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Critical Thinking & COVID-19: Generalization

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It is reasonable to wonder how the experts are coming up with the numbers of cases of COVID and calculating its lethality. Some might be concerned about or even skeptical because the numbers often change and they vary across countries, age groups, ethnicities and economic classes. This essay provides a basic overview of a core method of making inferences from samples to entire populations—this is what philosophers call the inductive generalization.

An inductive generalization is an inductive argument. In philosophy, an argument consists of premises and one conclusion. The premises are the reasons or evidence being offered to support the conclusion, which is the claim being argued for.  Philosophers generally divide arguments into inductive and deductive. In philosophy a deductive argument is such that the premises provide (or are supposed to provide) complete support for the conclusion. An inductive argument is an argument such that the premises provide (or are supposed to provide) some degree of support (but less than complete support) for the conclusion.  If the premises of an inductive argument support the conclusion adequately (or better) it is a strong argument. It is such that if the premises are true, the conclusion is likely to be true. If a strong inductive argument has all true premises, it is sometimes referred to as being cogent.

One feature of inductive logic is that a strong inductive argument can have a false conclusion even when all the premises are true. This is because of what is known as the inductive leap: the conclusion always goes beyond the premises. This can also be put in terms of drawing a conclusion from what has been observed to what has not been observed. Our good dead friend David Hume argued back in the 1700s that this meant we could never be sure about inductive reasoning and later philosophers called this the problem of induction. In practical terms, this means that even if we engage in perfect inductive reasoning using premises that are certain, our conclusion can still turn out to be wrong. But induction is often the only option—so we use it because we must. So, when the initial numbers about COVID-19 turn out to be wrong, this is exactly what we should expect.

What, then, is an inductive generalization? Roughly put, it is an argument in which a conclusion about an entire population is based on evidence from a sample of observed members of that population. The formal version looks like this:

Premise 1: P% of observed Xs are Ys.
Conclusion: P% of all Xs are Ys.

The observed Xs would be the sample and all the Xs would be the target population. As an example, if someone wanted to know the mortality rate for males over sixty, the target population would be all males over sixty.

While the argument is simple, sorting out when a generalization is a good one can be quite challenging. Without getting into the complicated statistics and methods for doing rigorous generalizations, I will go over the basic method of assessment—so you can make some sense when experts talk about such matters in the context of COVID-19 or anything. There will be various factors whose presence or absence in the sample can affect the presence or absence of the property the argument is concerned with, so a representative sample will have those factors in proportion to the target population. For example, if we wanted to determine the infection rate for all people, then we would need to try to ensure that our sample included all factors that impact the infection rate and we would also need to ensure that our sample mirrored our target population in terms of age, ethnicity, base health, and so on for all relevant features of the population. Sorting out what factors are relevant can be challenging—in the case of COVID-19 experts are engaged in taking samples and doing causal analysis to try to create even better samples to make stronger generalizations. To the degree that the sample mirrors the target population properly, it would be representative.

A sample is biased relative to a factor to the extent that the factor is not present in the sample in the same proportion as in the population. This sort of sample bias is a major problem when trying to generalize about COVID-19. One example of this is trying to draw a conclusion about the lethality of COVID-19. While the math to do this is easy (a simple calculation of the percentage of the infected who die from it) getting the numbers right is hard because we need to know how people have been infected and how many of them die from it.

Experts have been trying to determine the number of people who have been infected—this is done by testing and modeling—which are also inductive reasoning. In the United States, most of the testing is being done on people who are showing symptoms, and this will create a biased sample—to get an unbiased sample, everyone needs to be tested. Until testing is broad enough, inferences about the lethality of the virus will be weakened by this biasing factor. There is also the practical matter of the accuracy of the tests and the determination of the cause of death.

To use a concrete, but made up example, if 5% of those who tested positive for COVID-19 ended up dying, the generalization from that sample to the whole population would only be as strong as the representativeness of the sample—and if only sick people are being tested, the sample will not be representative and the conclusion about the lethality of the virus will be wrong.

There is also the challenge of sorting out the effect of the virus on different populations. While there will be an overall infection rate and lethality rate for the whole population, there will also be different infection rates and lethality rates for different groups within the human population. As an example, the elderly appear to have a higher lethality rate than the population as a whole.

In addition to representativeness, sample size is important—the larger, the better.  This brings us to two more concepts: Margin of error and confidence level. A margin of error is a range of percentage points within which the conclusion of inductive generalization falls; this number is usually presented in terms of being plus or minus. The margin of error depends on sample size and the confidence level of the argument. The confidence level is typically presented as a number and represents the percentage of arguments like the one in question that have a true conclusion.

When generalizing about large (10,000+) populations, a sample will need to have 1,000+ individuals to be representative (assuming the sample is taken properly). This table, from Moore & Parker’s Critical Thinking text, shows the connection between sample size and error margin (confidence level of 95%:

 

Sample Size Error Margin (%) Corresponding Range (percentage points)
10 +/- 30 60
25 +/- 22 44
50 +/- 14 28
100 +/- 10 20
250 +/- 06 12
500 +/- 04 8
1,000 +/- 03 6
1,500 +/- 02 4

 

The practical takeaway here is that sample size is particularly important: a small sample will have a large margin of error that can make it useless. For example, suppose that a group of 50 COVID-19 patients received hydroxychloroquine tablets and 10 of them recovered fully. Laying aside all causal reasoning (which would be a huge mistake) the best we could say is that 20% of patients treated with hydroxychloroquine +/-14% will recover fully. It is very important to say here that this is just a simple generalization and that a controlled experiment or study would be needed to properly assess a causal claim—something I will discus in the future.

There are various fallacies (mistakes in reasoning) that can occur with a generalization. I will discuss those in the next essay. Stay safe and I will see you in the future.

 

 

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Critical Thinking & COVID-19 IX: Straw Person, Steel Person and Just Kidding

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During a White House press briefing President Trump expressed interest in injecting disinfectants as a treatment for COVID-19. In response  medical experts and the manufacturers of Lysol warned the public against attempting this. Trump’s defenders adopted two main strategies. The first was to interpret Trump’s statements in a favorable way; the second was to assert they were “fact checking” the claim that Trump told people to inject disinfectant. Trump eventually claimed that he was being sarcastic to see what the reporters would do. From the standpoint of critical thinking, there is a great deal going on here involving rhetorical devices and fallacies. I will briefly go over how critical thinking can sort through this situation and how it can be used in analogous situations.

When interpreting or reconstructing claims and arguments made by others, philosophers are supposed to apply the principle of charity. Following this principle requires interpreting claims in the best possible light and reconstructing arguments to make them as strong as possible. There are three reasons to follow the principle. The first is that doing so is ethical. The second is that doing so avoids committing the straw person fallacy, which I will talk more about in a bit. The third is that if I am going to criticize a person’s claims or arguments, criticism of the best and strongest versions also takes care of the lesser versions.

The principle of charity must be tempered by the principle of plausibility: claims must be interpreted, and arguments reconstructed in a way that matches what is known about the source and in accord with the context. For example, reading quantum physics into the works of our good dead friend Plato would violate this principle.

Getting back to injecting disinfectants, it is important to accurately present Trump’s statements in context and to avoid making a straw person. The Straw Person fallacy is committed when one ignores a person’s actual claim or argument and substitutes a distorted, exaggerated or misrepresented version of it. This sort of “reasoning” has the following pattern:

 

Premise 1: Person A makes claim or argument X.

Premise 2: Person B presents Y (which is a distorted version of X).

Premise 3: Person B attacks Y.

Conclusion:  Therefore, X is false/incorrect/flawed.

 

This sort of “reasoning” is fallacious because attacking a distorted version of a claim or argument does not constitute a criticism of the position itself. This fallacy often makes use of hyperbole, a rhetorical device in which one makes an exaggerated claim. A Straw Person can be highly effective because people often do not know the real claim or argument being attacked. The fallacy is especially effective when the straw person matches the audience’s biases or stereotypes—they will feel that the distorted version is the real version and accept it.

While this fallacy is generally aimed at an audience, it can be self-inflicted: a person can unwittingly make a Straw Person out of a claim or argument. This can be done entirely in error (perhaps due to ignorance) or due to the influence of prejudices and biases.

The defense against a Straw Man, self-inflicted or not, is to take care to get a person’s claim or argument right and to apply the principle of charity and the principle of plausibility.

Some of Trump’s defenders have been claiming that Trump was the victim of a straw person attack; they are “fact checking” and asserting that Trump did not tell people to drink bleach. Somewhat ironically, they might be engaged in Straw Person attacks when attempting to defend Trump from alleged Straw Person attacks—warning people to not drink bleach or inject disinfectants  is not the same thing as claiming that Trump told people to drink bleach.

His defenders are right that Trump did not tell people to drink bleach. His exact words, from the official White House transcript, are as follows: “And then I see the disinfectant, where it knocks it out in a minute. One minute. And is there a way we can do something like that, by injection inside or almost a cleaning. Because you see it gets in the lungs and it does a tremendous number on the lungs. So it would be interesting to check that. So, that, you’re going to have to use medical doctors with. But it sounds — it sounds interesting to me.”

Trump does not, at any point, tell people to drink bleach—he does not even use those words. He does not even tell people to inject disinfectant. As such, the “Clorox Chewables” and similar memes can be seen as form of visual Straw Person attack against Trump—they can also be seen as the rhetorical device of mockery. To avoid committing the Straw Person fallacy, we need to use Trump’s actual statements—so attacking him for advocating drinking bleach would be an error. Somewhat ironically, Trump’s actual statements are so terribly mistaken that they sound like a Straw Person.

While Trump does not directly tell people inject disinfectants, he can be seen as engaging in a form of innuendo—a rhetorical technique in which something is suggested or implied without directly saying it. Anyone who understands the basics of how language and influence works would get that Trump’s remarks about injecting disinfectant would cause some people to believe that this was a good idea or at least lead them to think this was something worth considering. There is evidence for this in the form of calls to New York City poison control centers and similar calls in Maryland and other states. Although there have been some claims that people have been hospitalized because of misusing disinfectant, I have not seen adequate confirmation of these claims. One main feature of innuendo is that it allows a person to deny they said what they implied or suggested—after all, they did not directly say it. Holding someone accountable requires having adequate evidence that they did intend what their words imply or suggest—this can be challenging since it requires insights into their character and motives. There is also an obvious moral issue here about the responsibility of influential people to take care in what they say—something that goes beyond critical thinking. Spoiler: the president needs to be careful in what he says.

Trump clearly uses words that convey the idea that he thinks medical doctors should test injecting disinfectants into peoples’ lungs as a possible treatment for COVID-19. This takes us back to my earlier discussion of experts and my case that Trump is not an expert. I should not have to say this, but injecting disinfectants into lungs would be extremely dangerous—something that almost anyone should know. Given Trump’s well established record of dangerous ignorance, interpreting his words as meaning what they clearly state does meet the conditions of the principle of charity and the principle of plausibility: these are his exact words, in context and with full consideration of the source.

Some of Trump’s defenders have tried to use what I will call the Steel Person fallacy. The Steel Person fallacy involves ignoring a person’s claim or argument and substituting a better one in its place without justification.  This sort of “reasoning” has the following pattern:

 

Premise 1: Person A makes claim or argument X.

Premise 2: Person B presents Y (which is a better version of X).

Premise 3: Person B defends Y.

Conclusion:  Therefore, X is true/correct/good.

 

This sort of “reasoning” is fallacious because presenting and defending a better version of a claim or argument does not show that the actual version is good. A Steel Person can be highly effective because people often do not know the real claim or argument being defended. The fallacy is especially effective when the Steel Person matches the audience’s positive biases or stereotypes—they will feel that the improved version is the real version and accept it. The difference between applying the principle of charity and committing a Steel Person fallacy lies mainly in the intention: the principle of charity is aimed at being fair, the Steel Person fallacy is aimed at making a person’s claim or argument appear much better than it is and so is an attempt at deceit.

While this fallacy is generally aimed at an audience, it can also be self-inflicted: a person can unwittingly make a Steel Person out of a claim or argument. This can be done entirely in error (perhaps due to ignorance) or due to the influence of positive biases. The defense against a Steel Man, self-inflicted or not, is to take care to get a person’s claim or argument right and to apply the principle of plausibility.

In the case of Trump, he is clearly expressing interest in injecting disinfectants into the human body. Some of his defenders created a Steel Man version of his claims, contending that what he really was doing was presenting new information about using light, heat and disinfectant killing the virus. To conclude that Trump was right because of this unjustified better version of his statements has been offered would be an error in logic. While light, heat and disinfectant probably can destroy the virus, Trump’s claim is clearly about injecting disinfectant into the human body—which, while not telling people to drink bleach, is a dangerously wrong claim.

Trump himself undermined these defenders by saying “I was asking a question sarcastically to reporters like you just to see what would happen.” If this is true, then his defenders’ claims that he was not talking about injecting disinfectant would be false—he cannot both be saying something dangerously crazy to troll the press and be making a true and rational claim about cleaning surfaces.  Trump seems to be attempting to use a rhetorical device popular with the right (although anyone can use it). This method could be called the “just kidding” technique and can be put in the meme terms “for the lulz.”

One version of the “just kidding” tactic occurs when a person says something that is racist, bigoted, sexist, or otherwise awful and does not get the positive response they expected or are called out and held accountable for what they said. The person’s “defense” is that they did not really mean what they said, they were “just kidding. “As a rhetorical technique, it is an evasive maneuver designed to avoid accountability. The defense against this tactic is to assess whether the person was plausibly kidding or not—that is, did they intend to be funny without malicious intent and fail badly or are they trying to weasel out of accountability for meaning what they said? This can be difficult to sort out, since you need to have some insight into the person’s motives, character and so on.

Another version of the “just kidding” tactic is somewhat similar to the “I meant to do that” tactic. When someone does something embarrassing or stupid, they will often try to reduce the humiliation by claiming they intended to do it. In Trump’s injection case, he is claiming that intended to say what he said and that he was being sarcastic—thus he meant to do it but was just kidding.

If Trump was just kidding, he thought it was a good idea to troll the media during a pandemic—which is a matter for ethics rather than critical thinking. If he was not kidding, then he was attempting to avoid accountability for his claims—which is the point of this tactic. The defense against this tactic is to assess whether the person was plausibly kidding or not—that is, did they really mean to do it and what they meant to do was just kidding? This requires having some insight into the person’s character and motives as well as considering the context. In the case of Trump, the video shows him addressing his remarks to the experts rather than the press and he seems completely serious. There is also the fact that a president engaged in a briefing on a pandemic should be serious rather than sarcastic. As such, he does not seem to be kidding. But Trump has put himself in a dilemma of awfulness: he was either seriously suggesting a dangerous and stupid idea to the nation or trying to troll the press during a briefing on a pandemic that is killing thousands of Americans. Either way, he is terrible.

 

 

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Critical Thinking & COVID-19 VIII: The Prediction Fallacy

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As politicians and pundits debate about reopening America, some make the case that we can and should reopen soon because the dire predictions turned out to be wrong. On the face of it, this seems like good reasoning: things are not as bad as predicted, so we can start reopening sooner than predicted. To use an analogy, if a fire was predicted to destroy much of your house, but it only burned your garage to the ground, then it is time to start planning on rebuilding and moving back in. While this line of thought is appealing, it also can be a trap. Here is how the trap works.

Some politicians and pundits are pointing out that the dire predictions did not come true—for example, the governor of Florida recently noted that the hospitals were not overwhelmed as predicted and he wants to allow them to return to money making elective surgery. He also, like some other Republican governors, wants to reopen very quickly. This reasoning does initially seem sensible: the pandemic was not as bad as predicted, so we can quickly reopen. There are also those who sneer at the dire predictions and are upset at what they see as excessive precautions. This can also seem sensible: the experts predicted a really terrible outcome for COVID-19, but they were wrong. We overreacted and should roll back the precautions. So, re-open America.

While it is reasonable to consider whether the precautions are excessive and to update our assessment of when to re-open, there is a tempting fallacy that needs to be avoided. This can be called “the prediction fallacy.” It occurs when someone uncritically rejects a prediction and responses to the prediction when the outcome of a prediction turns out to be false. The error in the logic occurs because the person fails to consider what should be obvious: if an effective response is made to a prediction, then the prediction is going to be “wrong.” The form of the fallacy is this:

 

Premise 1: Prediction P predicted X (if we do not do R).

Premise 2: Response R was taken based on prediction P.

Premise 3: X did not happen, so prediction P is wrong.

Conclusion: We should not have taken Response R (or no longer need to take Response R).

 

To use a concrete example:

 

Premise 1: Experts predicted that the hospitals in Florida would be overwhelmed (if we did not respond with social distancing and other precautions).

Premise 2: People responded to this prediction with social distancing and other precautions.

Premise 3: The hospitals in Florida were not overwhelmed, so the prediction was wrong.

Conclusion: The response was excessive and we no longer need to practice all those precautions and can open Florida up.

 

While it is (obviously) true that a prediction that turns out to be wrong is wrong, the error is to uncritically conclude that this proves that the response based on the prediction need not have been taken (or that we no longer need to keep responding in this way). The prediction in question assumes that we do not respond (or do not respond a certain way) and the response is intended to address the prediction. If the response was effective, then the predicted outcome without it would not occur—that is the point of responding. To reason that the “failure” of the prediction shows that the response was mistaken or no longer needed would be a mistake in reasoning. You could be right—but you need to do more than to point to the failed prediction.

To use a silly, but effective analogy, imagine that we are in a car and driving towards a cliff. You make the prediction that if we keep going, we will go off the cliff and die. So, I turn the wheel and avoid the cliff. If backseat Billy gets angry and says that there was no reason to turn the wheel or that I should turn it back because we did not die in a fiery explosion, Billy is falling for this fallacy. After all, if we did not turn, then we would have died. And if we turn back too soon, then we die.

The same applies to COVID-19: by responding effectively to dire predictions, we change the outcome and the predictions turn out to be wrong. But to infer that the responses were excessive or that we should stop now simply because the results were not as dire as predicted would be an error.

This is not to deny what is obviously true: it is possible to overreact to COVID-19 and there will, one hopes, come a time we can end some of the responses. But making these decisions based on the prediction fallacy would be a bad idea. There is also another version of this fallacy.

A variation on this fallacy involves inferring the prediction was a bad one because it turned out to be wrong:

 

Premise 1: Prediction P predicted X if we do not do R.

Premise 2: Response R was taken based on prediction P.

Premise 3: X did not happen.

Conclusion: The prediction was wrong about X occurring if we did not do R.

 

While the prediction turned out to be wrong in the sense that the predicted outcome did not occur, this does not disprove the prediction that X would occur without the response when the response occurred. Going back to the car example, the prediction that we would die if we drove of the cliff if we do not turn is not disproven if we turn and then do not die. In fact, that is the result we want.

Getting back to COVID-19, the predictions made about what could occur if we did nothing are not disproven by the fact that they did not come true when we did something. So, to infer that these predictions must have been wrong in predicting what would occur if we did nothing would be an error. We do, of course, rationally assess predictions based on outcomes—but this assessment cannot ignore considering the effect of the response when judging the prediction. Sorting out such counterfactual predictions is hard—in complex cases you can probably never prove what would have happened, but good methods can guide us here—which is why we need to go with science and math rather than hunches and feelings.

This fallacy does draw considerable force from psychological factors, especially in the case of COVID-19. The response taken to the virus comes with a high cost and we want things to get back to normal—so, ironically, the success of the response makes us feel that we can stop now or that we did not really need such a response.  As always, bad reasoning can lead to bad consequences and in a pandemic, it can hurt and even kill many people.

Stay safe and I will see you in the future.

 

 

 

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Critical Thinking & COVID-19 VII: Argument Against Expertise

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In a previous essay I went over the argument from authority and the standards to use to distinguish between credible and non-credible experts. While people often make the mistake of treating non-experts as credible sources, they also make the mistake of rejecting credible experts because the experts are experts. This sort of fallacious reasoning is worthy of a name and the obvious choice is “argument against expertise.” It occurs when a person rejects a claim because it is made by an authority/expert and has the following form:Einstein

 

Premise 1: Authority/expert A makes claim C.

Conclusion: Claim C is false.

 

While experts can be wrong, to infer that an expert is wrong because they are an expert is obviously absurd and an error in reasoning. To use a geometry example, consider the following:

 

Premise 1: Euclid, an expert on geometry, claimed that triangles have three sides.

Conclusion: Triangles do not have three sides.

 

It must be noted that there are rational grounds for doubting an expert—as discussed in the essay on argument from authority. When a person rationally applies the standards of assessing an alleged expert and decides that the expert lacks credibility, this would not be an error. But to reject a claim solely because of the source is always a fallacy (usually an ad hominem) and rejecting a claim because it was made by an expert would be doubly fallacious, if there were such a thing.

Since experts are generally more likely to be right than wrong, this sort of reasoning will tend to lead to accepting untrue claims. While this is a bad idea in normal times, it is even more dangerous during a pandemic. In the case of COVID-19, there are those who use this reasoning to reject the claims of medical experts. This can, obviously enough, lead to illness and death. Because the fallacy lacks all logical force, it derives its influence from psychological factors, and these are worth considering when trying to defend against and respond to this dangerous fallacy.

Our first step in understanding the driving forces behind this fallacy take us back to ancient Athens to visit our good dead friend Socrates. One of Socrates friends went to the oracle of Delphi and asked them who was the wisest of men. It was, of course, Socrates. While many would accept such praise, Socrates believed that the gods were wrong and set out to disprove them by finding someone wiser. He questioned the poets, the politicians, the craftspeople—anyone who would speak with him. He found that everyone believed they knew far more than they did—and the more ignorant a person, the more they believed they knew. Reflecting on this, Socrates concluded that the gods were right: he was the wisest because he knew that he knew nothing, that his infinite ignorance eclipsed what little he knew. While some were grateful to Socrates, most were outraged at Socrates and saw to it that he was put on trial and sentenced to death. Sorry, spoilers.

While we now have smart phones, people have not changed since those times: most people believe they know far more than they do, and they resent anyone who would disagree. And resent most of all someone who reveals their ignorance. Technology has made this worse—thanks to the “university of Google” and social media, people not only doubt the experts, but regard themselves as equal to or better than them.

The fundamental lesson of philosophy provides the obvious defense against this arrogant ignorance: realizing, as Socrates did, that wisdom is recognizing that we know nothing. This is not to embrace empty skepticism in which everything is doubted, but to accept a healthy skepticism of the extent of our own knowledge and to develop a willingness to listen to those who have knowledge.

We can continue our philosophical adventure centuries past the death of Socrates by visiting our good dead friend John Locke. While Locke is best known for “life, liberty and property” he also wrote on enthusiasm. By enthusiasm he did not mean being really stoked about your sports team or a getting free guacamole—he was concerned with the tendency people have to believe a claim because they strongly feel it to be true. While Locke was very concerned with this in the context of religion, he held to a very sensible general principle that one should believe in proportion to the evidence rather than in proportion to the strength of feeling.

While psychologists and cognitive scientists have examined the various cognitive biases that contribute to what Locke calls enthusiasm, his basic idea is still correct: believing based on strong feeling is not a rational way to form beliefs. True beliefs can be backed up with evidence and reason. The power of this enthusiasm leads people to believe based on the strength of their feelings and they will often be wrong—thus leading them to reject what experts claim when there is disagreement. They will feel that they are right and that their strong feeling counts more than expertise.

The defense against this is not, obviously, to become unfeeling. Rather it is to be aware that feelings are not evidence and to endeavor to proportion belief to the evidence not the feeling. This is very difficult to do—it is hard to fight feelings. But rational decision making that can save your life and the lives of others requires this—especially now. How we feel about COVID, social distancing or alleged cures proves nothing. Only proof proves things.

The above applies universally to all people, but what about Americans in particular? Unfortunately, we are especially prone to rejecting experts because they are experts. This tendency feeds into stereotypes that often appear in fiction and these stereotypes then feed the tendency. For example, the idea that intellectuals (especially professors) are helpless outside of the ivory towers and that problems are solved by manly men with loud voices and a strong right hook is a common theme. The defense against this is to realize that the stereotypes are just that.

A mistaken American conception of democracy also serves to fuel this fallacy. While American political philosophy holds that everyone is equal and everyone has a right to free expression, these are wrongly interpreted as everyone being equal in knowledge and that all opinions are equally good (although mine is first among equals). The science fiction writer Isaac Asimov noted this: “There is a cult of ignorance in the United States, and there has always been. The strain of anti-intellectualism has been a constant thread winding its way through our political and cultural life, nurtured by the false notion that democracy means that my ignorance is just as good as your knowledge.” This view is also fed by relativism—the idea that there is no objective truth, that there are alternative facts.

The defense against this is not to reject democracy or freedom of expression but to realize that neither of these entail that “my ignorance is just as good as your knowledge.” We can accept democracy and accept that people have the right to express themselves, but the correctness of a claim is not a matter for a vote nor is any opinion automatically as good as another just because someone is free to express it. Almost everyone realizes this when it comes to very practical matters: while people do sometimes try to do their own dentistry, build rockets, or rewire their house on their own most people realize that root canals, major electrical work and rockets are best left to the experts. We turn to dentists, mechanics and engineers because they are experts and we are generally not. We should get that the same applies beyond these areas, such as to epidemiology. This is not to say that we should blindly believe the experts, but that we should accept claims made by credible experts over our own ignorance. Or accept authoritarians over authorities.

While the professed political values of America are contrary to authoritarianism, a significant percentage of Americans have embraced it. As noted in an earlier essay, authoritarian leaders and followers are generally inimical to real experts and the delusions and lies of authoritarians can motivate them to accept the fallacy. While a rejection of experts is not limited to the right (see, for example, the anti-vaccination movement), the American right has systematically waged a war on experts whose views conflict with their ideological claims and key economic interests. While the right did not, perhaps, intend to wage a war on all expertise, it has had this effect—distrust in experts has grown considerably and often with negative consequences. This is not to say that experts are blameless—there have also been clear failings among experts and those purporting to be experts. But the lessons of these failures have generally not been properly interpreted. For example, it is often claimed that the failures in the Vietnam War were due to the arrogance of experts. While this has some merit, the true lesson of The Best and the Brightest was that ignoring credible experts was a major factor behind the poor decision making.

Since rejecting experts has become a matter of political identity for some Americans, overcoming this aspect is extremely difficult. Also, overcoming decades of systematic undermining of expertise and science will also be extremely difficult. Neither is impossible, but it might be more realistic to focus on outvoting those who reject reason in favor of ideology. There is also some hope that the pandemic will shake some people out of their ideology—that they will realize that rejecting medical experts and going with their own beliefs is like trying to do their own surgery.

Stay safe and I will see you in the future.

 

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Critical Thinking & COVID-19 VI: Testing

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Every year I go through a section in Moore and Parker’s classic Critical Thinking book on medical testing. Until now, it has been a fairly abstract thing for my students, but now medical testing is a critical part of responding rationally to the pandemic. One type of test is to determine whether a person is infected. Another is to determine whether a person had the infection. While these tests are a critical source of information it is important to be aware of the limitations of testing. Since I am not a medical expert, I will not comment on the accuracy of specific methods of testing. Instead, I will look at applying critical thinking to testing.

An ideal medical test would always be accurate and never yield a false positive. Real medical tests have, for various reasons, less than 100% accuracy in the field and a good test will fall into the 90-99% range. This means that a test can falsely show that a person is or was infected or falsely show they are or were not infected. So how do you judge whether a person is infected or was infected based on a test result?

Intuitively, the chance a person was infected (or not) would seem to be the same as the accuracy of the test. For example, if a COVID-19 test has an accuracy of 90%, then the seemingly rational inference would be that if you test negative, then there is a 90% chance you did not have COVID. Or, if you test positive. There is a 90% chance you had COVID. While this seems sensible, it is not accurate and involves a confusion about conditional probabilities.  I will keep the math to a minimum because math, as Barbie said, is hard.

So, suppose that I test positive for having COVID and the test is 90% accurate. If I think there is a 90% chance, I had COVID, I am probably wrong and here is why. The mistake I would be making is failing to recognize that the probability that X given Y is distinct from the probability of Y given X. In the case of the test for COVID, testing positive is the effect of COVID and obviously not the cause. As such, a 90% accurate test for COVID does not mean that 90% of those who test positive (effect) will have had COVID (cause). It means that 90% of those who had COVID (cause) will test positive (effect). So, if I have COVID, then there is a 90% chance the test will detect it. The wrong way of looking at it would be to think that if I test positive, then there is a 90% chance I had COVID. So, what is the true chance I had COVID if I test positive on a test that is 90% accurate? The answer, right now, is that I do not know. But I do know how to do the math to sort it out.

To know my chance of having COVID I would also need to know the percentage of false positives that occur with the test and, very importantly, the base rate of the infection. The base rate of the infection is the frequency of the cause. Using my made-up test and some made-up numbers, here is how the math would go.

Suppose that the 90% accurate test has a 10% false positive rate and 1% of the population in question is infected. For every 1,000 people in the population:

 

  • 10 people will have COVID
  • 9 of the people with COVID will test positive.
  • 990 people will not have COVID.
  • 99 of the people without COVID will test positive.

 

While there will be 108 positive test results, only 9 of them will have had COVID. So, a person who tests positive has an 8% of having had COVID, not 90%.  In conditional terms and using these made-up numbers, if I had COVID, then there is a 90% chance I will test positive. But If I test positive, then there is an 8% chance I had COVID. The same math holds true for antibody testing to see if I had COVID.

At this point is tempting to think that testing is useless, but that would be a mistake. Testing is obviously useful in gathering data about infection rates. Testing is more likely to be right in populations with higher rates of COVID infections—this is a function of statistics rather than testing. To illustrate this, let us run the example again with one change—increasing the rate of infection to 10%. For every 1,000 people in the population:

 

  • 100 people will have COVID
  • 90 of the people with COVID will test positive.
  • 900 people will not have COVID.
  • 90 of the people without COVID will test positive.

 

There will be 180 positive test results and 50% of them will have COVID. So, if I test positive for COVID, then there is a 50% chance I had COVID. Again, this is a matter of statistics—the test accuracy, by hypothesis, has not changed. Because of this, testing groups that we know to have higher infection rates will give better statistical results that can be useful—but much of the use will be in terms of additional statistical analysis. NPR has provided an excellent discussion of antibody testing for COVID and they even included a calculator that will do the math for you.

In terms of putting your trust in a test, such as an antibody test to determine whether you had COVID or not, it is wise to keep the math in mind. Even if surviving COVID confers some immunity, a positive test might mean an 8% chance that you had COVID. And until we know the rate of infection, we are essentially guessing when doing the math. At this point the rational approach might seem to be a bit odd: assume you have COVID while also assuming that you have not had COVID.

 

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Critical Thinking & COVID-19 V: Argument from Authoritarian

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While it would be irrational to reject medical claims of health care experts in favor of those made by President Trump, there are those who do just that. Considerations of why people do this is mainly a matter of psychology, but the likely errors in reasoning are a matter for philosophy.Stalin

While those who accept Trump as a medical authority are falling victim to a fallacious appeal to authority, it is worth considering the specific version of the fallacy being committed. I am calling this fallacy the argument from authoritarian. The error occurs when a person believes a claim simply because it is made by the authoritarian leader they accept. It has this form:

Premise 1: Authoritarian leader L makes claim c.
Conclusion: Claim C is true.

The fact that an authoritarian leader makes a claim does not provide evidence or a logical reason that supports the claim. It also does not disprove the claim—accepting or rejecting a claim because it comes from an authoritarian would both be errors. The authoritarian could be right about the claim but, as with any fallacy, the error lies in the reasoning.

The use of my usual silly math example illustrates why this is bad logic:

Premise 1: The dear leader claims that 2+2 =7.
Conclusion: The dear leader is right.

 

At this point, you might be thinking about the consequences someone might suffer from not accepting what an authoritarian leader claims—they could be fired, tortured or even killed. While that is true, there is a critical distinction between having a rational reason to accept a claim as true and having a pragmatic reason to accept a claim as true or at least pretend to do so. Fear of retaliation by an authoritarian can provide a practical reason to go along with them but this does not provide evidence. No matter how brutally an authoritarian enforces their view that 2+2=7 and no matter how many people echo his words, 2+2=4. While fear can provide people with a motivation to accept an argument from authoritarian, there are other psychological reasons driving the bad logic. This takes us to a simplified look at the authoritarian leader type and the authoritarian follower type. The same person can have qualities of both, and everyone has at least some of these traits—the degree to which a person has them is what matters.

An authoritarian leader type is characterized by the belief that they have a special status as a leader. At the greatest extreme, the authoritarian leader believes that they are the voice of their followers and that they alone can lead. Or, as Trump put it, “I alone can fix it.” Underlying this is the belief that they possess exceptional skills, knowledge and ability that exceed those of others. Perhaps all others, in the extreme cases. As Socrates found out, people think they know far more than they do—but the authoritarian leader takes this to extremes and overestimates their abilities. This, as would be expected, leads them to make false claims and mistakes.

Since the authoritarian leader is extremely reluctant to admit their errors and limits, they must be dishonest to the degree they are not delusional and delusional to the degree they are not dishonest. Trump exemplifies this with his constant barrage of untruths and incessant bragging.

Because of the need to maintain the lies and delusions about their greatness and success, the authoritarian leader is intolerant of criticism, dissent and competition. To the extent they can do so, they use coercion against those who would disagree and resort to insults when they cannot intimidate. Because the facts, logic and science would tell against them, they tend to oppose all these things and form many of their beliefs based on their feelings, biases, and bad logic. They encourage their followers to do the same—in fact, they would not have true followers if no one followed their lead here.  This describes Trump quite accurately.

While an authoritarian leader might have some degree of competence, their grotesque overestimation of their abilities and their fear of competent competition even among those who serve them will result in regular and often disastrous failures. Trump’s handling of COVID-19 provides an example of this. Maintaining their delusions and lies in the face of failure requires explaining it away. One approach is denial—to ignore reality, something Trump has been doing. A second approach is to blame others—the leader is not at fault, because someone else is responsible. Trump has done this is well. One method here is scapegoating—finding someone else to bear undeserved blame for the leader’s failings. Trump has blamed Obama, the Democrats, the media and the WHO for his failings. For the authoritarian, there is something of a paradox here. They must affirm their special greatness at the same time they are blaming vastly inferior foes who somehow manage to thwart them. These opponents must be both pathetic and exceptional dangerous, stupid and brilliant, incompetent and effective and so on for a host of inconsistent qualities.

An authoritarian leader obviously desires followers and fortunately for them, there are those of the authoritarian follower type. While opportunists often make use of authoritarian leaders and assist them, they are not believers. The authoritarian follower believes that their leader is special, that the leader alone can fix things. Thus, the followers must buy into the leaders’ delusions and lies, convincing themselves despite the evidence to the contrary. Trump’s supporters incorrectly believe him to be honest and competent. Some believe his untruths about COVID-19. And this is very dangerous.

Since the leader will tend to fail often, the followers must accept the explanations put forth to account for them. This requires rejecting facts and logic.  The followers embrace lies and conspiracy theories—whatever supports the narrative of their leader’s greatness. Those who do not agree with the leader are not merely wrong, but as enemies of the leader—and thus enemies of the followers.  The claims of those who disagree are rejected out of hand, and often with hostility and insults. Thus, the followers tend to isolate themselves epistemically—which is a fancy way of saying that nothing that goes against their view of the leader ever gets in. This motivates a range of fallacies including what I call an accusation of hate.

When I have attempted to discuss COVID-19 with Trump supporters, it almost always ends with them accusing me of hating Trump and their rejection of whatever claim I make that is not consistent with what Trump claims. I do think they are being sincere—like everyone, they tend to believe and reject claims based on how they feel about the source. Since they like Trump, they believe him in the face of all evidence.  This is fallacious reasoning. Since I disagree with Trump’s false claims, it must follow that I hate Trump—otherwise I would just believe his untruths. It also follows, at least to them, that I am wrong. While this makes psychological sense, it is obviously bad logic and can be presented as a fallacy—the accusation of hate. It has this form:

Premise 1: Person A rejects Person B’s claim C.
Premise 2: Person A is accused of hating B.
Conclusion: Claim C is true.

As my usual silly math example shows, this is bad logic:

Premise 1: Dave rejects Adolph’s claim that 2+2=7.
Premise 2: Dave hates Adolph.
Conclusion: So, 2+2=7.

While hating someone would be a biasing factor, this does not disprove the alleged hater’s claim. It can have great psychological force—people tend to reject claims made by those they think hate someone they like. This is especially true in the case of authoritarian followers defending their leader.

Since authoritarian leaders are generally delusional liars who fail often, deny their failures and scapegoat others, they are extremely dangerous. The more power they have, the more harm they can do. They are enabled by their followers, which makes them dangerous as well. In a democracy, such as it is, the solution is to vote out the authoritarian and get a leader who does not exist in a swamp of lies and delusions. Until then, non-authoritarian leaders must step up to make rational decisions based on truth and good science—otherwise the pandemic will drive America into ruin while lies and delusions are spun.

 

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