I studied epistemic logic and philosophy of language with Dr. Hintikka while a graduate student at Boston University in the early 1990s. He was a very impressive intellectual figure—the author of dozens of scholarly books and hundreds of articles. But I understood his passion in life to be rather simple: it was to teach people to think—not what to think, but how to think. As a logician, he could see how helpless most people are at the mechanics of thought, and he wanted to help them.
Today, on the first anniversary of his passing, I am honoring Dr. Hintikka‘s memory with the following comedic horror story. Its plot rests on one of his insights: that public knowledge is but the tip of an iceberg of confidential, privately shared knowledge. It’s not what you know that matters, but who else knows that you know what you know.
The genre of this piece is uncertain: it starts out as screenplay, then for the sake of brevity lapses into libretto. (It can be respun into a movie script or even a musical, should anyone so desire.) I hope that it entertains you, and that after reading it you will never think about epistemology (or werewolves) in quite the same way again.
An old-fashioned lecture hall. Present are Prof. Tlöm and a Chorus of nerds. Among the Chorus there is a werewolf. The professor is plump, bespectacled and disheveled. His annunciation is slow and deliberate, his voice reedy and keening, sometimes becoming high-pitched and shrill (for emphasis).
Tlöm: As some of you now realize (gloweringly) having seen your grades from the last term… what matters is not that you know what you know… (laboriously writes “KβS” on the blackboard) …but that I know that you know what you know. (Adds “Kα” to the front of the expression.) Of course, (chuckles mirthlessly) your destiny will remain a mystery to you unless you know… (adds “Kβ” to the front of the expression) …that I know that you know what you know.
Choir: (Chanting, quietly at first, then louder) I know that you know that I know that you know...
Tlöm: (Screeching) Shut up!… (the Choir simmers down reluctantly; Tlöm continues nonchalantly) But then of course, if we were to obtain the full benefit of this exercise (chuckles sardonically) which we call… fffformal education (these last two words are emitted as a groan accompanied by an eye-roll) …then I would also have to know…” (adds a final “Kα” to the front of the expression, then, in spite of himself, breaks into a syncopated rhythm) …that you know… that I know… that you know… what you know! (tosses the piece of chalk in the general direction of the Choir and crosses his arms triumphantly).
Choir: (Breaking in at full volume, ecstatically) We know that you know that we know that you know that we know that you know that we know… (the Choir continues chanting and carrying on; curtain/fade).
Our protagonist, Johnny, is living in the mid-1990s suburban United States. One of his neighbors is a werewolf who, once per lunar month, kills a jogger, does whatever it is werewolves like to do with joggers, and buries the body in a thickly wooded area nearby.
One night, while Johnny is walking his dog, the dog catches the werewolf in mid-burial and starts snarling and snapping at him. In hot pursuit after his best friend, Johnny is just about to burst on the scene when he sees and hears a steel shovel make contact with his poor dog’s head. He panics and freezes, and remains standing still behind some trees a short distance away.
The werewolf stoops down, slowly pets the dead dog while droning something mournful, then tosses the body on top of the one already resting in the freshly dug grave. Johnny tries to hyperventilate as quietly as possible, but at one point he starts to shake so much that a branch snaps underfoot. The werewolf stops shoveling, but only for a moment, and not so much to look around as to scratch himself and rearrange his underwear. Then, just as Johnny is about to defecate in his, he resumes his work.
Humming a dreary tune, the werewolf finishes filling the grave, then, humming a slightly cheerier one, jumps around on top of it for a while, throws a pile of leaves on it, and stomps off dragging the shovel. Only after he disappears in the distance does Johnny collapse on the pile of leaves, get into the fetal position and start whimpering.
Johnny finds himself at home some time after sunrise, in a mental fog, trying to remember what happened. In a flashback, he remembers walking home after spending the night shivering in a pile of leaves, and must have presented an amusing spectacle to busloads of schoolchildren who pointed at him and jeered. This rattles his nerves even more. Several Bloody Marys later his body regains some semblance of homeostatic equilibrium and the mental fog lifts somewhat.
To help himself think, he takes out a notepad and a pencil. He writes down: “Go to the police.” Then he grows pensive. Everyone saw him dazed and stumbling home from the woods early in the morning, looking like he had spent the night in a pile of leaves, which is what he had done, next to a fresh grave that contains the remains of his dog and who knows what else. His story is that he saw a werewolf. Not good. He crosses out “Go to the police.”
He is sure that the werewolf didn’t see him, but can’t decide whether he heard him or not. If he did, then he knows that someone was there, which he might suspect anyway by inferring from the fact that dogs are most often accompanied by their owners. “Does he know big words like ‘infer’?” Johnny wonders. He takes courage from this thought, and serves himself another drink. “He is just some kind of perverted degenerate who lets his shovel do his thinking,” Johnny mutters to himself as his world turns fuzzy and tingly. He decides that he has had enough, and takes to his bed.
While Johnny sleeps off the Bloody Marys, Wolfie (for that has been his moniker since childhood), now looking only very slightly werewolf-like, wakes up from a sound sleep a minute or two ahead of his alarm clock, as usual, but is chagrined to discover that he once again climbed into bed wearing clothing soiled from the previous evening’s adventure. After a quick shower, Wolfie helps himself to some breakfast, then proceeds to put everything in order, from laundry to boot shining. Once he is again perfectly at peace with his surroundings, Wolfie turns on the computer, dials up the internet, and gets to work promoting some sort of financial pyramid scheme in a desperate, destitute country halfway across the globe.
A few hours later Wolfie takes a break from his work and, to rest his eyes, gazes out the window. He sees a dog run by, followed some distance behind by the dog’s owner. Wolfie sees tags dangling from the dog’s collar. His heart skips a beat. “The dog I buried had tags on its collar,” he reasons. “It has an owner, who may have been following not far behind, witnessed what happened to the dog, and will get the police involved, who will then excavate my entire quaint little columbarium!” And then it would be time to move, again. Wolfie doesn’t like the idea of moving. It takes time to arrange one’s recreation in a new place, and Wolfie values his time. No, he will not be dislodged by some ill-founded paranoia over a dead dog!
“If I knew who the owner was, then… depending on whether he was there and saw me well enough to identify me (a remote possibility, given my appearance at the time) or whether he just witnessed what happened to the dog, or whether he only knows that his dog has disappeared…” Wolfie reaches for a pencil and a piece of paper, to draw a diagram. A few circles and arrows later, he is stuck.
Then he remembers that he studied the math for this sort of thing, but hasn’t so much as looked at it since school. He walks over to a bookshelf and pulls out Conspiracy Theory by Prof. P.D.Q. Tlöm. “Ah, good old Professor Tlöm…” thinks Wolfie, blowing the dust off the compact little tome. “Remember not to bite down too hard when speaking tongue-in-cheek, professor!” He chuckles heartily, misty over the remembrance of his eager school days. “Now then, let’s see what bit of scholarly thunder good old Tlöm saved up for this particular situation…” Wolfie opens the book to a dog-eared page and runs down the list of formulas, pointing an index finger at each formula and carefully reading out its verbal interpretation.
“If you know that a certain person knows a certain fact, then this implies that you know that this person actually exists.”
“If you know that a certain person doesn’t know a certain fact, then this still implies that you know that this person actually exists.”
“If you don’t know whether a certain person knows a certain fact, then that still implies that you know that this person actually exists.
“If you only know that a certain thing exists, that doesn’t mean that you know what it is.”
“If there actually exists something that you know to correspond to a certain thing that you know of, then you actually know what this thing is.”
“If you only know that a certain person exists, that doesn’t mean that you know who this person is.”
“If there actually exists someone whom you know to be a certain person, then you know who that person is.”
“If you know that a certain thing exists and if it is officially identified as such, then you actually know what this thing is.”
“If you know that a certain person exists and is officially identified as such, then you know who that person is.”
No Ignorance of Ignorance
“If you don’t know that somebody knows something, then neither do you know that this somebody doesn’t know this something.”
No Partial Ignorance
“If you know that somebody else knows something, that implies that you yourself know this something.”
“If you know that somebody else knows that something exists, that implies that you yourself know that this something exists.”
“If you know that somebody else knows that you know that this somebody else knows something, then it can be said that you both know it.”
“If you know that somebody else knows that you know that this somebody else knows that something exists, then it can be said that you both know that it exists.”
Wolfie stares at the page, ruminating, then sits back, brow furrowed. Then he crumples up and tosses away the useless page of circles and arrows, and starts over.
First, the obvious. I know that my columbarium exists.”
“I also have reason to suspect that you, my dogless friend, exist, but I don’t know who you are:
“To find out who you are, I need Iβ: the information on the dog’s tags. There are also many other things which I do not know. I don’t know whether you know about the grave,
“I don’t know whether you know that I exist,
“…and if you do, I don’t know whether you know who I am:
“Unless I can find out whose dog that was, I don’t have a game. I must get that dog’s tags and figure out who the owner is. The only safe time to do that is at night.”
Wolfie types “date” into the command line on his virtual terminal program to find out what time it is, realizes that it’s lunchtime, and decides to go out. He has a new car that needs exercise, and there is a ritzy little village nearby that just opened a new vegetarian café. Who knows, maybe there is a waitress there would want to drive over later for a glass of Riesling and some safe sex?
Not so much to indulge his paranoia as to exercise his car, Wolfie makes a few laps through the area, and observes that there is no unusual police activity. All is quiet around the wooded area where his columbarium is situated. Calmly, he drives to the café and parks in its ample parking lot.
While waiting for his food, he grows reflective. Why does he choose to do his dirty deeds right here in this area? Why doesn’t he just fly to some impoverished country once a month and pay whatever it takes to do whatever he wants to do? “But those people,” Wolfie thinks, “they struggle for their livelihood, and not just for themselves, but for their families, their children. They have integrity. I can respect them as animals. These suburban joggers, on the other hand, are too mild and tepid. They are so superficial in their relationships that no-one cares or suffers much when they disappear. They are like cattle on a farm,” Wolfie thinks while thoughtfully masticating his tofu avocado and watercress on organic stone-ground multigrain artisanal bread.
Back at the house, it is finally dusk, and Wolfie dons his gravedigger garb: overalls, boots, work jacket, shovel. By the time he arrives at the columbarium, it is quite dark. All is peaceful and quiet, and nothing has been disturbed. Being neither lazy nor squeamish, Wolfie doesn’t mind the work. And there is the dog, and there are the tags, and there is Wolfie taking them off and pocketing them. The reburial and the stroll home proceed uneventfully.
Just as Wolfie is getting done cleaning up and putting his grave-digging gear in order, Johnny wakes up in his bed, hung over, with a pounding headache. The night spent shivering on a pile of leaves, the rattled nerves and the serial Bloody Marys all conspired to make him less than an entirely healthy specimen. He realizes that he skipped work, and didn’t even call in sick. Not exactly an alibi.
After a shower and something vaguely food-like out of the microwave oven, Johnny tries to think. In all likelihood, he is a prime suspect in a murder which is going to be investigated. Numerous people can place him near the time and the place of the crime in a disheveled and deranged state. His story, if he chooses to tell it, is that he saw a werewolf digging a grave. It seems that his best bet is to keep quiet and hope for the best. But then, if they find and dig up the grave, the tags on his dog’s collar will lead them directly to him! How would he plead then? Of course, if there are no tags on the dog… He is quite sure that he didn’t see the werewolf take them. If he did, the police would find it harder to find him, but the werewolf would find it easier! A chilling thought. “Oh, but I am sure that the generate is too dumb for this kind of logic,” Johnny thinks, trying to comfort himself.
After some thinking and pacing around in circles, Johnny finally decides that he must act. He must make sure that his dog’s tags are not in that grave. By the time he reaches this conclusion only a few hours remain before sunrise. He looks for a shovel. The best he is able to come up with is a red plastic snow shovel with a cracked handle. With it, he sets off for the patch of woods. Once there, the work proceeds slowly. It had rained and the soil is saturated with water. He keeps getting splinters from the shovel’s cracked handle, and the red plastic blade is slowly but surely coming apart. The first thing he encounters is something too big to be a dog neatly wrapped in contractor-grade garbage bags. Trying not to lose his footing, he probes around in the pit and finds his dog, buried head up. There are no tags on the dog’s collar.
Johnny’s first panicked thought is, “He is here somewhere! He is watching me!” He freezes and listens. All is quiet except for a few birds’ anticipation of dawn. He is running out of time. He covers up the grave as best he can and heads home just as the sky is turning blue. He drops the nearly destroyed shovel and the mud-encrusted jacket in the garage, showers, shaves, dresses, and drives to work.
Wolfie executes his usual morning routine with the effortless precision of a well-oiled machine. But instead of sitting down to work, he does a bit of investigating. First he calls the town’s Dog Officer: “Excuse me, there was a neighbor’s dog running around my yard, and it caused some damage. I’d like to discuss that with the owner, but I don’t know who the owner is. But I do have the tag number: it’s A-1523… Thank you!” Wolfie grins as he writes down Johnny’s full name, address and phone number. “Iβ!”
The next step is a house call. Wolfie strolls over to Johnny’s place, which is only a block away. Peering in through the window of the garage, he notices a snow shovel and a jacket, both encrusted with fresh, wet mud. “Ah, my dogless friend, you’ve been busy, haven’t you,” Wolfie thinks, frowning. (Wolfie takes a dim view of amateurs who disturb his graves.) “Your result is probably unacceptable; I will have to make another trip to the columbarium tonight,” he resolves.
Back at his desk, Wolfie updates the formulas. “Let’s see who knows what now… I know who you are:
“But I still don’t know whether you know who I am:
“Since you dug up the grave and found the dog tags missing, you know that I have the tags, and so you know that I know who you are:
“I know that you know about the current state of the grave:
“But I am sure that you don’t realize that I know that you know about it:
“Now, why didn’t you go straight to the police? Why did you go back and dig? Probably to get the tags. Was that because you are afraid that the police would consider you a prime suspect, or because you are afraid that I would use the tags to figure out who you are and get rid of you because you are a witness; or both? To solve this riddle, I need to know whether or not you are a witness. If you are a witness, I’ll have to get rid of you. But if you are not a witness, I should let the police do their job. Do you know who I am? I think it’s time for a nice friendly chat.”
Johnny’s workday is uneventful. Somewhat disconcertingly, no-one noticed his absence the previous day. He stays in his cubicle and pretends to be busy by making intermittent noises with his adding machine. The only unnerving moment occurs when a co-worker he’s been trying hard to befriend comes over and, making a feeble attempt at small talk, asks him: “How’s your doggy doing?” His strained and inexplicable reply is “Oh, just fine, thank you!” He then attempts to smile. The result is a grimace so ghastly that his co-worker just drops the conversation and walks off.
Home once again, Johnny decides that going into deep denial about his dog’s death is stupid and will only get him into more trouble. No more denial! His dog is gone, and the world will find that out one way or another. It… ran away. Fine! Good story.
Shortly after dinner, which consists of yet another vaguely food-like petroleum-based spin-off of radar technology, and just as Johnny is settling down to watch a television broadcast about people who accept marital advice from stuffed animals whom they believe to be extraterrestrials, the doorbell rings. Johnny surprises himself by not jumping out of his seat and walks over to the door while trying to wrest control of his adrenal glands. It’s Wolfie, looking almost entirely unlike a werewolf, and working hard at being charming:
“I am sorry to disturb you. I am a neighbor, and apparently your dog…” (he looks around) “…by the way, where is your dog?… In any case, your dog has dug up some flower beds in my garden. It’s a very minor matter, the landscaping crew will be happy to work a few extra hours, but I just thought I’d bring it to your attention, because perhaps it isn’t such a good idea to let that dog roam free. By the way, where is the dog?”
In spite of his uneasiness about the subject, Johnny feels relieved. Also, Wolfie’s charm is working. Johnny wants to tell him a story that he likes, so that they can both believe it. “He ran away,” he says with determination.
“Oh, I am sorry. How awkward to bring it up at such a time. But how could I have known? Have you reported it?” Johnny starts and is suddenly speechless. “To the police, I mean…”
“No, no, no I haven’t,” he finally stammers. His mind is blank.
“Well, it may not be such a bad idea… Of course, that’s entirely up to you.”
“He might come back in a day or two.”
“Of course, of course! Let’s not give up hope. Well, I don’t want to take up any more of your time. Good night.”
“Good night. Oh, and thank you!”
Just for the sake of thoroughness, Wolfie updates his formulas in light of recent events.
“Now then, I know exactly who you are…
“…and I now know that you don’t know who I am.
“Since you dug up the grave and found the tags missing, you know that I have the tags, so that you know that I know who you are
“I know that you know about the current state of the grave…
“…and I am sure that you don’t realize that I know that you know about it.
“Also, you don’t seem terribly eager to talk to the police. You took the extreme measure of digging up the grave to get the tags because you thought that with the tags on the dog you would be found guilty. Therefore, if I put the tags back on the dog, you will probably be found guilty. Since my columbarium is now compromised, I will now have to relocate in any case, and it would be most helpful not to leave any unsolved cases behind.”
“You thanked me!” thinks Wolfie while walking toward the grave a few hours later. He is touched. Like most monsters, he is sentimental. For a moment he is overcome with guilt and pity and maybe even remorse, and stands looking up into the dark sky, waiting for the tears that welled up in his eyes to dry. He sighs, and feels good once more; refreshed, even.
The grave is as big a mess as he suspected. Luckily, no-one seems to have visited it since Johnny’s exertions. Wolfie excavates it far enough to get at the dog’s head and reattaches the tags to the collar. Then he fills the grave, but instead of stomping it flat he erects a large, prominent funeral mound and adorns it with a makeshift cross which he fashions out of a couple of sticks and a piece of twine. “The good thing about murders which the authorities find easy to solve,” he reasons, “is that it is virtually impossible for the guilty party to ever stand accused of them.”
The story briefly appears on television news a week or so later.
A thorough excavation of the wooded area produces a plethora of forensic material. People’s Exhibit #1 is a red plastic snow shovel found in Johnny’s garage, matching pieces of which were found mixed into the soil over the grave.
A team of criminologists has a frustrating time probing Johnny’s unconscious, unable to comprehend how it is possible that none of his many crimes left any trace in his mind. They consider naming a syndrome after him, but then decide to name it after one of the criminologists instead (leaving at least one other criminologist jilted).
At Johnny’s trial, Wolfie briefly appears in the jury box, but is dismissed after he expresses well-founded apprehensions regarding his potential lack of objectivity due to his personal knowledge of the defendant, and of the defendant’s dog.
What a shaggy dog story!
So essentially, Johnny goes to jail because nobody believes in werewolves... hmmm...he might have reported the dog missing as soon as he realized the tags might be on him. People don't usually kill their own dogs. It was the bits of plastic shovel and the muddy clothes that did him in. Too many Bloody Marys. All throughout that Warren Zevon song kept playing in my head. Ah-rooo!
Funny story Dmitry. You're a wonderful writer.
Rinse and repeat endlessly. The War on Terror in a nutshell. The werewolves live among us now, hiding in plain sight, knowing they'll never be found out, since only raving loons believe in werewolves. I'm one of those raving loons.
But it doesn't really affect the way people naturally (and effectively, in small matters) navigate the local world -- stratagems & rules-of-thumb generally based on experience, prejudice, and seat-of-pants fuzzy logic, strongly skewed by early childhood troubles & neural darwinism -- ie the fact that 'Clumps of neurons that have partied together in the past Find Ways to restimulate themselves & thus keep themselves nourished.'
On larger matters, the commandment is Thou Shalt Not Be Unreasonable!' 'Reasonable' means 'expressed and assumed-true on national television.' Expressing beliefs that are not taken for granted in tv news or Gee-Whiz Scientism educational shows will quickly get one classified as 'Nutcase.'
So it doesn't just come down to whether you know that you know what you're talking about. Yes, there's some advantage to having people know-that-you-know -- but what you know can still be 'unreasonable' if the bulk of tv coverage is agin it.
Where this sort of thing really impacts thinking is the question: "When is it 'reasonable' to 'know what you know', to believe that you know that you know, etc." When there are too many things one knows but mustn't think, one is soon ready for The Little Fearmongers Shop... and when too many people start feeling that way...?
Frighteningly funny - wish my Logic 101 course back in the '60s had been even half as relevant and engaging. Also wish this story wasn't quite so relevant to our manifest societal cognitive fog facing the current crop of monsters, victims, patsies, and other-world officialdom. Thanks Dimitry - we owe you for these threads of sanity you keep offering. Up to us to follow them to their logical conclusions...
Best moment is "These people are so mild & tepid" while his sanitized alter ego blends in and eats their frou-frou sandwich... And it's vegetarian too!
I can't believe I'm still thinking about this. Why couldn't Johnny have contacted the police? After all, he had nothing to hide...
That's a joke. Lolol.
Wow Dmitry; that was quite a trip.
However, being one who lives a somewhat intuitive life; I couldn't possibly live like that.
Far too analytical for the likes of me...
Logical mistake :
1) Johnny never leave his dog before he had been killed by Wolfie.
2) So Johnny knows that his dog never destroyed the garden of that guy.
3) Now Johnny knows who is the werewolf.
4) He knows as well that the werewolf knows who he is.
=» He surely realise that he has something to do if he doesn't want to be killed by the werewolf or accused by the police. =» Tell the police or kill wolfie the werewolf now that he knows who he is.
Excuse my english I'm french.
Did not know that Hintikka had died. Sad.
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