1. Meta Pattern: Probability - The likelihood that something will occur again based on its past performance (measured by
occurrences ÷ opportunities).
A. The more something occurs the more we believe it will occur again. B. If something which is not very probable occurs it tends to validate the cause-effect belief which predicted it.
2. Verification of a Consequence - If a particular belief (B) implies a particular consequence (C) and we verify that consequence then it makes the belief more plausible (it does not prove it however). The degree of plausibility will be stronger if there is a lack of other probable causes.
IF B implies C AND C is true THEN B is more credible.
A. Successive Verification of Several Consequences.
B. Verification of an Improbable Consequence (Extremes).
3. Contingency - If a belief (B) presupposes (or requires as a pre- condition) some event or phenomenon and we verify this contingent event (C) then it makes the belief more plausible. The degree of plausibility will be stronger if the contingent phenomenon would not probably occur in and of itself.
IF B presupposes C AND C is true THEN B is more credible.
4. Inference from Analogy - A belief (B) is more plausible if an analogous conjecture (A) is proven true. If the analogy cannot be shown to be true but it can be shown to be credible then it still increases the plausibility of the analogous belief.
IF B is analogous to A AND A is true THEN B is more credible.
5. Disprove the Converse - The plausibility of a belief (B) increases if a rival conjecture (C) is disproved.
IF B is competing with C AND C is false THEN B is more credible.
6. Comparison with Random - If a belief can be shown to predict a particular result with better than random accuracy then it is more
credible.
*G. Polya, Mathematics and Plausible Reasoning Vol. II, Patterns of Plausible Inference, Princeton University Press, 1968
The first pattern is quite straightforward. It’s called the “pattern of
probability,” and it is simply the perceived likelihood that something will occur again based on its past performance, measured by occurrences divided by opportunities. In other words, the more that something occurs, the more we believe it will occur again.
By way of illustration, let’s say you go out on a date and you bring flowers to the person with whom you’re going out. You go out with them a second time, and you bring them flowers again. You go out with them a third time, and again you bring them flowers. The fourth time you go out with them, you bring them flowers yet again. Finally, you go out with them a fifth time, but this time you don’t bring them flowers. The response you get on that fifth date is likely to be something along the lines of, “Hey, where are my flowers? There’s something wrong here. I’m supposed to get flowers.” Thus, the more often something happens, the more likely we are to believe it will happen again.
Let’s look at number two, “verification of a consequence.” This pattern states that the verification of a consequence of a conjecture renders the conjecture more plausible. In other words, if a particular belief, B, implies a particular consequence, C, and you verify that C is true, that makes B more plausible. It’s important to note that the verification does not prove that B is actually true; it merely increases the plausibility of B. Also, the degree of plausibility will be greater if there is a lack of other probable causes for B.
The third pattern, closely related to the previous one, is called “successive verification of several consequences.” This pattern is the same as the previous one except that instead of verifying just one consequence, you verify several in a row. Thus, suppose that B implies C, D, E, and F. If you then verify that C, D, E, and F are all true, that makes B even more plausible than if you had verified only C. Each time another consequence is verified, B’s plausibility increases.
The fourth pattern is called “verification of an improbable consequence.” This one says that if something that is not very probable occurs, that occurrence tends to validate the cause effect belief that predicted it.
An example of this that I like to use comes from the work of Anthony Robbins. I used to work for Anthony Robbins and I’ve done a lot of fire walks with him. A fire walk is a fascinating thing because everyone has the belief that when we touch fire, we get burned. It’s amazing, then, to walk across hot coals and not get burned. Because that outcome is so unlikely to occur, it really does tend to validate all the cause-effect beliefs that Anthony has set up to prepare his students for the fire walk.
Another example I like to use is that of acupuncture. A lot of people believe acupuncture, and the reason they believe it is because they’ve had a verification of the improbable consequence. They go to an acupuncturist and are told that, “You have a headache, so I’m going to stick this needle in your foot. And
going to make your headache go away.”
Obviously, that doesn’t make any sense. You can’t perform an autopsy on a cadaver and point out the meridian lines. They’re not there. We’ve got nerves; we’ve got bones; we’ve got veins. You can see those things, but where’s the meridian line? It doesn’t seem to exist, right? So it’s not likely that anything is going to happen when the needle gets stuck in your foot.
But then the needle gets stuck in your foot and your headache does goes away. So you’ve verified the improbable consequence. The inference that many people tend to draw based on experiences like this is that you must really have meridians after all, and the whole acupuncture thing must be true.
Incidentally, people have gone so far as to have major surgery done using acupuncture as the only anesthetic. It would be hard to imagine a more
dramatically improbable consequence than that, so when it does indeed turn out successfully, it greatly increases the plausibility of whole explanatory apparatus of acupuncture that predicted it.
The fifth pattern is called “contingency.” This one says that if a belief presupposes or requires as a pre-condition some event or phenomenon and we verify that pre-condition, then it makes the belief more plausible. The degree of plausibility will be stronger if the contingent phenomenon would not probably occur in and of itself.
A variation of this pattern is used all the time in criminal prosecutions. Suppose, for example, that believe a particular person committed the crime. Suppose further that in order for them to have committed the crime, a certain pre- condition would have to have occurred. The verification of that pre-condition increases the plausibility of the belief that they did indeed commit the crime.
Now, Alice is a nice lady who has no criminal record and has never done
anything wrong in her life. Our initial reaction might be that she couldn’t possibly have done this horrible thing. Besides, where would she get the explosives? However, if the prosecution comes up with a receipt from Explosives ‘R Us showing that Alice did in fact buy explosives, that evidence increases the plausibility of the belief that she really was guilty after all.
The sixth pattern is called “inference from analogy.” According to this pattern, a belief, B, be is more plausible if an analogous belief, A, is proven to be true. If the analogy cannot be shown to be true, but it can be shown to be
credible – i.e., plausible – then it still increases the plausibility of the analogous belief. It’s interesting that much of science is based on analogy. This is because so much of scientific research employs animal testing, and animal testing is depends upon analogy.
Test animals have certain biological features that are similar to our own. Still, lab rats are not humans. Despite these similarities, they’re still different from us in many ways. That’s why the use of test animals is an analogy. If you give drug X to a rat and he has a particular response, the inference is that it’s very likely humans will have the same response. So if you can prove the analogy, it makes the belief more plausible.
The seventh pattern is called “disproving the converse.” This pattern says that the plausibility of a belief increases if a rival belief is disproven. Now this, of course, works best when there are only two competing beliefs. If B is competing with C and C is proven false, then B becomes more plausible. This happens all the time in politics. We often hear candidates say, in effect, “Vote for me. I’m not him. He’s bad; he’s wrong. Therefore, I must be good.” The fact that this
approach works so well is why we have such negative campaigning.
There was an election not too long ago, I believe in New Jersey, where candidate A was running pretty solely on the platform, “Vote for me because my
opponent, candidate B, is a crook.” Interestingly, candidate A was right; his opponent was a crook. When that fact came to light, candidate B withdrew from the race. Of course, that meant that candidate A had no more platform. His whole campaign had been, “I’m not the other guy.” Suddenly, the other guy was gone.
The opposing party then replaced the withdrawn candidate with someone better who actually had a track record and was a good guy. Candidate A had spent all his money on advertising that said, “I’m not candidate B.” He did succeed in proving he wasn’t candidate B, but with B out of the picture A had nothing left to offer, and he lost the election.
The eighth and final pattern is called “comparison with random.” This pattern also is used in science a great deal. It says that if a belief can be shown to predict a particular result with better than random accuracy, the plausibility of that belief is increased.
Now that we’ve learned the Polya Patterns, let’s have a little fun with them. I’m going to present a couple of test questions and you’re going to try to figure out which Polya pattern is being represented.
In the first one there are actually two patterns, so see if you can get both of them. Here are the facts for the first question: “In order to prove Dr. Rathbone and not Dr. Firsthammer, turned into the Incredible Green Monster last weekend, Dr. Firsthammer’s assistant examined footage from the security cameras at the Witch’s Supply Store. To his surprise, he found a video with images of Dr. Firsthammer buying dried newts.” Which patterns did you spot?”
Question number two: “Neurolinguistic programming is based on the proposition that because your brain is like a computer. It has input and output channels, hardware (i.e., the gray matter), and software (thoughts and beliefs). Everyone knows you can program, deprogram, and reprogram a computer. You
can do the same thing with a human being’s subjective experience.”
Question three: “I never thought I’d believe it but since last week, every time my dog Fido hears the National Anthem, he stands at attention and gets misty- eyed.”
Question four: “People behave just like Pavlov’s dogs, no different. If you squeeze someone’s knee at the same time that they’re feeling an emotion and repeat that like Pavlov, soon just squeeze their knee and they’ll feel that same emotion.”
Question five: “I was told that either drinking a Coke or drinking a ginger ale would settle my stomach, but I couldn’t remember which one it was. So next time I had an upset stomach, I drank a Coke, but it didn’t work. So that’s why I know drinking a ginger ale will do it for me next time I have an upset stomach.”
I’m not going to tell you the answers to these test questions. You can figure them out for yourself. The important point is that once you start hearing the Polya patterns at work, you’ll remember their main function. They make beliefs plausible. They don’t prove anything; they just increase plausibility. There may be many other reasons Dr. Firsthammer bought the newts. Ginger ale may be just as effective or ineffective as Coke for settling a stomach. Fido may be responding to an inaudible to humans pitch that the stereo emits when tuned to the radio station that broadcasts the game. People sometimes (maybe even usually) stop searching for answers once they’ve found one that satisfies them, whether or not it’s actually true.
So as a sleight of mouth sleuth, when you hear a Polya pattern, you can immediately start searching for ways to demonstrate to the person you’re trying to influence that their search for validation isn’t over yet. Counterexamples work brilliantly with Polya and any complex equivalences. For example with our test questions, you could ask, “So is the only reason Dr. Firsthammer could buy
newts is to turn into the Green Monster? Is it totally impossible that he might have purchased them for Dr. Rathbone?” Or, “Dr. Rathbone couldn’t possibly have acquired newts on the black market? And that somebody else entirely was involved here?”
This series of counterexamples injects doubt into the other person’s mind. By asking these the questions, you’re helping to loosen the person’s firm grip on this belief that might not be so useful to them.