Material Fallacies 3

Miscellaneous Fallacies of Reasoning

Compound Questions. Also called “poisoning the well,” this fallacy involves a question which at the same time presents a conclusion or consists of a conclusion in the guise of a question. The fallacy is committed by combining two or more questions which cannot be answered together (hence the name “compound questions”), or more often, by asking a question implying that a previous question has already been asked and answered in a particular way. The compound question thus prevents or avoids any opposing arguments and incriminates the answerer regardless of the response he gives because any answer would admit the preliminary conclusions built into the question. The classic, ancient example is, “Have you stopped beating your wife?” If you say, “no,” you admit that you beat her. But if you say, “yes,” you also admit that you used to beat her. Note the assumptions behind these questions:

• How often do you cheat on tests this year?
• How do you account for your incompetence?
• Why did you cause the Smiths’ divorce?
• Why do you want war?
• Are you trying to impose your outdated standards on me?
• Do you expect me to believe that lie?
• Where did you hide the murder weapon?
• Who made God?
• Have you always been such a fanatic?
• Why do you always commit logical fallacies when you talk?
• Why won’t you be convinced by obvious truth?

In another form of this fallacy, several questions which may each have a different answer are combined into one question for which a single response is demanded.

• Mr. Glass, did you or did you not visit the bank that morning–as our witnesses have established–and then rob it later that afternoon? Just answer yes or no.
• Are you planning to quit your job and thereby doom yourself to failure and despair?
• Don’t you think steamed lobster, boiled ox eyes, and steak with mushrooms are delicious?
• Aren’t you against immoralities like lust, kissing, and adultery?

The response to a compound question, of course, is to refuse to answer it as stated, identifying it as a compound question, and then breaking it down into its various components. Questions which imply previous conclusions should be responded to by objecting to the conclusions: “Have you stopped beating your wife?” “I do not now beat nor ever have beaten my wife.”

Note that if a previous question has indeed been asked and answered or if some circumstance establishes the answer to a previous question, a question that implies that previous answer is not fallacious. If someone takes a few shots at you, you are not being illogical to ask, “Why are you trying to shoot me?” If Johnny is always late coming home, his parents are not being illogical to ask, “Why are you always late coming home?”

Begging the Question (Petitio Principii). In its standard form, this fallacy occurs when the initially stated point to be proved (the thesis or assertion) is later used in the argument as an already accepted fact, to support some new point at issue which must be established to prove the initial point. Thus the original statement is eventually used to prove itself true, and hence the other name for this fallacy, circular reasoning. Thesis A is supported by point B; point B is then supported by thesis A (now called fact A).

(Note: The name of this fallacy is often confusing. “Question” here means “issue” rather than “a request for an answer.” Thus, a question-begging argument usually has no actual questions in it.)

• Many intelligent people believe in ghosts. This is clear because several intelligent people told me so. And I know they were intelligent because they all believed in ghosts.
• All of the best economists follow Keynes. Joseph Line told me, and he’s clearly one of the best economists because he follows Keynes.
• The fossils in this stratum are 200 million years old. How did I date them? Well they are in a stratum of that age. How do I know the stratum is that old? Because it contains these fossils, which are found in strata of that age.

Sometimes essentially the same assertion is changed into different words and used directly as “evidence” to prove itself as first given:

• Things are worse than before because they are not as good as they used to be.
• I think Jones is guilty. Why? Because I think he did it.

Another form of this fallacy, known as a question-begging definition, defines a term or phrase in such a way that, when used in an assertion, it proves the assertion true by the very way the term is defined. Any objection to the assertion is silenced by appealing to the definition. For instance, if an arguer says, “All properly informed people oppose mining ocean-floor mineral nodes,” anyone named to be in favor of such mining can be declared “not properly informed” by definition. Note the way the following implied definitions are question begging:

• All high-quality lamps use Snappo switches.
• Anyone who isn’t a complete dunce knows that I am right.
• All those entitled to judgment will agree with my position on airbags.
• Books expressing that view are not reliable.
• The only way to get those results is by sloppy technique.

Question-begging definitions are often the result of stipulative definitions taken to extremes. A stipulative definition is a special, customized meaning given to a word for the sake of exactness or better understanding. Many words are broad or even vague, and stipulative definitions can help to clarify an argument or presentation. For example, no logical problem arises when a writer specifies that “the term ‘current technology’ shall mean here ‘manufactured within the last two years'” or “by ‘hardwood cabinet’ I mean a cabinet made from boards of solid hardwood but a cabinet made from particle board, even though the particle board is made of hardwood chips.” These are both reasonable stipulative definitions, almost certainly not designed to rig an argument. But compare these similar definitions and their arguments:

• Well, I define current technology as “using the Elmo-Frimpson screw system,” and since our company is the only one using that system, we are the only one using current technology.
• By “hardwood cabinet” I mean “any cabinet containing any hardwood.” Our Flimsoplastik speaker cabinets contain hardwood braces inside, so these are therefore “hardwood cabinets.”

The test is whether the definition establishes a conclusion automatically and unfairly or whether it is a reasonable definition and clarification of a vague or loose term.

Condition Contrary to Fact. We all have fun speculating on what might have been different if certain events of history or the past had had different outcomes. Of course, we can never be sure what would have happened. A single event is a link in an infinitely branching chain, and to alter that event could result in an incomprehensible number of altered events after it. Thus, all we can do is imagine and guess–probably very inaccurately–what would have been if some circumstance had been different. To insist otherwise–to pretend to know what would have happened–commits the fallacy of condition contrary to fact.

• If the South had won the Civil War, we would still have slavery.
• If Tillotson had been appointed to the Federal Reserve Board, the inflation rate would be twice as high.
• If we had made our toasters hot pink instead of blue, we would have sold twenty million of them instead of only six.
• If I’d gone to another school, I’d be making straight A’s this semester.
• If Philadelphia had remained the seat of the U.S. government, the publishing industry would be centered there instead of in New York.

In another form of this fallacy, an arguer applies the premise of a conditional syllogism to a circumstance that does not have a necessary or automatic cause-and-effect relationship. We can seldom be sure what will follow a certain proposed event until the event actually occurs. We can argue for probability in such cases, but not for necessity. Note the difference between the premises of acceptable conditional syllogisms like these–

• If the power remains off for more that 48 hours, the food will spoil.
• If the system fails to transfer control to the program, the program will not run.

–and these examples of condition contrary to fact:

• If peanut price supports are eliminated, the price of peanuts will go up, not down.
• If we reduce the amount of reading required, students will learn less.
• If the U.S. put a 10,000-man standing army in the Middle East, armed conflict there would stop.
• If the California Inventory Tax is repealed, business will improve dramatically, and many new warehouses will be built in the state.

Note that any of these last statements would serve very well for the thesis of an essay, in which supporting evidence would help to establish that thesis. But none of the conclusions follow necessarily from the proposed (hypothetical) conditions. As in all other areas of critical thinking, you must use your good judgment to determine how probable each of these claims seems to be.

Contradictory Premises. Conclusions are drawn from the interactions of premises: where two premises contradict each other, there can be no interaction and hence no conclusion. Similarly, if the definitions of two terms conflict with or exclude each other, then those two terms cannot be simultaneously ascribed to a single object or event. The classic example of contradictory premises is the question, “What will happen if an irresistible force meets an immovable object?” The problem here is that in a universe where an irresistible force has been defined to exist, there cannot also exist an immovable object, because then the force would not be irresistible. Conversely, if there is discovered or defined such an item as an immovable object, then by definition there can be no such thing as an irresistible force.

This fallacy’s most popular appearance is in the form of a challenging question, because questions with contradictory premises are such brain teasers. In each case, though, no answer can be given because the premises cannot both be true.

• Into what shape of hole would a round square fit?
• If an object is all black and all white at the same time, what color is it?
• If an object is both stationary and traveling at an infinite rate of speed, how long will it take to meet itself?
• If God can do anything, can he make a stone so heavy that he cannot lift it?
• If God is all powerful, can he put himself out of existence and come back with twice the power he had before?

The Fallacy of Self-Refutation. Any statement asserting a universal truth or absolute application must itself be subject to and consistent with the doctrine it advances. Sometimes, however, a statement–especially of epistemological philosophy–logically contradicts the philosophy it advances; that is, the expression or assertion of a “truth” is itself an exception or contradiction to the truth so expressed or asserted. For example, the statement, “All generalizations are false,” is itself a generalization, so that if indeed all generalizations are false, the statement itself is false also. Thus the statement refutes itself and is therefore logically impossible. Note that the following statements all commit the fallacy of self-refutation because each one contradicts in itself the assertion it presents.

• To find truth we must begin without any a priori assumptions. [This statement is an a priori assumption.]
• Nothing must be admitted as true without empirical verification. [How is this rule to be verified empirically as true? This statement must not be admitted as true by its own requirement.]
• Nothing can be known with certainty. [Then this statement cannot be known with certainty.]
• All truth is subjective opinion. [If this statement is an objective conclusion about truth, it contradicts itself; if it is merely a subjective opinion about truth, it bears little weight as a principle of knowledge.]
• There are no absolutes. [Is this true absolutely? Is it true partly? If this is absolutely true–true in every case–it proves itself false by being an absolute. If it is not true in every case, there must be absolutes which are the exceptions, and thus the statement is still false. The statement expresses an absolute truth and so refutes itself.]
• Truth does not exist. [In that case, this statement is not true. In any other case, the statement is proved false.]
• Everything should be questioned and doubted until it is proved. [Then this assertion must be questioned and doubted until it is proved; therefore, the truth of this assertion is in doubt.]
• Everything I say is a lie. [Then what are we to make of this statement? How reliable is it?]
• I believe in nothing. [Do you really believe that?]
• Words convey no meaning–only deeds convey meaning. [Then, of course, this statement is meaningless.]

False Dilemma. This fallacy is also known as false alternatives or the either/or fallacy. We all sometimes get into the habit of viewing life as a series of antitheses: we hear one side of an argument and want to hear the “other” side; one party or position must be “right” and the other must be “wrong.” Actually, there may be ten or more sides to an argument, not just two; and one party or position may be a mixture of good, bad, and compromised ideas, just like the other. The real circumstances of life seldom align themselves exactly with our ideals of right and wrong, good and bad, virtue and vice; so we must be careful not to create false alternatives forced into correspondence with these ideals (for example, “This energy bill is either good or bad”).

Further, we must resist reducing complex situations and possibilities to only two alternatives (or three or four). Many alternative positions are not diametrically opposed to each other, but may be merely different mixtures of similar ingredients. Thus, to characterize two positions as mutually exclusive can be not only reductive, but completely false. For example, “This is a struggle between safety and liberty,” or “You support progress but we support ecology,” implies in each case that the two opposed elements cannot be reconciled or co-existent and that the hearer must choose between them.

A false dilemma is not always created by a careless or ignorant arguer. A few arguers purposefully establish such a one-or-the-other choice in order to oppose their position to an obviously false and easily rejectible position, thereby almost forcing agreement with theirs: “We must either put my plan into operation today or face anarchy and bloodshed tomorrow.”

• In today’s world you must make a choice between integrity and success.
• This is another obvious case of capitalism versus the working man.
• Are you going to marry me or are you going to live a miserable and lonely existence?
• Which are you for–property rights or human rights?

Be slightly suspicious when you read or hear expressions like, “Our choice is clear–we must have either . . .” or “Which will you have?” They are often followed by a false dilemma. (Do note that not every either/or usage is fallacious: “The patient is either alive or dead” or “Either God exists or he doesn’t” are both legitimate oppositions.)

Missing Comparison. Part of the empirical method is to compare one thing to another and then to announce how each measures up or ranks. A conclusion might be, “This thread has a higher tensile strength than that thread.” A fallacy occurs when a comparison or ranking is announced without naming the thing to which it is compared, because such a “comparison” provides no real information. Note the essential meaninglessness of a statement like, “This thread has a higher tensile strength.” To what has the thread been compared? Another thread? A hair? A blade of grass? Since it is impossible to make any assumption about the object of comparison, the statement tells us nothing about the thread, though it seems to make a claim of superiority.

The fallacy of missing comparison is popular because it permits an expression of superiority without the risk of actual commitment or the need for proof. Whatever assumptions (or self deceptions) the hearer of the argument makes are his own problem.

• Now Soapo is 23% stronger.
• You get 54% fewer cavities with Crest.
• Blade-O gives you a closer shave.
• Use DeeTurge for a cleaner, whiter wash.

Missing Range. Similar to missing comparison, this fallacy occurs when only one end of a range of values is given, thus misleading understanding or expectation. By presenting one extreme or the other, or worst case or best case estimates, the an arguer distorts reality. Suppose Tastee Tomato plants produce anywhere from 2 to 100 pounds of fruit per plant, with most producing about 20 pounds. What picture of their performance would you get by the following claims?

• Hey! Tastee Tomato plants produce up to 100 pounds of fruit each! Get one today!
• Aw, Tastee Tomato plants produce as little as 2 pounds of fruit each. What good are they?

Here are some other examples of the missing range fallacy:

• Come to Oval Tires. We have radial tires from $24.95.
• But his plan could cost as much as $45 million.
• Wrist watches as low as $2.95.

Phrases Often Used in Missing Range
up to	starting at
as much as	as little as
beginning at	as many as
as few as	from
as high as	as low as

Misleading Average. Making an assertion about an average often reveals little and more often obscures truth, first because there are three distinct kinds of average and second because each kind can easily distort reality.

The three kinds of average are as follows:

1. Mean or arithmetic average, the most common kind, is obtained by dividing the sum of all the items in a group by the number of items. For example, in the group 3, 3, 8, 10, the mean is 6 (3 plus 3 plus 8 plus 10 equals 24, divided by 4 equals 6).

2. Median or halfway point is the number at the point in an arithmetically arranged list where half the items are larger (or above) and half are smaller (or below). Thus, the median in the list of 42, 54, 79, 108, 929 would be 79, because it is at the midway point.

3. Mode average is the most frequently occurring item in a list. The mode of 6, 6, 9, 19, 19, 72, 72, 72, 108 would be 72 because it occurs the most often.

When an arguer does not specify the kind of average he refers to as just “the average,” a considerable amount of deceit and distortion can be perpetrated. Suppose you see an advertisement for real estate sales positions. It reads, “Earn up to $350,000 a year! Salesmen in our office average $59,000 a year!” Here are the facts from which that claim was taken:

Joe makes $350,000
Moe makes 83,000
Sam makes 13,000
Gus makes 12,500
Lil makes 12,000
Tom makes 6,000
Ron makes 6,000
Sue makes 6,000
Jim makes 6,000
mean is $59,000
median is $12,000
mode is $6,000

Yes, both claims in the advertisement are quite true: you can earn up to $350,000 a year and the mean average is indeed $59,000. But do those claims present the situation fairly, or give you information on which you can base an accurate estimate of your own earnings? Over 86% of the salesmen earn $13,000 or less. Therefore, by not naming the kind of average used here, and because each kind differs so largely, and because an unspecified average is a misleading average, this advertisement is fallacious. Here are some other examples:

• The average American used car is 3.6 years old.
• The average income these days is $24,000.

Another kind of misleading average occurs when an average of any kind makes diversity look like uniformity. When a group of items contains widely differing values, any average will be a distorted representation of that group.

This fallacy shows up frequently, usually as a result of the blender effect produced by the mean average. We Americans have an odd desire always to know what the “average” is, perhaps because we have most regrettably confused “average” with “normal.” As a result we are offered and try to adjust our lives by such dubious statistics as these:

• The average woman is 30, married, and has 2.3 children.
• The average American eats an average of 4.3 ounces of beef a day.
• The average American husband commits adultery an average of 0.06 times per year.
• The average person weighs 150 pounds.
• The average temperature in this desert area is 75 degrees. [It’s 115 in the summer and 35 in the winter–average it yourself!]

As these examples would indicate, often no kind of average can adequately represent a group. Here, for instance, is a list of grades given in a class:

A
A
A
A
B
C
D
D
F
F
F
mean average is C
median average is C
mode average is A

Even if one of the averages is specified (“The median average is a C”), does that information convey the true nature of the grades? We could avoid the unspecified average fallacy here, but any statement of average will commit the convergent average fallacy because this list cannot be accurately characterized by an average.

Here are some other examples of averages that produce fallacious convergence:

• The average man reads five comic strips a day; the average woman reads two.
• Nationwide mean average gasoline mileage for all cars is 15 mpg.
• An average of twenty-two minutes is required for the average American to eat the average meal.

False Compromise. Also called false mean and extremes, this fallacy exploits the seemingly innate desire we all have for moderation. To accuse someone of going too far or being at the extreme has long been a common way of criticizing a perceived departure from acceptability. Stability, security, and reasonableness are all associated with the middle–the mean between the extremes of either side.

But the desire to steer a middle course can be exploited in argument because the true mean and the nature and extent of the extremes are open to question and debate. In fact, any position can be represented as the mean between two extremes, so that what at first appears to be the middle road, the compromise, the position of reason and moderation, may actually be a fanatical view cleverly placed between two fabricated extremes. For this reason alone, “compromise” and “middle” positions should not be accepted blindly; but further, sometimes the best position is nearer one extreme than the other and is not right in the middle.

• Avoid the right wing fringe of the Republicans and the left wing fringe of the socialists: join the Democratic party.
• Avoid the rightist extreme of anarchy and the leftist extreme of big-government Democrats: join the party of moderation, the Republicans.
• Avoid the fanatic capitalism of the Democrats and Republicans, and avoid the other extreme of those totalitarian communists–join the socialists, the mean between extremes.
• At one extreme are those who oppose all abortion services, and at the other are those who want free, government paid abortions available to anyone. I favor a middle, moderate position of allowing abortions when paid for by the patient and approved by her doctor.

Exercise 1

For each discourse below, name the fallacy or fallacies committed. If the discourse contains no fallacy, so state. Feel free to make brief comments pertinent to uncertain or context-dependent cases.

1. One question I would like to ask my opponent: Why are you always trying to hide your real position?

2. All serious students get straight A’s. If you aren’t getting straight A’s, then you are obviously not a serious student.

3. We have discovered a very high statistical correlation between exposure to ultraviolet light at high intensities for prolonged periods and skin cancer. And there is a strong correlation between not having skin cancer and not being exposed to high levels of UV for long periods. I think these findings show a good probability that long exposure to UV at high levels will create a higher risk of skin cancer than with non exposure.

4. Describe what will happen if you take a laser beam that can burn through anything and turn it on against a wall that cannot be penetrated by anything.

5. It’s as simple as this: either we build the Advanced Technology Bomber right now and in quantity or we will always be a second rate military power, in danger of invasion or attack. What’s your choice?

6. This administration has been attacked for going too far on affirmative action and it has been attacked for not going far enough. I think that shows that we have taken the proper middle road.

7. I’ll tell you one thing: if we legalized heroin and marijuana, then organized crime couldn’t make any money on it and would stop pushing it. Its legality would also make it lose its appeal and soon there would be no drug problem in the U.S.

8. There are no believable statements for modern man to live by. Now we have only to choose which collection of myths we will adopt for our “philosophy.”

9. You can now save up to 75% on selected items at Frimpson’s Department Store.

10. The houses in this city sell for an average of $200,000.

Review

Terms and Concepts
compound questions
begging the question
condition contrary to fact
contradictory premises
self refutation
false dilemma
missing comparison
missing range
missing average
false compromise

Questions

1. Distinguish between a contrary to fact fallacy and an acceptable conditional syllogism. What are the factors that permit you to judge?

Test Yourself

For each question, choose the single best answer.

1. But despite such public accolades, a sober, sometimes even bitter argument rages within the profession itself. Specifically, it is whether psychotherapy is a science or a superstition ennobled as a discipline. Are the emotionally distressed the recipients of the fruits of a true psychological revolution or the victims of a cheap psychic nostrum? –Martin L. Gross

A. compound questions
B. contradictory premises
C. false dilemma (either/or fallacy)
D. self refutation
E. no fallacy

2. Since I define “mental processes” as the conscious experiences of which someone is aware, the concept of “unconscious mental processes” is, in my opinion, an unacceptable contradiction in terms. –Arturo Rosenblueth

A. begging the question
B. compound questions
C. contrary to fact
D. genetic error
E. no fallacy

3. Do you or do you not agree that granola, wheat germ, whiskey, and soybean meal are health foods?

A. begging the question
B. compound questions
C. contrary to fact
D. genetic error
E. no fallacy

4. Unlike those intemperate people who get drunk every night, and still unlike those sourpuss teetotalers who never drink at all, I favor the happy medium of getting drunk on weekends. Everyone should agree with this middle position, which favors neither extreme.

A. missing comparison
B. false dilemma
C. false compromise
D. begging the question
E. no fallacy

5. If we had changed advertising agencies when I suggested it, we would have had a successful fourth quarter for our product, rather than the slow sales we have just had.

A. begging the question
B. compound questions
C. contrary to fact
D. genetic error
E. no fallacy

6. I don’t care for philosophy because I believe that all statements are meaningless, just empty wind.

A. missing comparison
B. false dilemma
C. self refutation
D. begging the question
E. no fallacy

7. Today, every scientist who has been keeping up with the field, and who is competent to judge the issue, agrees that the “Big Bang” theory is true.

A. missing comparison
B. false dilemma
C. false compromise
D. begging the question
E. no fallacy

8. If you have all the quarters in existence in one hand and one more quarter in the other hand, how many quarters do you have?

A. begging the question
B. compound questions
C. contrary to fact
D. contradictory premises
E. no fallacy

9. Come down to Discount Tire Center. We have steel belted radial tires with a 40,000 mile guarantee for all cars, starting at just $29.95.

A. contradictory premises
B. false dilemma
C. missing range
D. missing comparison
E. no fallacy

10. New Slash N Burn aftershave, for the better shave–54% better.

A. contradictory premises
B. false dilemma
C. missing range
D. missing comparison
E. no fallacy

Answers to Test Yourself: 1C2A3B4C5C6C7D8D9C10D