Intuition Pumps and Other Tools for Thinking

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What is an Intuition Pump

Marcel Kinsbourne suggests that whenever we find thinking hard, it is because the stony path to truth is competing with seductive, easier paths that turn out to be dead ends. Most of the effort in thinking is a matter of resisting these temptations.

According to the story—and like most famous stories, this one has many versions—a colleague approached him one day with a puzzle that had two paths to a solution, a laborious, complicated calculation and an elegant, Aha!-type solution. This colleague had a theory: in such a case, mathematicians work out the laborious solution while the (lazier, but smarter) physicists pause and find the quick-and-easy solution. Which solution would von Neumann find? You know the sort of puzzle: Two trains, 100 miles apart, are approaching each other on the same track, one going 30 miles per hour, the other going 20 miles per hour. A bird flying 120 miles per hour starts at train A (when they are 100 miles apart), flies to train B, turns around and flies back to the approaching train A, and so forth, until the two trains collide. How far has the bird flown when the collision occurs? “Two hundred and forty miles,” von Neumann answered almost instantly. “Darn,” replied his colleague, “I predicted you’d do it the hard way, summing the infinite series.” “Ay!” von Neumann cried in embarrassment, smiting his forehead. “There’s an easy way!”

Hand Tools of the mind
Labels. Sometimes just creating a vivid name for something helps you keep track of it while you turn it around in your mind trying to understand it. Among the most useful labels, as we shall see, are warning labels or alarms, which alert us to likely sources of error. 
Examples. Some philosophers think that using examples in their work is, if not quite cheating, at least uncalled for—rather the way novelists shun illustrations in their novels. The novelists take pride in doing it all with words, and the philosophers take pride in doing it all with carefully crafted abstract generalizations presented in rigorous order, as close to mathematical proofs as they can muster. Good for them, but they can’t expect me to recommend their work to any but a few remarkable students. It’s just more difficult than it has to be. 
Analogies and metaphors. Mapping the features of one complex thing onto the features of another complex thing that you already (think you) understand is a famously powerful thinking tool, but it is so powerful that it often leads thinkers astray when their imaginations get captured by a treacherous analogy. 
Staging. You can shingle a roof, paint a house, or fix a chimney with the help of just a ladder, moving it and climbing, moving it and climbing, getting access to only a small part of the job at a time, but it’s often a lot easier in the end to take the time at the beginning to erect some sturdy staging that will allow you to move swiftly and safely around the whole project. Several of the most valuable thinking tools in this book are examples of staging that take some time to put in place but then permit a variety of problems to be tackled together—without all the ladder-moving.

reductio ad absurdum,1 in which one takes one’s opponents’ premises and derives a formal contradiction (an absurd result), showing that they can’t all be right. One of my favorites is the proof attributed to Galileo that heavy things don’t fall faster than lighter things (when friction is negligible). If they did, he argued, then since heavy stone A would fall faster than light stone B, if we tied B to A, stone B would act as a drag, slowing A down. But A tied to B is heavier than A alone, so the two together should also fall faster than A by itself. We have concluded that tying B to A would make something that fell both faster and slower than A by itself, which is a contradiction.

This is an incredible thought experiment. I'm in awe of you

Whimsical Jailer. Every night he waits until all the prisoners are sound asleep and then he goes around unlocking all the doors, leaving them open for hours on end. Question: Are the prisoners free? Do they have an opportunity to leave? Not really. Why not?
the importance of getting timely information about genuine opportunities, soon enough for the information to cause us to consider it in time to do something about it. In our eagerness to make “free” choices, uncaused—we like to think—by “external forces,” we tend to forget that we shouldn’t want to be cut off from all such forces; free will does not abhor our embedding in a rich causal context; it actually requires it.

When Doug Hofstadter and I composed The Mind’s I back in 1982, he came up with just the right advice on this score: consider the intuition pump to be a tool with many settings, and “turn all the knobs” to see if the same intuitions still get pumped when you consider variations. So let’s identify, and turn, the knobs on the Whimsical Jailer. Assume—until proved otherwise—that every part has a function, and see what that function is by replacing it with another part, or transforming it slightly. 1. Every night 2. he waits 3. until all the prisoners 4. are sound asleep 5. and then he goes around unlocking 6. all the doors, 7. leaving them open for hours on end. Here is one of many variations we could consider: One night he ordered his guards to drug one of the prisoners and after they had done this they accidentally left the door of that prisoner’s cell unlocked for an hour.

the philosophers’ favorite tactic: “going meta”—thinking about thinking, talking about talking, reasoning about reasoning. Meta-language is the language we use to talk about another language, and meta-ethics is a bird’s-eye view examination of ethical theories. As I once said to Doug, “Anything you can do I can do meta-.” This whole book is, of course, an example of going meta: exploring how to think carefully about methods of thinking carefully

My own intuition pumps
Basketball Hoop - It's hard to tell a basket from an airball without the net

Making Mistakes

Sometimes you don’t just want to risk making mistakes; you actually want to make them—if only to give you something clear and detailed to fix. Making mistakes is the key to making progress. Of course there are times when it is really important not to make any mistakes—ask any surgeon or airline pilot. But it is less widely appreciated that there are also times when making mistakes is the only way to go.

we philosophers specialize in all the ways there are of getting things so mixed up, so deeply wrong, that nobody is even sure what the right questions are, let alone the answers. Asking the wrongs questions risks setting any inquiry off on the wrong foot. Whenever that happens, this is a job for philosophers! Philosophy—in every field of inquiry—is what you have to do until you figure out what questions you should have been asking in the first place. Some people hate it when that happens. They would rather take their questions off the rack, all nicely tailored and pressed and cleaned and ready to answer. Those who feel that way can do physics or mathematics or history or biology. There’s plenty of work for everybody. We philosophers have a taste for working on the questions that need to be straightened out before they can be answered. It’s not for everyone. But try it, you might like it.

Evolution is one of the central themes of this book, as of all my books, for the simple reason that it is the central, enabling process not only of life but also of knowledge and learning and understanding. If you attempt to make sense of the world of ideas and meanings, free will and morality, art and science and even philosophy itself without a sound and quite detailed knowledge of evolution, you have one hand tied behind your back.

Many topics beckon back to evolution and that's interesting. For example The Nature of Value takes an evolutionary approach as well

The chief trick to making good mistakes is not to hide them—especially not from yourself. Instead of turning away in denial when you make a mistake, you should become a connoisseur of your own mistakes, turning them over in your mind as if they were works of art, which in a way they are.

Try to acquire the weird practice of savoring your mistakes, delighting in uncovering the strange quirks that led you astray. Then, once you have sucked out all the goodness to be gained from having made them, you can cheerfully set them behind you, and go on to the next big opportunity. But that is not enough: you should actively seek out opportunities to make grand mistakes, just so you can then recover from them.

Evolution works the same way: all the dumb mistakes tend to be invisible, so all we see is a stupendous string of triumphs. For instance, the vast majority—way over 90 percent—of all the creatures that have ever lived died childless, but not a single one of your ancestors suffered that fate. Talk about a line of charmed lives!

“BY PARODY OF REASONING”:
USING REDUCTIO AD ABSURDUM

The crowbar of rational inquiry, the great lever that enforces consistency, is reductio ad absurdum—literally, reduction (of the argument) to absurdity. You take the assertion or conjecture at issue and see if you can pry any contradictions (or just preposterous implications) out of it. If you can, that proposition has to be discarded or sent back to the shop for retooling. We do this all the time without bothering to display the underlying logic: “If that’s a bear, then bears have antlers!”

Rapoports Rules

How to compose a successful critical commentary: 
You should attempt to re-express your target’s position so clearly, vividly, and fairly that your target says, “Thanks, I wish I’d thought of putting it that way.”  
You should list any points of agreement (especially if they are not matters of general or widespread agreement).
You should mention anything you have learned from your target.  
Only then are you permitted to say so much as a word of rebuttal or criticism.

One immediate effect of following these rules is that your targets will be a receptive audience for your criticism: you have already shown that you understand their positions as well as they do, and have demonstrated good judgment (you agree with them on some important matters and have even been persuaded by something they said).

Sturgeon's Law

Sturgeon’s Law is usually put a little less decorously: Ninety percent of everything is crap.

A good moral to draw from this observation is that when you want to criticize a field, a genre, a discipline, an art form, . . . don’t waste your time and ours hooting at the crap! Go after the good stuff, or leave it alone. This advice is often ignored by ideologues intent on destroying the reputation of analytic philosophy, evolutionary psychology, sociology, cultural anthropology, macroeconomics, plastic surgery, improvisational theater, television sitcoms, philosophical theology, massage therapy, you name it. Let’s stipulate at the outset that there is a great deal of deplorable, stupid, second-rate stuff out there, of all sorts. Now, in order not to waste your time and try our patience, make sure you concentrate on the best stuff you can find, the flagship examples extolled by the leaders of the field, the prize-winning entries, not the dregs.

Occam's Razor

“Do not multiply entities beyond necessity.” The idea is straightforward: don’t concoct a complicated, extravagant theory if you’ve got a simpler one (containing fewer ingredients, fewer entities) that handles the phenomenon just as well.

Occam's Broom

Occam’s Broom, to describe the process in which inconvenient facts are whisked under the rug by intellectually dishonest champions of one theory or another.

Conspiracy theorists are masters of Occam’s Broom, and an instructive exercise on the Internet is to look up a new conspiracy theory, to see if you (a nonexpert on the topic) can find the flaws, before looking elsewhere on the web for the expert rebuttals. When Brenner coined the term, he wasn’t talking about creationism and conspiracy theories; he was pointing out that in the heat of battle, even serious scientists sometimes cannot resist “overlooking” some data that seriously undermine their pet theory. It’s a temptation to be resisted, no matter what.

Joosting

there are always scads of unexamined presuppositions of any theoretical set-to, but trying to negate them one at a time until you find a vulnerable one is not a good recipe for success in science or philosophy.

When you are confronting a scientific or philosophical problem, the system you need to jump out of is typically so entrenched that it is as invisible as the air you breathe. As a general rule, when a long-standing controversy seems to be getting nowhere, with both “sides” stubbornly insisting they are right, as often as not the trouble is that there is something they both agree on that is just not so. Both sides consider it so obvious, in fact, that it goes without saying. Finding these invisible problem-poisoners is not an easy task, because whatever seems obvious to these warring experts is apt to seem obvious, on reflection, to just about everybody. So the recommendation that you keep an eye out for a tacit shared false assumption is not all that likely to bear fruit, but at least you’re more likely to find one if you’re hoping to find one and have some idea of what one would look like.

Rhetorical Question

Just as you should keep a sharp eye out for “surely,” you should develop a sensitivity for rhetorical questions in any argument or polemic. Why? Because, like the use of “surely,” they represent an author’s eagerness to take a short cut. A rhetorical question has a question mark at the end, but it is not meant to be answered. That is, the author doesn’t bother waiting for you to answer since the answer is so flipping obvious that you’d be embarrassed to say it! In other words, most rhetorical questions are telescoped reductio ad absurdum arguments, too obvious to need spelling out. Here is a good habit to develop: Whenever you see a rhetorical question, try—silently, to yourself—to give it an unobvious answer. If you find a good one, surprise your interlocutor by answering the question. I remember a Peanuts cartoon from years ago that nicely illustrates the tactic. Charlie Brown had just asked, rhetorically, “Who’s to say what is right and wrong here?” and Lucy responded, in the next panel, “I will.”

TOOLS FOR THINKING ABOUT MEANING OR CONTENT

The first step in any effective exploration is to get as clear as we can about our starting point and our equipment. Words have meanings.

AN OLDER BROTHER LIVING IN CLEVELAND

Imagine we can implant beliefs into people's heads. Let's say we implant the single idea "You have an older brother in Cleveland" into the mind of an only child. What would we expect would happen when asked "Do you have any siblings?" What would we expect happen with every follow up question? What's his name? How old is he? The lesson here is a belief is highly tied with a number of other beliefs

What if we implanted multiple supporting beliefs?
How much probing would it take to unveil the truth?
At what point does the person begin to seek the evidence of the lie even though its true? "What did you do to my older brother?"
How possible is it to get back to the truth in the persons mind?
How easily would it be to spark back up the lie again after confirming the truth?

“DADDY IS A DOCTOR”

A young child is asked what her father does, and she answers, “Daddy is a doctor.” Does she believe what she says? In one sense, of course, but what would she have to know to really believe it? (What if she’d said, “Daddy is an arbitrager” or “Daddy is an actuary”?) Suppose we suspected that she was speaking without understanding, and decided to test her. Must she be able to produce paraphrases or to expand on her claim by saying her father cures sick people? Is it enough if she knows that Daddy’s being a doctor precludes his being a butcher, a baker, a candlestick maker? Does she know what a doctor is if she lacks the concept of a fake doctor, a quack, an unlicensed practitioner? For that matter, how much does she need to understand to know that Daddy is her father? (Her adoptive father? Her “biological” father?) Clearly her understanding of what it is to be a doctor, as well as what it is to be a father, will grow over the years, and hence her understanding of her own sentence, “Daddy is a doctor,” will grow. Can we specify—in any nonarbitrary way—how much she must know in order to understand this proposition “completely”? If understanding comes in degrees, as this example shows, then belief, which depends on understanding, must come in degrees as well, even for such mundane propositions as this. She “sorta” believes her father is a doctor—which is not to say she has reservations or doubts, but that she falls short of the understanding that is an important precondition for any useful concept of belief.

Unstarred

Dunk (exclude from study)

Intuition Pumps and Other Tools for Thinking

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