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Factual knowledge is not a substitute for logical understanding, and
logical understanding is not a substitute
for factual knowledge. Both are important, yet today there is an
abundance of knowledge but a dearth of logic except by those
relatively few people who deduce and confirm the conclusions they then
pass on to
others who learn them in the form of -- facts -- not
necessarily logical understanding why they are true and how they were
discovered. While knowledge has grown collectively over the
centuries, little has changed in
the amount of individual logical understanding or reasoning ability
time of Socrates, who discovered that while many adults had specific
knowledge, few had basic understanding or much ability to reason.
Knowledge is what is sought and taught, moreso than
logical understanding. And when tests are developed to assess
logical reasoning ability and understanding, that goal is thwarted by
those who teach their content
as facts to be memorized. And while today, lip service is paid to
teaching reasoning in the name of "critical thinking", it is still too
often taught as recipes
by those who don't themselves reason very well. With sufficient
knowledge, one can become quite successful, as many were in Socrates'
day, and so knowledge is avidly pursued. The
problem with only being knowledgeable about particular facts, and not
being good at reasoning logically, is that when a new circumstance arises, one
either misapplies the facts one has or is simply stuck without knowing
what to do. Without logical understanding, one often doesn't even
recognize that circumstances have changed in a significant way and just
blindly keeps going. In this paper, I will try to show how lack
of logical understanding and reasoning skills explains many of the seemingly
stupid choices people make in all areas of life, many of which lead to
fiascoes or to catastrophes that end up making headlines after the
damage is done, and long after it should have been foreseen and
I used to believe, and wrote an essay to the effect, that many people were not reasonable or rational because they didn't know what it meant to be reasonable (Reasoning: What It Is To Be Rational). I thought that if they did know, they would be. And so that essay was intended to explain that being reasonable meant that your evidence had to be not only true, but that it also had to be logically relevant to the conclusions you draw, and that if anyone held a conclusion that was contrary to yours, you had to show that their argument either contained at least one false premise (i.e., statement of evidence) or that its conclusion did not really follow logically from its premises (i.e., from the evidence) and thus, even if the premises were true, they didn't prove the conclusion and were not sufficient reason to believe it. So when any conclusion is false, either the evidence is mistaken (which most people understand) or the reasoning that uses it is flawed (which most people do not understand), or both.
Examples of these two kinds of flaws occur in criminal court cases or investigations. Evidence can be shown to be false, for example, by a solid alibi that shows a witness was mistaken when he identified the accused as going into the victim's apartment at a particular time, if a number of independent people, with no reason to lie, who know the accused were with him at the time in another city, far away, and there is incontrovertible video tape confirmation, cell phone tower usage confirmation, and travel confirmation, of his presence in that city at that time.
But it also sometimes happens that evidence presented by the prosecution, though true, is not sufficient to imply beyond a reasonable doubt that the defendant is guilty. When the prosecution rests its case, the defense may ask for a summary dismissal, by agreeing that all the evidence presented was true -- that the accused did have a disagreement with the victim a week prior to the murder, that the accused did stand to gain from the victim's death, and that the crime was a brutal one that deserves justice -- but pointing out that it doesn't mean the defendant committed the murder any more than any disagreement between two people where they each stand to gain from the other person's death, means that one would kill the other, and that the prosecution produced no physical evidence that the defendant was at the crime scene other than his alibi of being home alone could not be confirmed. That is not sufficient evidence to show the murder was committed by the defendant. At most it shows he might have done, but so could other people.
Or as an example of insufficient evidence, the defense may produce confirmed testimony that other people also fit all the evidence for guilt that the prosecution presented, and that any of them, and perhaps others as well, might have killed the victim. Unfortunately, if sufficient jurors are unreasonable and don't understand the logic of evidence, they might convict an innocent person anyway in this kind of case, believing that the accused looks guilty and that if the police feel he did it, he probably is guilty, and that is sufficient evidence for them to convict him.
In many areas of life, people behave in ways, and make decisions, that are not reasonable, and I no longer believe it is always just because they don't understand what it is to be reasonable, but that it is often because many people, including people with college degrees, those in positions of power, and/or those who are smart and are otherwise knowledgeable, simply cannot tell that a conclusion does not follow from evidence in any but the most obvious cases. The best they can do otherwise is to concentrate on whether the evidence is believable (or true) or not, and not whether it logically implies the claim for which it is given as support. They believe that if the evidence is true, the conclusion must be reasonable.
I teach college ethics courses and logic (or critical thinking) courses, and teaching either of those courses is like bailing water out of the Titanic with a coffee cup, because many students can't see how to reason from evidence to a conclusion, not just in difficult or complex cases, or in regard to topics they don't care about, but in any and every case. In the ethics courses, students have a really difficult time following any argument whose conclusion disagrees with something they are sure is right because they were taught it as a child and have always used it, and they immediately dismiss your evidence of the flaw in it as being "just your opinion". If you present a case for a better replacement principle that will do what they think their principle does, but without the problems or potential mistakes, they either cannot understand the principle if it is at all complex, or they cannot understand how it was derived or how to use it, or they will say your formulation is just a matter of semantics, because they cannot see the different implications of those phrasings which are subtly different in appearance but significantly different in meaning. Or they will often dismiss your inclusion of important distinctions they can't really understand and your inclusion of clear exceptions in general principles as being too "gray", and say they believe ethics is "black and white". Or they will claim the teacher is trying to impose his/her views on them. In the nearly 2500 years since Socrates, not much has changed in how people respond to questioning the logic of their ethical views.
In the logic classes, as opposed to the ethics classes, students tend to believe that the teacher must be right when the subject turns to general principles, but that the subject then is just too complicated and difficult for them to understand, and unnecessary and too arcane for the kinds of knowledge they use and need. They may say it is "like math" and they are "just not good at math" as though that means they don't have to be, in the way one might say one is not good at basketball or painting. But if you discuss specific cases of logical error about something they think correct, they again think the teacher is mistaken and trying to impose his/her view on them, though only about how to think and not about what is morally right or wrong.
In one ethics class I taught, I introduced a math problem whose answer is counter-intuitive, in order to show my students you can't just rely on what seems intuitively obvious, not only in ethics, but even in something as objective as math. The problem was: to qualify for a particular race, you have to average 60 miles an hour for two laps around a one mile long track. On the first lap, you have some sort of engine problem that only lets you go 30 mph, but it miraculously clears up right at the end of that first lap, and you have full power. How fast do you have to do the second lap, in order to average 60 mph for both of them together? Most people say 90 mph, because they add the 30 and the 90 and divide by 2, to get 60; a few say 120 mph, particularly if you tell them 90 is wrong.
The correct answer is that no rate of speed, no matter how fast, will let you qualify, because in order to average at least 60 mph over two miles, which is one mile per minute, you have to cover the whole distance in two minutes or less. But because you drove the first lap at 30 mph, you used up the whole two minutes just doing the first lap, so therefore no matter how fast you go on the second lap, you can't qualify for the race. The day I presented this, one of the smartest students was absent at the beginning of the class when I covered it, but although he was really good at remembering things he had been taught or had read, he tended to dismiss evidence that what he had read was not right or that it was only right under certain conditions or with qualifications, or only if interpreted very precisely in a certain way. I predicted to the class that if he showed up he would give 90 mph as the answer and that when we explained to him why that was not right, he would say, as he often did "No, it can't be. That's messed up." He came in late and he responded exactly as predicted in both cases and the class cracked up. I explained to him what they were laughing at, and he laughed at himself and his predictability. But he was still shaking his head at the evidence that 90 mph couldn't be the right answer.
I still believe that many people don't understand, in all but the most obvious cases, that true evidence can lead to a false, doubtful, or unproved conclusion and so that is why they concentrate only on arguing that their own evidence is true and the other person's evidence is false or not believable, usually for irrelevant reasons that seem perfectly reasonable and relevant to them. But I now also believe that it is at least as much a problem that many people cannot distinguish good from bad deductions or even recognize when a deduction or inference is being implied or drawn. They cannot see that some statements are meant to serve as evidence for others. They just see them all as different facts or different statements about the same topic.
In very, very obvious cases, they can see that evidence is not relevant to the conclusion. For example, the old joke giving the facts about how many people are on a bus when you get on it, and then how many people get on and how many get off at each subsequent stop, and then asking "What is the bus driver's name?". The answer is "Ralph" or "Norman" (or whatever name you want to use), and when they ask how you know that, you say "Because it was on his name tag." They, of course, say "But that has nothing to do with the number of passengers getting on and off the bus." Of course not; that is why it is a stupidly funny or absurd joke. Or, when I was young, "nonsense jokes" (many of them "elephant jokes") became popular for a while. "What's the difference between an orange?" [No, not "an orange and something else", but just "an orange; what's the difference between an orange?"] Answer: "A monkey, because elephants can't walk on lily pads." Or "What are the three ways you can tell there is an elephant in your refrigerator?" Answer: "You can smell peanuts on its breath, see its footprints in the jello, and you can't get the door closed." Now, everyone can see those are logically silly or ridiculous. But the minute you try to show that any reasoning more subtle has the same logical lack of relationship between premise and conclusion, many students can't see it, particularly if you try to generalize about the form of the argument and any argument in the same form. Let's start with a simple argument:
1) If President Abraham Lincoln was assassinated, he'd be dead.Now all three of those statements are true, and most Americans know that, but the first two do not prove the conclusion, because someone can be dead without having been assassinated or murdered. So even though the conclusion is true, you cannot know it from the two premises, and that is not the way people learned that Lincoln was assassinated; it was taught just as a fact on its own. For example, consider an analogy:
1') If President George Washington was assassinated, he'd be dead.In that argument, the first two statements are also true, but the third one, the conclusion, is not. This should show that there is something wrong with the form of the reasoning itself, which is:
But many people cannot see that means there is something wrong with the Lincoln argument or its form, and they say it doesn't show anything of the sort because the first argument is about Abraham Lincoln who was assassinated, and the second one is about George Washington who was not, so there is "no real analogy". These are the kinds of people for whom no analogy or counter-example can ever work to show their reasoning or argument is flawed because they always point to the differences between their argument and the analogy, and ignore the similarities because the similarities just don't mean anything to them or seem relevant in any way. That is a problem with their reasoning ability. Instead of seeing the differences as minor and the similarities as major, they see the differences as major and the similarities as irrelevant.1) If statement P is true, then statement Q is true.
When students in logic courses cannot see how that specific case works, they then cannot at all see the general principles involved with four different argument forms related to it:
Without going into the full explanation here, the above Lincoln/Washington arguments are in form B, and they are flawed; and in fact every argument in Form B is flawed because the first premise just says (somewhat oversimplified) basically that P is a cause of Q, but it doesn't say there can't be other causes. And every argument in form D is also flawed, since just because the cause mentioned in the first premise didn't occur, that doesn't mean there can't be another cause of Q which did, and nothing in the first premise rules out other possible causes of Q. On the other hand, every argument in Forms A and C, have good reasoning, and if the premise statements are true, the conclusions will have to be true.
Now the statement after the "if", is called the antecedent, and the statement after the "then" is called the consequent. The first premise or "if, then" statement in each form makes the claim that the antecedent in some particular case implies the consequent. The second premise in Form A says that the antecedent is true and concludes that the consequent must be true. The second premise in Form B says that the consequent is true, and concludes that the antecedent must be true. The second premise in Form C says the consequent is false, and concludes that the antecedent must be false. And, finally, the second premise in Form D says the antecedent is false and concludes that the consequent must then be false also. These are all common, everyday forms of reasoning.
The easy way to remember which forms work and which ones don't, is to just use the example initial statement: If someone was murdered, he is dead. That statement is always true.
Then suppose you find out: A) the antecedent is true -- the person was indeed murdered. You know then the consequent is true -- he is dead. That will be the same for every argument in Form A. If the antecedent is true, the consequent must be.Another way of seeing this is that the first premise in each of these forms says that P leads to Q, which can be represented visually as P --> Q. The second premise than says whether P is true or false of whether Q is true or false. Since the arrow leads only from P to Q, you know that whenever P is true, Q is also; and you know that if Q is false, then P must be also (because if P were not false, then Q would not be false either). And since the arrow leads only from P to Q, and that doesn't rule out that other things could also lead to Q, just knowing that Q is true doesn't let you know that P is true, and knowing that P is false doesn't let you know that Q is false.
That is a lot of verbiage, and if you just read it without really thinking about each part of it, it will seem like an overwhelming amount of information. But if you follow each step and "see" how it works, you will be able to understand it all very easily. Explaining ideas in words often makes ideas seem much more difficult or complex than they are. But if you follow the logic, and read for logical understanding, at some point the idea will often become clear, and you don't have to remember any of the words. It is like having driving directions to some place with each turn and distance you travel till the next turn. The list could be fairly long and formidable, but if you drive the route a few times, you learn it and don't need any of the directions on the list. You just know how to get there and don't really have to think about it. It is far simpler than the verbal directions make it look. It is a common phenomenon that when someone asks you directions, you say truthfully "I know how to get there, but I am not sure I can tell you correctly." Or the common way of saying it is going to sound more complicated than it is, is to say first "You can't get there from here."
Now, in teaching logic, many of my students, including successful college seniors, cannot follow any of that or any other explanations of inferences and deductions, and one wrote one time, of an argument which she, to her credit, able to see was in form B, but then said that "it was just like the argument where you find out the person is dead, and you conclude they were therefore murdered, so it is a good argument." My guess is that she probably could not "see" the logic of the murdered/dead forms above and had tried to memorize them, and got confused. Understanding material lets one utilize it much more easily and correctly than does trying to memorize it without understanding.1
I think that most people are born with the capacity to reason, because one can see evidence of little children doing it at a rudimentary level, and of primary grade students reasoning quite well even with complex material (often better than the teachers)2, but many lose it as it is not exercised or if it is systematically thwarted, as schools unfortunately to often do. I have seen older students recapture the ability to reason and then hone it, but I see many in my ethics and my logic classes who seem totally unable to follow any line of reasoning at all, or even to recognize it when they have to find it in paragraphs that contain it in prose form. And I have not been able to find a way to help them even begin to do it. Children seem to do better, so that is why my guess is that people are born with the capacity to reason but can lose it if 1) it is not exercised and developed, and particularly if 2) they face opposition to their trying to figure things out and make sense of them as they grow up, and if 3) they are taught to memorize things whether they make sense or not, particularly those things which make no sense to them (or to anyone).
When people, particularly those who make rules, laws, or policies, have difficulty understanding when one thing logically implies another or not, it causes all kinds of problems in all kinds of areas. And there is no reason to believe that if college students, including seniors, cannot reason, that they learn to reason any better after they have their degrees. And, if I am correct, it also explains why appealing to many people logically is futile and why they seem so stupid or blind. They are not necessary stupid, but they are blind -- logically blind, or blind to reasoning. They have no more awareness of reasoning than a psychopath has of reality or a sociopath does of other people's feelings. They have no sense of logical coherence or logical implication. And it is not that they just have insufficient skill that needs honing; it is that they have no skill (any longer, if they ever did at all) to be improved. If they are intelligent, they can learn to appear to be reasoning by learning other people's arguments or reasons for certain points, or by freely associating related facts, even though the specific relationships are not logically relevant. But they cannot see connections and cannot see when there is a subtle or a complex lack of connection. They are like sociopaths who can fake empathy by saying things they know empathetic people say in certain situations or like color blind people who have learned by association to say tomatoes and fire trucks are red because that is what people who can see color say about them. As I explain in Having Understanding Versus Knowing Correct Explanations, knowing what other people understand is not necessarily the same thing as understanding what they know.
As I wrote before, some people attribute the problem to logic's being like math to them and they say they are not good at math. But the reverse is probably closer to the truth; they can't do math because math is a form of logic, and they can't do logic or make reasonable deductions, or detect whether a deduction is reasonable or not. When I was growing up, teachers and relatives often gave us logic problems that they usually referred to then as 'brain teasers'. A couple of teachers had index cards in a box on their desk that contained such problems and when you were done with your assigned work, you could come up to the desk and take an index card with a problem on it to see whether you could solve it. Some of us found it fun, but people blind to logic would not, and they are probably good kinds of problems to see who can do logic at all and understand deductions and who cannot. But the problems have to be new to you, otherwise you can just go through steps you have been taught as a recipe or algorithm to get the answer without really thinking about it or understanding it. And not being able to derive the answer on your own is not necessarily a sign you are not able to do logic, because some times you cannot discover a solution to a specific problem at a specific time, but it is problematic if you can't understand the answer already given if it is pretty clear and logical.
For an example of the sort of thing I am talking about: there are three people all standing in a line, one in front of the other; all are very logically competent. The third person can see both people in front of him; the middle person can see the person in front of him, but not the person behind him. The first person, at the front, can see neither of the other two. They all know the following: there are five hats, two of which are white, and three of which are black. Three hats are chosen by someone else from these five hats and one each will be placed on the heads of the three people in the line. None of them will be able to see their own hat color, but the middle person can see the hat color of the front person, and the person at the back of the line can see the hat color of both of the two people in front of him. They can all hear each other and the questioner, who first asks the guy at the back of the line "What color hat is on your head?" He says "I don't know." Then the middle person is asked what color hat he has on his head, and he says "I don't know." The guy at the front of the line is then asked what color is the hat on his head, and he knows and says correctly which color hat he has. What color hat does he have, and how did he and you know?
Now, at first sight this might seem like a math problem, because it involves numbers. But it is not really, particularly since there are only five hats. Insofar as it involves "math" at all, it is very, very low level math. This is not algebra or calculus. The answer is: The person in front is wearing a black hat, and here is how he and you should know that. Since the person in back does not know what color his hat is, that means the hats on both people in front of him cannot both be white. Since there were only two white hats in the original group of five hats, if both the front two were white, the third man would know his hat has to be black and he would have said he was wearing a black hat. Since he says he doesn't know what color his hat is, that means either the first two hats are both black or at least one of them is black. When the middle person then says he doesn't know what color hat he has on, that means the first person cannot be wearing a white hat, because if he were, that would mean the middle man would know he had to be wearing a black hat. Since the middle person doesn't know what color his own hat is, that means the first person's hat has to be black, and he can figure that out for himself using the reasoning we just went through.
If someone can deduce that answer and explanation him/herself, without having heard a similar problem before, that is a sign s/he understands deduction and implication. But if one cannot deduce it her or himself, that is not necessarily a sign s/he can not understand deduction and implication, because one cannot always creatively figure out a solution to a problem. What is important is whether as the answer is being explained, one can follow it or not, since it is a fairly simple and straightforward deduction that is being explained.
And if you want to see a logic problem devoid of all numbers and math, consider the following: You are walking along a path that leads directly to a village you are seeking, call it Village A. But suddenly you come to an unexpected fork and don't know which way to go. But along come two local inhabitants who know the way. The problem is one of them always tells the truth and the other always lies, but you don't know which one is which, and to make matters worse, you are only allowed to ask one question and you can only address it to one of them. There is at least one question you can ask that will let you know from the answer you get which fork you should take to get to the village you want. What is that question?
Now this one is extremely difficult to figure out, but it should be easy to recognize how the right solution works, and then explain it yourself, once you are told it and think about it a minute, if you have any understanding of deduction. You ask either person, and it doesn't matter which, "Which path would the other person say is the correct path to Village A?" Then, no matter which path you are told, you should take the other one, because the other one will be the correct one. The reason is: 1) You will either be asking the truth teller or the liar, and you don't know which, but 2) if it is the liar, he will lie about what the truth teller would have said, and so he will lie about the true path, and thus tell you wrong. But 3) if you had asked the truth teller that question, he will tell you the truth about what the liar would have said, which would have been the wrong path. So whether you hear the lie about the truth or the truth about the lie, you will be given the wrong path, and thus you know to take the other one.
Of course, like most logic riddles these are far-fetched and contrived, but that is necessary to keep people from knowing or arguing about the content of more realistic problems, where they may have either knowledge that does not require reasoning or where they think they do. Logic is about deducing what we don't know directly from what we do know already. If we could know everything directly, we would not need to use logic. That is why it is seductive to think that if we just learn enough facts, we won't need to know logic or how to reason. But we usually can't come to know all the facts we might need or want, and are then left to have to deduce them. When we play poker, you know what is in your own hand, by looking at it. You don't have to deduce what cards you already have. But since you don't know directly what is in the other players' hands without cheating, you have to use logic based on knowing the odds of different hands, which cards have been played that they then cannot have, and possibly their betting quirks and telltale signs, to deduce what they likely have. And when people are asked to reason about something with which they have some familiarity, and they get it right, it is difficult to tell when they are reasoning for themselves and making deductions versus when they are just saying what they already know or believe. For example, now that you know about the truth teller/liar riddle, you could answer it correctly without either figuring it out or understanding the answer I gave. So if you give the correct answer to it, it does not show you can reason. However, if after the answer was explained to you, you still could not answer it correctly, that might be a sign you cannot reason.
If the preceding is correct, and if it is true that many people, even otherwise intelligent and successful people, cannot reason at all and cannot tell when evidence is being given for a point or whether that evidence logically implies that point or not, it would explain the following sorts of phenomena, all of which are frustratingly difficult to fathom otherwise, because they exasperatingly seem to be cases of clear reasoning not being heeded, when in fact they are merely examples of logic not being understood in the first place, at all.
It would explain, for example, why when evidence is given about the fatal flaws in any regulation or policy, that is not sufficient to get those in charge of those regulations or policies to change or rescind it. For example, it is fast becoming widespread medical insurance practice not to pay doctors or hospitals for patients whose problems recur or need additional follow up treatment because that is claimed to be a sign they were not treated correctly the first time, which was already paid. Yet, there are all kinds of reasons a patient, particularly one with a difficult condition or one who doesn't follow his/her treatment as directed, might have a follow-up problem that has nothing to do with inadequate or improper care. And as one doctor put it, apparently it would be a sign of successful treatment if the patient just dies, since then there would be no recurring health problems or necessary follow-up medical treatments. But the policy is not changed.
By the way, sacrcasm, satire, and cynicism of that sort, based on logic, does no good for changing the minds of logipaths for two reasons: 1) they don't get it, and 2) they think that it is merely ridiculous, unfair criticism that makes no sense and that rudely mocks them. They can see it mocks them, but they don't know why, and think it is just because the person presenting it simply disagrees with their views and is being arrogant or condescending about it. Instead of being educated or persuaded to change through such logic, they are merely offended.
Lack of basic reasoning ability explains why businesses and other institutions have many really stupid policies and rules, and why those are not changed when they are shown to be stupid. Instead some formal procedure is pointed to that makes them legitimately instituted and thus "perfectly reasonable" to logipaths. For many people, being reasonable just means following the rules, and the rules are reasonable if they were passed by the proper procedure according to the rules for making rules and policy. My college degree is in philosophy, and when the International Baccalaureate diploma became available in some local high schools, one of the courses in it is "Theory of Knowledge" which is basically a philosophy course. I called the State Board of Education to find out what it would take to become certified to teach it, given that I already had an MA in philosophy. Could I just take some education courses? I was told no, that would not be sufficient. In order to teach a philosophy type of course in a high school, you need an education certificate in Social Studies, and philosophy courses don't count toward a degree in social studies, so I would basically have to start from scratch to get a degree in education with a social science major. I could not teach a philosophy course with a degree in philosophy, but I could teach it with a degree in social studies which has nothing to do with philosophy, any social studies field. And I then distilled it in that manner for the person telling me the regulations, who agreed that was an accurate charcterization of the policy, and when I said "And I'll bet that makes perfectly good sense to you, doesn't it?" she said, "Yes, those are the rules that the board members passed, and so that is the way it should be."
Lack of basic reasoning skills also explains why bad management can remain in place to keep making bad decisions, and why reports of problems caused by those decisions are considered to be signs of disloyalty to the company or disobedience to the chain of command instead of valid concerns that need to be heeded about flaws that need to be remedied. Supervisors in business, government, and in medicine, and superior officers in the military, often make terrible decisions and policies, and those too often result in the loss of life through reckless disregard for (product or per personnel's) safety and human life (think Ford Pinto, for example), not to mention vast amounts of wasted, unpaid, or robbed labor that is the ultimate result of poor financial decisions. The catastrophic loss of the space shuttle Challenger was an example of poor reasoning by management. Engineers warned administrators that the fuel seals might not hold in the extreme, unseasonably cold temperatures occurring at launch time in Florida that morning. They begged for the launch to be postponed till the temperatures were much warmer. Administrators said there was no evidence of such danger. But there was no such evidence only because tests had not been conducted at such low temperatures that were never expected to happen at the launch site, and the managers ignored evidence based on theoretical understanding of the properties of the materials involved. Here is a supremely sophisticated, complex engineering project, run by administrators who ignore the warnings of engineers. And they do that when the price of postponement is paltry compared with the cost of catastrophe. Surely this displays a total lack of reasoning ability, not just some uncharacteristic mistake or understandable occasional human error in judgment.
It also explains why form and traditional or standard procedure, and "business as usual" (or as it is extrapolated by mere intuition without much logical reasoning that it should be done), often take precedence over substance and results or consequences. For many people, if the standard or required forms and procedures are followed, and/or if traditional practices in the field are pursued or even just approximated, any harm done is unfortunate but not wrong, and not a sign of anything unreasonable or wrong in the process. It is only when someone or something important to somebody in a higher position of authority or when overwhelmingly sufficient people protest that the results are a sign of mismanagement, that consequences begin to matter and policies get ostensibly examined and possibly changed (though still, often not), or people fired or prosecuted (though again, often not). The view is that if the rules or standard procedures (or some freely associated approximation to them) are followed, nothing can go wrong, and if something does go wrong, it is not because of the rules or following them. That there could be something wrong with properly instituted rules, makes no sense to those without basic reasoning skills. And the admonition is always if you "don't like" the rules (as if it is not about problems with the rules, but about whether enough people like the rules or not), you should work to get them changed, rather than breaking them, no matter how bad the consequences (for others usually) would be in following them. Following rules and standard procedures is a poor substitute for understanding, particularly moral understanding, but many people simply don't know the difference or that there is a difference.
This was taken a step further in Major League Baseball's ruling on the clearly mistaken umpire call that cost Detroit pitcher Armando Galarraga a perfect game on the last out when a runner was called safe at first, and instant replay showed him clearly out. The umpire, Jim Joyce, saw the replay later and tearfully apologized to Galarraga afterward for his terrible mistake. But baseball doesn't have a rule to allow instant replay, and the commissioner's office used that excuse not to reverse the call. I don't think they need one for this because they are not understanding their own rule already in place that governs it:
The clarity of the instant replay takes this particular play out of the realm of "judgment call", which is basically a call for which there is no clear or incontrovertible evidence that can show what actually happened or that an umpire's call is wrong, even though many people might disagree with it, as is pretty much inevitable. In such cases, someone's decision has to count and so the "judgment" of the umpire is relied upon and is final, even if it may be arbitrary or (unable to be known to be) mistaken. But when even the umpire admits he was mistaken, and every baseball fan who saw the game or the news reports and replay later knows the call was wrong, it seems most irrational to say the call has to stand, even though reversing it would affect nothing other than the 27th and 28th batters' batting averages negligibly, and would give Galarraga the significant credit for the amazing and rare performance of pitching a perfect game that he deserves. In football, the precedence of "judgment call" is preserved even with the instant replay rules, in that it takes conclusive evidence in the replays to override the call on the field by the official. And part of the significance of that is when replay evidence is inconclusive from all angles, meaning there is likely no possible way to tell what actually happened, whichever way the referee judged it will be the call. Had the official called it the other way, that would have been what stood. Those are the kinds of cases where what is in some sense the arbitrariness or luck of the call can and should stand, simply because that arbitrariness and luck cannot be avoided. But in cases where the evidence is definitive, it is bizarre to say one has to still consider it a judgment call, and that the mistake needs to be officially accepted as correct. (Some television commentators added that part of the wonder and beauty of baseball is that it has a history of human error, and should not be changed in that way. Good thing these people are not in charge of medical progress, making pronouncements like 'the beauty of the history of medicine is that lots of people died in the past of things we could cure now if we chose to, but we shouldn't choose to do that and spoil such a wonderful tradition.')"9.02 (a) Any umpire’s decision which involves judgment, such as, but not limited to, whether a batted ball is fair or foul, whether a pitch is a strike or a ball, or whether a runner is safe or out, is final. No player, manager, coach or substitute shall object to any such judgment decisions."
Absense of basic logical abilities, explains why public debates usually center around the truth of claims and reasons, rather than whether the reasons which are given as evidence don't logically imply or support the positions taken even if those reasons are true to begin with. And it explains why people give lame reasons as long as they can argue they are true. It doesn't matter to them or their constituents that evidence can be true but still not be reasonable or relevant. So instead, other means besides logic are employed to persuade politicians, such as marches in the street, large rallies, poll survey results, huge petition drives, visible political pressure in large numbers, donors threatening to cut off campaign contributions or promising to make very generous ones, etc. -- things that affect their position of power, or that show them a majority of their voting constituents have changed their minds. In such cases, politicians and elected officials follow public opinion, no matter which way it goes, rather than helping lead and shape it through reasonable explanations to their constituents about what is right and why, given the best possible evidence. The only politicians immune to public opinion are those locked in to an ideological position, but those positions tend to be impervious to logic and rational argument also. In many cases, politicians' beliefs, based simply on likes and dislikes or on feelings of what is right, simply are the same as the majority of their voting constituents, and what gets them elected is not the logic of either the constitutent or the candidate, but the fact that the candidate can articulate or express the beliefs of those constituents in a way that allows them to feel well-represented by him or her.
And that may help to explain why the Supreme Court so far has equated (or confused) campaign contributions with freedom of speech. If the only "logic" a candidate can understand, or a contributor can express, is approval or disapproval of political positions by the giving or withholding of significant campaign funds, then money is their form of "argument". Moreover, insofar as a majority of voters confuses advertising with the logical presentation and scrutiny of political positions, and money is needed to increase advertising, then one can, in some stretch of logic, maintain that money is necessary for free speech even if it is not equated with it. And a majority of the court, as of this writing, either think at least some of that is a reasonable form of argument or think they have to let it count as such to those who believe it.
Even research scientists often misinterpret their data and don't have a good sense of what constitutes legitimate evidence. A current obsession in medical research in the United States is with random, double-blind, placebo-control trials as being the only good evidence even though there is good reason for other sorts of evidence being just as good and often more appropriate and ethically superior (see, for example, A Perspective on the Ethics of Clinical Medical Research on Human Subjects or Smith, Gordon C S and Pell, Jill P. Hazardous Journey: Parachute use to prevent death and major trauma related to gravitational challenge: systematic review of randomised controlled trials, BMJ 2003;327:1459-1461 (20 December), doi:10.1136/bmj.327.7429.1459r3).
Students often give answers that make little or no sense, or that won't stand up to any kind of scrutiny, and I try to explain to them what the problems are with each of their answers. Part way through each term in my ethics courses, I get comments from some of them saying "Oh, you want us to think deeply about what is right in these cases, not just give a surface answer to get credit just for 'doing' the assignment", while others say "I just don't understand what you want. None of this (meaning the reasoning and the examples and analogies given in the explanations in the readings and in the discussions) makes any sense to me." In the first instance what the student considers "thinking deeply", I consider just "thinking". Often students will say they have read the material three or four times and they still don't understand anything. Upon questioning them, it will be clear they are right, that they don't understand anything. So I will then ask some probing questions to see what they understand, and the conversation typically goes something like this:
Me: Do you remember the example about the 100 correctly convicted murderers on a train headed toward a school bus with 10 children on it.
Student: Kind of, but I didn't understand it.
Me: Okay. There are 100 rightly convicted murderers being transported by train to another prison. But a school bus with ten young students on it is stuck on the tracks. You can stop the train from hitting the bus only by switching it to run off a washed out bridge over a cliff. (The engineer will be saved or is already dead, but he will not be killed with the murderers. Likewise any prison guards.) What should you do, save the people on the train or the kids on the bus?
Student: I don't know. I guess I would save the children on the bus.
Me: Yes, isn't that what you should do?
Student: Okay, but what does that have to do with anything?
Me: Well that was one of the situations I gave to show that the principle of utilitarianism -- that you should always do what brings the greatest good to the greatest number of people -- is wrong. And there were ten other different kinds of cases where it would also be wrong to do the greatest good for the greatest number of people. Do you see that?
Student: I guess. I'll go back and read that again and see what it says. Maybe I'll get it now. But I just can't remember all this stuff. There is a lot there.
Me: But this is not about memorizing anything; I said that in the announcements. It is about understanding it as you read. You should see what the examples illustrate, and think about the principles they help show are right or wrong. Some are meant to show what is right about a principle; others are meant to show what is wrong with some principle.
Student: I didn't know that. Okay, I'll read it again.
There is not much reason to believe students like that will understand reasoning or logic any better in the work place or the military. A friend of mine was in charge of the computer programming and data for a national company. He was invited to a meeting where they discussed the idea of buying a half million dollar computer system for the company. He explained to them why it would not serve their purposes well and thought it was unnecessary and would be a waste of the money. They held more meetings without him and then bought the system. It didn't do what they wanted it to, and so it was basically a half million dollar loss for them. He later asked one of the bosses why they had not had him at the other meetings, and was told: "You had such good reasons for why it was not a good idea to buy it, that we were afraid you would talk us out of it. And we wanted to buy it." Those people all had college degrees, but apparently either couldn't reason or didn't realize that reasoning had anything to do with reality.
The reason many children get turned off to math is that it is too often taught by rote (memorization and drill) rather than by understanding. That works for doing calculations that are already set up, but it doesn't help students learn about number relationships; so when they get to word problems or to algebra or any kind of higher level math that requires understanding number relationships, they are lost. They know how to calculate what they are told, but don't know how to figure out what kinds of calculations they need to do to solve problems they have to think about. And they often lose all common sense in trying to just follow recipes. One student somewhere else in the country wrote me for help one time with a word problem, in which he said there were two planes flying in opposite directions at the same speed (forget about wind, zero wind factor) and after two hours one of the planes had traveled twice as far as the other. Then he went on to ask the question. I pointed out that it was impossible for one thing to go twice as far as another if they are both going the same speed for the same amount of time. If two things go at the same speed for the same amount of time, they have to travel the same distance. If you are running a race with a friend who runs exactly as fast as you do, you will be neck and neck throughout the race, no matter how long you both run. He then reread the problem and sent me the correct version of it.
But even many teachers who think math needs to be understood, not memorized, think understanding cannot be fostered by instruction (but only by the child's self-discovery), and they confuse any attempt to do so with merely manipulating the child to get the answer the teacher "wants" by some kind of imposed form. They cannot see that 1) children can "discover" things that actually turn out to be mistaken, and 2) that there are ways to break down an idea into component logical steps that children can grasp and see the consequences of, though adults often cannot. The Socratic Method4 paper gives an example of how to do that, which the students figured out perfectly, but which adult teachers I practiced on first could not do. I have received emails from other teachers who subsequently read that paper, saying that though they have taught elementary math and place-value to students for years, this is the first time they themselves really understood how it worked. The children's answers showed them how it all went together. Yet one math teacher who thinks that children have to construct their own understanding of math said I was merely psychologically leading the students in that Socratic Method exercise. She couldn't see the difference between logically leading students to discover insights and psychologically leading them in ways that just got them to give the answer without really understanding what they were doing. If my questions were merely psychologically leading ones, the adult teachers should have been able to answer them correctly too. As to self-discovery's being wrong. I once was working with a different third grade class to teach them "place-value" using a method involving "color value" of poker chips (or color tiles). One girl showed me she had discovered a method in second grade for subtracting two digit (and larger) numbers. I had her show it to me, and it was something I had never seen before, and was really weird in that I couldn't see any reason why it would work, and it intuitively seemed mistaken. But with each problem I gave her, she got it right using her method. So I went off to the side of the room to think about it a bit, and finally saw why it worked, but also saw what the conditions had to be for it to work, and I saw it would not work if the number from which she was subtracting had zeroes in it. So I gave her some problems where I knew it wouldn't work and had her check her answers against a calculator. Once she saw there was a problem, I was able to explain to her why her method worked in the cases she had shown me, and why it didn't work reliably in general though. And she was able to see it.
But the most serious problem, it seems to me, probably because I think ethics is one of the most important areas of life and involves all activity, is that too many people cannot reason well about ethical issues. They basically give the same answers they would have given in a fifth grade Sunday school class, which involves rules such as the Ten Commandments, or the Golden Rule, or "being nice", sharing, and doing what they have been taught, being obedient, etc. Those sorts of mores work in everyday social situations for the most part, particularly in a fairly homogenous culture. The problem is they don't work in complex situations or ones that have conflicts between different rights or different rules, or conflicts between rights or normal obligations on the one hand amounts of good missed or harm done by honoring those rights and obligations. I usually begin my college ethics course by asking students (many of whom are older adults) to tell which conditions make it right to break a date, and why they think it is right in those conditions. The students are surprised to find out how difficult that is for them and how much disagreement there is among them. They find it very difficult to resolve those disagreements, and they find it almost impossible to derive general principles from (or see patterns in) the different conditions on the class list that survive scrutiny. Later in the term if you raise questions about what seem to them to be clear cut standard practices in business or about any social custom (such as how much they as the owner of a company should pay their employees, and what should determine it), they are often surprised to discover those practices involve ethical questions that are difficult to answer and ethical assumptions that are difficult to justify. They had never thought of those things as involving ethics. It is no wonder that people in all walks of life make egregious ethical decisions openly and without a moment's thought, because it never occurs to them that a standard practice is an ethical matter at all or has an ethics component. And even if they did know that, they don't have the logic skills or understanding of general moral principles to be able recognize, analyze, and evaluate the best options. I am not talking about cases simply of disagreement about what is right or wrong in a given circumstance or scenario; I am talking about not being able to recognize ethical components of some choices at all or even beginning to be able to give anything other than the most simplistic attempts at justifying one's beliefs, which will not stand up to scrutiny at all. And I am talking about not being able to understand counterexamples or other sorts of evidence against one's beliefs, or knowing how to have a rational discussion to resolve and remedy the problems.
In short, it is an error for education to be mostly about facts and rote learning, rather than deeper understanding of all sorts of topics from math to social and natural sciences to business, to management, to finance, to medicine, etc. Students begin school with the capacity to understand material and reason about it, but we diminish that capacity by not nourishing, stimulating, challenging, and honing it. That causes a great loss in potential, and it allows some of the really terrible mistakes and misjudgments that make the headlines, unfortunately all too often.
In the second semester of introductory calculus my freshman year in college, we had a midterm coming up in week 8 of a 15 week term, and it was looking to be really difficult. The midterm covered two chapters of the textbook, and in each chapter there were some 30 or so formulas apiece we had to know to work the problems. Working on the homework every night and on weekends showed it was really difficult to remember which formulas went with which kinds of problems. During week 6 or 7 of the term, they announced they were postponing the midterm until week 12, so they could include a third chapter, because the three of them together made a better unit. I didn't see anything about the first two chapters that made them at all a "unit" in the first place, so I didn't see how adding another 20 or 30 formulas was going to make this any more unified. And it didn't; it was really difficult trying to keep track of all the formulas. I should have asked what the unifying factor was, but assumed it was something I was supposed to see and that if I asked, it would show my ignorance. So I futilely just kept trying to figure it out on my own.
The night before the exam, I was working problems with the same result as previously, getting them right fairly often, but missing far too many because I used the wrong formula. I knew that under the pressure of exam conditions, it was going to be worse, and really bad. I finally just went out for a walk in the night air to try to clear the cobwebs a bit. While I was walking, I still kept fretting over their talking about all this making a better "unit" and wondering why they said that or how it could possibly be. Suddenly an image flashed into my mind of the first page of the first of the three chapters (which I had gone over and over and over), and I noticed in my memory that it had more bold print than usual. I had always thought the first line of bold print in each chapter was some sort of stylistic art feature that had no significance, but since this page had so much bold, it made me wonder. It occurred to me perhaps the first formula in the first chapter was some sort of general principle from which all the other formulas were derived. I went back to my room to test that theory, and, sure enough it was right. It turned out that all you needed to know was that main formula, and you could derive the ones you needed, given the information in any of the problems. I felt like a fool that it took me so long to see that, but I was relieved I saw it the night before the exam, rather than the night after it. This was a large course with some 1500 students scattered throughout 60 classrooms each day, and they gave everyone the same exam at night in auditoriums around campus, and then graded and curved the exams that night, and gave back the papers and results the next day. I finished the exam early and it had been pretty easy. The next day, however, the teacher came in to the classrooom looking stricken and upset. It turned out the test results across the whole course were terrible, and the professors had been really upset at the instructors like him. He passed out the exams, and I saw my score was an 83, and though I didn't know how many possible points there were on the test, I figured I was somewhat safe at least. It turned out, as the teacher explained, there were 84 possible points, and no one had got an 84. There was one 83, and the next highest score was 56, with the course median (across all 1500 students) at 30. The reason I had not got an 84 was that I had made a careless error when I simplified an answer I didn't need to have simplified. I had the right answer as the square root of 2, but I simplified it to 1.414 and forgot to put the plus-or-minus sign in front of it. I hid my test score from my friends. It turned out that I was not the last student in the course to see how all these problems were logically related; I was the only one. Now many of the students were far better at math than I was, but I happened to have had this one insight about these problems in time to do well on this exam; and the insight did not come from just a mathematical deduction but also from their comment about the unity of these three chapters that let me know there was something I must not have been seeing. If I had had to rely on just memory of the formulas, I would have done far worse, as they did. It is just better to work from understanding than from memory, when there is a lot to remember and particularly when you are under pressure.
And although I have a pretty decent memory when I study hard, I have always found it difficult to give a speech from memory. I could never be an actor. Yet I have no trouble teaching in a class or giving a lecture to a group without notes, because I am talking about things I understand and have organized for a presentation in a way that makes sense to me and that I can get to make sense to my audience.
And I think this is related to a totally different kind of activity -- learning and performing a dance routine. I cannot hear a beat in music. I can in poetry, but not in music. I cannot clap my hands or tap my foot to any music and don't understand what people are clapping to or how they can all do it simultaneously in unison the way they do. So when I watch dancers or figure skaters do a dance routine to a long piece of music, I marvel at how they can keep all those steps memorized in their heads; I can't. I have since found out that dancers don't have to memorize the steps in the way I would; they can feel which steps go with which parts of the music, and so as the music plays, they just naturally (after much rehearsal and practice) can dance to and with the music. I can't do that. I can do dance moves, but not to music. So I am not really dancing, but just doing "dance motions" (or something akin to them) while music is playing. Without "understanding" or perceiving the relationship between motions and the music, I am having to rely on memory, and it fails. I think students in a course that requires critical thinking have a similar problem -- they try to memorize which kinds of statements go with which kinds of questions or problems, because they cannot "see" or "feel" or "perceive directly" what is right. To them one answer makes as much sense as another, just as to me, one dance step fits as well to any part of the music as another. In both cases there is no perceived connection at all. (Return to text.)
For example, see The Socratic Method: Teaching by Questions (Return to text from footnote 2.) (Return to text from footnote 4.)
An article showing the pathetic dearth of random, double-blind, placebo-control trials for the efficacy of parachutes during jumps or falls from great heights, particularly airplanes. (Return to text.)