MIT ESD02 ESSENTIALS OF ENGINEERING
LOGIC
ERRORS OF LOGIC
Reference: Fallacies and Pitfalls of Language: The Language Trap
S. Morris Engel, Prentice Hall, 1994
Aristotle, one of the greatest philosophers, was intrigued by the debates of the Sophists. Studying their methods he compiled a complex set of "errors of logic," which the Sophists used to confound and take advantage of others. Aristotle reduced the discussions to fundamental statements, which he called "categorical propositions" such as "The table is brown" or "The sky is clear." Combining these seemingly simple declarations, the Sophists would create a "syllogism" or argument, e.g.
"All people who try to deceive others by uttering what they know to be false are liars."
"You are such a person,"
"Therefore you are a liar."
[Mathematically, one can think of set theory to determine whether such syllogisms must be true, may be true, may not be true, or must be false.
If B is a subset of A and C is also a subset of A, does it follow that B=C? Of course not, because there is nothing to state that the two subsets B and C must be identical subsets. The Sophists (and others) use such tricks to prove that "black is white."]
Aristotle enumerated 256 argument forms, only 15 or which he considered valid. Modern philosophers have developed other classifications, twenty of which are outlined in Morris Engel’s text on Fallacies and Pitfalls of Language. Many of these the student will readily recognize as it was necessary to have exceptional logical reasoning skills in order to pass all those tests required for admission to MIT! You will learn more such "errors of logic," not so much from your classroom experience, but from interactions with your classmates, over dinner, in late night debates and most importantly through MIT humor.
MIT humor is not necessarily unique, but much of it tends to focus on fallacies of logic, showing how the common person is unable to cope, in real time, with the complex set theory of language.
"If you are what you eat; I’m dead meat."
"I intend to live forever — so far, so good."
"Age doesn’t always bring wisdom. Sometimes age comes alone."
"If you are going to try cross-country skiing, start with a small country."
"If we aren’t supposed to eat animals, why are they made of meat?"
"Save the whales! Trade them for valuable prizes."
"If you cannot complete your work in 24 hours a day — work nights."
"The early bird gets the worm, but the second mouse gets the cheese."
"A clear conscience is the sign of a bad memory."
Engel lists the following fallacies: [There is a separate chapter in his text devoted to each if you are really interested!]
1. Amphiboly: applies to statements that, because of some ambiguity, admit of a double interpretation:
"With her enormous nose aimed toward the sky, my mother rushed to the plane."
[Whose nose? The plane’s or my mother’s?]
"Clean and Decent Dancing Every Night Except Sunday."
"Killer says dead man was chasing him with a razor."
"The accused will be given a fair trial before hanging."
2. Accent: depending on the tone of voice the meaning changes.
"Only I hit him in the eye yesterday." (I alone did it.)
"I only hit him in the eye yesterday." (I didn’t kill him.)
"I hit only him in the eye yesterday." (I hit him and no one else.)
"I hit him only in the eye yesterday." (I hit him there and nowhere else.)
"I hit him in the only eye yesterday." (He was a one-eyed monster, and so I let him have it.)
"I hit him in the eye only yesterday." (It happened only yesterday.)
"I hit him in the eye yesterday only." (It’s not something I do every day.)
"I wish you all the good fortune you deserve."
"I could care less."
"The Mass is ended. Thanks be to God."
"After living with her husband for 55 years. She departed in hope of a better life."
3. Hypostatizing: to attribute to things that are not persons (but only ideas or concepts) qualities and properties that only persons can have.
"The city is aroused."
"Science makes progress."
"Ask not what your country can do for you; ask what you can do for your country."
4. Equivocation: Many words have multiple meanings. When the meanings become mixed, absurdity can result.
"Everything that runs has feet.
The river runs.
Therefore, the river has feet."
"The miracles of science."
"If a tree falls in the forest and no one is present to hear it, does it make a sound?"
5. Division and Composition: Division attributes the properties of the whole among the parts or members. It’s opposite, composition, tries to compose the whole out of the properties or qualities possessed by each of its parts."
"How can we love our country and not love our countrymen?"
"It is not going to help the energy crisis to have more people ride buses instead of cars. Buses use more gas than cars."
"Each manufacturer is perfectly free to set his own price on the product he produces. So there can be nothing wrong with all manufacturers getting together to fix the prices of the articles made by all of them."
6. Sweeping (or Hasty) Generalization: This assumes that what is true for one is true for all.
"I know one union representative and he is a terrible person. I wouldn’t trust any of them."
"Under the capitalist system, there are many poor people. Therefore, capitalism should be abandoned."
7. Bifurcation: Sometimes called the "black-or-white fallacy" or the "either/or fallacy," this presumes that a certain distinction proposed is exclusive or exhaustive when other alternatives exist.
"We can become independent of Arab oil only by ruining our environment."
"Volvo: the car for people who think."
"Either you drive a Jaguar, or you don’t drive at all."
"Life is like that, take it or leave it."
"Give me liberty or give me death."
8. Begging the Question: a logic lapse committed when, instead of offering proof for its conclusion, an argument simply reasserts the conclusion in another form.
"When many people are out of work, unemployment results."
"China is a large country inhabited by many Chinese."
"Death for traitors is justified; because it is right to put to death those who betray our country."
"Why did he lose the election? He didn’t get enough votes."
9. Question-begging epithets: are statements that state a judgement and treat it as a fact.
"The scoundrel hounded his wife to the grave."
"This criminal is being charged with the most vicious crime known to man."
[When such judgements are made against you, it is often useful to "cloud" the judgement by calmly acknowledging that there may be some truth in what has been said and then replacing the uncomplimentary terms with more neutral or even laudatory ones.
Boss: Diane, sometimes you seem to take twice as long as other times to get your work done.
Diane: It does seem that I am more productive on some days than I am on others.
Boss: Maybe you should be paying a little more attention to your duties.
Diane: I’m sure there are times I should be a little more attentive.
Boss: Maybe you aren’t getting enough rest, and shouldn’t stay out so late on a week night.
Diane: You could be right. If I feel the need for more sleep, I’ll get in earlier.
A little humor doesn’t hurt either:
In-Law: My daughter deserves a husband who is more ambitious.
Paul: I probably could be more ambitious than I am.
In-Law: I don’t know what she ever saw in you, anyway.
Paul: I don’t know what she sees in me either but I’m glad she does.
Nor does a bit of foggy generalizing:
In-Law: Sometimes just your presence irritates me.
Paul: People often irritate other people.
And gentle self-deprecation:
In-Law: Don’t you have anything more to say?
Paul: I guess I haven’t had a lot to say, have I?]
10. Complex questions: Some questions contain implicit assumptions, which may not be true. It is important to question the question.
"Have you stopped beating your wife?"
"When should you buy your first Cadillac?"
"Why is a ton of lead heavier than a ton of feathers?"
"Will you be paying by a check or a credit card?"
"Would you rather watch your baby sister or mow the lawn?"
11. Special pleading: Using a positive term for oneself and a negative term for another.
"I know how to be thrifty but Larry is a tightwad."
"Our patriotic troops were fighting the savage enemy."
12. Imperfect or False analogy: Although some analogies are excellent for teaching, analogies which distort the facts represent another form of fallacy.
"No body can be healthful without exercise, neither natural body nor politic; and , certainly, to a kingdom, or estate, a just and honorable war is the true exercise. A civil war, indeed, is like the heat of a fever; but a foreign war is like the heat of exercise, and serveth to keep the body in health; for in a slothful peace, both courages will effeminate and manners corrupt." [Of the True Greatness of Kingdoms]
"By what conceivable standard can the policy of price-fixing be a crime, when practiced by businessmen, but a public benefit, when practiced by the government? There are many industries in peacetime–trucking, for instance–whose prices are fixed by the government. If price-fixing is harmful to competition, to industry, to production, to consumers, to the whole economy, and to the "public interest"–as the advocates of the antitrust laws have claimed–then how can that same harmful policy become beneficial in the hands of the government?"
13. False cause: assumes that two events juxtaposed in time or space, have a cause and effect relationship.
"Twenty-five years after graduation, alumni of Harvard College have an average income five times that of men of the same age who have no college education. If a person wants to be wealthy, he or she should enroll at Harvard."
Letter from George Bernard Shaw to Jakob Heifetz ater listening to Heifetz’s concert.
"My dear Heifetz:
Your recital has filled me and my wife with anxiety. If you provoke a jealous God by playing with such superhuman perfection, you will die young. I earnestly advise you to play something badly every night before going to bed, instead of saying your prayers. No mortal should presume to play so faultlessly.
G. Bernard Shaw"
14. Irrelevant thesis: attempts to prove a conclusion that is not the one at issue.
"The United States had justice on its side in waging this war. To question this would give comfort to our enemies and would therefore be unpatriotic."
"I do not permit questions in my class, because if I allow one student to ask a question, then everyone starts asking questions and the first thing you know, there is no time for the lecture."
"Vegetarianism is an injurious and unhealthy practice. For if all people were vegetarians, the economy would be seriously affected and many people would be thrown out of work."
15. Genetic fallacy: attempts to prove a contention false or unsound by condemning its source or genesis.
"It must be false that in a capitalistic economy small business tends to disappear, because this is said in the Communist Manifesto, and the only person I have ever heard affirm this was a communist."
"Congress shouldn’t bother to consult the Joint Chiefs of Staff about military appropriations. As members of the armed forces, they will naturally want as much money for military purposes as they think they can get."
"Smoking is unhealthy. You should quit."
"Hey! Look who’s talking! You smoke!"
"Far too much fuss has been made over our Central Intelligence Agency’s espionage abroad. Other countries are just as deeply engaged in spying as we are."
16. Appeal to authority: attempts to justify the conclusion by quoting an authority in its support.
"No federal aid should be provided for public schools. My banker, my dentist, my doctor, my minister, and all my business associates are opposed to it."
"I join two presidents, twenty-seven senators, and eighty-three Congressmen in describing Drew Pearson as an unmitigated liar."
17. Appeal to ignorance: uses an opponent’s inability to disprove a conclusion as proof of the conclusion’s correctness.
"No responsible scientist has proved that the strontium 90 in nuclear fallout causes leukemia. Therefore we can disregard the alarmists and continue testing nuclear weapons with a clear conscience."
"If there were any real evidence for these so-called flying saucers, it would be reported in our reputable scientific journals. No such report has been made; therefore there is no real evidence for them."
18. Mob appeal: crowds are anonymous and anonymity breeds irresponsibility.
"One American custom has never changed: a friendly social drink."
"The U.S. is Enemy No. 1 of humanity"–Iranian radio broadcast."
"It is a struggle between Islam and the infidels"–Khomeini speech"
19. Appeal to pity:
"Streaks of pain etching his youthful face, the boy drags his withered legs along the sidewalk, two crutches biting into the pavement one short step ahead. The minutes seem like hours, but the thinly built boy finally makes it to his destination, hangs up his coat and prepares for his day’s activities.
When a handicapped boy pains himself by walking grueling distances on hard wooden crutches, it proves that the handicapped will go out of their way to improve their lives. Now we ask you to do a little out of your way to help the handicapped.
"My client is the sole support of his aged parents. If he is sent to prison, it will break their hearts, and they will be left homeless and penniless. You surely cannot find it in your hearts to reach any other verdict than "not guilty."
20. Appeal to fear:
"You must believe with me that this woman is guilty of the crime of which she is accused, for if you do not find her guilty of it, she will be released and you may end up being her next victim."
"Don’t argue with me, young man. Remember who pays your salary."
Desegregation of labor unions is not desirable, and any official who thinks it is will discover his error at the next election."
It is not always easy to recognize fallacious arguments. Firstly, the 20 different methods listed above is a large number to sift through. Secondly, the arguments are not usually presented in such compact form as the examples given above. Nonetheless, categorizing the methods helps you, with practice, to recognize the errors of logic and will hopefully make you better able to counter or expose the errors.