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Overconfident Inference from Unknown Statistics

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An American Affair
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Yet another fallacy.

Description:

This fallacy is committed when a person places unwarranted confidence in drawing a conclusion from statistics that are unknown.

  1. “Unknown” statistical data D is presented.
  2. Conclusion C is drawn from D with greater confidence than D warrants.

Unknown statistical data is just that, statistical data that is unknown. This data is different from “data” that is simply made up because it has at least some foundation.

One common type of unknown statistical data is when educated guesses are made based on limited available data. For example, when experts estimate the number of people who use illegal drugs, they are making an educated guess. As another example, when the number of total deaths in the Iraqi war is reported, it is (at best) an educated guess because no one knows for sure how many people have been killed.

Another common type of unknown statistical date is when the data can only be gathered in ways that are likely to result in incomplete or inaccurate data. For example, statistical data about the number of people who have affairs is likely to be mostly in this category.

Obviously, unknown statistical data is not very good data.  However, drawing an inference from such data is not, in itself, an error. In some cases, such inferences can be quite reasonable.

For example, while the exact number of people killed in the Iraq war is unknown, it is reasonable to infer from the data that many people have died. As another example, while the exact number of people who do not pay their taxes is unknown, it is reasonable to infer that the government is losing some revenue because of this.

The error that makes this a fallacy is to place too much confidence in a conclusion drawn from such unknown data. Or, to be a bit more technical, to overestimate the strength of the argument based on statistical data that is not adequately known.

This is an error because, obviously enough, a conclusion is being drawn that is not adequately justified by the premises.

Naturally, the way in which the statistical data is gathered also needs to be assessed to determine whether or not other errors have occurred.

Example #1

“Several American Muslims are known to be terrorists or at least terrorist supporters. As such, I estimate that there are hundreds of actual and thousands of potential Muslim-American terrorists. Based on this, I am certain that we are in grave danger from this large number of enemies within our own borders.”

Example #2

“Experts estimate that there are about 11 million illegal immigrants in the United States. While some people are not worried about this, consider the fact that the experts estimate that illegals make up about 5% of the total work force. This definitely explains that percentage of American unemployment since these illegals are certainly stealing 5% of America’s jobs.”

Example #3

Sally: “I just read an article about cheating.”

Jane: “How to do it?”

Sally: “No! It was about the number of men who cheat.”

Sasha: “So, what did it say?”

Sally: “Well, the author estimated that 40% of men cheat.”

Kelly: “Hmm, there are five of us here.”

Janet: “You know what that means…”

Sally: “Yes, two of our boyfriends are cheating on us. I always thought Bill and Sam had that look…”

Janet: “Hey! Bill would never cheat on me! I bet it is your man-he is always given me the eye!”

Sally: ‘What! I’ll kill him!”

Janet: “Calm down. I was just kidding. I mean, how can they know that 40% of men cheat? I’m sure none of the boys are cheating on us. Well, except maybe Sally’s man.”

Sally: “Hey!”

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Illicit Inductive Conversion

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Description:

This fallacy occurs when someone makes illicit use of the conversion rule from categorical logic in the context of inductive reasoning.  This fallacy has the following form:

  1. Premise 1: P% (or “some”, “few”, “most”, “many”, etc.) of Xs are Ys.
  2. Conclusion: Therefore P% (or “some”, etc.) of Ys are Xs.

In deductive logic, conversion is a rule that allows the subject and predicate claims of a categorical claim to be exchanged. In categorical logic there are four sentence types (All S areP , No S are P, Some S are P, and Some S are not P) and this rule applies correctly to two of them: No S are P and Some S are P. A conversion is legitimate when the converted claim logically follows from the original (and vice versa). Put another way, the rule is applied correctly when its application does not change the truth value of the claim.

For example, “No cats are hamsters” converts legitimately to “no hamsters are cats.” Interestingly, “some dogs are huskies” converts correctly to “some huskies are dogs”, at least in categorical logic. In categorical logic, “some” means “at least one.” Hence, “at least one dog is a husky” is converted to “at least one husky is a dog.” In this case, the inference from one to the other is legitimate because it is made in the context of categorical logic.

The illicit use of conversion is, not surprisingly, an error.  This error occurs in two ways. The first is when the rule is applied incorrectly in the context of categorical logic: if conversion is applied to an All S are P or a Some S are not P claim, then the rule has been applied improperly.  This can be easily shown by the following examples. While it is true that all dogs are mammals, the conversion of this claim (that all mammals are dogs) is not true.  As another example, the claim that some dogs are not huskies is true while its conversion (that some huskies are not dogs) is false.

The second occurs when the conversion rule is applied outside of the context of categorical logic.  To be specific, it occurs in contexts in which “some” and comparable terms such as “few”, “most”, “many” and so on are not taken to mean “at least one.” This is the sort of error that defines this specific fallacy. For example, to infer that most people who speak English are from Maine because most people from Maine speak English would be an obvious error.  This is because “most” in this context is not taken to mean “at least one.”

Not surprisingly, people generally do not make such obvious errors in regards to conversion. However, people do fall victim to conversions that seem plausible. For example, when people hear that a medical test for a heart condition is 80% accurate they might be tempted to infer that 80% of those who test positive have the condition. However, to convert “80% of those who have the condition will test positive” (that is what it means for a test to be 80% accurate) to “80% of those who test positive have the condition” is an illicit use of conversion.

Example #1

“Very few white men have been President of the United States. Therefore very few Presidents have been white men.”

Example #2

“A fairly small percentage of automobile accidents involve drivers over 70. Therefore a fairly small percentage of drivers over 70 are involved in automobile accidents.”

Example#3

“Most conservatives are not media personalities on Fox News. Therefore, most of the media personalities on Fox News are not conservative.”

Example #4

“Most wealthy people are men so most men are wealthy.”

Example #5
“Most modern terrorists are Muslims, therefore most Muslims are terrorists.”

Example #6

“Most modern terrorists are religious people, therefore most religious people are terrorists.”

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Automakers & Socrates

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Portrait of Socrates. Marble, Roman artwork (1...
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While Toyota‘s woes are the big news, there are numerous other cases of companies inflicting defective or dangerous products onto the public. In the case of Toyota, there also seems to be some evidence that the government was aware of the problems for quite some time, yet acted in ways that seem contrary to the public interest. Toyota has also been accused of covering up problems.

Of course, Toyota has paid for these actions. Millions of vehicles have been recalled for repairs and consumer confidence has been shaken. In my own case, I bought a Toyota in 2001 based largely on Toyota’s reputation. While the truck has worked out well for me, I cannot say that I would buy a new Toyota today.  I suspect many other people are also wary of the company now.

Given the damage caused by such problems, one wonders why companies do such things.

In regards to problems with cars, the answer can be both simple and honest: cars are complex machines and can have various problems that do not become evident until they are exposed to a wide variety of conditions. Such potential problems are simply part of the nature of an imperfect world.

Of course, this cannot be used as an excuse across the board-eventually a somewhat vague line is crossed and a corporation can be justly regarded as producing a defective product. For example, I do accept that my PC might have problems if I attach certain peripherals or load certain software. However, if my video card catches on fire due to shoddy manufacturing, then the company is at fault.  In the case of cars, I accept that certain unusual conditions might create unanticipated problems. But, the brakes and accelerator in cars need to work properly and failures in this area are not acceptable.

Not surprisingly, companies do not intentionally make products to cause them trouble. Rather, they produced such products through negligence or in an attempt to make money by cutting corners. When a problem is found, the natural tendency is to cover it up rather than face up to it.

One reason to do this is to avoid having to pay for the consequences of the problem. For example, if a company accepts responsibility for a defect, this makes it much easier for laws suits to succeed in this area. Also, if a company can cover it up, it can avoid having to pay for the repairs. So, money is an important factor.

Another reason to do this is to avoid the harm to the brand reputation. After all, if the problem stays hidden, the company retains its reputation. This also motivates individuals. For example, Spitzer, Clinton and Stanford did their best to hide their affairs.

A third reason to do this is that people are naturally inclined to hide their failures and resent those who would correct them.

However, the tactic of the cover up is generally a poor strategy. In addition to the obvious ethical issues, the strategy often creates more damage in the long run than being honest.

In his Apology, Socrates noted this. He pointed out that people who do misdeeds prefer to remain hidden and uncorrected, but that they should be grateful for a gadfly who keeps them on track. After all, by being corrected, they will be more likely to do what is correct. But, if they are free to hide their misdeeds, then they will be even more inclined to act poorly and thus end up in a worse situation than if they had been open to criticism.

Toyota seems to be in this situation: they were aware serious problems and seem to have acted to try to conceal them by using their relation with the regulatory folks and by other means.  It seems that getting away with such things might be habit forming. In any case, it does seem to be natural for people to slack when they know they can get away with it. As such, Toyota can be faulted for doing wrong, but the folks who were supposed to be their gadfly also deserve blame.

When Socrates was on trial, he told his accusers that they were doing themselves harm. He seems to have been right. While companies would no doubt prefer to get away with whatever they wish to do, this actually turns out to harm them. While Toyota did enjoy a delay in the consequences of its failures, it is now paying the price. If the company had been properly regulated and brought to task for past problems, it might not bee going trough the disaster it is facing today. Hiding misdeeds just allows them to grow, as Socrates well knew.  As such, proper regulation can actually be very good for companies by helping keep them from hurting themselves.

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Fallacy

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As a philosophy professor, I have waged a never-ending and largely pointless battle against people using “fallacy” when they mean “factual error.” For example, someone might say “people often think that dogs won’t eat anything that is bad for them, but that is a fallacy.” This is, of course, a mistake. A fallacy is a mistake in reasoning that occurs when the premises presented in an argument fail to adequately support the conclusion.

So, to think that a dog won’t eat anything that is bad for them is not a fallacy. Rather it is just a factual error. After all, dogs will consume anti-freeze and that will kill them.

Naturally enough, people might argue that words should mean whatever people say they mean. So, of folks use “fallacy” in place of “factual error”, then that is just they way things are.

While that has some appeal, since language is mostly a matter of convention, this sort of use is problematic. After all, there is an important distinction between an error in logic and a factual error. It certainly seems important to distinguish between those two mistakes. To see why, think about balancing your checkbook. You can make a mistake by doing the math incorrectly (adding $500 + $50.50 and getting $555) and you can make a mistake by entering the wrong amount (for example, $50 instead of $500) for a check. These errors are different and calling them the same would be a mistake and would also cause confusion.

Now, if people insist that “fallacy” should mean the same as “factual error”, then a new word would be needed to name what we used to call “fallacies.” However, since we already have a perfectly good word for fallacies, namely “fallacies”, then it makes sense to simply stick with the current usage.

A minor problem with using “fallacy” for “factual error” is that it makes teaching logic a bit more challenging. To be specific, it is quite challenging to make the distinction between assessing the quality of reasoning and assessing the quality of a claim without adding to the confusion by using two terms for the same thing.

As such, it would be nice if people would stop using “fallacy” in place of “factual error.” One refers to a mistake in reasoning and the other refers to being wrong about a fact and these are not the same things.

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