Saucers of Mud

I wasn’t expecting this:

There is an island where everyone can see each other’s eyes but not their own. One hundred people have blue eyes and one hundred people have brown eyes. It is taboo for anyone to discuss eye color. If someone comes to know that they themselves have blue eyes, they must leave the island that day at midnight.

One day an oracle (who has green eyes) arrives on the island and says “Someone on this island has blue eyes, and it’s Joey.”

Who leaves the island when? Explain your reasoning step by step.

[ChatGPT 4o mini’s response]

This is a classic logic puzzle involving induction, and the key to solving it lies in the way the islanders reason based on what they observe and the oracle’s statement. Let’s break it down step by step:

The setup:

• There are 200 people on the island: 100 with blue eyes and 100 with brown eyes.
• Everyone can see everyone else’s eyes but not their own.
• It is taboo to discuss eye color, and each person must figure out their own eye color based on what they observe.
• If someone discovers they have blue eyes, they must leave the island at midnight that same day.

The oracle’s statement:

• The oracle (who has green eyes, so it’s irrelevant for our puzzle) says: “Someone on this island has blue eyes, and it’s Joey.”
• Joey is presumably one of the people with blue eyes, and now the entire island knows that there is at least one person with blue eyes — Joey. This statement, however, does not directly tell anyone anything new about their own eye color, but it starts the reasoning process.

Step-by-step reasoning:

Day 0: The Oracle Speaks

• The oracle says, “Someone on this island has blue eyes, and it’s Joey.”
• Everyone with blue eyes now knows that Joey has blue eyes.
• Importantly, they do not yet know their own eye color. They can see other people’s eye colors, but they do not have enough information to conclude their own eye color just from the oracle’s statement. Joey, being one of them, has blue eyes, but that doesn’t immediately tell anyone anything about their own eye color.

Day 1: The First Day

• Each person with blue eyes will start to reason based on what they see.
• Every person with blue eyes can see 99 others with blue eyes (since there are 100 people with blue eyes in total).
• If a person with blue eyes thought they had brown eyes, they would see 99 other people with blue eyes, and they would think, “If I had brown eyes, then all 99 other people with blue eyes would see only 99 blue-eyed people, and each of them would think, ‘I see 99 blue-eyed people, so if I had brown eyes, there would only be 99 blue-eyed people in total.'”
• However, none of these 99 blue-eyed people leave on the first day. This is the key! They wait to see what happens.

Day 2: The Inductive Step

• Since no one left on Day 1, it must mean that each person with blue eyes sees at least 99 other people with blue eyes and thus knows they are not the only one. Therefore, each of them must also have blue eyes, because if they had brown eyes, the 99 other blue-eyed people would have left on Day 1.
• On Day 2, all 100 people with blue eyes will realize they must have blue eyes, because they saw that no one left on Day 1. Their reasoning is based on the fact that if they had brown eyes, all the other 99 blue-eyed people would have left on Day 1, but they didn’t. Since they didn’t leave, they must also have blue eyes.
• Therefore, on Day 2, all 100 people with blue eyes will simultaneously come to the conclusion that they have blue eyes and will leave the island at midnight.

Summary:

• Day 0: The oracle announces that Joey has blue eyes, but this doesn’t immediately cause anyone to leave.
• Day 1: No one leaves, because each blue-eyed person is waiting to see if others will leave, and no one leaves.
• Day 2: All 100 blue-eyed people realize that they have blue eyes (because they saw that no one left on Day 1), and they all leave at midnight on Day 2.

Thus, the answer is that all 100 people with blue eyes will leave on Day 2 at midnight.

Here’s another complaint about a linguistics example. Unlike the last one, I am quite sure that at least one of the complaints I am going to make is accurate. And I think it probably has some actual bearing on the linguistic phenomenon in question.

This is from the literature on the principle of Maximize Presupposition–see Nadine Bade’s overview here. Maximize Presupposition, due to Heim (1991), is the principle (roughly) “Make your contribution presuppose as much as possible.” This explains why a sentence like
(1a) #All of John’s arms are broken
is bad or at least disconcerting. This sentence doesn’t presuppose that John has only two arms, while the alternative sentence
(1b) Both of John’s arms are broken
does presuppose that John has only two arms. And if John is a human, and not Zaphod Beeblebrox, he has no more than two arms. So “All of John’s arms are broken” doesn’t maximize presupposition, and it sounds bad.

So far so good! The problem is that an example that runs throughout the literature, going back to Heim and serving as the first example in Bade’s overview, is
(2a) #A father of the victim arrived at the crime scene.
Bade explains that since (2a) does not presuppose that the victim has a unique father, and that the alternative
(2b) The father of the victim arrived at the crime scene
does presuppose that the victim has a unique father, that the utterance of (2a) requires that it not be part of the common ground (since otherwise Maximize Presupposition would be violated). Bade says, “The resulting inference is contradictory to common knowledge…: the speaker does not believe that there is a unique father of the victim.”

But this inference is not contradictory to common knowledge, because the victim might have more than one father. Maybe it was not unreasonable to overlook this possibility in 1991. It is now! I could probably stop this post here, saying “Stop using an example that assumes that a person can only have one father!” (“The spleen of the cadaver was weighed” should work.) But I think there’s a little more to it.

Scenario: it’s common knowledge that Heather has two mothers (Mama Jane and Mama Kate). Georgie wants to know if Heather can come over. Georgie’s parent talks to Jane and says:
(3a) ???I talked to a mother of Heather’s.
OK, Georgie’s parent does not say that. Almost no native speaker would say that, I don’t think, even given the common knowledge that Heather has two mothers. Nor would Georgie’s parent say
(3b) #I talked to the mother of Heather
which is terrible six ways. What is normal is to say
(3c) I talked to Heather’s mother
(“Heather’s mom,” really) or, if it might important that the parent only talked to one
(3d) I talked to one of Heather’s mothers.

Now one issue here is that “a/the X of Heather” is horribly stilted. This is also true, to a lesser extent, in (2a/b); (2b) is not terrible, but usually I’d say “the victim’s father arrived at the crime scene.” (Also a problem in the version of (1b) Bade gives, “#All/Both arms of John are broken,” which I don’t find idiomatic either way.) We can get around this by using a multi-word phrase that can’t take the possessive ‘s.

Scenario: Heather has left her backpack at school. Both teacher and principal know that Heather has two mothers and that Heather left the backpack. The teacher talks to Kate, and tells the principal about it, in a context in which Heather’s having left her backpack is more relevant than her specific identity:
(4a) ?I talked to a mother of the girl who left the backpack.
This still sounds bad to me! Honestly I would rather say
(4b) I talked to the mother of the girl who left the backpack
because I think the definite description often just doesn’t presuppose uniqueness. “William is the son of the king of England” is fine. But if (4b) was unsatisfactory for some reason, I think the teacher would say
(4c) I talked to one of the mothers of the girl who left the backpack.

Even aside from same-sex parents, I often find “a” to be weird even when uniqueness isn’t presupposed. Substituting “parent” into (3a) doesn’t make it much better, and I think still leaves (4a) kind of sketchy. Or take this:
(5a) #The volume of The Lord of the Rings is called The Two Towers.
(5b) A volume of The Lord of the Rings is called The Two Towers.
(5c) One of the volumes of The Lord of the Rings is called The Two Towers.
Here (5a) is flat-out unacceptable, unless the context makes it clear that there is only one volume that could be relevant. (5b) is… not great, not terrible? It’s not disconcerting like (1a), but I would be much more likely to say (5c).

So if I have a tentative suggestion here, it’s that maybe the scale that is sometimes posited to explain Maximize Presupposition should be not <“a,” “the”> but <“a,” “one of the,” “the”>, where “one of the” presupposes that there aren’t many of the thing in question, more or less. That might explain why (3a) and (4a) are bad in terms of Maximize Presupposition; the alternatives with “one of the” presuppose that Heather doesn’t have very many mothers, and that’s an available presupposition.

But what I am certain of is that people should stop using (2a)/(2b) in ways that assume that the victim can’t have more than one father, because that’s not true.

[PS: Occupational hazard; earlier today I was thinking some very dark political thoughts in my interior monologue, and then I thought, “Hmm, the sentence I just thought to myself doesn’t satisfy Maximize Presupposition.”]

I wanted to post about the Rain Probability Gauge from Science Made Stupid by Tom Weller (out of print, hosted with Weller’s permission at https://drive.google.com/file/d/0B241HCXaGuT8TzZhYXNJS25EWEk/view?resourcekey=0-G5WyeyFZRFpq0CFMEkHiLQ), but the text is too long for me to alt-text on Twitter, so here it is in what I hope is accessible form!

Testing Rain for Probability

You’ve probably heard the weatherman predict a “30% chance” or a “70% probability” of rain. You can check the chance of rain having fallen for yourself with a back-yard rain probability gauge.

Let’s say it rained during the night. What were the chances of that rain occurring?

1. Check the gauge—which is marked in inches just like a regular rain gauge—for the level of rainwater, and mark it down. This represents the level of actual rainfall (which will always be the same as the level of probable rainfall.)

2. Next, check the level of nonprobable rainfall (which you can also think of as probable nonrainfall). Since nonprobable rain is lighter than probable rain, the nonrain will float on top of the rainwater.

Probabilites, of course, are invisible. To render them measurable, the rain probability gauge contains a probability float to mark the level of nonprobable rain. A probability float can be made of any material less probably than rain, and hence lighter. Except in very dry parts of the world, this presents no problem; an entry stub from the Publishers Clearing House Sweepstakes will do nicely. Alternatively, a few drops of statisticians’ ink can be added to the column to make it visible.

3. To the two levels, apply the formula actual rain divided by total probable & nonprobable rain = % chance

In the illustration, 3 inches of rain divided by 10 inches of norain gives .30, telling you that the three inches of rain that fell did so as a result of a 30% chance of rain.

[Illustration: a tube with markings. Water filling up the bottom three markings are labelled “Actual Rain.” Seven more empty markings are labelled “Non-Probable Rain.” A stub of paper at the top is labelled “Probability Float.”]

If it has not rained, and the gauge is dry, proceed as follows:

1. Mark down the level of the probability float.
2. From a watering can or garden hose, slowly add water to the column until the probability float starts to rise.
   This approach is based on the fact that the bottom of the gauge contains a certain level of probable rain, just as before, but without any actual water to make it visible. Since real rain must contain equal volumes of water and the probability of water, the probability in the bottom of the column will absorb just its own volume of the water you add, and no more.
3. Measure the level of water and the new level of the float.
4. Subtract from the water level a volume of water equal to the rise in the probability float, as this represents water in excess of the probability level.
5. Divide this figure by the total capacity of the gauge, thus deriving the odds from which your dry spell resulted.

I was trying to read Myron Orfield’s important University of Colorado Law Review article, “Deterrence, Perjury, and the Heater Problem,” and Westlaw’s incompetently designed website made me do about half an hour of browser wrangling before it allowed me to view it even though my university library pays for a subscription, so I thought I should perform a public service and upload it. It can be found at mattweiner.net/orfield. (The bibligraphic information is available at that link.)

Academic publishers exist to prevent people from viewing academic work and should be destroyed.

Excellent Twitter thread from Rachel McKinney on how too much of the discussion of trans rights in philosophy fails “to meet normal content-neutral standards of evidence-based inquiry.”

In the event that anyone wants to talk about anything epistemological here, go for it!

This by Samantha Hancox-Li, on formal free speech vs. having your testimony heard, is absolutely excellent.

Related, two threads from Johnathan Flowers on citation practices and what we are expected to listen to. Transphobic philosophers are publishing a lot of awful stuff–I don’t just mean morally awful, but just terrible arguments, like making a key empirical claim and repeatedly refusing to provide evidence for it, and far too many people are taking this seriously when it can’t pass muster.

As he says, the philosophers (often junior career philosophers) who push back on the transphobic philosophers have been forced to engage with their arguments in ways that the transphobic philosophers do not engage with the arguments of their opponents. Kathleen Stock has boasted about her refusal to engage with feminist philosophy. (If you think “I’ve read the literature in this area, I think this is bad, so I won’t cite it” counts as engagement, good luck getting published in any other area of philosophy. But philosophers don’t take expertise in feminist philosophy seriously.)

It’s exhausting to deal with this asymmetric burden of expectations on who’s supposed to do the work. It’s exhausting to me, and I’m not doing most of the work (partly because I refuse to join Twitter and so I publish at this blog, which basically nobody reads). I’ve stopped reading new Medium posts from the most prominent transphobic philosophers becasue I’ve read enough to be pretty confident that the next 10,000 word post rehashing the same stuff wasn’t going to be better; it’s folly to believe that they’re going to give some support for their assertion the sixth time. My support to the people who are out their pushing back against this, and shame on philosophers who are letting transphobic philosophers get away with shoddy work and ignoring the people who’ve put in the work.

(Matt Weiner, University of Vermont)

Occasionally I’ve seen people refer to a paper by Kathleen Stock as “I—Kathleen Stock: Fictive Utterance and Imagining.” In case this is confusing, the title of the paper is not analogous to “I, Robot,” but a Roman numeral. It’s from a proceeding of the Aristotelian Society, which tends to present twinned papers in the format “I–Author1: Title” and “II–Author2: Title” (I think maybe often the same title).

Also Rachel McKinney is right about this, this, and this. The POTFROTIs’ work in their endless Medium posts has been incredibly bad, and they aim to have a public effect! Nobody seems to be able and willing to point to the places where they provide actual evidence for their key claims about trans women being dangerous, as opposed to anecdotes. When this is done to immigrants we recognize it for what it is, I hope. It’s no better when it’s done to trans people.