Logical Fallacies

Readers often ask about critical thinking and how to reason better. One of the best ways is to learn about logic, which is both fun and useful. Following are examples of the most common logical fallacies. You can use them as exercises to find the flaws in your own thinking.

Simple errors arising from ambiguity.

The same word may be used in different senses (called equivocation): “Marriage is a subject of great gravity, so getting married will make us gain weight.” Or a sentence construction may produce a double meaning (amphiboly): “We’re having some friends for dinner.” Or a word may be emphasized inappropriately (accent): Contrast “I just love my dog!” with “I just love my dog!” Or words that are similar in form may not be similar in sense (figure of speech): “Does he have cold feet?” Who asked: Your husband’s mother or his doctor?!

Confusing the parts with the whole.

We may mistakenly assume that what is true of the parts must be true of the whole (composition): “A chimpanzee is an intelligent animal and even grasps certain numerical concepts, such as the difference between one and two. So a dozen chimpanzees probably would be able to divide a dozen bananas among themselves equally.” Not too likely, right?! But what about this? “Every member of a congressional committee is bright and understands fiscal policy. So the committee likely would be able to successfully restructure the country’s fiscal policy.” It’s the same fallacy.

And sometimes we assume that what is true of the whole must be true of the parts (division): “A group of musicians is wildly popular. Therefore, if they break up, each will be wildly popular.” Of course, that’s incorrect. But how about this? “A corporation consisting of several subsidiaries produces goods of high quality and is profitable. Therefore, each subsidiary can be expected to produce goods of high quality and be profitable.” Again, it’s the same fallacy.

Considering the form of an argument.

We’ve all heard of “if-then” arguments: If this is so, then that must be so. One source of error is assuming “this” defines the only way in which “that” can occur (affirming the consequent): “If a person has full-blown AIDS, then his or her T-cell count will be low.” True. But the following is false: “A person has a low T-cell count. Thus, he or she has AIDS.” Other conditions cause low T-cell counts. A twin error occurs in the opposite manner (denying the antecedent): “A person does not have AIDS. Thus, he or she does not have a low T-cell count.” False, and for the same reason: Other conditions cause low T-cell counts.

Learning about deductive reasoning.

Have you ever heard this? “Every man is mortal; Socrates is a man; therefore, Socrates is mortal.” It’s a famous “syllogism,” a form of deductive reasoning that consists of a major premise, a minor premise, a “middle,”and a conclusion. (The “middle” appears in both premises, linking them.)

An error occurs when the middle contains a term used in two different senses (four terms): “Wool coats shrink if they get wet. Sheep have wool coats. Thus, sheep get smaller when they stand in the rain.” Obvious, right? But what about this? “Many people pay no taxes. The working class is composed of many people. Thus, the working class pays no taxes.” Obviously wrong!

Or the middle term may be used inappropriately to link the two premises (undistributed middle): “Truffles often are found by dogs trained to locate them by scent. Illegal drugs often are found by dogs trained to locate them by scent. Thus, truffles are often illegal drugs.” Oops! This is wrong, just as wrong as the following. “Executives often are ambitious and want to make a lot of money. Criminals often are ambitious and want to make a lot of money. Thus, successful executives are criminals.”

One error occurs when the conclusion is broader than the major premise allows (illicit major): “Politicians are actually reasonable people and not biased nitwits. All politicians are human beings. Therefore, no human beings are unreasonable or biased nitwits.” Another error occurs when the conclusion is broader than the minor premise allows (illicit minor): “Politicians love power. All politicians are human beings. Therefore, all human beings love power.”

Considering the fabric of an argument.

Capital punishment is the source of many an argument, both good and bad. Following are some bad ones, all containing an irrelevant conclusion (ignoratio elenchi). In this one, the opponent is attacked instead of the premise of the debate (argumentum ad hominem): “Capital punishment is wrong because people who favor it tend to be less religious.” And in this one, the opponent is attacked by means of a countercharge (tu quoque): “Capital punishment is right because those who oppose it are more likely to be criminals themselves.”

Abortion is also the source of many bad arguments. The following contain irrelevant conclusions, too. This form uses an appeal to pity (argumentum ad misericordium): “Abortion is wrong; what have these innocent babies ever done to deserve such a cruel fate?” And this form uses an appeal to popular passion (argumentum ad populum): “Pro-choice is right; if your daughter became pregnant as the result of a rape, should she be forced to bear the child?” This form relies on an authority (argumentum ad verecundiam): “Abortion is wrong because my religion says so.”

One last form of irrelevant conclusion is used by just about everyone, so let’s look at an example that is hard to criticize. This form maintains that because a premise is not known to be untrue, it may indeed be true (argumentum ad ignorantium): “No one has ever disproved the existence of the Tooth Fairy. Therefore, it won’t hurt to put your grandfather’s previous set of false teeth under your pillow every night. After all, she may be easy to fool.”

Circular Arguments

Scientists and creationists are always at odds, of course. The following fallacy is called “vicious circle.” In it, the conclusion also appears as an assumption (circulus in probando): “The story of divine creation as related in Genesis must be true because God would not deceive us.” Another fallacious argument is called “begging the question.” The conclusion appears as an assumption, but in a different form (petitio principii): “Miracles cannot occur because they would defy the laws of nature.” (All those talk show hosts who say, “And that begs the question…” when they mean, “And that prompts the question…” are simply wrong.)

Errors of Principles

Evolution has long been the target of illogical arguments that use presumption (secundum quid). One is called “direct accident,” in which the truth of an abstract principle is applied to a specific circumstance: “The theory of evolution maintains that man evolved from apes. Thus, the apes in our wildlife preserves will someday be found reading the newspaper.” Wrong, right?! So is the one called “converse accident,” which is the reverse: “Because the apes in our wildlife preserves will never be found reading the newspaper, man did not evolve from apes.”

Contradiction, Diversion, and Superstition

In one fallacy, the argument declares that an assumption is false if a contradiction can be drawn from it (reductio ad absurdum): “Intelligent people have open minds. Politicians are supposed to be intelligent. But anyone who says that recreational drugs should not be legalized has a closed mind. Therefore, politicians are not intelligent people.” In another fallacy, the argument takes the form of a question phrased so that a direct reply (instead of a denial) supports the implications of the question (plurimum interrogationum): “How many family members have you put at risk with the handgun you bought for self-defense?” Yet another fallacy (“after this, therefore because of it”) is the source of much of the world’s superstition, a legacy from early times (post hoc, ergo propter hoc). Can you imagine the audience reaction if a speaker were to be struck by lightning while denouncing creationism from an outdoor podium? It would make news all over the world!

That just doesn’t follow!

And in the notorious fallacy of non sequitur, the conclusion doesn’t follow from the argument, as in this example: “Because fish have gills and birds have wings, because dinosaurs are extinct and snakes are not, because the duckbilled platypus and the spiny anteater have characteristics of both reptiles and mammals, because animals need the waste products of plant respiration to survive and plants need the waste products of animal respiration, because plenty of plants need insects for fertilization but earthworms don’t even need another earthworm, because dolphins are intelligent and whales can sing, because crustaceans look so much like big bugs and primates look so much like humans, and because nearly every meat on the planet doesn’t taste all that much different from chicken, the theory of evolution is correct.” That just doesn’t follow!