Self-locating evidence and bearers of epistemic good

In the case of non-epistemic goods, it’s an obvious feature of life that someone there is a choice to be made by an individual between their own first-order good and the first-order good of the community—each requires the sacrifice of the other. In the case of epistemic goods, this is less obvious.

In the pragmatic case, the typical reason for such competition between goods is due to limited resources. This, of course, also happens in the epistemic sphere. Suppose Alice is much more intellectually talented than Bob, but only Bob has the money to go to university. If Bob spends the money on himself, he will gain private epistemic goods, but will contribute little epistemically to society as a whole. But if he gives the money to Alice, she may become a brilliant scholar or scientist, significantly contributing to society’s knowledge.

More interesting than these, however, are cases of competition between private and communal epistemic goods that are not due to epistemic resources. I find it interesting that some cases of self-locating evidence appear to be such.

Suppose there are ten billion people in the world, currently isolated from one another. A device produced by a mad scientist has a 99.9% chance at noon today of triggering a death ray that randomly kills 99.9999% of the world population. Noon has just passed. You are still alive. Should you think the device worked? Sleeping Beauty style arguments say “No”. This time I want to think about this in terms of individual epistemic goods. In N runs of the device, 0.001N runs will have you survive because the device doesn’t trigger and 0.999 ⋅ 0.000001N runs will have you survive despite the device triggering. Thus, the vast majority of the runs where you survive are runs where the device didn’t trigger. Hence, it’s best for you individually to adopt the epistemic policy of thinking the device didn’t trigger.

But on the other hand, suppose we all adopt the epistemic policy of thinking the device didn’t trigger. Then 99.9% of the time, we are unanimously collectively wrong. And if we all adopt the epistemic policy of thinking the device did trigger, then 99.9% of the time, we are unanimously collectively right. It seems thus that if we look at the epistemic goods of society, then a policy of thinking the device did trigger is best.

If this is right, it points to a potential diagnosis of why the problems about self-locating evidence (doomsday, multiverses, Sleeping Beauty, etc.) are so difficult. For there may be different bearers of epistemic goods at play—say, society vs. the individual—and it could be that different answers are appropriate depending on whose goods we are pursuing. Maybe.

Is there some sort of a probability problem with a humongous but finite universe?

It’s easy to generate probabilistic paradoxes in a universe (or multiverse) with infinitely many people (e.g., if infinitely many people roll a die, equal numbers of people get 1 as get more than 1, so why think it’s more likely to get more than 1?). But what about a very large but finite universe? I used to think: “The only relevant difference is between finite and infinite. Really big but finite—no problem.” Now I am not so sure.

Paul Heyl measured the gravitational constant G as 6.670 × 10⁻¹¹ m³ kg⁻¹ s⁻², and denote the latter quantity by G₀. Consider two theories:

• H₁: The gravitational constant is between 6.665 × 10⁻¹¹ m³ kg⁻¹ s⁻² and 6.675 × 10⁻¹¹ m³ kg⁻¹ s⁻².

• H₂: The gravitational constant is between 7.676 × 10⁻¹¹ m³ kg⁻¹ s⁻² and 7.686 × 10⁻¹¹ m³ kg⁻¹ s⁻².

It seems obvious that:

1. Heyl’s measurement strongly supports H₁ but does not completely rule out H₂.

But let’s think this through. Suppose Heyl’s evidence is the proposition E which he would express as “I measured G to be G₀.” But, very plausibly, it is an essential property of a human being that they exist in a world with such-and-such a gravitational constant. One way of getting to this conclusion is to say that the forces of gravity are part of our causal history, and then to apply the essentiality of origins. Another is to say that we couldn’t have been made of completely different matter, but the forces exerted by the matter in our bodies are an essential property of that matter.

Given this essentiality of gravitational constant assumption, it follows that at least one of H₁ and H₂ is incompatible with Heyl’s existence. Now, to get (1), we need prior probabilities on which P(H₁|E) > P(H₂|E) > 0. Such prior probabilities will assign a non-zero value to H₁E and to H₂E. But at least one of these two claims is impossible since E entails Heyl’s existence, and a probability assignment that assigns a non-zero value to something impossible is screwed up, and we should be quite suspicious of what we get from it.

We might try to avoid this by using self-locating evidence. But my colleague Yoaav Isaacs has this great paper that gives a pretty strong argument that there isn’t a good way to working with self-locating evidence. So suppose we put this option aside.

Or we might make a distinction between logical impossibility and metaphysical impossibility. I find that suspicious, too.

So, what’s left? Well, here’s one remaining suggestion. Heyl’s evidence is equivalent to the proposition that Heyl measured G to be G₀, a proposition that rigidly refers to Heyl, and hence won’t be compatible with both H₁ and H₂. But we can weaken Heyl’s evidence to something that is compatible with H₁ and H₂, something purely qualitative, like:

• E_Q: A physicist named “Paul Heyl”, who married someone named “Lucy Daugherty”, and who …, measured G to be G₀.

Here, “…” is all the other purely qualitative stuff we know about Paul Heyl, so that E_Q is compatible with both H₁ and H₂.

But now here is a problem. Suppose we live in a vast but finite universe with, say, 10¹⁰¹⁰ people. In such a universe, we might well expect large numbers of people named “Paul Heyl” who satisfy all the conditions in E_Q, including the measurement of G to be G₀, even if in fact G is in the range indicated in H₁ (measurement error!). Thus, P(E_Q|H₂) is close to 1 as is P(E_Q|H₁). Granted, we do have P(E_Q|H₁) > P(E_Q|H₂) > 0. But because the two probabilities are so close to each other, the support E_Q gives to H₁ over H₂ is very slight, and hence we no longer have (1).

It follows that unless we can find some other way of solving the problem that the essentiality of the laws of nature to humans poses for Bayesian reasoning, a fair amount of fundamental physics research would be undercut by a large enough—even if finite—universe.

Of course, maybe we can find some other way of solving it. But maybe we can’t. And if we can’t, then the E_Q solution might be our best bet—and it’ll work just fine in a universe that isn’t too vast.

Finetuning the multiverse

It has occurred to me that there is a kind of fine-tuning of multiverse theories.

If there is too large a variety of universes within a multiverse, we get skeptical problems. For instance, if all possible laws of nature are realized, then induction-friendly laws like “Gravity is always attractive” are either outnumbered by or at least do not outnumber nasty laws like “Gravity is attractive until the end of March 2026 and repulsive afterwards”. Or if there are too many kinds of material arrangements, we would expect scenarios with local order, like Boltzmann brains to outnumber or at least not be outnumbered by scenarios like brains arising by evolution.

On the other hand, if there are too few universes, then the laws by which universes are generated need to be themselves fine-tuned or else there won’t be life.

So, a multiverse theory needs to be tuned as to the variety of universes it supposes. I don’t have a a great argument that this tuning is highly improbable, but it might be. My intuition says, for what it’s worth, that the on naturalism we should either expect a single universe or a very wide and varied multiverse, and the latter is likely to engender skepticism.

Combining epistemic utilities

Suppose that the right way to combine epistemic utilities or scores across individuals is averaging, and I am an epistemic act expected-utility utilitarian—I act for the sake of expected overall epistemic utility. Now suppose I am considering two different hypotheses:

• Many: There are many epistemic agents (e.g., because I live in a multiverse).

• Few: There are few epistemic agents (e.g., because I live in a relatively small universe).

If Many is true, given averaging my credence makes very little difference to overall epistemic utility. On Few, my credence makes much more of a difference to overall epistemic utility. So I should have a high credence for Few. For while a high credence for Few will have an unfortunate impact on overall epistemic utility if Many is true, because the impact of my credence on overall epistemic utility will be small on Many, I can largely ignore the Many hypothesis.

In other words, given epistemic act utilitarianism and averaging as a way of combining epistemic utilities, we get a strong epistemic preference for hypotheses with fewer agents. (One can make this precise with strictly proper scoring rules.) This is weird, and does not match any of the standard methods (self-sampling, self-indication, etc.) for accounting for self-locating evidence.

(I should note that I once thought I had a serious objection to the above argument, but I can't remember what it was.)

Here’s another argument against averaging epistemic utilities. It is a live hypothesis that there are infinitely many people. But on averaging, my epistemic utility makes no difference to overall epistemic utility. So I might as well believe anything on that hypothesis.

One might toy with another option. Instead of averaging epistemic utilities, we could average credences across agents, and then calculate the overall epistemic utility by applying a proper scoring rule to the average credence. This has a different problematic result. Given that there are at least billions of agents, for any of the standard scoring rules, as long as the average credence of agents other than you is neither very near zero nor very near one, your own credence’s contribution to overall score will be approximately linear. But it’s not hard to see that then to maximize expected overall epistemic utility, you will typically make your credence extreme, which isn’t right.

If not averaging, then what? Summing is the main alternative.

Presentism, multiverses and discrete time

Suppose time is in fact continuous and modeled by the real numbers.

It seems odd indeed to me that the real numbers should be the only possible way for time to run. The real numbers are a very specific mathematical system. There are other systems, such as the hyperreals or the rationals or even the integers, that seem to be plausible alternatives. I know of no argument that the time sequence has to be numbered by the real numbers.

Thus, given our initial supposition, it should be possible to have time sequences corresponding to ordered sequences numbered by the integers or the hyperreals. Here, then, is a further intuition. It is possible to have a multiverse with radically different spacetime structures in each universe of it. If so, then we would expect the possibility of a multiverse where different universes in a multiverse have time sequences based on very different ordered sets.

Suppose presentism is necessarily true. Then even in such a multiverse, there would be an absolute present running across all of these timelines in the different universes. And that would be rather odd. Imagine that in one universe the time-line is corresponds to the integers and in the other it corresponds to the reals, and both are found in one multiverse. What happens in the universe whose time-line is based on the integers when the line of the present moves continuously across the uncountable infinity of times numbered by the real numbers? Does it stay for infinitely moments at the same integer? But then at infinitely many moments of time it would be at one moment, which is a contradiction. Or does the universe with the integer time-line pop out of existence when the present doesn’t meet up with these integers? Maybe that’s the best view, but it’s a weird view.

Perhaps the presentist’s best bet is to say that there is a privileged mathematical structure that models what a time-line could be like. If so, my intuition says that the only candidate for that privileged structure would be a discrete structure like the integers. For there are arguments in the history of philosophy for time having to be discrete (arguments from Zeno through myself), but none for time having to be modeled by specifically the real numbers, or the rational numbers, or some specific hyperreal field.

Inferentialism and the fictitious isolated hydrogen atom

This is another attempt at an argument against inferentialism about logical constants.

Given a world w, let w^* be a world just like w except that it has added to it an extra spatiotemporally disconnected island universe containing exactly one hydrogen atom with a precisely specified wavefunction ψ₀. Suppose that in in the actual world there is no such isolated hydrogen atom. Now, given a nice first-order language L describing our world, let L^* be a language whose constants are the same as the constants of L with an asterisk added to every logical constant, name and predicate. Given a sentence ϕ of L, let ϕ^* be the corresponding sentence of L^*—i.e., the sentence with all of L’s logical constants asterisked.

Let the rules of inference of L^* be the same as those of L with asterisks added as needed.

Let the semantics of L^* be as follows:

• Every predicate P^* in L^* means the same thing as P in L.

• Every name a^* in L^* means the same thing as a in L.

• Any sentence ϕ^* in L^* without quantifiers means the same thing as ϕ in L.

• But if ϕ^* has a quantifier, then ϕ^* means that ϕ would be true if there were an extra spatiotemporally disconnected island universe containing exactly one hydrogen atom with wavefunction ψ₀.

Thus, ϕ^* is true in world w if and only if ϕ is true in w^*.

Observe that because L contains only names for things that exist in the actual world, and hence not for the extra hydrogen atom or its components, an atomic sentence P(a₁,...,a_n) in L is true if and only if the corresponding sentence P^*(a₁^*,...,a_n^*) is true in L^*.

Logical inferentialism tells us that the logical constants of L^* mean the same thing as those of L, modulo asterisks. After all, modulo asterisks, we have the same inferences, the same meanings of names, and the same meanings of predicates. But this is false: for if ∃^* in L^* were an existential quantifier, then it would be true that there exists an isolated hydrogen atom with wavefunction ψ₀. But there is none such.

Metaphysical universism

Here’s a metaphysical view I haven’t seen: the fundamental obejcts (priority version) or the only objects (existence version) are universes, but there can be more than one of these. Call this metaphysical universism (as distinguished from Quisling’s philosophy).

If in fact there is only one universe, metaphysical universism extensionally coincides with monism. But even in that case, metaphysical universism is a different theory, because it has different modal implications. And if we live in a multiverse, metaphysical universism is extensionally different from monism, since monism says that the one fundamental (priority) or one and only (existence) entity is the multiverse as a whole, not the universes.

I can think of two main advantages of metaphysical universism over monism.

First, suppose there is only one universe. It is plausible that there could be another in addition to this one. Metaphysical universism embraces this possibility. Monism only says that The One could have been bigger so as to comprise two spatiotemporally disconnected regions.

Second, there is an old intuition that being and unity are connected. In a multiverse, monism violates this intuition, for in a multiverse it is the universes that have unity, not the multiverse. Indeed quantum entanglement arguments for monism in the context of a non-Everettian multiverse seem to me to point more towards metaphysical universism than monism.

On the other hand, monism has a significant advantage over metaphysical universism insofar as monism solves the problem of truthmakers of negative and universal claims by making The One be the truthmaker of all of them.

Of course, both theories are false.

A sloppy fine-tuning argument

This argument is an intuition-pump. I don’t know if it can be made rigorous.

Start with some observations. Let Q₀ be the nomic parameters of our universe—the exact values of all the constants in the laws of nature. To avoid serious problems with higher infinities and probability, I will make a technical assumption, which I will assume to be neutral be theism and atheism:

0. There are at most countably many universes.

Now:

1. For no non-zero countable cardinality n does theism have a bias against the hypothesis that there are countable many universes with cardinality at least n.

2. The parameters Q₀ are life-permitting.

3. For any fixed countable cardinality n of universes, theism has a significant bias in favor of distributions of parameters that include more universes with life-permitting parameters.

4. If (2) and (3), then for any countable cardinality n of universes, theism has a significant bias in favor of at least one of them having the parameters given by Q₀.

5. Thus, theism has a bias in favor of a universe with Q₀.

6. Thus, the obtaining of Q₀ is evidence for theism.

Some thoughts on the premises.

Regarding 1: Theism actually seems to have a bias in favor of the hypothesis that there are at least n universes. After all, theism has a bias in favor of the hypothesis that there is at least one universe: that there is a universe is quite surprising on atheism, but not so on theism, given that God is by definition perfectly good, and the good tends to spread. But the same reasoning suggests a bias on theism in favor of larger numbers of universes.

Regarding 2: Obvious.

Regarding 3: I think the main way to challenge (3) is to say that God would only care about having one universe with life-permitting parameters, and wouldn’t care about having a larger number. But I think this is implausible given that the good tends to spread. In fact, it seems likely that God would create only universes with life-permitting parameters, which would induce a strong bias in favor of such parameters.

Regarding 4: This is a very substantial assumption. It won’t hold for every set of exact parameters, because some sets of parameters might be life-permitting but would be likely to generate a universe that is really unfortunate in some regard. I don’t think the parameters Q₀ behind our universe are like that, but this is a matter of dispute, and intersects with the problem of evil. Note also that it is important for the “significant” in (4) that even if n is (countably) infinite, the probability getting exactly Q₀ on atheism is low (in fact, infinitesimal).

The big technical difficulty, which makes me doubtful that the argument can be made rigorous, are the infinities involved.

The multiverse objection to the fine-tuning argument for theism

Consider a fine-tuning argument like this:

1. On theism, it is moderately likely that there would be a fine-tuned universe.

2. On naturalism, it is extremely unlikely that there would be a fine-tuned universe.

3. So, the existence of a fine-tuned universe is very significant evidence for theism over naturalism.

These days, the main response to this is to invoke a rich multiverse, and to note:

4. On multiverse naturalism, it is nearly certain that there would be a fine-tuned universe.

It follows from (1) and (4) that the existence of a fine-tuned evidence is moderate evidence for multiverse naturalism over theism.

If (4) undercuts anything in the argument (1)–(3), it is (2). How could (4) undercut (2)? It would have to be roughly as follows:

5. On naturalism, prior to the evidence of a fine-tuned universe, it is not very unlikely that there is a multiverse.

When we combine (4) with (5), we do indeed get that it’s not extremely unlikely that there would be a fine-tuned universe.

But (5) is dubious. For prior to the evidence of a fine-tuned universe, the rational credence in a naturalistic multiverse should be extremely small. This is because one of the prior ratioanl constraints on credences is that they should make skeptical hypotheses extremely unlikely. And a naturalistic multiverse is a kind of skeptical hypothesis, for multiple reasons. First, it denies the uniformity of nature (at least if it’s the kind of multiverse relevant to fine-tuning, where the laws of nature vary between universes). Second, it implies intuitively absurd claims, such as that probably there are fairies and Greek gods out of sight of our observation (namely in other universes). Third, on many versions it threatens most of our common-sense knowledge by making Boltzmann brains at least as likely as ordinary brains. Fourth, at least the infinite versions of the multiverse hypotheses endanger probabilistic reasoning, since crazy things happen infinitely many times and non-crazy things happen infinitely many times in a multiverse, and it’s hard to say that the crazy things are less likely.

I suppose it is possible that (a) the rational credence in a naturalistic multiverse is extremely small, but (5) is still true. But the only way that could be is if the prior probability of naturalism is quite low. And while I am happy to say that, I think few naturalists will be. Thus a typical naturalist should, I think, deny (5), and should hold that prior to the evidence of a fine-tuned universe, even on naturalism, a multiverse would be very and maybe even extremely unlikely. The evidence of fine-tuning will greatly raise the probability of a naturalistic multiverse, but given that it started extremely small relative to theism, it is going to stay small.

Open futurism and many-worlds quantum mechanics

I’ve been thinking about some odd parallels between the many-worlds interpretation of quantum mechanics and open future views.

On both sets of views, in the case of genuinely chancy future events there is strictly no fact of the matter about what will turn out. On many-worlds, the wavefunction provides a big superposition of the options, but for no one option is it true that it will eventuate. The same is true for open future views, except that what we have instead of a superposition depends on the particular temporal logic chosen.

Yet, despite no fact about outcomes, on both sets of views one would like to be able to make probabilistic predictions about “the outcome”. For instance, one wants to say that if one tosses an indeterministic coin, it is moderately likely that the coin will land on heads and extremely unlikely that it will land on heads. In both cases, this is highly problematic, because on both views it is certain that it is not true that the coin will land on heads. So how can something that is certainly not going to happen be more likely than another event? In both cases, there is a literature trying to answer this problem (and I am not convinced by it).

Anyway, I wonder how far we can take the parallel. The wavefunction in the many-worlds interpretation is a superposition of many options about what the present is like, and is interpreted as a plurality of worlds in which different options are true. Why not do the same in the open-future case? Why not just say that there are now many worlds, including some where the coin will land on heads, some where the coin will land on tails, and some where it will land on edge? After all, if it is reasonable to interpret the superposition this way, why is it not reasonable to interpret the temporal logic this way?

There is, however, one crucial difference. The open futurist insists that reality will collapse: that once the coin lands, there will be a fact about which way it landed. On many-worlds, there is no collapse: there is never a fact about how the coin landed. Nonetheless, this could be accommodated in a many-worlds interpretation of an open-future view: we just suppose that once the coin lands, a lot of the worlds disappear.

So what if there is a parallel? Why does it matter?

Well, here are some things that we might say.

First, in both cases, there is an underlying metaphysics (a non-classical truth assignment to future facts, or a giant superposition), and then we need to interpret that underlying metaphysics. I wonder if it might not be true:

1. A many-worlds interpretation of the underlying metaphysics is reasonable in the quantum case if and only if it is reasonable in the open-future case.

Suppose (1) is true. Most people think a many-worlds interpretation of open-future is absurd. But then why isn’t the many-worlds interpretation of quantum mechanics (or, more precisely, a quantum mechanics with exceptionlessly unitary evolution and all the facts supervening on the wavefunction) also absurd?

Second, it may well be that the open-futurist finds plausible the standard criticism of many-worlds interpretations that it does not make sense of probabilistic predictions. If so, then they should probably find equally problematic probabilistic predictions on open-future views.

Does my existence by itself confirm a multiverse?

Suppose I am considering two hypotheses, H₁ and H₂, and according to H₂ there are more people. Does the fact that I exist give me reason to prefer H₂, all other things being equal? If so, then my existence is apt to confirm the existence of a multiverse over a single universe.

Here is one reason to think this works. The probability that I exist in a given world, all other things being equal, seems proportional to the number of people in that world. Each person in that world corresponds to another opportunity for me to exist.

While this is tempting, here is a toy model that should give us pause. Suppose that I am defined by a real number parameter between 0 (inclusive) and 1 (not inclusive). According to hypothesis H₁, a single real number is picked uniformly at random in the range, and the person with that parameter is created. According to hypothesis H₂, two real numbers are picked uniformly and independently in the range, and persons corresponding to these are created. Learning that a person with my parameter is created seems to provide me with evidence for H₂, since it’s twice as likely on H₂ as on H₁.

But this is tricky. In classical probability theory, it is correct to say that my parameter is twice as likely to be generated on H₂ as on H₁, but that’s only because both probabilities are zero, and zero is twice zero, so while H₂ is twice as likely as H₁, it is also true that H₁ is twice as likely as H₂!

Perhaps, though, we want to depart from classical probability theory in some way, say by allowing non-zero infinitesimal probabilities or by an intuitive handwavy “this is twice as likely as that”. However, it is then no longer clear that on H₂ there is twice as big a chance of hitting my parameter. For there are (infinitely) many ways of picking a number between 0 and 1 uniformly randomly.

Here’s one way:

1. You write down “0.”, then roll a fair ten-sided die infinitely many times, writing down the results as the digits after the decimal point, thereby generating a decimal representation of a number. If the number ends with infinitely many nines, try again.

(The final proviso is to ensure that intuitively each number is equally likely. Without that proviso, 1/10 would be more likely than 1/3, as there would be two ways of getting 1/10, namely 0.1000... and 0.0999..., but only one way to get 1/3, namely 0.3333.....)

Here is another way:

2. You write down “0.”, then roll a fair ten-sided die infinitely many times, omitting the results of the first die throw, but writing down the results as the digits after the decimal point, thereby generating a decimal representation of a number. If the number ends with infinitely many nines, try again.

Intuitively, method B has ten times the probability of generating any given number than method A has, as long as literally the numerically same die throws occur in the two cases. For consider the number 1/3 = 0.3333.... By method A to generate it you need every die to show a three. By method B, to generate 1/3, all you need is for all the die throws other than the first one to be threes, and so there are ten times as many ways to generate the number.

Now, if the single selection of a parameter on H₁ uses method B while the double selection of a parameter on H₂ uses method A, then intuitively we are five times as likely to generate my parameter on H₁ than on H₂. Thus merely saying that on both hypotheses the parameters are generated uniformly is insufficient to determine how the comparison between the probabilities of generating my parameter goes.

We might insist that in both hypotheses the same method for generating parameters is used. But notice that in cosmological applications, this is implausible. If H₂ is some multiverse hypothesis and H₁ is a single universe hypothesis, we are unlikely to be able to count on the two hypotheses involving even the same laws of nature, much less the same selection process for the parameters of the persons. (Besides all this, it is really unclear what it even counts to say that there are two different runs of method A.)

So, here’s what I am thinking. On classical probability theory, there is no difference in the probability of my parameter getting generated on H₂ than on H₁, because both probabilities are zero. On non-classical probability theory, we can perhaps make sense of a difference between the probabilities, but cannot count on the hypothesis with more people being more likely to generate my parameter.

Given all this, there does not seem to be a way of making sense of comparing the evidential impact of my existence on the two hypotheses using probabilistic methods. Maybe all we have is intuition.

Multiverses as a skeptical hypothesis

1. A multiverse hypothesis that counters the fine-tuning argument posits laws of nature that vary across physical reality.

2. A hypothesis that posits laws of nature that vary across physical reality contradicts the uniformity of nature.

3. A hypothesis that contradicts the uniformity of nature is a global skeptical hypothesis.

4. Global skeptical hypotheses should be denied.

5. So, a multiverse hypothesis that counters the fine-tuning argument should be denied.

The thought behind (1) is that the constants in the laws of nature are part and parcel of the laws. This can be denied. But still, the above argument seems to have some plausibility.

Predictions and Everett

Imagine this unfortunate sequence of events will certainly befall you in a classical universe:

1. You will be made to fall asleep.

2. Upon waking up, you will be shown a red square.

3. You will be made to fall asleep again.

4. While asleep, your memory will be reset to that which you had in step (1).

5. Upon waking up, you will be shown a green triangle.

6. You will be made to fall asleep for a third time.

7. While asleep, your memory will be reset again to that which you had in step (1).

8. Upon waking up, you will be shown a green circle.

9. You will then be permanently annihilated.

Questions:

10. How likely is it that you will be shown a green shape?

11. How likely is it that you will be shown a red shape?

The answers to these questions are obviously: one and one. You will be shown a green shape twice and a red shape one, and that’s certain.

Now consider a variant story where personal identity is not maintained in sleep. Perhaps each time in sleep the person who fell asleep will be annihilated and replaced by something that is in fact an exact duplicate, but that isn’t identical with the original according to the correct metaphysics of diachronic personal identity. (We can make this work on pretty much any metaphysics of diachronic personal identity. For example, we can make it work on a materialist memory theory as follows. We just suppose that before step (1), you happen to have three exact duplicates alive, who are not you. Then during the nth sleep cycle, the sleeper is annihilated, and a fresh brain is prepared and memories will be copied into it from your nth doppelganger. Since these memories don’t come from you, the resulting brain isn’t yours.)

And in the variant story, let’s ask the questions (10) and (11) again. What will the answers be? Again, it’s easy and obvious: zero and zero. You won’t be shown any shapes, because you will be annihilated in your sleep before any shapes are shown.

Now consider Everettian branching quantum mechanics. Suppose there is a quantum process that will result in your going to sleep in an equal superposition of states between having a red square, a green triangle and a green circle in front of your head, so that upon waking up an observation of the shape will be made. Now ask questions (10) and (11) again.

I contend that this is just as easy as in my classical universe story. Either the branching preserves personal identity or not. If it preserves personal identity, the answer to the questions is one and one. If it fails to preserve personal identity, the answer to the questions is zero and zero. The only relevant ontological difference between the quantum and classical stories is that in the quantum stories the wakeups might count as simultaneous while in the classical story the wakeups are sequential. And that really makes no difference.

In none of the four cases—the classical story with or without personal identity and the branching story with or without personal identity—are the answers to the questions 2/3 and 1/3. But those are in fact the right answers in the quantum case, contrary to the Everett model.

Now, one might object that we care more about decisions than predictions. Suppose that you have a choice between playing a game with one of two three-sided fair quantum dice:

• Die A is marked: red square, green triangle, green circle.

• Die B is marked: green square, red triangle, red circle.

And suppose pain will be induced if and only if the die comes up red. Which die should you prudentially choose for playing the game? Again, it depends on whether personal identity is preserved. If not, it makes no difference. If yes, clearly you should go for die A on the Everett model—and that is indeed the intuitively correct answer. But the reason for going for die A on the Everett model is different from the reason for going for it on a non-branching quantum mechanics. On the Everett model, the reason for going for die A is that it’s better to get pain once (die A) rather than twice (die B).

So far so good. But now suppose that you’ve additionally been told that if you go for die A, then before you roll A, an irrelevant twenty-sided die will be rolled. (This is a variant of an example Peter van Inwagen sent me years ago, which was due to a student of his.) Then, intuitively, if you go for die A, there will be twenty red branches and forty green branches on Everett. So on die A, you get pain twenty times if personal identity is preserved, and on die B you get pain only twice. And so you should surely go for die B, which is absurd.

One might reasonably object that there are in fact infinitely many branches no matter what. But then on the no-identity version, the choice is still irrelevant to you prudentially, while on the identity version, no matter what you do, you get pain infinitely many times no matter what you choose. And that doesn’t work, either. And if there is no fact about how many branches there will be, then the answer is just that there is no fact about which option is preferable on the identity version, and on the no-identity version, indifference still follows.

This is all basically well-known stuff. But I like the above way of making it vivid by thinking about classically sequentializing the story.

Boltzmann brain blackouts

Some cosmological theories lead to the worrisome conclusion that most people with present brain states like ours are Boltzmann brains—random aggregations of molecules in space that came together to form a brain in a little bubble of oxygen. Usually when people talk about Boltzmann brains, they talk of how this induces a sceptical problem for the theory that generates them. Thinking about Boltzmann brain issues that way leads to messy epistemological questions such as whether we get to simply assume that we have hands, and the like. Moreover, if there is evidence for the cosmological theory, then that becomes evidence for Boltzmann brains, which then undermines the evidence for the cosmological theory, and that’s all a mess.

Here is how I suggest we think about what happens when a cosmological theory T leads to a Boltzmann brain issue. The vast majority of Boltzmann brains—even ones with brain states like ours—are short-lived. Their bubble of oxygen dissipates in the absence of gravity, and after a brief moment of hypoxia they die. So think of the point this way. If a cosmological theory predicts a large ratio of Boltzmann brains to ordinary evolved brains, then the theory makes an empirical prediction: in a moment you are extremely likely to start blacking out. So just do the experiment: wait a moment and see if you’re blacking out. If you’re not, then you’ve got very strong disconfirmation of the cosmological theory, and you’re done with it. You don’t have to worry about self-defeat, Moorean questions about whether you have two hands, or anything deep like that. (And if you are blacking out, then if it’s a Boltzmann brain related blockout, you’ll be dead in a moment. If you do come back to, and not in the afterlife, that’s massive evidence against the theory again, but now you should see a doctor about your blackout problem.)

In fact, you don’t even have to wait: on cosmological theories that generate too many Boltzmann brains, you should expect to already be starting to black out—because most of the Boltzmann brains will be extremely short-lived.

Objection: There will be long-lived Boltzmann brains, too.

Response: Sure. But for entropic reasons they will be much less common than the short-lived ones. You might, of course, worry that in many of these cosmological scenarios there are infinitely many Boltzmann brains, and infinitely many are short-lived and infinitely many are long-lived, and you can’t say that the short-lived ones are more common. The short-lived ones will be more common in a “typical” large finite region, but overall we just have infinity. Now, if you are worried about this—and I think you should be—then that worry already applied at the beginning of the story when you looked at the ratio of ordinary to Boltzmann brains, because there will be infinitely many of each on such a cosmological theory, and the formulation of the problem that I gave at the beginning, namely that Boltzmann brains greatly outnumber ordinary brains, is inaccurate. (I think if you do have this worry, then the theory has another problem, namely that probabilistic reasoning makes no sense in a world described by the theory. That is a kind of sceptical and self-defeat problem, but of a different nature.)

My point in this post is modest: if you want to say that Boltzmann brains greatly outnumber ordinary brains, then instead of thinking deep stuff about self-defeat of theories and scepticism, you should just think of the theory that generates this prediction as falsified by future observation.

What I think is wrong with Everettian quantum mechanics

One can think of Everettian multiverse quantum mechanics as beginning by proposing two theses:

1. The global wavefunction evolves according to the Schroedinger equation.

2. Superpositions in the global wavefunction can be correctly interpreted as equally real branches in a multiverse.

But prima facie, these two theses don’t fit with observation. If one prepares a quantum system in a (3/5)|↑⟩+(4/5)|↓⟩ spin state, and then observes the spin, one will will observe spin up in |3/5|^2=9/25 cases and spin down in |4/5|^2=16/25 cases. But (roughly speaking) there will be two equally real branches corresponding to this result, and so prima facie one would expect equally likely observations, which doesn't fit observation. But the Everettian adds a third thesis:

3. One ought to make predictions as to which branch one will observe proportionately to the square of the modulus of the coefficients that the branch has in the global wavefunction.

Since Aristotelian science has been abandoned, there has been a fruitful division of labor between natural science and philosophy, where investigation of normative phenomena has been relegated to philosophy while science concerned itself with the non-normative. From that point of view, while (1) and (less clearly but arguably) (2) belong to the domain of science, (3) does not. Instead, (3) belongs to epistemology, which is study of the norms of thought.

This point is not a criticism. Just as a doctor who has spent much time dealing sensitively with complex cases will have unique insights into bioethics, a scientist who has spent much time dealing sensitively with evidence will have unique insights into scientific epistemology. But it is useful, because the division of intellectual labor is useful, to remember that (3) is not a scientific claim in the modern sense. And there is nothing wrong with that as such, since many non-scientific claims, such as that one shouldn’t lie and that one should update by conditionalization, are true and important to the practice of the scientific enterprise.

But (3) is a non-scientific claim that is absurd. Imagine that a biologist came up with a theory that predicted, on the basis of their genetics and environment, that:

4. There are equal numbers of male and female infant spider monkeys.

You might have thought that this theory is empirically disproved by observations of a lot more female than male infant spider monkeys. But our biologist is clever, and comes up with this epistemological theory:

5. One ought to make predictions as to the sex of an infant spider monkey one will observe in inverse proportion to the ninth power of the average weight of that sex of spider monkeys.

And now, because male spider monkeys are slightly larger than females, we will make predictions that roughly fit our observations.

Here’s what went wrong in our silly biological example. The biologist’s epistemological claim (5) was not fitted to the actual ontology of the biologist’s theory. Instead, basically, the biologist said: when making predictions of future observations, make them in the way that you should if you thought the sex ratios were inversely proportional to the ninth power of the average weights, even though they aren’t.

This is silly. But exactly the same thing is going on in the Everett case. We are being told to make predictions in the way you should if the modulus squares of the weights in the superposition were chances of collapse. But they are not.

It is notorious that any scientific theory can be saved from empirical disconfirmation by adding enough auxiliary scientific hypotheses. But one can also save any scientific theory from empirical disconfirmation by adding an auxiliary philosophical hypothesis as to how confirmation or disconfirmation ought to proceed. And doing that may be worse than obstinately adding auxiliary scientific hypotheses. For auxiliary scientific hypotheses can often be tested and disproved. But an auxiliary epistemological hypothesis may simply close the door to refutation.

To put it positively, we want a certain degree of independence between epistemological principles and the ontology of a theory so that the ontology of the theory can be judged by the principles.

Yet another formulation of my argument against a theistic multiverse

Here’s yet another way to formulate my omniscience argument against a theistic multiverse, a theory on which God creates infinitely concretely real worlds, and yet where we have a Lewisian analysis of modality in terms of truth at worlds.

1. Premise schema: For any first order sentence ϕ: Necessarily, ϕ if and only if God believes that ϕ.

2. Premise schema: For any sentence ϕ: Possibly ϕ if and only if ∃w(at w: ϕ).

3. Premise: Possibly there are unicorns.

4. Premise: Possible there are no unicorns.

5. Necessarily, there are unicorns if and only if God believes that there are unicorns. (Instance of 1)

6. Possibly, God believes that there are unicorns. (3 and 5)

7. Possibly God believes that there are unicorns if and only if ∃w(at w: God believes that there are unicorns). (Instance of 2)

8. ∃w(at w: God believes that there are unicorns). (6 and 7)

9. ∃w(at w: God believes that there are no unicorns). (from 1, 2, 4 in the same way 8 was derived from 1, 2, 3)

So, either there is a world at which it is the case that God both believes there are unicorns and believes that there are no unicorns, or what God believes varies between worlds. The former makes God contradict himself. The content of God’s beliefs varying across worlds is unproblematic if the worlds are abstract. But if they are concrete, then it implies a real disunity in the mind of God.

Premise schema (1) is restricted to first order sentences to avoid liar paradoxes.

Ethics and multiverse interpretations of quantum mechanics

Somehow it hasn’t occurred to me until yesterday that quantum multiverse theories (without the traveling minds tweak) undercut half of ethics, just as Lewis’s extreme modal realism does.

For whatever we do, total reality is the same, and hence no suffering is relieved, no joy is added, etc. The part of ethics where consequences matter is all destroyed. There is no point to preventing any evil, since doing so just shifts which branch of the multiverse one inhabits.

At most what is left of ethics is agent-centered stuff, like deontology. But that’s only about half of ethics.

Moreover, even the agent-centered stuff may be seriously damaged, depending on how one interprets personal identity in the quantum multiverse.

Consider three theories.

On the first, I go to all the outgoing branches, with a split consciousness. On this view, no matter what, there will be branches where I act well and branches where I act badly. So much or all of the agent-centered parts of ethics will be destroyed.

On the second, whenever branching happens, the persons in the branches are new persons. If so, then there are no agent-centered outcomes—if I am deliberating between insulting or comforting a suffering person, no matter what, I will do neither, but instead a descendant of me will insult and another descendant will comfort. Again, it’s hard to fit this with the agent-centered parts of ethics.

The third is the infinitely many minds theory on which there are infinitely many minds inhabiting my body, and whenever a branching happens, infinitely many move into each branch. In particular, I will move into one particular branch. On this theory, if somehow I can control which branch I go down (which is not clear), there is room for agent-centered outcomes. But this is not the most prominent of the multiverse theories.

Monotheism and anthropomorphism

Xenophanes famously lambasted Greek religion for its anthropomorphism:

if cattle or lions had hands, so as to paint with their hands and produce works of art as men do, they would paint their gods and give them bodies in form like their own-horses like horses, cattle like cattle.

Two and a half millenia later, accusations of anthropomorphism continue to be made against monotheistic religions, typically by naturalists.

I was thinking about this, and had an odd thought. According to monotheism, the root of all explanation is the activity of God. According to standard naturalism, the root of all explanation is the activity of the fundamental physical entities, either particles or fields. But humans are more like fundamental physical entities than like the God of the monotheistic religions. The difference between us and the fundamental physical entities is merely finite. The difference between us and God is infinite. Thus, in an important sense, it is standard naturalism that is more anthropomorphic in its fundamental explanatory agents than monotheism.

If we do not feel this—if we feel ourselves more God-like than electron-like—then we are infinitely elevating ourselves or infinitely demoting God or both.

That said, the three Western monotheistic religions do think that the physical universe is made for us. Thus, while the religions are not anthropomorphic, they do have an anthropocentric view of our physical universe. Interestingly, though, to some (albeit lesser) extent so does the most plausible current naturalist view, namely a multiverse theory together with the weak anthropic principle.

A potential explanation why we don't observe violations of the PSR

A standard puzzle for the opponent of the Principle of Sufficient Reason (PSR) is to explain why we don’t observe objects coming into existence ex nihilo. Here is a thought that I think hasn’t been explored enough. Maybe when an object comes into existence ex nihilo, it is unlikely that the object would end up being spatiotemporally related to things already in existence. In other words, perhaps the typical object coming into existence ex nihilo forms a new universe, not spatiotemporally related with any other universe.

If this is right, then the opponent of the PSR should take multiverse hypotheses very seriously.

That said, such random multiverse hypotheses lead to very compellingly sceptical scenarios.

An argument against a giant multiverse

Tariq Nazeem emailed me a really cool and simple argument against certain kinds of gigantic multiverses. I’ve tweaked the argument a little, and here it is.

Start with this, as the target of the reductio ad absurdum:

1. Every metaphysically possible kind of substance exists.

But:

2. It is metaphysically possible to have a substance that has the causal propensity to turn every colorable object red every second.

(Colorable objects are things are like trees and dogs, but not numbers, photons or electromagnetic fields.)

Well, it follows from (1) and (2) that:

3. So, there is a substance that has the causal propensity to turn every colorable object red every second.

4. So, every colorable object turns red every second.

5. But I am a colorable object that does not turn red every second. (Empirical observation)

6. Contradiction!

My initial objection to Nazeem’s argument was that in a typical philosophical giant multiverse theory, the multiverses exist in separate spacetimes. (I think Nazeem’s own target was a view where they were in a single spacetime, but that is a less common view.) But then I realized that there is nothing absurd about a substance affecting things that are not spatiotemporally connected to it—classical theists think God is like that. Substances have causal propensities that specify the types of things they affect and the circumstances in which they affect them, and there is nothing absurd about a specification of these things and circumstances that makes no reference to a spatiotemporal connection. Therefore, (2) is pretty plausible, notwithstanding the fact that the colorable objects might exist in other spacetimes than the substance making them red does.

A different objection to this argument is what to say about conflict. What if reality included a substance that constantly made everything colorable red and another substance that constantly made everything colorable blue? Would I then be red all over and blue all over at the same time? But that’s impossible.

I am not completely clear on what to say to this objection.

One thought is: So much the worse for our giant multiverse—there are metaphysically possible pairs of kinds of substances, like the constant-reddenner and the constant-bluer, that simply cannot both be exemplified.

But on the other hand, maybe the possibility of conflict suggests that when we fully specify the causal propensities of a substance, we need to specify how they would interact with other causal propensities. Thus, we might have a constant-reddener that in the absence of other color-setters turns everything red, but in the presence of a constant-bluer, turns everything purple. However, it seems metaphysically possible to also have an overriding-reddener which makes everything red notwithstanding whatever other things exist. Then there could also be an overriding-bluer which makes everything blue notwithstanding whatever other things exist. And again this refutes (1).