiness which, using our everyday intuitions, prevents two bodies from occupying the same position. In Lucretius’ atomic theory, the atoms were in solid shapes like billiard balls (but not necessarily round) which excluded each other due to their solidity. Very different was St. Roger Joseph Boscovich‘s 1763 proposal that atoms are merely mathematical points exerting force on other mathematical points.

In modern physics, there’s nothing inherently wrong in general with two objects occupying the same position, since you can write down equations in which this is allowed. The default, in the absence of interactions, is for two bodies to pass right through each other. That this does not occur for real solid bodies is due to a combination of electromagnetic forces and the Pauli exclusion principle for electrons.†

So I agree with Carroll that there have been changes in our attitude to causality in Physics. Now let’s see whether this should change our views about Metaphysics. As a reminder, Metaphysics is the branch of philosophy which studies the fundamental nature and relationships between various beings (abstracting from the particular descriptions of the particular things as studied by more specialized fields like Physics or Biology). It asks questions like these:

Do individual things have a particular essence or nature which does things?
In what sense does causality exist, and if so what kinds are there?
Is there really a physical universe?
Are there really minds?
Can everything be reduced to physics, or can everything be reduced to mental properties, or are these two independent realities, or are they both dependent on something else?
In what sense do mathematical entites like “7” or “isoscoles triangles” exist?
In what sense does morality exist?
Does some type of God exist, and if so what is he/she/it like?
What are the relationships between these different types of existence?
Do the “holes” in doughnuts really exist, or are they merely the absence of doughnut?
Are the questions I just asked even meaningful, or are some of them silly word games?

(The subset of questions about what exists are also sometimes also called Ontology. In case you’re wondering, analytic philosophers really do debate the one about holes. Personally I consider the one about God to be more important. But I figured that given my last question, I needed to include at least one question which I consider to be a silly word game…)

Now, these questions raise some difficult and contentious issues, and philosophers have been debating them for thousands of years. But rather then tackle them head-on, let’s ask to what extent developments in Physics and other Sciences help answer these questions.

There are two opposite extreme approaches one might take:

1. One is the view that our Metaphysics should essentially follow immediately from our Physics. Once we learn from experiment what specific Laws of Physics are true, that tells us everything we need to know about Metaphysics. People with this view tend to be scientistic and dismissive of philosophical arguments. (You might think from the quotation above that this is Sean Carroll’s view, that once we work out the correct physical model there are no more interesting questions to ask. But in fact his view is more subtle, since he acknowledges that there are interesting philosophical questions not obviously resolved by Science.)

2. The opposite extreme would be to say that developments in Physics have little or no bearing on Metaphysics. For example, there are modern day followers of St. Thomas Aquinas (typically but not always Roman Catholics) who believe that something similar to Aristotle’s metaphysical views follow necessarily, given that the world is rationally explicable at all, and that the very possibility of doing Science depends implicitly on accepting them. In this view, the basic concepts of metaphysical reality such as substance/accident or act/potency are written in stone, although identifying the particular “substances”‡ which actually exist, and their properties, depends on empirical Science. One such philosopher is St. Ed Feser, whose blog is on my sidebar. (I recently read his book Scholastic Metaphysics in which he presents his arguments for this position. On a first pass, I found it serious and interesting but ultimately unconvincing, though giving my reasons would take this post too far afield.)

But it seems to me that the correct view is in the middle, that Physics has some bearing on Metaphysics but it doesn’t fully determine it. Physical models and metaphysical views have, not a 1-to-1 relationship, or even a 1-to-many relationship, but a many-to-many relationship!

People who agree on the Laws of Physics (to the extent that we are able to discover them at present) can still have radical disagreements about Metaphysics. Of these metaphysical views, some seem irrational and silly, like the Monadic view that all distinctions are illusory and that only one thing exists. But it seems to me that there are several possible reasonable (i.e. non-crazy) views. So even after we agree on a single physics model, multiple metaphysical views can be reasonable. The variety of interpretations of Quantum Mechanics is one prominent example. Choosing between these interpretations requires philosophical arguments; doing an experiment is not enough.

On the other hand, it seems rather unlikely that the philosophical considerations by themselves are sufficient to pin down an exact Metaphysics either. That would be to say that every single view about the nature of Being, besides one, can be decisively refuted by philosophical arguments. That would seem to me almost as surprising as a claim that the Laws of Physics can be deduced from pure Reason. There are just too many possible sets of belief, and logical consistency plus noncraziness is too weak of a constraint. (Especially since our notion of noncraziness needs to be flexible enough to include things like interpretations of QM and the mind-body problem, where nearly all views seem “crazy” in one way or another.)

Given that there are multiple possible views about Metaphysics, we need all the help we can get to choose one. So it would be absurd not to rely on Physics to some extent, especially as it impinges on relevant questions. How could anyone have an informed position on the nature of time without thinking about what General Relativity says about spacetime? But we also need to recognize that Physics is not enough, and that abstract arguments about what “makes sense” are also called for. Even together these are not sufficient to bring all reasonable Philosophers into agreement.

That means that Carroll is moving much too quickly when he says that “This kind of Aristotelian analysis of causation was cutting edge stuff 2,500 years ago. Today we know better. Our metaphysics must follow our physics.”

If there are multiple possible metaphysical views, then we can’t just dismiss the views of Aristotle (or whoever) just for being old, without carefully thinking about their compatibility with Modern Science. Maybe people switched to modern views because of updates in physical knowledge (some of which, like Determinism, may themselves be out of date!). Or maybe they changed because of philosophical arguments, in which case we need to check whether those arguments are good or bad. Or maybe the old views simply became unfashionable. Most likely, it was some combination of these four causes, and we need to be careful! As St. Lewis writes concerning Owen Barfield:

In the first place he made short work of what I have called my “chronological snobbery”, the uncritical acceptance of the intellectual climate common to our age and the assumption that whatever has gone out of date is on that account discredited. You must find out why it went out of date. Was it ever refuted (and if so by whom, where, and how conclusively?) or did it merely die away as fashions do? If the latter, this tells us nothing about its truth or falsehood. From seeing this, one passes to the realization that our own age is also a “period”, and certainly has, like all ages, its characteristic illusions. They are the likeliest to lurk in those widespread assumptions which are so ingrained in the age that no one dares to attack or feels necessary to defend them.

While I don’t accept St. Feser’s arguments that Aristotelianism is compulsory, I think that studying it is a useful antidote to thinking that there’s only one possible view. Certain aspects of modern thought might be unreasonable inheritances from the Enlightenment, or from Positivism. The easiest way to notice that we are making unnecessary presuppositions, is by comparison to what previous thinkers have thought. If we dismiss previous metaphysical views out of hand, that makes it hard to notice our own modern blindness towards certain issues and problems.

We need to be especially careful given the tendency for theories to be expressed in the language of the existing philosophical structures. This can cause us to think that those theories depend on a certain Metaphysics, when really they don’t. Just because theologians expressed Trinitarian doctrines using Aristotelian terminology, or early 20th century physicists expressed QM using Positivist concepts, doesn’t necessarily mean that these ideas can’t be transplanted to certain other systems.

Aristotelianism became unpopular long before QM was discovered. But suppose that somehow the medieval European or Muslim world had discovered QM. I bet that their “interpretations” would have been radically different from anything we have now, even if the mathematics which they developed ultimately turned out to be equivalent to ours (as happened to Heisenberg and Schrödinger)!

None of what I have said here is a positive argument for Theism. It is merely my attempt to sweep away Carroll’s strong claim that once we have a physical model, all of our work is done and there is no place to ask further metaphysical questions. On the contrary, we can continue to ask questions, and we can judge possible answers to those questions by whether they make logical or intuitive sense to us.

Perhaps at the end of the day, a person might conclude that the certain questions about the origin of the Universe are meaningless, or that that they are meaningful but that Theism is not the correct answer to them. But that has to come after considering the merits of different rival views, not beforehand.

Notes:
† The Pauli exclusion principle forbids two fermions from occupying the same state, which sounds a bit like the principle that solid objects cannot occupy the same space, except that:

(i) “state” refers not just to position but rather to all properties including both position and velocity (to the extent that both can be simultaneously measured in Quantum Mechanics).

(ii) It follows from a much more abstract mathematical principle, which I will cite without explaining, that identical types of fermions (e.g. electrons) have antisymmetric wavefunctions. This means that the complex number describing the quantum mechanical amplitude for one electron to be in position $x$ and the other in position $y$ is minus the amplitude for the first to be at $y$ and the other at $x$. This is called Fermi-Dirac statistics.

(iii) It doesn’t apply to bosons, which have symmetric wavefunctions. Therefore you can have a bunch of identical bosons in the same state, as in lasers or Bose-Einstein condensates.

‡ “Substance” is a technical term in Aristotelian metaphysics. It means an individual entity which possesses existence independently, as opposed to an “accident” which “inheres” in a substance and can be changed without affecting the underlying nature of the thing in question. Sort of like the difference between nouns and adjectives. Not to be confused with the more recent chemical notion of substances. This confusion of terminology causes great misunderstanding when Roman Catholics try to explain their doctrine of transubstantiation to modern people!

Different Views about Time

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Updated to ask readers more directly for their thoughts, if you have any…

A random thought. Suppose we ask whether the world has a Beginning or an End, or whether it is eternal is one or both directions. It seems like there are 5 possible views, which I will name by association to various cultural groups who supposedly have had these views:

Norse view: the world began, and it will end.
Greek view: time is infinite in both directions
Hindu view: time goes in a circle
Hebrew view: the world began, but it will never end.
Nobody ever: time had no beginning, but it will still end!

I find it interesting that the first four views all have some intuitive appeal, to different people, but the fifth view just seems horribly wrong and perverse! Why do you suppose that is?

My best guess is that there’s is a certain obvious symmetry to treating the past and future in the same way, which makes views (1-3) seem reasonable. And there is also an argument that the past is not like the future, but if so it had better be like (4) rather than like (5)! I guess we all know deep down (it’s really the Second Law of Thermodynamics) that it makes sense for the universe to start from a simple initial condition and then develop complexities from there. But if we have to deal with infinite regresses AND we don’t even get an eternal universe out of it, that seems a bridge too far… but if anyone has any further thoughts on this, I’d be interested.

My cultural names are a brutal oversimplification, and you shouldn’t take my assigning these views to different cultures too literally. For one thing, there were lots of different Greeks and there are lots of different Hindus who believe all sorts of different things. For another, there is a conceptual difference between the world—in the sense of an ordered cosmology with a history—beginning, and time (a much more abstract notion) having a beginning. It takes a certain amount of intellectual sophistication to think about the latter question.

Norse mythology begins with fire and ice swirling around a bottomless pit for aeons; it is only later that a bit of fire strikes a bit of ice and spontaneously generates a giant and a cow, from whom later the jotun and gods emerge by various removes. (As you can see, the Norse were ultimately Materialists even about their so-called divinities.) At the end, the cruel jotun defeat the merry gods and the world is destroyed, plunging back into chaos. So it’s not really clear that time has a beginning or end, just that the story has a beginning and an end.

The Hebrews had the notion of divine Creation in Genesis 1:1 and elsewhere, but it is controversial whether Genesis 1:1 actually teaches the creation ex nihilo of later theology. St. Augustine is usually credited with the idea that there was not even time before creation, but in fact Philo, a 1st century Hellenistic Jew, got there first.

Similarly, our current best “concordance cosmology” appears to begin with an initial singularity, but has no end in time. (Well, really we should talk about spacetime, which allows time to end in some places, e.g. inside black holes, but not others.) This appears at first sight to be like the Hebrew view. At late times the universe expands exponentially forever, thinning matter out to a very cold but finite temperature. This is in accordance with the Generalized Second Law of Thermodynamics, which tells us that the universe will reach a boring maximum entropy state at late times. Thus, the story ends at finite time, and we really have the heroic defiance against inevitable destruction, as in the Norse view.

Even in Hebrew cosmology, there is that little matter of the whole universe being destroyed and then recreated again:

“See, I will create
new heavens and a new earth.
The former things will not be remembered,
nor will they come to mind.
But be glad and rejoice forever
in what I will create,
for I will create Jerusalem to be a delight
and its people a joy.
I will rejoice over Jerusalem
and take delight in my people;
the sound of weeping and of crying
will be heard in it no more.

Never again will there be in it
an infant who lives but a few days,
or an old man who does not live out his years;
the one who dies at a hundred
will be thought a mere child;
the one who fails to reach a hundred
will be considered accursed.
They will build houses and dwell in them;
they will plant vineyards and eat their fruit.
No longer will they build houses and others live in them,
or plant and others eat.
For as the days of a tree,
so will be the days of my people;
my chosen ones will long enjoy
the work of their hands.
They will not labor in vain,
nor will they bear children doomed to misfortune;
for they will be a people blessed by the Lord,
they and their descendants with them.
Before they call I will answer;
while they are still speaking I will hear.
The wolf and the lamb will feed together,
and the lion will eat straw like the ox,
and dust will be the serpent’s food.
They will neither harm nor destroy
on all my holy mountain,”
says the Lord. (Isaiah 65:17-25)

It’s really this “new heavens and new earth” that will last forever. Christianity is about Death and Resurrection, both for the universe and for each person. Science can get us as far as the doomed-to-die bit, but it can’t get us any farther. That is Law, the rest is Grace, revealed in Jesus Christ.

Separation of Physics and Theology?

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Down in the comments section of this post, reader St. TY has the following kind thing to say about me:

What an excellent blog. I have been looking for one like this for a long time. I tell what I like about it: Although we all know St. Aron’s Christian bias, but he does not let it intrude into his physics and, as one with a mathematical background, I like that separation of Church and State.

As for the format I’m old fashioned and I like the written word because good writing demands clarity and coherence I must add honesty, and so I like reading Aron’s pieces and the comments.

I would like Aron to put all of this meaty stuff in a book.
Would you, Aron?
Thank you.

Thanks so much for your gracious compliments about my blog! It’s too bad really, that I must strongly disagree with you when you say that

Although we all know St. Aron’s Christian bias, but he does not let it intrude into his physics and, as one with a mathematical background, I like that separation of Church and State.

Your proposal that I keep a separating wall is not really very undivided, is it? I expressed a different aspiration in my About page:

“Undivided Looking” expresses the aspiration that, although compartmentalized thinking is frequently helpful in life, one must also step back and look at the world as a whole. This involves balancing specialized knowledge with common sense to keep both kinds of thinking in perspective.

So in response I would say, that one’s physics views can and should be influenced by one’s theological views (or vice versa), if there is a legitimate reason why it should do so. There is, after all, only one universe, and therefore no compartments can be kept completely watertight. For example, most economists don’t need to know much about chemistry, but if they’re talking about buying things that might explode then there needs to be some cross-talk.

Christianity is not a “bias”, but a “belief”, one which happens to be true. Deducing things from one’s beliefs is not bias unless it is done in an irrational and capricious manner. But perhaps you were speaking in a semi-humorous way, in the way that we might say that all scientists seek to be biased towards the truth!

Reasonable physicists will probably have similar intuitions about how physics should be done (I’m excluding unreasonable people like Young Earth Creationists), regardless of whether they are atheists or theists. Or rather, people have different intuitions about physics but they mostly don’t correlate with religious views! But if on a particular matter (e.g. the universe having a beginning in time) somebody happens to be influenced by their religion (or lack thereof) to think that one viewpoint is more likely than another, I don’t think that should be taboo.

Far from corrupting the scientific process, I think science usually works better when people explore a variety of intuitions and options. As I said in discussing the importance of collaboration in science:

Healthy scientific collaboration encourages reasonable dissent. Otherwise group-think can insulate the community from effective criticism of accepted ideas. Some people say that scientists should proportion their beliefs to the evidence. However, there’s also some value in diversity of opinion, because it permits subgroups to work on unpopular hypotheses. I suppose things work best when the scientific community taken as a whole proportions its research work to the evidence.

It doesn’t necessarily matter whether the source of the original intuition is something that could be accepted by all scientists. What matters is that the resulting idea can be tested. Sometimes, the original motivation for a successful scientific theory is rather dubious (e.g the Dirac sea motivation for antimatter), but nevertheless the resulting theory is confirmed by experiment and later is motivated by a different set of considerations.

So I don’t believe in the complete separation of Physics and Theology, hence the blog. But maybe I believe in something else which has some similar effects on my writing. You must after all be detecting something about what I am doing which provoked your favorable statement.

Perhaps it is this: I believe in being honest. I must to the best of my ability weigh the evidence on fair scales, and be open about what I am doing. It would be dishonest if, because I want to prove the truth of Theism, I were to report the relevant Physics data in an imbalanced way, playing up anything which might seem to help my case and playing down anything which does not. People often do this kind of thing reflexively when they argue, even to the extent of first deceiving themselves before they deceive others. But it’s still unfair tactics, especially when deployed by the expert against the layman.

It is not dishonesty for me to have my own views about what’s important in Physics and what’s not, but it would be dishonest if I implied that all physicists agreed with me about that when they don’t. Nor would it be dishonest if my views about speculative physics are influenced to some extent by my theological views—I think this is inevitable, and possibly not even fully conscious—but to pretend that a view is based on purely physical considerations when it is not, or to distort the data about Physics to match a preconceived agenda (theological or otherwise) is repugnant to me.

So I’ll do the best I can to be honest, and hopefully that will tilt the scales in the right direction.

Once upon a time, a college friend and I planned to write a book about Science-and-Religion topics, but that never got off the ground. A few of the ideas from that time are being recycled here.

I originally started this blog because an elder Christian whom I respect back in Maryland told me (and gave me to understand that it was a divine revelation to him, and I trust him to know the difference) that I should not neglect my gift of teaching when I went to Santa Barbara. At first I tried to start a Bible study with my church, but it already had lots of other groups, and it kept not working out for various reasons; then I thought of the idea of blogging instead.

Once I reach a critical mass on the blog, perhaps some of them could be organized into book format. But I don’t need to decide that yet. For the time being, the informal blogging environment seems more fruitful for developing ideas.

Reasonable Unfalsifiable Beliefs

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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:

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.
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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.
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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.
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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 (*).
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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.
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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.
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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.
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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.
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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.

Must Science be Falsifiable?

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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.