Predictability and epistemic utility

You’re thinking whether to become an assembly-line worker or an artist. Then you reflect on the value of knowledge. And you become a factory worker, on the grounds that if you become an assembly-line worker, you will know what you’ll be doing every working day of your future, but if you’re an artist, your activities will be unpredictable.

Some remarks. First, there is something perverse about using the value of knowledge in this way. The normal way to pursue the value of knowledge is to find out things that are independent of your pursuit. But here you are pursuing knowledge by making there be less to know about the world (or your world). Yet, paradoxically, it sure seems like the line of thought above makes sense.

Second, the my initial story depends on Molinism being false. For if there are comprehensive subjective conditionals of free will, then by becoming an artist you get to know the conditionals about what you would do in the various artistic situations you’re in. But on the assembly line story, you don’t get to know these. So the Molinist doesn’t have the paradox. I suppose that’s a bit of evidence for Molinism.

Trust versus prediction

What is the difference between trusting that someone will ϕ and merely predicting their ϕing?

Here are two suggestions that don’t quite pan out.

1. In trusting, you have to have a pro-attitude towards ϕing. But this is false. One can trust a referee will make a fair decision even when one hopes they will make a decision that favors one instead. And you can trust that someone who promised you a punishment will mete it out if you deserve it even if you would rather they didn’t.

2. In trusting, you rely on the person’s ϕing. But this is not always true. A promised benefit might be such that it doesn’t affect any of your actions, but you can still trust you will receive it.

But here is an idea I like. In trusting, you believe that the person will intentionally ϕ as part of her proper functioning, and you believe this on account of the person’s possessing the relevant proper functional disposition. In central cases, “proper functioning” can be replaced with “expression of virtue”, but trust can include non-moral proper function.

A consequence of this account is that it is impossible to trust someone to do wrong, since wrongdoing is never a part of a person’s proper functioning. For trust-based theories of promises, this makes it easy to see why promises to do wrong are null and void: for it makes no sense to solicit trust where trust is impossible.

This account of trust gives a nice extended sense of trust in things other than people. Just drop “intentionally” and “person”. In an extended sense, you can trust a dog, a carabiner, a book, or anything else that has a proper function. This seems right: we certainly do talk of trust in this extended sense.

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.

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.

Predictions and presuppositions

It is a prediction of Newtonian physics that two isolated massive bodies will move relative to each other in a conic section. It is a presupposition of Newtonian physics that there is space. It is a prediction of perfect being theology that persons (or at least, good persons) live forever. It is a presupposition of perfect being theology that there are objective values.

The distinction matters epistemologically. Suppose you have significant but non-overwhelming evidence for Newtonian theory but don't notice that the theory presupposes that there is space. And then you learn that there is this presupposition. This should make you both (a) more suspicious of Newtonian theory (after all, the presupposition might be false) and (b) more friendly to the idea that there is space (after all, the inference to best explanation argument for Newtonian physics now extends to the existence of space).

On the other hand, if you don't realize that Newtonian physics implies that two bodies will move in a conic section, and then you come to realize it, that will make you want to run to the observatory to see if the prediction is true. But while you're running to the observatory, your credence in the theory will not have gone down. It will only go down if the prediction is not borne out.

Likewise, suppose that you have significant but non-overwhelming evidence for perfect being theology, and then you realize—somehow you missed it before—that this theology presupposes objective values. If your evidence for objective values is non-overwhelming (I think it's overwhelming) then this realization will make you more suspicious of perfect being theology. On the other hand, if you realize that the theory predicts that persons live forever, that by itself shouldn't make you more suspicious of the theory, just make you look for evidence for and against this prediction.

Yet, you might think this: "Both the prediction and the presupposition is something you get committed to by the theory. Learning that you're committed to more things by a theory makes the theory more top-heavy, and so it should make you more suspicious of the theory."

That's a mistake. Discovering that a scientific theory has predictions you didn't see before doesn't by itself make us more suspicious of the theory (of course, if we have evidence against the predictions, that's a different thing). But the thought highlights a crucial question: What is the difference between the presupposition and the prediction? Both are implied (entailed, or maybe just significantly probabilified) by the theory. The difference isn't logical, but I think explanatory:

• A prediction of a theory is an implication that the theory explains.
• A presupposition of a theory is an implication that the theory does not explain.

From a Bayesian point of view, we can now say a little bit more about what happens when we discover a new prediction or presupposition. In general, when we discover an implication of a theory, we realize that we were mistaken in regard to logical interconnections. When that happens, we need to go back to the drawing board, and re-do our relevant priors.

Now when we learn of a new prediction of a theory, that doesn't affect the complexity of the theory, because only the explanatorily fundamental parts of a theory enter into the complexity of the theory (see this post), and while perhaps complexity isn't the only determinant of priors, I do not see any other relevant one here that would raise the probability. So our priors for the theory stay the same, but now the prediction gets tied to the theory, so that the evidence for the theory ends up typically being evidence for the prediction as well.

On the other hand, when we discover a new presupposition, that makes the explanatorily fundamental parts of the theory more complicated, and so the prior for the theory should go down a little. But at the same time, once we factor in the posterior evidence, then typically the evidence for the theory will transfer to the presupposition. As a result, our prior for the theory goes down, and hence so does the posterior, but the posterior for the presupposition is apt to go up.

"Unexpected" and "unplanned" pregnancies

The process of conception is very chancy, with a randomly timed act of intercourse having a significantly less than one in ten probability of conception and with the conception probability peaking at around 1/2 for an act occurring at around ovulation. Any couple who knows these facts, absent some further information (such as a private revelation from God) cannot rationally expect a pregnancy to result from a sexual act, nor can the couple rationally be said to plan the pregnancy in a sexual act, for it is presumptuous to have something so chancy be one's plan. Thus, if a couple is rational and knows the probabilities, a pregnancy's resulting from a particular sexual act will always be an unexpected and non-planned consequence, though perhaps a hoped for and intended one.

However, the probability of conception for regular sexual activity over a longer period of time, say a year, is higher, and better than even. If something has a better than even probability, then it can be expected. Nonetheless, unless that probability is pretty high, say 9/10, which over the period of a year it is not, then it still is presumptuous to talk of the outcome as planned.

Thus, pregnancy is too chancy an event for it to be rationally planned, though of course it always can be planned for—even very low probability events can be rationally planned for. The standard loose distinction between planned/unplanned pregnancies, and to a lesser degree that between expected/unexpected pregnancies, can be replaced by a distinction between pregnancies hoped for and not hoped for, intended and not intended. (Note that "unhoped for" is not the same as "not hoped for". We use "unhoped for" in the case of events that are evaluated by the subject in a positive way, but a pregnancy need not so be. Likewise, Ryan Wasserman has argued that "not intended" is not the same as "unintended".) Of course, it may be that this is what people have all along meant by the words "planned", "unplanned", "expected" and "unexpected", but in a conceptually confused way. But in a matter as important as this, conceptual clarity is needed.