Priors in the supernatural

A friend of mine recently told me the following anecdote.

Years back, she had visited an astrologer in India with her boyfriend, who told her the following things: (1) she would end up marrying her boyfriend at the time, (2) down the line they would have two kids, the first a girl and the second a boy, and (3) he predicted the exact dates of birth of both children.

Many years down the line, all of these predictions turned out to be true.

I trust this friend a great deal, and don’t have any reason to think that she misremembered the details or lied to me about them. But at the same time, I recognize that astrology is completely crazy.

Since that conversation, I’ve been thinking about the ways in which we can evaluate our de facto priors in supernatural events by consulting either real-world anecdotes or thought experiments. For instance, if we think that each of these two predictions gave us a likelihood ratio of 100:1 in favor of astrology being true, and if I ended up thinking that astrology was about as likely to be true as false, then I must have started with roughly 1:10,000 odds against astrology being true.

That’s not crazily low for a belief that contradicts much of our understanding of physics. I would have thought that my prior odds would be something much lower, like 1:1010 or something. But really put yourself in that situation.

Imagine that you go to an astrologer, who is able to predict an essentially unpredictable sequence of events years down the line, with incredible accuracy. Suppose that the astrologer tells you who you will marry, how many kids you’ll have, and the dates of birth of each. Would you really be totally unshaken by this experience? Would you really believe that it was more likely to have happened by coincidence?

Yes, yes, I know the official Bayesian response; I read it in Jaynes long ago. For beliefs like astrology that contradict our basic understanding of science and causality, we should always have reserved some amount of credence for alternate explanations, even if we can’t think of any on the spot. This reserve of credence will insure us against jumping in credence to 99% upon seeing a psychic continuously predict the number in your heads, ensuring sanity and a nice simple secular worldview.

But that response is not sufficient to rule out all strong evidence for the supernatural.

Here’s one such category of strong evidence: evidence for which all alternative explanations are ruled out by the laws of physics as strongly as the supernatural hypothesis is ruled out by the laws of physics.

I think that my anecdote is one such case. If it was true, then there is no good natural alternative explanation for it. The reason? Because the information about the dates of birth of my friend’s children did not exist in the world at the time of the prediction, in any way that could be naturally attainable by any human being.

By contrast, imagine you go to a psychic who tells you to put up some fingers behind your back and then predicts over and over again how many fingers you have up. There’s hundreds of alternative explanations for this besides “Psychics are real science has failed us.” The reason that there are these alternative explanations is that the information predicted by the psychic existed in the world at the time of the prediction.

But in the case of my friend’s anecdote, the information predicted by the astrologer was lost far in the chaotic dynamics of the future.

What this rules out is the possibility that the astrologer somehow obtained the information surreptitiously by any natural means. It doesn’t rule out a host of other explanations, such as that my friend’s perception at the time was mistaken, that her memory of the event is skewed, or that she is lying. I could even, as a last resort, consider that possibility that I hallucinated the entire conversation with her. (I’d like to give the formal title “unbelievable propositions” to the set of propositions that are so unlikely that we should sooner believe that we are hallucinating than accept evidence for them.)

But each of these sources of alternative explanations, with the possible exception of the last, can be made significantly less plausible.

Let me use a thought experiment to illustrate this.

Imagine that you are a nuclear physicist who, with a group of fellow colleagues, have decided to test the predictive powers of a fortune teller. You carefully design an experiment in which a source of true quantum randomness will produce a number between 1 and N. Before the number has been produced, when it still exists only as an unrealized possibility in the wave function, you ask the fortune teller to predict its value.

Suppose that they get it correct. For what value of N would you begin to take their fortune telling abilities seriously?

Here’s how I would react to the success, for different values of N.

N = 10: “Haha, that’s a funny coincidence.”

N = 100: “Hm, that’s pretty weird.”

N = 1000: “What…”

N = 10,000: “Wait, WHAT!?”

N = 100,000: “How on Earth?? This is crazy.”

N = 1,000,000: “Ok, I’m completely baffled.”

I think I’d start taking them seriously as early as N = 10,000. This indicates prior odds of roughly 1:10,000 against fortune-telling abilities (roughly the same as my prior odds against astrology, interestingly!). Once again, this seems disconcertingly low.

But let’s try to imagine some alternative explanations.

As far as I can tell, there are only three potential failure points: (1) our understanding of physics, (2) our engineering of the experiment, (3) our perception of the fortune teller’s prediction.

First of all, if our understanding of quantum mechanics is correct, there is no possible way that any agent could do better than random at predicting the number.

Secondly, we stipulated that the experiment was designed meticulously so as to ensure that the information was truly random, and unavailable to the fortune-teller. I don’t think that such an experiment would actually be that hard to design. But let’s go even further and imagine that we’ve designed the experiment so that the fortune teller is not in causal contact with the quantum number-generator until after she has made her prediction.

And thirdly, we can suppose that the prediction is viewed by multiple different people, all of whom affirm that it was correct. We can even go further and imagine that video was taken, and broadcast to millions of viewers, all of whom agreed. Not all of them could just be getting it wrong over and over again. The only possibility is that we’re hallucinating not just the experimental result, but indeed also the public reaction and consensus on the experimental result.

But the hypothesis of a hallucination now becomes inconsistent with our understanding of how the brain works! A hallucination wouldn’t have the effect of creating a perception of a completely coherent reality in which everybody behaves exactly as normal except that they saw the fortune teller make a correct prediction. We’d expect that if this were a hallucination, it would not be so self-consistent.

Pretty much all that’s left, as far as I can tell, is some sort of Cartesian evil demon that’s cleverly messing with our brains to create this bizarre false reality. If this is right, then we’re left weighing the credibility of the laws of physics against the credibility of radical skepticism. And in that battle, I think, the laws of physics lose out. (Consider that the invalidity of radical skepticism is a precondition for the development of laws of physics in the first place.)

The point of all of this is just to sketch an example where I think we’d have a good justification for ruling out all alternative explanations, at least with an equivalent degree of confidence that we have for affirming any of our scientific knowledge.

Let’s bring this all the way back to where we started, with astrology. The conclusion of this blog post is not that I’m now a believer in astrology. I think that there’s enough credence in the buckets of “my friend misremembered details”, “my friend misreported details”, and “I misunderstood details” so that the likelihood ratio I’m faced with is not actually 10,000 to 1. I’d guess it’s something more like 10 to 1.

But I am now that much less confident that astrology is wrong. And I can imagine circumstances under which my confidence would be drastically decreased. While I don’t expect such circumstances to occur, I do find it instructive (and fun!) to think about them. It’s a good test of your epistemology to wonder what it would take for your most deeply-held beliefs to be overturned.

Patterns of inductive inference

I’m currently reading through Judea Pearl’s wonderful book Probabilistic Inference in Intelligent Systems. It’s chock-full of valuable insights into the subtle patterns involved in inductive reasoning.

Here are some of the patterns of reasoning described in Chapter 1, ordered in terms of increasing unintuitiveness. Any good system of inductive inference should be able to accommodate all of the following.


If A implies B, then finding that B is true makes A more likely.

Example: If fire implies smoke, smoke suggests fire.

Asymmetry of inference:

There are two types of inference that function differently: predictive vs explanatory. Predictive inference reasons from causes to consequences, whereas explanatory inference reasons from consequences to causes.

Example: Seeing fire suggests that there is smoke (predictive). Seeing smoke suggests that there is a fire (diagnostic).

Induced Dependency:

If you know A, then learning B can suggest C where it wouldn’t have if you hadn’t known A.

Example: Ordinarily, burglaries and earthquakes are unrelated. But if you know that your alarm is going off, then whether or not there was an earthquake is relevant to whether or not there was a burglary.

Correlated Evidence:

Upon discovering that multiple sources of evidences have a common origin, the credibility of the hypothesis should be decreased.

Example: You learn on a radio report, TV report, and newspaper report that thousands died. You then learn that all three reports got their information from the same source. This decreases the credibility that thousands died.

Explaining away:

Finding a second explanation for an item of data makes the first explanation less credible. If A and B both suggest C, and C is true, then finding that B is true makes A less credible.

Example: Finding that my light bulb emits red light makes it less credible that the red-hued object in my hand is truly red.

Rule of the hypothetical middle:

If two diametrically opposed assumptions impart two different degrees of belief onto a proposition Q, then the unconditional degree of belief should be somewhere between the two.

Example: The plausibility of an animal being able to fly is somewhere between the plausibility of a bird flying and the plausibility of a non-bird flying.

Defeaters or Suppressors:

Even if as a general rule B is more likely given A, this does not necessarily mean that learning A makes B more credible. There may be other elements in your knowledge base K that explain A away. In fact, learning B might cause A to become less likely (Simpson’s paradox). In other words, updating beliefs must involve searching your entire knowledge base for defeaters of general rules that are not directly inferentially connected to the evidence you receive.

Example 1: Learning that the ground is wet does not permit us to increase the certainty of “It rained”, because the knowledge base might contain “The sprinkler is on.”
Example 2: You have kidney stones and are seeking treatment. You additionally know that Treatment A makes you more likely to recover from kidney stones than Treatment B. But if you also have the background information that your kidney stones are large, then your recovery under Treatment A becomes less credible than under Treatment B.


Even if A suggests B and B suggests C, this does not necessarily mean that A suggests C.

Example 1: Your card being an ace suggests it is an ace of clubs. If your card is an ace of clubs, then it is a club. But if it is an ace, this does not suggest that it is a club.
Example 2: If the sprinkler was on, then the ground is wet. If the ground is wet, then it rained. But it’s not the case that if the sprinkler was on, then it rained.


Just learning that a proposition has changed in credibility is not enough to analyze the effects of the change; the reason for the change in credibility is relevant.

Example: You get a phone call telling you that your alarm is going off. Worried about a burglar, you head towards your home. On the way, you hear a radio announcement of an earthquake near your home. This makes it more credible that your alarm really is going off, but less credible that there was a burglary. In other words, your alarm going off decreased the credibility of a burglary, because it happened as a result of the earthquake, whereas typically an alarm going off would make a burglary more credible.


All of these patterns should make a lot of sense to you when you give them a bit of thought. It turns out, though, that accommodating them in a system of inference is no easy matter.

Pearl distinguishes between extensional and intensional systems, and talks about the challenges for each approach. Extensional systems (including fuzzy logic and non-monotonic logic) focus on extending the truth values of propositions from {0,1} to a continuous range of uncertainty [0, 1], and then modifying the rules according to which propositions combine (for instance, the proposition “A & B” has the truth value min{A, B} in some extensional systems and A*B in others). The locality and simplicity of these combination rules turns out to be their primary failing; they lack the subtlety and nuance required to capture the complicated reasoning patterns above. Their syntactic simplicity makes them easy to work with, but curses them with semantic sloppiness.

On the other hand, intensional systems (like probability theory) involve assigning a function from entire world-states (rather than individual propositions) to degrees of plausibility. This allows for the nuance required to capture all of the above patterns, but results in a huge blow up in complexity. True perfect Bayesianism is ridiculously computationally infeasible, as the operation of belief updating blows up exponentially as the number of atomic propositions increases. Thus, intensional systems are semantically clear, but syntactically messy.

A good summary of this from Pearl (p 12):

We have seen that handling uncertainties is a rather tricky enterprise. It requires a fine balance between our desire to use the computational permissiveness of extensional systems and our ability to refrain from committing semantic sins. It is like crossing a minefield on a wild horse. You can choose a horse with good instincts, attach certainty weights to it and hope it will keep you out of trouble, but the danger is real, and highly skilled knowledge engineers are needed to prevent the fast ride from becoming a disaster. The other extreme is to work your way by foot with a semantically safe intensional system, such as probability theory, but then you can hardly move, since every step seems to require that you examine the entire field afresh.

The challenge for extensional systems is to accommodate the nuance of correct inductive reasoning.

The challenge for intensional systems is to maintain their semantic clarity while becoming computationally feasible.

Pearl solves the second challenge by supplementing Bayesian probability theory with causal networks that give information about the relevance of propositions to each other, drastically simplifying the tasks of inference and belief propagation.

One more insight from Chapter 1 of the book… Pearl describes four primitive qualitative relationships in everyday reasoning: likelihood, conditioning, relevance, and causation. I’ll give an example of each, and how they are symbolized in Pearl’s formulation.

1. Likelihood (“Tim is more likely to fly than to walk.”)

2. Conditioning (“If Tim is sick, he can’t fly.”)
P(A | B)

3. Relevance (“Whether Tim flies depends on whether he is sick.”)

4. Causation (“Being sick caused Tim’s inability to fly.”)
P(A | do B)

The challenge is to find a formalism that fits all four of these, while remaining computationally feasible.

If all truths are knowable, then all truths are known

The title of this post is what’s called Fitch’s paradox of knowability.

It’s a weird result that arises from a few very intuitive assumptions about the notion of knowability. I’ll prove it here.

First, let’s list five assumptions. The first of these will be the only strong one – the others should all seem very obviously correct.


  1. All truths are knowable.
  2. If P & Q is known, then both P and Q are known.
  3. Knowledge entails truth.
  4. If P is possible and Q can be derived from P, then Q is possible.
  5. Contradictions are necessarily false.

Let’s put these assumptions in more formal language by using the following symbolization:

P means that P is possible
KP means that P is known by somebody at some time


  1. From P, derive KP
  2. From K(P & Q), derive KP & KQ
  3. From KP, derive P
  4. From ◇P & (P → Q), derive ◇Q
  5. ◇[P & -P]

Now, the proof. First in English…


  1. Suppose that P is true and unknown.
  2. Then it is knowable that P is true and unknown.
  3. Thus it is possible that P is known and that it is known that P is unknown.
  4. So it is possible that P is both known and not known.
  5. Since 4 is a contradiction, it is not the case that P is true and unknown.
  6. In other words, if P is true, then it is known.

Follow all of that? Essentially, we assume that there is some statement P that is both true and unknown. But if this last sentence is true, and if all truths are knowable, then it should be a knowable truth. I.e. it is knowable that P is both true and unknown. But of course this can’t be knowable, since to know that P is both true and unknown is to both know it and not know it. And thus it must be the case that if all truths are knowable, then all truths are known.

I’ll write out the proof more formally now.


  1. P & –KP                Provisional assumption
  2. K(P & –KP)        Assumption 1
  3. ◇(KP & KKP)     Assumption 2
  4. ◇(KP & –KP)        Assumption 3
  5. -(P & –KP)            Reductio ad absurdum of 1
  6. P → KP                 Standard tautology

I love finding little examples like these where attempts to formalize our intuitions about basic concepts we use all the time lead us into disaster. You can’t simultaneously accept all of the following:

  • Not all truths are known.
  • All truths are knowable.
  • If P & Q is known, then both P and Q are known.
  • Knowledge entails truth.
  • If P is possible and P implies Q, then Q is possible.
  • Contradictions are necessarily false.

Objective Bayesianism and choices of concepts

Bayesians believe in treating belief probabilistically, and updating credences via Bayes’ rule. They face the problem of how to set priors – while probability theory gives a clear prescription for how to update beliefs, it doesn’t tell you what credences you should start with before getting any evidence.

Bayesians are thus split into two camps: objective Bayesians and subjective Bayesians. Subjective Bayesians think that there are no objectively correct priors. A corollary to this is that there are no correct answers to what somebody should believe, given their evidence.

Objective Bayesians disagree. Different variants specify different procedures for determining priors. For instance, the principle of indifference (POI) prescribes that the proper priors are those that are indifferent between all possibilities. If you have N possibilities, then according to the POI, you should distribute your priors credences evenly (1/N each). If you are considering a continuum of hypotheses (say, about the mass of an object), then the principle of indifference says that your probability density function should be uniform over all possible masses.

Now, here’s a problem for objective Bayesians.

You are going to be handed a cube, and all that you know about it is that it is smaller than 1 cm3. What should your prior distribution over possible cubes you might be handed look like?

Naively applying the POI, you might evenly distribute your credences across all volumes from 0 cm3 to 1 cm3 (so that there is a 50% chance that the cube has a volume less than .50 cm3 and a 50% chance its volume is between greater than .50 cm3).

But instead of choosing to be indifferent over possible volumes, we could equally well have chosen to be indifferent over possible side areas, or side lengths. The key point is that these are all different distributions. If we spread our credences evenly across possible side lengths from 0 cm to 1 cm, then we would have a distribution with a 50% chance that the cube has a volume less than .125 cm3 and a 50% chance that the volume is greater than this.

Cube puzzle

In other words, our choice of concepts (edge length vs side area vs volume) ends up determining the shape of our prior. Insofar as there is no objectively correct choice of concepts to be using, there is no objectively correct prior distribution.

I’ve known about this thought experiment for a while, but only recently internalized how serious of a problem it presents. It essentially says that your choice of priors is hostage to your choice of concepts, which is a pretty unsavory idea. In some cases, which concept to choose is very non-obvious (e.g. length vs area vs volume). In others, there are strong intuitions about some concepts being better than others.

The most famous example of this is contained in Nelson Goodman’s “new riddle of induction.” He proposes a new concept grue, which is defined as the set of objects that are either observed before 2100 and green, or observed after 2100 and blue. So if you spot an emerald before 2100, it is grue. So is a blue ball that you spot after 2100. But if you see an emerald after 2100, it will not be grue.

To characterize objects like this emerald that is observed after 2100, Goodman also creates another concept bleen, which is the inverse of grue. The set of bleen objects is composed of blue objects observed before 2100 and green objects observed after 2100.

Now, if we run ordinary induction using the concepts grue and bleen, we end up making bizarre predictions. For instance, say we observe many emeralds before 2100, and always found them to be green. By induction, we should infer that the next emerald we observe after 2100 is very likely going to be green as well. But if we thought in terms of the concepts grue and bleen, then we would say that all our observations of emeralds so far have provided inductive support for the claim “All emeralds are grue.” The implication of this is that the emeralds we observe after time 2100 will very likely also be grue (and thus blue).

In other words, by simply choosing a different set of fundamental concepts to work with, we end up getting an entirely different prediction about the future.

Here’s one response that you’ve probably already thought of: “But grue and bleen are such weird artificial choices of concepts! Surely we can prefer green/blue over bleen/grue on the basis of the additional complexity required in specifying the transition time 2100?”

The problem with this is that we could equally well define green and blue in terms of grue and bleen:

Green = grue before 2100 or bleen after 2100
Blue = bleen before 2100 or grue after 2100

If for whatever reason somebody had grue and bleen as their primitive concepts, they would see green and blue as the concepts that required the additional complexity of the time specification.

“Okay, sure, but this is only if we pretend that color is something that doesn’t emerge from lower physical levels. If we tried specifying the set of grue objects in terms of properties of atoms, we’d have a lot harder time than if we tried specifying the set of green or blue objects in terms of properties of atoms.”

This is right, and I think it’s a good response to this particular problem. But it doesn’t work as a response to a more generic form of the dilemma. In particular, you can construct a grue/bleen-style set of concepts for whatever you think is the fundamental level of reality. If you think electrons and neutrinos are undecomposable into smaller components, then you can imagine “electrinos” and “neuctrons.” And now we have the same issue as before… thinking in terms of electrinos would lead us to conclude that all electrons will suddenly transform into neutrinos in 2100.

The type of response I want to give is that concepts like “electron” and “neutrino” are preferable to concepts like “electrinos” and “neuctrons” because they mirror the structure of reality. Nature herself computes electrons, not electrinos.

But the problem is that we’re saying that in order to determine which concepts we should use, we need to first understand the broad structure of reality. After which we can run some formal inductive schema to, y’know, figure out the broad structure of reality.

Said differently, we can’t really appeal to “the structure of reality” to determine our choices of concepts, since our choices of concepts end up determining the results of our inductive algorithms, which are what we’re relying on to tell us the structure of reality in the first place!

This seems like a big problem to me, and I don’t know how to solve it.

History is Lamarckian

I just finished this novel, and loved every bit of it. It’s a plodding epic chronicling the colonization of Mars, and the first of a trilogy (Red Mars, Blue Mars, Green Mars) which I plan to continue.

Here’s one of my favorite exchanges, between the fiery revolution-minded anarchist Arkady and the group of more conventional thinkers among the first one hundred colonists of Mars. While I’m inclined to dismiss Arkady-types in the real world as wild-eyed idealists whose dreams are not anchored to the realities of human history, this was a passage that made me think hard, through the sheer force of its eloquence and originality.

Over a dessert of strawberries, Arkady floated up to propose a toast. “To the new world we now create!”

A chorus of groans and cheers; by now they all knew what he meant. Phyllis threw down a strawberry and said, “Look, Arkady, this settlement is a scientific station. Your ideas are irrelevant to it. Maybe in fifty or a hundred years. But for now, it’s going to be like the stations in Antarctica.”

“That’s true,” Arkady said. “But in fact Antarctic stations are very political. Most of them were built so that countries that built them would have a say in the revision of the Antarctic treaty. And now the stations are governed by laws set by that treaty, which was made by a very political process! So you see, you cannot just stick your head in sand crying ‘I am a scientist, I am a scientist!’ ” He put a hand to his forehead, in the universal mocking gesture of the prima donna. “No. When you say that, you are only saying, ‘I do not wish to think about complex systems!’ Which is not really worthy of true scientists, is it?”

“The Antarctic is governed by a treaty because no one lives there except in scientific stations,” Maya said irritably. To have their final dinner, their last moment of freedom, disrupted like this!

“True,” Arkady said. “But think of the result. In Antarctica, no one can own land. No one country or organization can exploit the continent’s natural resources, without the consent of every other country. No one can claim to own those resources, or take them and sell them to other people, so that some profit from them while others pay for their use. Don’t you see how radically different that is from the way the rest of the world is run? And this is the last area on Earth to be organized, to be given a set of laws. It represents what all governments working together feel instinctively is fair, revealed on land free from claims of sovereignty, or really from any history at all. It is, to say it plainly, Earth’s best attempt to create just property laws! Do you see? This is the way entire world should be run, if only we could free it from the straitjacket of history!”

Sax Russell, blinking mildly, said, “But Arkady, since Mars is going to be ruled by a treaty based on the old Antarctic one, what are you objecting to? The Outer Space Treaty states that no country can claim land on Mars, no military activities are allowed, and all bases are open to inspection by any country. Also no martian resources can become the property of a single nation —the UN is supposed to establish an international regime to govern any mining or other exploitation. If anything is ever done along that line, which I doubt will happen, then it is to be shared among all the nations of the world.” He turned a palm upward. “Isn’t that what you’re agitating for, already achieved?”

“It’s a start,” Arkady said. ”But there are aspects of that treaty you haven’t mentioned. Bases built on Mars will belong to the countries that build them, for instance. We will be building American and Russian bases, according to this provision of the law. And that puts us right back into the nightmare of Terran law and Terran history. American and Russian businesses will have the right to exploit Mars, as long as the profits are somehow shared by all the nations signing the treaty. This may only involve some sort of percentage paid to UN, in effect no more than bribe. I don’t believe we should acknowledge these provisions for even a moment!”

Silence followed this remark.

Ann Clayborne said, “This treaty also says we have to take measures to prevent the disruption of planetary environments, I think is how they put it. It’s in Article Seven. That seems to me to expressly forbid the terraforming that so many of you are talking about.”

“I would say that we should ignore that provision as well,” Arkady said quickly. “Our own well-being depends on ignoring it.”

This view was more popular than his others, and several people said so.

“But if you’re willing to disregard one article,” Arkady pointed out, “you should be willing to disregard the rest. Right?”

There was an uncomfortable pause.

“All these changes will happen inevitably,” Sax Russell said with a shrug. “Being on Mars will change us in an evolutionary way.”

Arkady shook his head vehemently, causing him to spin a little in the air over the table. “No, no, no, no! History is not evolution! It is a false analogy! Evolution is a matter of environment and chance, acting over millions of years. But history is a matter of environment and choice, acting within lifetimes, and sometimes within years, or months, or days! History is Lamarckian! So that if we choose to establish certain institutions on Mars, there they will be! And if we choose others, there they will be!” A wave of his hand encompassed them all, the people seated at the tables, the people floating among the vines: “I say we should make those choices ourselves, rather than having them made for us by people back on Earth. By people long dead, really.”

Phyllis said sharply, “You want some kind of communal utopia, and it’s not possible. I should think Russian history would have taught you something about that.”

“It has,” Arkady said. “Now I put to use what it has taught me.”

“Advocating an ill-defined revolution? Fomenting a crisis situation? Getting everyone upset and at odds with each other?”

A lot of people nodded at this, but Arkady waved them away. “I decline to accept blame for everyone’s problems at this point in the trip. I have only said what I think, which is my right. If I make some of you uncomfortable, that is your problem. It is because you don’t like the implications of what I say, but can’t find grounds to deny them.”

“Some of us can’t understand what you say,” Mary exclaimed.

“I say only this!” Arkady said, staring at her bug-eyed: “We have come to Mars for good. We are going to make not only our homes and our food, but also our water and the very air we breathe—all on a planet that has none of these things. We can do this because we have technology to manipulate matter right down to the molecular level. This is an extraordinary ability, think of it! And yet some of us here can accept transforming the entire physical reality of this planet, without doing a single thing to change our selves, or the way we live. To be twenty-first century scientists on Mars, in fact, but at the same time living within nineteenth century social systems, based on seventeenth century ideologies. It’s absurd, it’s crazy, it’s—it’s—” he seized his head in his hands, tugged at his hair, roared “It’s unscientific! And so I say that among all the many things we transform on Mars, ourselves and our social reality should be among them. We must terraform not only Mars, but ourselves.”

History is Lamarckian, in exactly the sense declared by Arkady. But this of course does not imply that the social systems we build are not subject to the same forces of selection that have caused the downfall of so many past societies.


Anyway, I highly recommend this book, and to give you a flavor, here are a few more of my favorite quotes, presented with zero context…

“We were too old!”

“We were not too old. We chose not to think of it. Most ignorance is by choice, you know, and so ignorance is very telling about what really matters to people.”

“Come on,” he said. He propped himself up on an elbow to look at her. “You really don’t know what beauty is, do you?”

“I certainly do,” Nadia said mulishly.

Arkady ignored her and said, “Beauty is power and elegance, right action, form fitting function, intelligence, and reasonability.”

“We didn’t mean to be selfish,” Hiroko said slowly. “We wanted to try it, to show by experiment how we can live here. Someone has to show what you mean when you talk about a different life, John Boone. Someone has to live the life.”

Sax Russell rose to his feet. He looked the same as ever, perhaps a bit more flushed than usual, but mild, small, blinking owlishly, his voice calm and dry, as if lecturing on some textbook point of thermodynamics, or enumerating the periodic table.

“The beauty of Mars exists in the human mind,” he said in that dry factual tone, and everyone stared at him amazed. “Without the human presence it is just a concatenation of atoms, no different than any other random speck of matter in the universe. It’s we who understand it, and we who give it meaning. All our centuries of looking up at the night sky and watching it wander through the stars. All those nights of watching it through the telescopes, looking at a tiny disk trying to see canals in the albedo changes. All those dumb sci-fi novels with their monsters and maidens and dying civilizations. And all the scientists who studied the data, or got us here. That’s what makes Mars beautiful. Not the basalt and the oxides.”

He paused to look around at them all. Nadia gulped; it was strange in the extreme to hear these words come out of the mouth of Sax Russell, in the same dry tone that he would use to analyze a graph. Too strange!

“Now that we are here,” he went on, “it isn’t enough to just hide under ten meters of soil and study the rock. That’s science, yes, and needed science too. But science is more than that. Science is part of a larger human enterprise, and that enterprise includes going to the stars, adapting to other planets, adapting them to us. Science is creation. The lack of life here, and the lack of any finding in fifty years of the SETI program, indicates that life is rare, and intelligent life even rarer. And yet the whole meaning of the universe, its beauty, is contained in the consciousness of intelligent life. We are the consciousness of the universe, and our job is to spread that around, to go look at things, to live everywhere we can. It’s too dangerous to keep the consciousness of the universe on only one planet, it could be wiped out. And so now we’re on two, three if you count the moon. And we can change this one to make it safer to live on. Changing it won’t destroy it. Reading its past might get harder, but the beauty of it won’t go away. If there are lakes, or forests, or glaciers, how does that diminish Mars’s beauty? I don’t think it does. I think it only enhances it. It adds life, the most beautiful system of all. But nothing life can do will bring Tharsis down, or fill Marineris. Mars will always remain Mars, different from Earth, colder and wilder. But it can be Mars and ours at the same time. And it will be. There is this about the human mind; if it can be done, it will be done. We can transform Mars and build it like you would build a cathedral, as a monument to humanity and the universe both. We can do it, so we will do it. So—” he held up a palm, as if satisfied that the analysis had been supported by the data in the graph – as if he had examined the periodic table, and found that it still held true – “we might as well start.”

Constructing the world

In this six and a half hour lecture series by David Chalmers, he describes the concept of a minimal set of statements from which all other truths are a priori “scrutable” (meaning, basically, in-principle knowable or derivable).

What are the types of statements in this minimal set required to construct the world? Chalmers offers up four categories, and abbreviates this theory PQIT.


P is the set of physical facts (for instance, everything that would be accessible to a Laplacean demon). It can be thought of as essentially the initial conditions of the universe and the laws governing their changes over time.


Q is the set of facts about qualitative experience. We can see Chalmers’ rejection of physicalism here, as he doesn’t think that Q is eclipsed within P. Example of a type of statement that cannot be derived from P without Q: “There is a beige region in the bottom right of my visual field.”


Here’s a true statement: “I’m in the United States.” Could this be derivable from P and Q? Presumably not; we need another set of indexical truths that allows us to have “self-locating” beliefs and to engage in anthropic reasoning.


Suppose that P, Q, and I really are able to capture all the true statements there are to be captured. Well then, the statement “P, Q, and I really are able to capture all the true statements there are to be captured” is a true statement, and it is presumably not captured by P, Q, and I! In other words, we need some final negative statements that tell us that what we have is enough, and that there are no more truths out there. These “that’s all”-type statements are put into the set T.


So this is a basic sketch of Chalmer’s construction. I like that we can use these tags like PQIT or PT or QIT as a sort of philosophical zip-code indicating the core features of a person’s philosophical worldview. I also want to think about developing this further. What other possible types of statements are there out there that may not be captured in PQIT? Here is a suggestion for a more complete taxonomy:

p    microphysics
P    macrophysics (by which I mean all of science besides fundamental physics)
Q    consciousness
R    normative rationality
normative ethics
C    counterfactuals
mathematical / logical truths
I     indexicals
T    “that’s-all” statements

I’ve split P into big-P (macrophysics) and little-p (microphysics) to account for the disagreements about emergence and reductionism. Normativity here is broad enough to include both normative epistemic statements (e.g. “You should increase your credence in the next coin toss landing H after observing it land H one hundred times in a row”) and ethical statements. The others are fairly self-explanatory.

The most ontologically extravagant philosophical worldview would then be characterized as pPQRECLIT.

My philosophical address is pRLIT (with the addendum that I think C comes from p, and am really confused about Q). What’s yours?

Moving Naturalism Forward: Eliminating the macroscopic

Sean Carroll, one of my favorite physicists and armchair philosophers, hosted a fantastic conference on philosophical naturalism and science, and did the world a great favor by recording the whole thing and posting it online. It was a three-day long discussion on topics like the nature of reality, emergence, morality, free will, meaning, and consciousness. Here are the videos for the first two discussion sections, and the rest can be found by following Youtube links.


Having watched through the entire thing, I have updated a few of my beliefs, plan to rework some of my conceptual schema, and am puzzled about a few things.

A few of my reflections and take-aways:

  1. I am much more convinced than before that there is a good case to be made for compatibilism about free will.
  2. I think there is a set of interesting and challenging issues around the concept of representation and intentionality (about-ness) that I need to look into.
  3. I am more comfortable with intense reductionism claims, like “All fact about the macroscopic world are entailed by the fundamental laws of physics.”
  4. I am really interested in hearing Dan Dennett talk more about grounding morality, because what he said was starting to make a lot of sense to me.
  5. I am confused about the majority attitude in the room that there’s not any really serious reason to take an eliminativist stance about macroscopic objects.
  6. I want to find more details about the argument that Simon DeDeo was making for the undecidability of questions about the relationship between macroscopic theories and microscopic theories (!!!).
  7. There’s a good way to express the distinction between the type of design human architects engage in and the type of design that natural selection produces, which is about foresight and representations of reasons. I’m not going to say more about this, and will just refer you to the videos.
  8. There are reasons to suspect that animal intelligence and capacity to suffer are inversely correlated (that is, the more intelligent an animal, the less capacity to suffer it likely has). This really flips some of our moral judgements on their head. (You must deliver a painful electric shock to either a human or to a bird. Which one will you choose?)

Let me say a little more about number 5.

I think that questions about whether macroscopic objects like chairs or plants really REALLY exist, or whether there are really only just fermions and bosons are ultimately just questions about how we should use the word “exist.” In the language of our common sense intuitions, obviously chairs exist, and if you claim otherwise, you’re just playing complicated semantic games. I get this argument, and I don’t want to be that person that clings to bizarre philosophical theses that rest on a strange choice of definitions.

But at the same time, I see a deep problem with relying on our commonsense intuitions about the existence of the macro world. This is that as soon as we start optimizing for consistency, even a teeny tiny bit, these macroscopic concepts fall to pieces.

For example, here is a trilemma (three statements that can’t all be correct):

  1. The thing I am sitting on is a chair.
  2. If you subtract a single atom from a chair, it is still a chair.
  3. Empty space is not a chair.

These seem to me to be some of the most obvious things we could say about chairs. And yet they are subtly incoherent!

Number 1 is really shorthand for something like “there are chairs.” And the reason why the second premise is correct is that denying it requires that there be a chair such that if you remove a single atom, it is no longer a chair. I take it to be obvious that such things don’t exist. But accepting the first two requires us to admit that as we keep shedding atoms from a chair, it stays a chair, even down to the very last atom. (By the way, some philosophers do actually deny number 2. They take a stance called epistemicism, which says that concepts like “chair” and “heap” are actually precise and unambiguous, and there exists a precise point at which a chair becomes a non-chair. This is the type of thing that makes me giggle nervously when reflecting on the adequacy of philosophy as a field.)

As I’ve pointed out in the past, these kinds of arguments can be applied to basically everything in the macroscopic world. They wreak havoc on our common sense intuitions and, to my mind, demand rejection of the entire macroscopic world. And of course, they don’t apply to the microscopic world. “If X is an electron, and you change its electric charge a tiny bit, is it still an electron?” No! Electrons are physical substances with precise and well-defined properties, and if something doesn’t have these properties, it is not an electron! So the Standard Model is safe from this class of arguments.

Anyway, this is all just to make the case that upon close examination, our commonsense intuitions about the macroscopic world turn out to be subtly incoherent. What this means is that we can’t make true statements like “There are two cars in the garage”. Why? Just start removing atoms from the cars until you get to a completely empty garage. Since no single-atom change can make the relevant difference to “car-ness”, at each stage, you’ll still have two cars!

As soon as you start taking these macroscopic concepts seriously, you find yourself stuck in a ditch. This, to me, is an incredibly powerful argument for eliminativism, and I was surprised to find that arguments like these weren’t stressed at the conference. This makes me wonder if this argument is as powerful as I think.