Disguised Queries

Imag­ine that you have a pe­cu­liar job in a pe­cu­liar fac­tory: Your task is to take ob­jects from a mys­te­ri­ous con­veyor belt, and sort the ob­jects into two bins. When you first ar­rive, Su­san the Se­nior Sorter ex­plains to you that blue egg-shaped ob­jects are called “bleggs” and go in the “blegg bin”, while red cubes are called “rubes” and go in the “rube bin”.

Once you start work­ing, you no­tice that bleggs and rubes differ in ways be­sides color and shape. Bleggs have fur on their sur­face, while rubes are smooth. Bleggs flex slightly to the touch; rubes are hard. Bleggs are opaque; the rube’s sur­face slightly translu­cent.

Soon af­ter you be­gin work­ing, you en­counter a blegg shaded an un­usu­ally dark blue—in fact, on closer ex­am­i­na­tion, the color proves to be pur­ple, halfway be­tween red and blue.

Yet wait! Why are you call­ing this ob­ject a “blegg”? A “blegg” was origi­nally defined as blue and egg-shaped—the qual­ifi­ca­tion of blue­ness ap­pears in the very name “blegg”, in fact. This ob­ject is not blue. One of the nec­es­sary qual­ifi­ca­tions is miss­ing; you should call this a “pur­ple egg-shaped ob­ject”, not a “blegg”.

But it so hap­pens that, in ad­di­tion to be­ing pur­ple and egg-shaped, the ob­ject is also furred, flex­ible, and opaque. So when you saw the ob­ject, you thought, “Oh, a strangely col­ored blegg.” It cer­tainly isn’t a rube… right?

Still, you aren’t quite sure what to do next. So you call over Su­san the Se­nior Sorter.

“Oh, yes, it’s a blegg,” Su­san says, “you can put it in the blegg bin.”
You start to toss the pur­ple blegg into the blegg bin, but pause for a mo­ment. “Su­san,” you say, “how do you know this is a blegg?”
Su­san looks at you oddly. “Isn’t it ob­vi­ous? This ob­ject may be pur­ple, but it’s still egg-shaped, furred, flex­ible, and opaque, like all the other bleggs. You’ve got to ex­pect a few color defects. Or is this one of those philo­soph­i­cal co­nun­drums, like ‘How do you know the world wasn’t cre­ated five min­utes ago com­plete with false mem­o­ries?’ In a philo­soph­i­cal sense I’m not ab­solutely cer­tain that this is a blegg, but it seems like a good guess.”
“No, I mean...” You pause, search­ing for words. “Why is there a blegg bin and a rube bin? What’s the differ­ence be­tween bleggs and rubes?”
“Bleggs are blue and egg-shaped, rubes are red and cube-shaped,” Su­san says pa­tiently. “You got the stan­dard ori­en­ta­tion lec­ture, right?”
“Why do bleggs and rubes need to be sorted?”
“Er… be­cause oth­er­wise they’d be all mixed up?” says Su­san. “Be­cause no­body will pay us to sit around all day and not sort bleggs and rubes?”
“Who origi­nally de­ter­mined that the first blue egg-shaped ob­ject was a ‘blegg’, and how did they de­ter­mine that?”
Su­san shrugs. “I sup­pose you could just as eas­ily call the red cube-shaped ob­jects ‘bleggs’ and the blue egg-shaped ob­jects ‘rubes’, but it seems eas­ier to re­mem­ber this way.”
You think for a mo­ment. “Sup­pose a com­pletely mixed-up ob­ject came off the con­veyor. Like, an or­ange sphere-shaped furred translu­cent ob­ject with writhing green ten­ta­cles. How could I tell whether it was a blegg or a rube?”
“Wow, no one’s ever found an ob­ject that mixed up,” says Su­san, “but I guess we’d take it to the sort­ing scan­ner.”
“How does the sort­ing scan­ner work?” you in­quire. “X-rays? Mag­netic res­o­nance imag­ing? Fast neu­tron trans­mis­sion spec­troscopy?”
“I’m told it works by Bayes’s Rule, but I don’t quite un­der­stand how,” says Su­san. “I like to say it, though. Bayes Bayes Bayes Bayes Bayes.”
“What does the sort­ing scan­ner tell you?”
“It tells you whether to put the ob­ject into the blegg bin or the rube bin. That’s why it’s called a sort­ing scan­ner.”
At this point you fall silent.
“In­ci­den­tally,” Su­san says ca­su­ally, “it may in­ter­est you to know that bleggs con­tain small nuggets of vana­dium ore, and rubes con­tain shreds of pal­la­dium, both of which are use­ful in­dus­tri­ally.”
“Su­san, you are pure evil.”
“Thank you.”

So now it seems we’ve dis­cov­ered the heart and essence of bleg­gness: a blegg is an ob­ject that con­tains a nugget of vana­dium ore. Sur­face char­ac­ter­is­tics, like blue color and furred­ness, do not de­ter­mine whether an ob­ject is a blegg; sur­face char­ac­ter­is­tics only mat­ter be­cause they help you in­fer whether an ob­ject is a blegg, that is, whether the ob­ject con­tains vana­dium.

Con­tain­ing vana­dium is a nec­es­sary and suffi­cient defi­ni­tion: all bleggs con­tain vana­dium and ev­ery­thing that con­tains vana­dium is a blegg: “blegg” is just a short­hand way of say­ing “vana­dium-con­tain­ing ob­ject.” Right?

Not so fast, says Su­san: Around 98% of bleggs con­tain vana­dium, but 2% con­tain pal­la­dium in­stead. To be pre­cise (Su­san con­tinues) around 98% of blue egg-shaped furred flex­ible opaque ob­jects con­tain vana­dium. For un­usual bleggs, it may be a differ­ent per­centage: 95% of pur­ple bleggs con­tain vana­dium, 92% of hard bleggs con­tain vana­dium, etc.

Now sup­pose you find a blue egg-shaped furred flex­ible opaque ob­ject, an or­di­nary blegg in ev­ery visi­ble way, and just for kicks you take it to the sort­ing scan­ner, and the scan­ner says “pal­la­dium”—this is one of the rare 2%. Is it a blegg?

At first you might an­swer that, since you in­tend to throw this ob­ject in the rube bin, you might as well call it a “rube”. How­ever, it turns out that al­most all bleggs, if you switch off the lights, glow faintly in the dark; while al­most all rubes do not glow in the dark. And the per­centage of bleggs that glow in the dark is not sig­nifi­cantly differ­ent for blue egg-shaped furred flex­ible opaque ob­jects that con­tain pal­la­dium, in­stead of vana­dium. Thus, if you want to guess whether the ob­ject glows like a blegg, or re­mains dark like a rube, you should guess that it glows like a blegg.

So is the ob­ject re­ally a blegg or a rube?

On one hand, you’ll throw the ob­ject in the rube bin no mat­ter what else you learn. On the other hand, if there are any un­known char­ac­ter­is­tics of the ob­ject you need to in­fer, you’ll in­fer them as if the ob­ject were a blegg, not a rube—group it into the similar­ity cluster of blue egg-shaped furred flex­ible opaque things, and not the similar­ity cluster of red cube-shaped smooth hard translu­cent things.

The ques­tion “Is this ob­ject a blegg?” may stand in for differ­ent queries on differ­ent oc­ca­sions.

If it weren’t stand­ing in for some query, you’d have no rea­son to care.

Is athe­ism a “re­li­gion”? Is tran­shu­man­ism a “cult”? Peo­ple who ar­gue that athe­ism is a re­li­gion “be­cause it states be­liefs about God” are re­ally try­ing to ar­gue (I think) that the rea­son­ing meth­ods used in athe­ism are on a par with the rea­son­ing meth­ods used in re­li­gion, or that athe­ism is no safer than re­li­gion in terms of the prob­a­bil­ity of causally en­gen­der­ing vi­o­lence, etc… What’s re­ally at stake is an athe­ist’s claim of sub­stan­tial differ­ence and su­pe­ri­or­ity rel­a­tive to re­li­gion, which the re­li­gious per­son is try­ing to re­ject by deny­ing the differ­ence rather than the su­pe­ri­or­ity(!)

But that’s not the a pri­ori ir­ra­tional part: The a pri­ori ir­ra­tional part is where, in the course of the ar­gu­ment, some­one pulls out a dic­tio­nary and looks up the defi­ni­tion of “athe­ism” or “re­li­gion”. (And yes, it’s just as silly whether an athe­ist or re­li­gion­ist does it.) How could a dic­tio­nary pos­si­bly de­cide whether an em­piri­cal cluster of athe­ists is re­ally sub­stan­tially differ­ent from an em­piri­cal cluster of the­olo­gians? How can re­al­ity vary with the mean­ing of a word? The points in thingspace don’t move around when we re­draw a bound­ary.

But peo­ple of­ten don’t re­al­ize that their ar­gu­ment about where to draw a defi­ni­tional bound­ary, is re­ally a dis­pute over whether to in­fer a char­ac­ter­is­tic shared by most things in­side an em­piri­cal cluster...

Hence the phrase, “dis­guised query”.