Values of disagreement

We live in a deeply epistemically divided society, with lots of different views, including on some of the most important things.

Say that two people disagree significantly on a proposition if one believes it and one disbelieves it. The deep epistemic division in society includes significant disagreement on many important propositions. But whenever two people significantly disagree on a proposition, one of them is wrong. Being wrong about an important proposition is a very bad thing. So the deep division implies some very bad stuff.

Nonetheless, I’ve been thinking that our deep social disagreement leads to some important advantages as well. Here are three that come to mind:

1. If two people significantly disagree on a proposition, then by bivalence, one of them is right. There is a value in someone getting a matter right, rather than everyone getting it wrong or suspending judgment.

2. Given our deep-seated psychological desire to convince others that we’re right, if others disagree with us, we will continue seeking evidence in order to convince them. Thus disagreement keeps us investigating, which is beneficial whether or not we are right. If everyone agreed with us, we would be apt to stop investigating, which would mean we would either get us stuck with a falsehood, or at least likely provide us with less evidence of the truth than is available. Moreover, continued investigation is apt to refine our theory, even if the theory was already basically right.

3. To avoid getting stuck in local maxima in our search for the best theory, it is good if people are searching in very different areas of epistemic space. Disagreement helps make that happen.

Committee credences

Suppose the members of a committee individually assign credences or probabilities to a bunch of propositions—maybe propositions about climate change or about whether a particular individual is guilty or innocent of some alleged crimes. What should we take to be “the committee’s credences” on the matter?

Here is one way to think about this. There is a scoring rule s that measures the closeness of a probability assignment to the truth that is appropriate to apply in the epistemic matter at hand. The scoring rule is strictly proper (i.e., such that an individual by their own lights is always prohibited from switching probabilities without evidence). The committee can then be imagined to go through all the infinitely many possible probability assignments q, and for each one, member i calculates the expected value E_pis(q) of the score of q by the lights of the member’s own probability assignment p_i.

We now need a voting procedure between the assignments q. Here is one suggestion: calculate a “committee score estimate” for q in the most straightforward way possible—namely, by adding the individuals’ expected scores, and choose an assignment that maximizes the committee score estimate.

It’s easy to prove that given that the common scoring rule is strictly proper, the probability assignment that wins out in this procedure is precisely the average p̄ = (p₁+...+p_n)/n of the individuals’ probability assignments. So it is natural to think of “the committee’s credence” as the average of the members’ credences, if the above notional procedure is natural, which it seems to be.

But is the above notional voting procedure the right one? I don’t really know. But here are some thoughts.

First, there is a limitation in the above setup: we assumed that each committee member had the same strictly proper scoring rule. But in practice, people don’t. People differ with regard to how important they regard getting different propositions right. I think there is a way of arguing that this doesn’t matter, however. There is a natural “committee scoring rule”: it is just the sum of the individual scoring rules. And then we ask each member i when acting as a committee member to use the committee scoring rule in their voting. Thus, each member calculates the expected committee score of q, still by their own epistemic lights, and these are added, and we maximize, and once again the average will be optimal. (This uses the fact that a sum of strictly proper scoring rules is strictly proper.)

Second, there is another way to arrive at the credence-averaging procedure. Presumably most of the reason why we care about a committee’s credence assignments is practical rather than purely theoretical. In cases where consequentialism works, we can model this by supposing a joint committee utility assignment (which might be the sum of individual utility assignments, or might be consensus utility assignment), and we can imagine the committee to be choosing between wagers so as to maximize the agreed-on committee utility function. It seems natural to imagine doing this as follows. The committee expectations or previsions for different wagers are obtained by summing individual expectations—with the individuals using the agreed-on committee utility function, albeit with their own individual credences to calculate the expectations. And then the committee chooses a wager that maximizes its prevision.

But now it’s easy to see that the above procedure yields exactly the same result as the committee maximizing committee utility calculated with respect to the average of the individuals’ credence assignments.

So there is a rather nice coherence between the committee credences generated by our epistemic “accuracy-first”
procedure and what one gets in a pragmatic approach.

But still all this depends on the plausible, but unjustified, assumption that addition is the right way to go, whether for epistemic or pragmatic utility expectations. But given this assumption, it really does seem like the committee’s credences are reasonably taken to be the average of the members’ credences.

Rachels on doing and allowing

Rachels famously gives us these two cases to argue that the doing–allowing distinction is morally vacuous:

1. You stand to inherit money from a young cousin, so you push them into a tub so they drown.

2. You stand to inherit money from a young cousin, and so when you see them drowning in a tub, you don’t pull them out.

The idea is that if there is a doing–allowing distinction, then (1) should be worse than (2), but they both seem equally wicked.

But it’s interesting to notice how things change if you change the reasons from profit to personal survival:

3. A malefactor informs you that if you don’t push the young cousin into the tub so they drown, you will be shot dead.

4. A malefactor informs you that if your currently drowning cousin survives, you will be shot dead.

It’s clear that it’s wrong to drown your cousin to save your life. But while it’s praiseworthy to rescue them at the expense of your life, unless you have a special obligation to them beyond cousinage, you don’t do wrong by failing to pull them out. And it seems that the relevant difference between (3) and (4) is precisely that between doing and allowing: you may not execute a drowning to save your life, but you may allow one.

Or consider this variant:

5. A malefactor informs you that if you don’t push the young cousin into the tub so they drown, two other cousins will be shot dead.

6. A malefactor informs you that if your currently drowning cousin survives, two other cousins will be short dead.

I take it that pretty much every non-consequentialist will agree that in (5) it’s wrong to drown your cousin, but everyone (consequentialist or not) will also say that in (6) it’s wrong to rescue your cousin.

So there is very good reason to think there is a morally relevant doing–allowing distinction, and cases similar to Rachels’ show it. At this point it is tempting to diagnose our intuitions about Rachels’ original case as based on the fact that the death of your cousin is not sufficiently good to justify allowing the drowning—their death is disproportionately bad for the benefit gained—so we want to blame the agent who cares about their financial good more than the life of their young cousin, an we don’t care whether they are actively or passively killing the cousin.

But things are more complicated. Consider this pair of cases:

7. Your recently retired cousin has left all their money to famine relief where it will save fifty lives but if your cousin survives another ten years their retirement savings will be largely spent and won’t be enough to save any lives. So you push the cousin into the tub to drown them.

8. Your recently retired cousin has left all their money to famine relief where it will save fifty lives but if your cousin survives another ten years their retirement savings will be largely spent and won’t be enough to save any lives. So when your cousin is drowning in the tub, you don’t rescue them.

Now it seems we have proportionality: your cousin’s death is not disproportionately bad given the benefit. Yet I have the strong intuition that it’s both wrong to drown them and to fail to save them. I can’t confidently put my finger on what is the relevant difference between (8), on the one hand, and (4) and (6), on the other hand.

But maybe it’s this. In (8), your rescue of your cousin isn’t a cause of the death of the people. The cause of their death is famine. It’s just that you have failed to prevent their death. On the other hand, in (4) and (6), if you rescue, you have caused your own death or the death of the two other cousins, admittedly by means of the malefactor’s wicked agency. In (8), rescuing blocks prevention of deaths; in (4) and (6), rescuring causes deaths. Blocking prevention is different from causing.

This is tricky, though. For drowning someone can be seen as blocking prevention of death. For their breathing prevents death and drowning blocks the breathing!

Maybe the difference lies between blocking a natural process of life-preservation (breathing, say) and blocking an artificial process of life-preservation (sending famine relief, say).

Or maybe I am mistaken about (4) and (6) being cases where rescue is not obligatory. Maybe in (4) and (6) rescue is obligatory, but it wouldn’t be if instead the malefactor told you that if you rescue, then the deadly consequences would follow. For maybe in (4) and (6), you are intending death, while in the modified cases, you are only intending non-rescue? I am somewhat sceptical.

There is a lot of hard stuff here, thus. But I think there is still enough clarity to see that there is a difference between doing and allowing in some cases.

Video splitter python script

I'm working on submitting my climbing record to Guinness. They require video--including slow motion video!--but they have a 1gb limit on uploads, and recommend splitting videos into 1gb portions with five second overlap. I made a little python script to do this using ffmpeg. You can specify the maximum size (default: 999999999 bytes) and the aimed-at overlap (default: 6 seconds, to be on the safe side for Guinness), and it will estimate how many parts you need, and split the file into approximately these many. If any of the resulting parts is too big, it will try again with more parts.

Doing, allowing and trolleys

Consider a trolley problem where the trolley is heading for:

• Path A with two people,

but you can redirect it to:

• Path B with one person.

If that’s the whole story, and everyone is a stranger to you, redirection is surely permitted, and probably even required.

But add one more ingredient: the one person on Path B is you yourself. I am far from sure of this, but I suspect that you aren’t morally required to save two strangers at the expense of your life, though of course it would be praiseworthy if you did. (On the other hand, once the number on Path A is large enough, I think it becomes obligatory to save them.)

Now consider a reverse version. Suppose that the trolley is heading for Path B, where you are. Are you permitted to redirect it to Path A? I am inclined to think not.

So we have these two judgments:

1. You aren’t obligated to redirect from two people to yourself.

2. You aren’t permitted to redirect from yourself to two people.

This suggests that in the vicinity of the Principle of Double Effect there is an asymmetry between doing and allowing. For you are permitted to allow two people to be hit by the trolley rather than sacrifice your life, but you are not permitted to redirect the trolley from yourself to the two.

Now, you might object that the whole thing here is founded on the idea, which I am not sure of, that you are not obligated to save two strangers at the expense of your life. While I am pretty confident that you are not obligated to save one stranger at the expense of your life, with two I become unsure. If this is the sticking point, I can modify my case. Instead of having two people fully on Path A, we could suppose that there is one person fully on Path A and the other has a limb on the track. I don’t think you are obligated to sacrifice your life to save one stranger’s life and another’s limb. But it still seems wrong to redirect the trolley from yourself at the expense of a stranger and a limb. So we still have an allowing-doing asymmetry.

Another interesting question: Are you permitted to redirect a trolley heading for you in a way that kills one stranger? I am not sure.

A second indoor climbing world record

On July 15, 2023, I set (still uncertified) my second indoor world climbing record: fastest vertical mile (male), doing 112 climbs, at 14.4 meters each, in a total of 1 hour 42 minutes and 58 seconds (continuous time, including descents and breaks; descents do not count towards the mile). The official best time was Andrew Dahir's 1 hour 51 minutes and 37.5 seconds. I am still working on preparing all the materials for submission to Guinness. [Later note: The record has since been officially certified.]

This was a fastest-time for fixed distance (one mile) record. In December, I got a longest-distance (about a kilometer) for a fixed-time (one hour) record. The video below shows the first and last climbs at normal speed and runs the middle 110 climbs at 30X.

I am grateful to Baylor Recreation for all the encouragement I have received, and to the volunteers who made this possible (two timekeepers, two witnesses, two additional safety officers).

Here are some details:

• I am incredibly impressed with Andrew Dahir who had set both of the records in one day! There is no way I would have the endurance for that.
• My vertical speed was 938 meters per hour, somewhat lower than the 1014 meters per hour of my December record, but I had to keep it up for a longer time. Still, I think I was less tired this time: the lower pace compensated for the greater distance.
• The route was a 5.6. 
• Unlike in my previous record, an auto-belay was used.
• I started by doing 12 climbs at a slightly higher pace than I could keep up for the full length, followed by a  minute break, followed by ten sets of ten, with about 1.5-2 minute breaks in between. 
• I got a cramp in the upper right thigh around climb #100, and had to rely more on upper body for the remainder.
• I had a pacing sheet with dual target times both for beating the record by about 1.5 minutes and for beating the record by about 5 minutes. I consistently stayed ahead of both.
• I wore my comfy 5.10 lace-up Anasazi shoes (pinks).
• Mid-way I ducked into the storage room to change into a dry T-shirt.
• I did a lot of short practices with 1-5 climbs at maximum pace (which I wouldn't be able to keep up much longer) to get my muscle memory of all the moves.
• I did three full-length practices starting around May. The first one was slightly slower than Dahir's time. The second was about two minutes ahead of the record, and the third about five.
• I did one mid-length practice about a week ahead, where I unofficially beat my December one hour record.
• To avoid mishaps with video evidence, I had five cameras pointed at the event. Guinness rules require slow motion footage to be available for one-mile events. That makes sense for a run, but is surprising for a nearly two-hour climb, and to satisfy this requirement one of the cameras was a GoPro capturing at 120fps.

Because Guinness wanted the witnesses to log the individual time of each climb, I have a nice graph of how long each ascent took. I started a little faster, slowed down towards the end. The average ascent was 36 seconds. The fastest was 26 seconds (#1) and the slowest was 50 seconds (#111).

 

Partially defined predicates

Is cutting one head off a two-headed person a case of beheading?

Examples like this are normally used as illustrations of vagueness. It’s natural to think of cases like this as ones where we have a predicate defined over a domain and being applied outside it. Thus, “is being beheaded” is defined over n-headed animals that are being deprived of all heads or of no heads.

I don’t like vagueness. So let’s put aside the vagueness option. What else can we say?

First, we could say that somehow there are deep facts about the language and/or the world that determine the extension of the predicate outside of the domain where we thought we had defined it. Thus, perhaps, n-headed people are beheaded when all heads are cut off, or when one head is cut off, or when the number of heads cut off is sufficient to kill. But I would rather not suppose a slew of facts about what words mean that are rather mysterious.

Second, we could deny that sentences using predicates outside of their domain lack truth value. But that leads to a non-classical logic. Let’s put that aside.

I want to consider two other options. The first, and simplest, is to take the predicates to never apply outside of their domain of definition. Thus,

1. False: Cutting one head off Dikefalos (who is two headed) is a beheading.

2. True: Cutting one head off Dikefalos is not a beheading

3. False: Cutting one head off Dikefalos is a non-beheading.

4. True: Cutting one head off Dikefalos is not a non-beheading.

(Since non-beheading is defined over the same domain as beheading). If a pre-scientific English-speaking people never encountered whales, then in their language:

5. False: Whales are fish.

6. True: Whales are not fish.

7. False: Whales are non-fish.

8. True: Whales are not non-fish.

The second approach is a way modeled after Russell’s account of definite descriptors: A sentence using a predicate includes the claim that the predicate is being used in its domain of definition and, thus, all of the eight sentences exhibited above are false.

I don’t like the Russellian way, because it is difficult to see how to naturally extend it to cases where the predicate is applied to a variable in the scope of a quantifier. On the other hand, the approach of taking the undefined predicates to be false is very straightforward:

9. False: Every marine mammal is a fish.

10: False: Every marine mammal is a non-fish.

This leads to a “very strict and nitpicky” way of taking language. I kind of like it.

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.