Logical Fallacies

March, 2008

In a previous (and generous) serving of well-argued hooey, Professor Plum raised the intriguing question,

Hey! How come loony and harmful fad "movements" (such as whole language and learning styles and brain-based teaching) catch on in education.  Why aren't they hooted off the stage with significant vigor as soon as their proponents show up with red nose, fright wig, clown shoes, and fake flower squirt?

Here’s one answer. The feeblemindedness and moral disorders embedded in faddish movements are hidden within cleverly disguised logical fallacies of which teachers, administrators, ed students, and families are unaware.  They are therefore easily gulled by treacly wording ("Our extra fuzzy math is child-centered, authentic, developmentally appropriate, and enables youngsters to construct knowledge through an inquiry-based discovery learning pedagogy that is child-centered, authentic, and developmentally appropriate.  And we're not $hitting you.") and evocative images.

Now these same fallacies would never work in other situations.  For example, let’s say you are visiting Uncle Ned (perhaps YOUR Uncle Ned) in London, England, and you order a large shipment of fish and chips (or perhaps jellied eels). And you are instead served a bowl of foul gruel.  You say to the gruel purveyor, "Hey, what's this mess?  This isn't what I ordered." And the purveyor of said gruel says, "All the BEST people are eating gruel.  In fact, Her Majesty, The Queen, tucks into her luncheon rations with great delight."  And you say, "The Queen.  The Queeeen!  I don't care WHAT 'The Queen' tucks into.  Since when is she an authority on lunch?"

In other words, you're not taken in for one second by this OBVIOUS fallacy called appeal to authority. 

Why, then, are we such idiots when it comes to eduillogic?  An ed perfesser or conference speaker spouts, "Piaget says...." and everyone nods like an amiable cow chewing its noonday portion of cud.

I think it's because the world of daily life (outside schools and ed schools) has pretty clear consequences, and these keep us alert to nonsense and other forms of oompus-boompus.  I mean, if you don't find SOMEthing wrong with the Her-Majesty-The-Queen scam, you're going to end up with a bowl of gruel.  But teachers and ed students don't KNOW what's going to happen if they fail to challenge the drivel they get in conferences, workshops, and courses.  And so, they willfully suspend disbelief.  The null hypothesis---"Oh, iz zat so?  Baloney!"---never occurs to them.

Professor Plum has written this essay in hopes it will make his Dear Readers hypercynical to what they read and hear in Edland. 

"Oh, yeah, sez you!"

In other words, Readers will see everything presented by the ed establishment as an opportunity to test the null hypothesis--which in this case is, "What bunk.  Pure nonsense. Odious piffle."

Second, this essay provides tools for identifying hidden hooey. 
So, here we go...

              Common Fallacies of Relevance and Ambiguity

Fallacies of relevance and ambiguity have to do with logical errors in everyday (and research) arguments. The errors may the result of sloppy thinking; they may be unintentional slips; or they may be rhetorical tricks to sway gullible audiences. By studying these fallacies, you will become fluent at spotting errors in your own and in other persons' arguments. Definitions of the fallacies are from the work of Copi (1986) and Downes (1996). Useful exercises involve spotting fallacies in articles and books, TV commercials, political speeches, and everyday conversation. For example:

"My husband was having, you know, personal difficulties," says Mrs. Reginald Waddington Bassett-Bassett of Upper Bingley.  "But now he takes Niagara!!  And what a difference!  He's up all night!!" 

[So, based on ONE case--an anecdote--we should all run out and get a bottle of Niagara?]

1. Arguing Against the Person (argumentum ad hominem)
The fallacy of ad hominem is committed when an argument attacks an opponent (e.g., a person or group with a different view) rather than the opponent's evidence and logic. Sometimes, the person or group is said to have negative qualities; and therefore, the opponent's argument should not be accepted. This is the abusive version of the ad hominem argument. For example:

"You can’t accept the implications of B.F. Skinner's research. After all, he was a behaviorist."

Sometimes the ad hominem argument is that a person's or group's position should not be accepted because of their special circumstances. This is the circumstantial version of the ad hominem argument. For example:

"Oglethorpe is an engineer. Of course she advocates focused and systematic math instruction based on solid research. She must be biased."

In other words, it's implied that the opponent's argument is invalid because the opponent benefits from the argument or because the opponent has to believe what he or she says, and therefore the argument cannot be trusted. However, these considerations are irrelevant to the validity of the opponent's argument.

Ad hominem arguments can be handled by: (1) determining whether the arguer presents credible evidence in support of his own position and/or against the opponent's position; (2) identifying the negative characterization of the opponent and revealing how this characterization is used to invalidate the opponent's argument or position; and (3) showing what sort of solid evidence is needed to invalidate the opponent's position and/or support the arguer's position.

2. Prejudicial Language
This invalid argument uses emotionally loaded words to persuade an audience that the arguer's position, conclusion, or suggestion is reasonable and acceptable because it seems morally good, or that an opponent's position, conclusion, or suggestion is unacceptable because it seems morally bad. The emotive words "pump up" the audience, and give the audience the sense that it is on the side of right. For example,

"In contrast to the rigid, piece-meal and conformity-fostering curricula forced on children by advocates of explicit instruction, our child-centered curriculum provides children with a seamless series of authentic and meaningful experiences that foster self-esteem and enable children to develop their inner potentials."

Appealing as it sounds--assuming that pure twaddle has an appeal--this argument gives no data on what "explicit" vs. "child-centered" curricula actually do and what the curricula actually yield--so that a reasoned comparison and choice can be made. Instead, the arguer uses words (not precisely defined) appealing to the audience's negative sentiments about conformity and piece-meal instruction, and positive sentiments for children, authenticity, and development. The implication is that anyone who disagrees with the arguer is against children, individual development, and authenticity.

This argument can be handled by: (1) identifying prejudicial words and showing how they are used to sway the audience; and (2) showing that the arguer has no credible evidence for his or her position or against his or her opponent's position.

3. False Dilemma
In this fallacy, an arguer makes it seem as if there are two or three (and only two or three) opposing options; e.g., two possible ways to understand things, two ways to interpret data, two conclusions that can be drawn, or two responses to a problem. Then the arguer tries to discredit or invalidate the position(s) he or she opposes. This appears to leave only the arguer's position--which, by elimination, the audience is logically bound to accept--if the audience falls for the false dilemma. For example:

"There are only two kinds of data--quantitative (numbers) and qualitative (meanings, interpretations, narrations).  Quantitative data say nothing about how children make sense of their school achievements. But this is just the sort of information we need. Therefore, we must choose qualitative over quantitative data."

The false dilemma, here, is that research cannot be divided neatly: (1) into qualitative vs. quantitative data, and (2) into data that tell about persons' experiences vs. data that do not tell about persons' experiences. In fact, quantitative data can speak to how persons see things (e.g., teachers can count the number of times per day that they blame students for not getting the material); and some qualitative data say nothing about how persons see things. So, the argument gives a false choice. The way out of this argument is to show that the forced, limited choice is false and to suggest additional options.

4. Appeal to Popularity (argumentum ad populum)
This invalid argument involves persuading an audience to accept a speaker's or writer's conclusions because other persons and groups already do so. For example,

"Hundreds of schools and businesses in the United States have school-to-work programs. So do some foreign countries. There is substantial government funding for these programs.  Obviously, Smith's opposition goes against the trend."

The implication is, "How can Smith argue against these programs? How can Smith be right and so many other persons and groups be wrong?"

Unfortunately, this argument is often effective. For instance, a study by Solomon Asch showed that at least one-third of the participants in his experiments agreed with the majority's judgment about which line was longer even when the group's judgment was obviously wrong. Subjects went along to avoid being the lone nonconformist. Similarly, jurors in trials of teachers and day care workers accused of child abuse said they went along with the majority even though they believed the defendants were innocent; they just could not see how they alone could be right when so many other persons had the opposite opinion.

This fallacy can be handled by: (1) showing how the arguer appeals to popularity to support his or her conclusions; and (2) showing that the popularity of a position is not evidence for the validity of the position. For example, jurors have convicted innocent persons; our species long thought the sun revolved around the earth; and education in the United States and other countries has been dominated by faddish ideas and methods that later proved worthless.

5. Appeal to Pity (argumentum ad misercordiam)
This fallacy is similar to the appeal to the population; it, too, relies on emotion. An arguer implies that his or her explanations, conclusions, positions, or suggestions should be accepted, and/or that alternative explanations, conclusions, positions, or suggestions should be rejected, because failure to agree would injure the arguer or some other persons.

For example, before there was much research on whether full inclusion of students with special needs did any good, many groups advocated full inclusion of children with severe mental retardation in classes for typically developing children by appealing to readers' sympathies.

"Will we continue to keep these children in a shadowland--outside the circle of warmth and protection with their fellow human beings? Will we add even more misery to their lives? Or will we at last provide them with their rightful place?"

The appeal to pity can be handled by: (1) showing how the argument appeals to the audience's sensibilities (e.g., about the difficult lives of many persons with disabilities); (2) showing that the argument does not give direct evidence that supports the position (e.g., that inclusion leads persons with disabilities out of a "shadowland," decreases "misery," or helps them achieve a "rightful place") or that refutes opposing positions; and (3) that the argument (e.g., advocating full inclusion) may be against the interests of persons whom the argument claims to support.

6. Fallacy of Division
This fallacy is the argument that the characteristics of a whole (e.g., an automobile engine is heavy) apply to all of the elements (therefore all of its parts are heavy). An example of the fallacy of division in education would be an argument that the average test scores in a school are high; therefore, all children in the school (or all classes in the school) got high scores (or were proficient). In fact, some classes may have gotten very high scores, which pulled up the average (school) scores.

7. Fallacy of Composition
This fallacy is the flip side of the fallacy of division. It's the fallacy of arguing that the characteristics of elements (e.g., an engine's parts are light) apply to the whole (therefore the engine is light). An example of the fallacy of composition is arguing that: (1) since all of the children and teachers in a school improved their skills a great deal, therefore, (2) the school as a whole improved a great deal.

The problem is that the school is a social organization; it has features (organizational features) that its elements (individual human beings) do not have. Teachers and students (elements) may have learned new skills, but: (1) the school division of labor (a feature of the whole) may still involve a high degree of specialization and little collaboration among teachers; (2) there may have been no change in patterns of power; and (3) there may have been no change in relationships with families.

8. Argument From Ignorance (argumentum ad ignorantiam)
There are two forms of this fallacious argument:

1.  There is no solid evidence that supports a position, conclusion, or suggestion. Therefore, the position, conclusion or suggestion must be false, invalid, or generally unacceptable. Or,

2.  There is no solid evidence that a position, conclusion, or suggestion is false, invalid, or unacceptable. Therefore, the position, conclusion or suggestion must be true, valid or acceptable.

For example:

Ms. White: "You say new teachers should be assessed for  licensure by portfolios. But you don't have evidence that portfolio assessment leads to the selection of better teachers?"

Ms. Wong: "Maybe not. But you don't have evidence that portfolio assessment doesn’t lead to selection of better teachers."

Ms. White is right; Ms. Wong is wrong. Advocates for a conclusion, technique, treatment, curriculum, or social policy are obliged to provide positive evidence (supporting data) for what they advocate. In other words, lack of evidence is not evidence. That's why prosecuting attorneys must prove that defendants committed a crime; defendants don't have to prove that they didn't.

9. Slippery Slope
In this argument, a person claims that failure to accept his or her conclusions or suggestions, and/or acceptance of an opponent's conclusions or suggestions, will have increasingly bad effects. For example:

"If state boards of education require publishers to have empirical evidence that their textbooks or curricula are effective, that will be the thin end of the wedge by which school boards take away more teacher autonomy. Soon they will require that we submit lesson plans to school boards for approval. Moreover, this policy will inhibit publishers from developing new materials, and so we will have to use increasingly obsolete materials."

This is an appeal to fear. No evidence is presented that adverse effects will occur or cannot be stopped.

10. False Cause (post hoc ergo propter hoc)
"Post hoc ergo propter hoc" is Latin for "After this, therefore because of this." An argument commits this fallacy when a person claims that because one event follows another event, it was caused by the prior event. However, the fact that one event follows another event may be coincidence. There may be no causal connection at all. Each event may be caused by a separate chain of causation. Or two events may be caused by a third, unknown event. Here is an example of post hoc ergo propter hoc.

"We pre-tested students' math skills. Then we implemented the new 'Creative Calculus' math curriculum. And then we gave students a post-test. Post-test scores were much higher than the pre-test scores. Therefore, Creative Calculus is effective."

After Creative Calculus, therefore because of Creative Calculus. Math scores may have changed, but not because of the new curriculum. Perhaps teachers communicated to students that they had high expectations that students would succeed (which they did not communicate with the old curriculum); or perhaps the post-test was easier than the pre-test; or perhaps some students with the lowest math aptitude dropped out after the pre-test (and so their likely low post-test scores could not drag the average down). Many other extraneous factors could account for the findings.

We could more clearly show whether the curriculum does or does not work by conducting an experiment with equivalent groups. One group gets the new math and the other gets the old math. If the group that receives the new math has higher pre-test to post-test differences, and if all other extraneous variables are pretty much equal across the two groups, then we can begin to suspect that the curriculum makes a difference.

11. Wrong Direction
In this fallacy, the direction of cause and effect is reversed. For example,

"The rates of mental illness increase as we examine data from suburban to inner city areas. Therefore, inner city areas cause mental illness more than suburban areas."

It is more likely that as some persons who live in suburban areas become mentally ill, and cannot hold their jobs, they lose income, abuse drugs and alcohol, lose their families, and end up homeless in the inner city. In other words, moving into the inner city does not cause mental illness. It’s the other way around; some people move into the inner city because of impairments resulting from mental illness.

Here is another example of the fallacy of wrong direction.

"When you observe cooperative learning groups, you find that the high status students end up running discussions and learning the most. Therefore, cooperative learning groups produce social inequality."

It's just as likely that causation runs in the opposite direction; students who enter cooperative learning groups with high social status and skills control discussions from the start. The cooperative learning format may sustain inequality, but inequality was already there.

12. Begging the Question (petitio principii)
In this fallacy, no empirical evidence is given to support a conclusion. Instead, the conclusion merely restates the premise. For example,

1.  "God exists." (premise)

2.  "I know God exits because if something exists I will know it."  (evidence)

3.  "Since I know God exists, God must exit." (conclusion)

Well, that clears things up nicely! Here's another example:

1.  "Children who are most disruptive in class have ADD (conclusion)  because

2.  Children with ADD usually engage in a lot of disruptive behavior  (premise)."

It may be true that ADD is associated with (indeed is partly defined by) disruptive behavior. However, this does not imply that most disruptive behavior in classes can be traced to children with ADD. Children without ADD also engage in disruptive behavior.

Read the two statements again. Note that the conclusion and the premise say virtually the same thing. If you aren't careful, the premise seems to provide good reason for the conclusion.

Here's still another example of petitio principii (begging the question).

1.  "Whole language is an effective way to teach children to read  (conclusion) because

2.  "Whole language uses literature rich environments and authentic  materials which are conditions that foster reading skill (premise:  evidence)."

Again, the premise that is supposed to provide good reason (evidence) for the conclusion merely restates the conclusion. However, no empirical evidence is given on, for example, how many children in a group could read before and after whole language, in contrast to a comparison group that received an explicit phonics curriculum.

13. Converse Accident (Hasty Generalization)
The fallacy of hasty generalization is committed when a generalization is made from an exceptional case (or what later turns out to be an exceptional case) to a larger population of events. For example, I helped develop a curriculum for autistic children. This curriculum was quite successful. However, it would have been a hasty generalization to imply that the curriculum would be as effective with other autistic children in the larger population. Why? Because our sample of 35 children may have been exceptional in some way--i.e., not representative of the larger population of autistic children. The children we worked with may have been younger; less impaired; living with parents who were more skilled at teaching their children. What worked with our sample of children may not have worked with other children. Therefore, before generalizations were made about how the curriculum might be used with other children, it was replicated with more and more samples of children--younger, older, more impaired, less impaired, single-parent families, two-parent families, families with much social support, families with less social support, etc. The more times the curriculum was replicated with different samples, and still shown to be effective, the more confident we could be about making generalizations to the larger population of children with autism and their families.

14. Equivocation
This fallacy is committed when the meaning of one or more important words changes during an argument to make the conclusion seem valid. For example,

"Virtually all of experience consists of constructs such as time, space, objects and cause-effect (premise). Therefore, we may say that children construct their own experiences (conclusion)."

The conclusion that children construct experience seems plausible--because the meaning of "construction" changes between the premise and the conclusion. In the premise, "construct" is a noun. Constructs are things--tools--by which children create experience. In the conclusion, "construct" is used again--only now it is a verb synonymous with "make." Since the same word is used in the premise and conclusion, a reader may accept the conclusion, just as one would accept the argument, "A rose is a rose is a rose." Well, of course it is! However, just because experience consists of constructs, does not mean that experience is constructed. Constructs (and experience) could be transmitted through communication, shaped without a child's noticing as the child interacts with her environment and learns language.

We have examined informal fallacies--arguments using words in a way that makes false or unsupported conclusions seem reasonable--to an inattentive or naive audience.  But we are no longer  inattentive  or naive.  We will not be fooled again.