

The following are ideas about what reasoning is and about what it is to be reasonable. It also offers some conjectures about why many people don't seem to have good reasoning skills or to be very reasonable. It is offered here for students whose teachers do not seem to think very highly of their work, but who themselves do not make very clear what they think is wrong with it. In some cases students and professors may have very different ideas about what it is to show good reasoning in a paper or class or to present a case in a reasonable manner.



If little children are playing with chess pieces and a chess board, but are making arbitrary moves in what they think is emulation of adults they have seen playing chess, it is not just that they are playing chess badly. It is that they are not playing chess at all, regardless of what they think they are doing or what they call it. There are some things that are difficult to distinguish between whether they are being done badly or whether they are not even being done at all. It is crucial to understand the difference, for it is often not helpful to try to improve the performance of someone who is not even doing what you are trying to get him to do better. He won't see you as improving his performance but as merely changing it. It will generally not serve much purpose, for example, to correct the children's chess moves until you explain to them what chess is and what the rules and goal are. Otherwise if you try to "correct" a move, they may simply say "but we do it this way." There are common exaggerated uses of the distinction between doing something badly and not doing it at all. If a person dances very poorly, other people might say they are not sure what he is doing, but he is certainly not dancing. We say of some people's culinary efforts not just that they are bad cooks but that they "can't cook at all." And we say some people "cannot sing a note," though they may think they are singing. These seem to me to be satirical applications of the distinction rather than real examples of it, as in the above chess case. But there are some cases where it is not clear how we might describe the situation. Yet an accurate description or understanding of the case may be crucial for improving someone's performance. Suppose someone does a math problem very poorly, using algebraic language and symbols but utilizing "reasoning steps" that seem to us very bizarre, and when asked to explain why he used those steps, says "I am using algebra". If his steps and reasons were so far removed from anything remotely approaching GOOD algebraic reasoning, we may be quite tempted to feel that he did not use algebra but merely what he mistakenly thought was algebra. It may be not just that he does not understand how to work this problem, but that he does not understand what algebra "is about" in general. These are two different difficulties, requiring two different approaches to remedy. Or students may write an exam answer or do an assignment in such a way that it incorporates all the features a teacher requires, but does it in such a way that shows either the student does not understand those features well or that he did not get the point of the features. Knowing the cause of the problem is important to correcting it effectively. Recently it occurred to me in one of those all-encompassing revelations that "reasoning" itself is an activity that some people sometimes seem to do so badly that it is more accurate and more helpful to think of them as not actually reasoning at all, though they may mistakenly think they are, and though they may be doing something that seems like reasoning. What makes this "all-encompassing" is that it explains a great deal of what seems to be poor decision-making and poor logical ability on the part of a great many people, not all of whom are students, and not all of whom are outside positions of wealth, power, influence, and authority. When teaching, I have always concentrated, not just on presenting "factual" subject content, but, on trying to get students to see logical relationships in the material and, when necessary, trying to improve general reasoning skills, so that the conceptual and logical aspects of the subject matter would make sense to students and so that they could derive needed or new material, thereby depending less on memory. I pointed out various sorts of common fallacies and I required myself and students to justify our views in class, trying to expose fallacious or weak reasoning wherever it appeared. Many students seemed to catch on and to become skilled, but there were students who seemed not to get it at all and who were either just debating to try to score trivial points or who gave reasons that just seemed to make no sense or were repetitions of points we had just shown flawed. Many of these students were quite intelligent, as are many quite successful adults who nevertheless seem quite often not to be very sensible or reasonable about various matters. I think it is not so much that these people reason badly as that they are not reasoning at all, but merely emulating the outward behavior of people they believe to be reasoning. They are behaving like the above children who are moving chess pieces. In teaching my own courses (as opposed to teaching isolated topics in another teacher's course or in a one-time forum) I had explained what it was to be logical and reasonable, but I now believe that even when I did that, I did it too summarily, and incorrectly assumed the students understood what "being reasonable" is. I thought they only needed to improve or focus their reasoning skills. I now believe that most people do not know what it is to be logical or rational or reasonable; and I think that, like children moving chess pieces or students merely using algebraic lingo without understanding, too many people are merely mimicking what rational discussion sounds like to them, but don't have any real understanding of what they are trying to accomplish. So before one can improve their reasoning skills, one has to show them what reasoning is; i.e., what counts as reasoning and what its point is. Without doing that, one turns reasoning only into a game to these people, a game whose point is arbitrary or unclear and whose rules or methods are external, behavioristic, contrived, and capricious. I suspect there are a number of incorrect things people are doing when they are being what they consider "reasonable". Some seem to think that being reasonable means merely "having reasons". It does not matter to them that their reasons are untrue or improbable or that they may not even be relevant to their conclusion. When you point out problems with their reasons and their conclusions, they say things like "Well, I have my reasons, and you have yours." And if you are bold enough to say something like "But yours are no good! That is what I have been trying to show you!", they dismiss you with "But they are my reasons!" Some seem to think that reasons are only meant to persuade oneself or others. If they do persuade others, as in a debate, political campaign, or courtroom, that is all that matters. Truth, for people with this perspective, is irrelevant or is merely what people can get each other to believe. And if one fails to persuade others of one's viewpoint, that is unfortunate but also unimportant if one has the power to do what he wants to do anyway. Such people see no distinction between good objections to their views and bad objections to their views; they only see persuasive and unpersuasive objections. One friend of mine was invited to sit in on company discussions about the purchase of a half-million dollar system of some sort and he voiced objections, explaining why it would not successfully do what they wanted it to do. He was not invited to ensuing meetings; the system was purchased; it did not meet their needs; and the company took a half-million dollar loss. Later he asked why he had not been wanted at the meetings where the decisions were actually made about purchasing the system and he was told that he had such good arguments for not buying the system, they were afraid he would talk them out of it, and it was something they really wanted to buy. They apparently understood logic as persuasion, not as something to do with facts or reality which might let them know ahead of time whether something would actually work or not. Some people seem to think that "being reasonable" only means "seeing" both (or all) sides of an issue. One does not really need to UNDERSTAND either side or the reasoning on either side; one only needs to recognize that different people believe different sides, and perhaps know what those sides are. One may even be able to state both sides and any reasons each side gives. But the reasons themselves don't actually mean anything to the third party who simply takes some sort of impartial, uncritical, egalitarian approach to the whole thing. If he has to decide between them, he often tends to believe the best decision is one that angers both of the involved parties, as if something that both sides believe to be wrong is somehow more likely to be right or better than an explanation of why one side is more reasonable than another or than an alternative idea that genuinely satisfies both sides. Hence, if one witness thinks he saw a yellow getaway car and another thinks he saw a blue one, green is the color the police ought to note on their reports; or if one side thinks we need all-out military action and another thinks we should not use military action at all, the proper course must be to use limited (insufficient) military action. Government and business leaders are fond of saying they get criticism from both sides of various issues, so they assume they are doing the right thing. How reasonable is such a view? Would they not get such criticism also if they were simply doing the totally wrong thing? Finally, many people, including some scientists and some scholars, tend to believe that what is reasonable is what conforms to rules, traditions, or accepted procedures, and it does not matter whether those things have reasonable justification themselves. Often some reasons are given in attempted justification of methodologies, rules, or traditions, and they are considered sufficient regardless of how true or relevant they are. Nor does it matter whether an alternative may be more logical; too frequently logic seems to have nothing to do with methodology or with what is right. It takes years before conflicting "facts" outside of a given methodology are able to be accepted as facts or evidence, and the "traditional" methodology then seen to be inadequate in some kinds of situations. One person told me he thought that being reasonable was "making things make sense"; i.e., that "something is reasonable when it makes sense." That, I believe, is a step in the right direction. Perhaps it needs to be added that what needs to make sense is ALL the available relevant information, and that ignoring relevant information is not the same thing as making sense out of it. However, the notion of making sense out of things is perhaps vague, and I would like to suggest another way of looking at what it is to be reasonable. I think that every high school and every college student needs to be taught what reasoning is and what it means to be reasonable. I offer the following as such a description. I believe it applies to all disciplines. At the end of this essay, there is an example, with commentary, of a position that is meant to be logical and reasonable stated in a fully explicit manner to show the various reasoning steps. Being reasonable means holding beliefs and views for which (1) one can give true or probable evidence that (2) actually (or sufficiently and relevantly) supports them. And it means also (3) having true or probable evidence about what is wrong with beliefs that oppose or challenge your conclusions or the truth or sufficiency of your evidence.* For the only ways any views can be reasonably challenged are by the supported claim that (1) the conclusion is not true, (2) that the evidence is not true, or (3) that the evidence is insufficient to justify the conclusion. The only ways you can have mistaken beliefs of any sort is to have faulty evidence -- evidence that is not true or that, even if it is true, still does not support your beliefs. (As an example of the latter point, the view that the sun moves around the earth does not follow from the appearance that it does, because that very same appearance can be explained by a rotation of the earth instead. So even though the reason for believing that the sun is revolving around the earth is true -- that we see the sun going from east to west each day -- that reason does not necessarily lead to the conclusion that the sun is revolving around the earth.) Showing evidence to be not true or to be inconclusive does not, by itself, show a conclusion to be false, but it shows it unreasonable or unwarranted to believe it on the basis of that evidence. Other people's evidence that your conclusion is false must itself be faulty in some way if your conclusion is true; otherwise your conclusion must be false and there must be something wrong with YOUR evidence for it. Whenever there is evidence that a belief or a conclusion is true, and other evidence that it is false, there must be something wrong with at least one of those sets of evidence. As a corollary, this all means being able to support your reasons or evidence itself, insofar as is necessary. So, if someone challenges the truth of any of your reasons, you need to be able to give the evidence you believe that reason itself is true, and you then need to show why you think their challenge is itself faulty. In other words, you will be looking at the reason under attack as a conclusion itself -- a conclusion of a "prior" argument or of prior evidence. In one episode of the television series "Law and Order", the defense attorney challenged the eyewitness testimony of an elderly woman who had positively identified his client as the perpetrator of a crime. He asked her age and he asked her about failing vision. When she denied any problem with her vision, he asked her to identify a mural on a far wall in the courtroom. She said it was some part of Manhattan in the seventeenth century. When he sarcastically asked her whether she was familiar with 17th century Manhattan, her response annihilated his attack on her credibility as an eyewitness from the standpoint of her allegedly having impaired vision: "No, young man, but I can read the legend at the bottom of the mural." (The legend was in small script.) As another corollary, it means having true or probable, relevant, sufficient evidence against other people's conclusions you dispute, or against the truth, probability, or sufficiency of their evidence. (Whenever possible and feasible this may include expressing not only what you think is untrue or irrelevant but what you think the correct or relevant points are. Sometimes, however, this latter is not possible, as when one knows, and can demonstrate, something is wrong, but does not know what is right to replace it.) Evidence and conclusions can be disputed as being either false, unproved, improbable, unclear, or meaningless. Being reasonable, when evidence is only probable at best, does not necessarily mean being right, just as being right does not necessarily mean being reasonable. Betting the mortgage on a pair of kings in a high stakes poker game will be a winning bet in those cases where no one is able to draw a better hand, but it is not normally a reasonable bet. Oppositely, betting a high, but affordable, amount on a straight flush may be quite reasonable, but may lose to someone who has the rare and improbable royal flush. Being reasonable in situations involving only probable evidence gives you the best chance of being right, but does not guaranty being right. Being good at being reasonable is not easy and may always be prone to mistake. One of my favorite real life examples is the brochure a pharmaceutical company put out to give information about, and promote, a flu vaccine they make. It is a vaccine for a strain of flu called HiB, if I remember the name correctly. The flu is the disease that causes 95 percent of meningitis. And the vaccine is 100 percent effective in preventing this flu. My pediatrician thought that was sufficient grounds to give the vaccine to my children, but I asked for time to make the decision, since the evidence sounded suspiciously like some I had heard before in a different context, and which did not support the conclusion for which it was presented. (That argument was that since 90 percent of heroin addicts first used marijuana, marijuana use tends to lead to heroin addiction. That is a fallacious argument since 100 percent of heroin addicts first drank their mothers' milk or formula as infants, but that does not make mothers' milk or formula lead to heroin addiction. The important statistic is not what percentage of heroin addicts took marijuana, but what percentage of marijuana users take, or become addicted to, heroin.) The pharmaceutical brochure made the same kind of error even though the reasonable argument that the pharmaceutical company needed, and which gave strong support to the wisdom of using the vaccine, was available to them. What is important is not what percentage of meningitis comes from this flu but 1) what percentage of this flu leads to meningitis, 2) what percentage of the population gets this flu, and 3) what the risks are from the vaccine. That is, what are the side-effects of the vaccine and how likely are they? For, if the vaccine is riskier than taking a chance on getting the flu coupled with the chance of getting meningitis from the flu, the vaccine is a poor risk. (As I understand it now, smallpox vaccine is not routinely given any more in the United States since the risk of dying from the vaccination is greater than the risk of getting smallpox.) A call to the public health department ascertained no information about (1) and (2), but sufficient information about (3) to allow a reasonable decision. After a number of years of vaccine use, there were no known side effects by any child. Hence, since there was some risk involved with getting the meningitis and no risk involved with the vaccine, I had my children given the vaccine. I presume the pharmaceutical company used the fallacious argument, instead of the reasonable evidence which gave them a stronger sales pitch, not because they were trying to deceive anyone, but because they thought they really had a good argument, good evidence, for using their product. Now, not every issue requires long deliberation. What degree of examination to use is itself a reasonable question. A woman I knew whose EX-husband was a philosopher used to justifiably resent his examining everything she said in minute detail. She got tired of explaining things like precisely what she meant by "medium" toast. Education is one means of teaching the known pitfalls of irrelevance, untruth, improbability, vagueness, unnecessary analysis and indecision, meaninglessness, and the like; but we may not have yet discovered all the ways we sometimes, frequently, or even systematically go wrong, whether in specific subject areas or in general. And it is easy to make mistakes that one, in some sense, "knows better" but forgets or does not recognize at the time. But however difficult helping someone to improve their reasoning is, it is infinitely more difficult when the student does not even understand what you are trying to do. For example, a student may have a view with some evidence for it, and you may have three different objections, one about the truth of one of his reasons, one about the truth of his conclusion, and one about the relevance or sufficiency of his reasons even if they were all true. If you try to attack one of his reasons, he shifts to others or to a different argument altogether, or thinks you are attacking the truth of his conclusion and does not see how your reasons have anything to do with it. If you try to show his conclusion is false, he falls back on his reasons. If you try to show his reasons would be irrelevant or insufficient even if they were true, he cannot understand what you are getting at at all. And if you try to do this by an analogy he gets distracted by the analogy and starts arguing about it, or does not see what this totally different subject matter has to do with his conclusion and evidence at all. The fact that the form or logic of the argument in the analogy and the form or logic in his argument are exactly the same, and that the form is what determines whether the conclusion follows from the evidence and reasons, mean nothing to him. In short, he does not understand how his evidence is supposed to relate to his views, if he can even distinguish concluding views from supporting reasons; and he cannot then understand how your disputing any elements of his views affects any of the other elements. Finally, he cannot generally distinguish your conclusions from your evidence or see how one is relevant to the other. You can draw diagrams of his argument(s) and your rebuttal to it till you are blue in the face, but the problem for his seeing it is not the particular points at issue; it is reasoning or logical argument in general that he does not understand. Each particular point about this particular argument just confuses him more, since he just does not understand what significance all these different points have in regard to what he believes or wants to believe. And each of the numerous students afflicted with this problem has the same battle in each of his courses every time something conceptual or logical arises. And each teacher has to face the specific problems because no one teaches the general concept of what reasoning is. If people understood what the relationship in general is supposed to be between evidence and conclusions, if they understood what sufficient relevance is, and if they understood which kinds of points differing rebuttals are attacking, and why, there would be far less difficulty in achieving understanding and agreement. And I think teaching and learning would be far easier tasks. That is why I think it crucial that students (and teachers) learn in general the simple idea of what being reasonable is about. The purpose of education is to produce rational and skilled people, but we seldom teach what it is to be rational. In some of my more optimistic conjectural moments I even tend to think that reasonable people (seeking truth, not just power or personal gain) working from the same evidence and spending sufficient time in discussion (presenting all the evidence and clearing up mistakes, arranging complex material in ways it can be kept track of, etc.) would logically come to the same conclusions (even if that means knowing and agreeing there is insufficient evidence or logical understanding at the time to be definitive) and that, contrary, to the frequently evoked maxim, reasonable people could not disagree. I believe most honest disagreements come from different evidence (often based on different experiences) or from faulty logic. (Sometimes there is not time or mutual inclination to look at all the evidence with an open mind or to pursue the logic wherever it might lead, but that should not be true of really important issues; and when it is, it is a problem of spirit and honesty, not one of knowledge or reason. The fact that some people cannot or will not solve problems does not mean those problems are insoluble.) Even in ethics classes, if you first use elemental types of moral situations (about which there is little disagreement generally) to derive principles of ethics, then you can discuss extremely complex issues in a way that tends to foster agreement rather than the kind of discordant, passionate controversy such issues tend to generate in the media and public at large. Complex issues can frequently be analyzed in terms of more elemental components which are not controversial at all, but the public and media do not tend to do that very often and instead tend to miss key elements or to focus on different aspects of the issues and erroneously apply the results to all aspects. It is frequently analogous to people trying to do complex math, science, or engineering problems without analyzing them into the individual components for which solutions are readily available. Conflicts and confusion arise that do not need to. Below is one of the arguments designed for the affirmative side of a debate tournament where the point was to make a case for the claim that "When there is a conflict between them, a higher value should be placed on cultural sensitivity than on the commercial use of free speech." In normal usage, arguments are seldom given spelled out in this explicit, stilted way, but it is important for you to be able to present any argument this way, so that you can see whether your reasons make sense, seem clear and true, and seem to logically lead to the conclusion you wish. Moreover, you should be able to support each of the reasons themselves if challenged about their truth. If you can do all this, you also will be more likely to be able to detect flaws in the arguments made by people who disagree with you or who question or attack your position. In footnote 1 there is a sub-argument for the first premise that is intended to forestall any objection that one does not have to be accountable for speech. In footnote 2, an argument is given in support of premise 8. Those were two premises I felt likely to be challenged during the debate. One can never know ahead of time what someone else listening to or reading your arguments will challenge, so the best course is normally to be as explicit and complete as time or space allows, and then to answer any unanticipated objection as it is given. In high school and college courses, the general problem is that students haven't had sufficient experience being challenged in their ideas for them to know when they are not being clear or complete enough. Students tend to overgeneralize, without realizing it; and teachers often grade work without giving the student a chance to respond to the teacher's objections. Spelling out one's position in the following manner helps prevent that because it requires one to be able to examine each reason to see how it is specifically used, and to see whether it makes sense, whether it can be supported or not, or whether it needs a modification. This was an argument that I helped my daughter develop from the vague idea she had that "there should be some sort of accountability for companies that say bad things about minorities". The difficulty was in trying to show this in a way that made sense and was "solid" in its logic. The gist of the argument was fairly simple, but it turned out that premises 5 and 10 were the most difficult to figure out how to word in a way that captured what was needed and that made sure there were no gaps in the logic. It took me three hours to develop those two premises the way they are. They can be supported if necessary. The lines of the argument in bold print are derived from preceding lines within the argument. The lines not in bold are reasons which are introduced into the argument from outside of it and would have to be supported, if challenged, by additional evidence or prior argument.

1.) Corporations are (and ought to be) accountable for those actions and behaviors of theirs which cause harm(1), whether intentionally, through negligence, or through callous indifference and reckless disregard for the well-being of others. 2.) Speech is a behavior that can cause harm. 3) Commercial, free speech is speech. Hence, 4) Corporations are (and ought to be) accountable for that commercial, free speech of theirs which causes harm, whether intentionally, through negligence, or through callous indifference and reckless disregard for the well-being of others. 5.) If any commercial, free speech which causes harm were valued above or equal to the harm it causes, commercial, free speech would be a behavior that is not accountable for its harm. Hence, 6) any commercial, free speech which causes harm should not be valued more highly than, nor equal to, the harm it causes. Hence, 7) harmful commercial, free speech should always be valued less highly than the harm it causes. 8) Speech which is insensitive to any culture or minority is harmful(2) (to that culture). Hence, 9) Commercial, free speech which is insensitive to a culture or minority should be valued less highly than its harm. Hence, 10) whatever prevents the harm of insensitive commercial, free speech should be valued more highly than insensitive commercial, free speech itself, if that preventive is not more harmful in some other way to society. 11) Cultural sensitivity conflicts with, and prevents the harm of, insensitive commercial, free speech, and it is not more harmful in any other way to society. 12) Hence, when in conflict, cultural sensitivity ought to be valued more highly than commercial free speech. (Return to text.)

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1. This is not just true about physical harm; there are many different crimes based just on speech. Obstruction of justice, contempt, and perjury are all punishable offenses because they are considered to harm the administration of justice. Executive commands to employees to break the law, make those executives responsible for the ensuing illegal actions of their employees in obedience of those commands. They are not protected by free speech. Slander and libel are not protected, neither for individuals nor for commercial entities such as newspapers. Conspiracy to commit a crime is also speech that is punishable by law. (Return to text.)



























































2. It is harmful, over time, to the culture directly and indirectly - directly first by being humiliating and emotionally hurtful, and also by causing the minority not to value itself, as its impressionable children grow up; indirectly, by fostering a climate that permits and encourages a range of harms from minor humiliations to hate crimes against victims who are considered, because of the message being promulgated, not to be human beings who are worthy in their own right, deserving of being spared pain, suffering, and murder. (Return to text.)















































































































Although students tend to do it more, or more egregiously, overgeneralization is easy for anyone to do by mistake. I used to have a generalization I was totally sure of until one day I thought of a counter-example after seeing an actual situation that had relevance to my contention; I had to amend my position. It was meant to illustrate a point about probability and utility. The point that I was illustrating is that one has to take into account not only probabilities but also utilities (i.e., value) in deciding what is the wisest course to pursue. For example, it might be okay to risk a $1 bet to win $1,000,000 if the probability is one in 500, but it is quite another thing for the average person to risk $50,000 to win $1,000,000 if the probability is one in 400. Even with better odds in the second case, the risk is too great because the utility or value of $50,000 is much greater than the utility or value of $1. (That might not be true for a billionaire, because $50,000 does not mean as much to him/her, but it is true for the average person. "Value" has more to do with significance than it has to do with mere numbers or relative numbers.) You have to judge the value of what you are risking versus the value of what you are likely to gain, as well as taking into account the likelihood of success or failure. An example I used to illustrate the point was from American football, where after a touchdown, a team could choose to kick the ball through the goal posts for one point, or they could choose to try to run or pass the ball into the endzone for two points. The kick is much more likely to succeed, though there is some risk to it. The specific example I chose to illustrate the importance of utility, however, was the case in which a team scored a touchdown at the very end of a game in which there would be no (further) overtime -- a touchdown that left them behind by two points with no time left on the clock for any plays after the extra-point attempt. For years I pointed out that no coach would ever opt for the kick even though it had the higher probability, because the value of the kick was to insure a loss even if it was successful. The kick was not worth just one point at this time in the game; it was worth a loss. The only thing of value was to try to tie the game even if the odds were less you would be successful. That seemed an obvious point to me. However, it occurred to me one day there is at least one possible situation where a team and coach might opt for the kick. That is in a case where their kicker had a chance to break a college career record for (consecutive) successful field goals, and this was his last career game. If the team had a losing record anyway, and this game did not really mean as much as helping the kicker set such a prestigious record, the coach and the team might opt to give him the opportunity. So what had seemed obviously true to me for years turned out not to be true for all cases, but just for almost all cases. When I use that example now, I explain the exception to it as well, for the story still makes the point; but now it does it more accurately. It is not difficult to overgeneralize. One just tends to do it less the more one thinks and writes about things and is challenged. When I write about philosophy of education, I tend to forget sometimes that I need to point out I may be talking about education in a middle or above-middle class suburb. I have clear in my mind what situation I am discussing, but if I don't convey that specifically to the reader, they will think I have overgeneralized. In terms of what I actually wrote, as opposed to what I had in mind, I will have overgeneralized. I wrote a political argument one time against passing a tax increase (until the school administration changed its proposal) to fund smaller classrooms in our community because no training was going to be given to teachers to help them teach using more individualized instruction. In the classrooms where size had already been reduced, it made no difference in the instructional approach the teachers used, and children were not learning any more. The paper I wrote fell into the hands of the opposition before it was printed and distributed, and they hooted at my claim that teachers did not teach differently in smaller classes, because their younger children were all receiving much more personal attention from their teachers, who knew their names and interests, etc. more readily when classes were smaller. I had time to revise the argument I gave before it was published to point out that I was talking about instruction and not attention, and that although it was true that students might receive more personal attention in smaller classes, it would not matter for their instruction if the instruction itself was just as bad as it had been. Personal attention did not translate automatically into personalized instruction. The derision had helped me see that I had not written what I had really meant, and that essentially I had overgeneralized about the lack of change in teaching when class sizes were reduced. 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*The following is a merely technical point that I include in this footnote for those who might be interested in greater analytic precision than is probably either necessary or interesting for most people on this topic: The explanation of what it is to be reasonable above is what makes an argument or a position be one that is reasonable. For a person to be reasonable, it must also be that the person sees (or thinks s/he sees) the logic of the argument, and is not just stating memorized reasons someone else has given. Stating someone else's argument is not the same thing as reasoning. There is a difference between giving reasons in which one sees the logic, and giving what one is told are reasons, even if the list of reasons is the same, and even if one believes the reasons must be correct because some expert says so. The value and the strength or weakness of the argument or the position is the same in either case, and the argument is reasonable or unreasonable in exactly the same way in either case, but when one gives the reasons that one "sees" (or thinks one sees) are logically related to the conclusion, one is then reasoning, whereas when one gives a list of reasons one has simply memorized and about which one does not really understand the supposed logical significance, one is not reasoning but simply verbally copying or reciting an argument, not really reasoning for oneself. This point is simply to distinguish between reasonable and unreasonable arguments on the one hand, and, on the other hand, people who are either reasoning or not reasoning when they give those arguments. When one simply states a conclusion with a list of reasons for that conclusion, one is not necessarily reasoning, even if one is stating a reasonable argument. This is similar to a point in the essay "Having Understanding, Versus Knowing Correct Explanations": interpreting or explaining anything (whether it is art, literature, science, experience, or any sort of phenomenon) is different from learning an interpretation or explanation by being taught or told that interpretation or explanation. To learn an interpretation of anything is not necessarily, and not usually, the same thing as interpreting it. (Return to text)















































