Fallacies in academic writing Chad Nilep There are many possible sources of fallacy – an idea that is mistakenly thought to be true, even though it may be untrue – in academic writing. The phrase logical fallacy often refers to a formal fallacy in a logical argument; that is, an invalid argument that is mistakenly thought to be valid. Often people talk about various kinds of rhetorical fallacies, writing or speech that appears to be based on an argument but is not logically entailed by premises. Research writing can also be prone to statistical fallacy: mistaken use of statistics, or conclusions based on misunder- standing statistics. Below I discuss a few common fallacies in academic writing. Logical (formal) fallacies Affirming the consequent. Implication is a valid form of logical argument. The truth of one idea (call it an antecedent, meaning it comes first) may imply a consequence. If the antecedent is true then the consequent (the thing that happens after or sometimes because of the antecedent) must be true. For example, if a person is murdered that person is dead. This is necessarily true because it is part of the meaning of murder. If Taro was murdered, we can conclude that he is dead. That is a valid argument from implication. But the opposite is not a valid argument: the truth of the consequent does not imply the truth of the antecedent. If Taro is dead, we cannot conclude that he was murdered; he might have died from a disease or an accident. The consequent does not imply the truth of the antecedent. Denying the antecedent. On the other hand, if an antecedent implies a consequent and that consequent is not true, then the antecedent must not be true. Think about the murder example again: if Taro was murdered, he is dead. If he is not dead, then we know that he was not mur- dered. But again the opposite is not a valid argument: a false antecedent does not imply a false consequent. Even if we know that Taro was not murdered, we don’t know whether he is dead. He may be alive, but he may have died naturally or accidentally. Syllogistic fallacies We discussed syllogisms in class. In a syllogism, two premises add up to a conclusion. If the syl- logism is valid and the premises are true, then the conclusion must be true. Be careful, though: there are several fallacies that can make a syllogism invalid. VALID SYLLOGISMS All P is M. Some P is M. All P is M. All M is Q. All M is Q. No M is Q. (All M is not-Q) Therefore, all P is Q. Therefore, some P is Q. Therefore P is not Q. Undistributed middle. All syllogisms must have a middle term that is “distributed” – true for all – in at least one premise. If the middle term is not distributed, the syllogism is not valid. NOT VALID SYLLOGISMS All P is M. Some P is M. All P is M. All Q is M. Some M is Q. Some M is not Q Therefore, all P is Q. Therefore, some P is Q. Therefore P is not Q. We’ve seen the first non-valid argument in class: “All rabbits run fast; Usain Bolt runs fast. Therefore, Usain Bolt is a rabbit.” I also mentioned an example of the second pattern: “Some students in this class are women; some women are over 60 years old. Therefore, some students in this class are over 60 years old.” Here is an example of the third pattern: “All students in this class are graduate students. Some graduate students do not study logic. Therefore, students in this class do not study logic.” None of the conclusions are proved true since the syllogisms are invalid. Four terms. A valid syllogism must have three terms, like the ones labeled P, M, and Q above. If the conclusion or one of the premises introduces a fourth term, it is not valid. Consider this argument: “Socrates is a human. All humans are mortal. Therefore, Socrates is Japanese.” The wrongness of that syllogism is obvious. But sometimes it can be hard to spot this fallacy when the same words express two different ideas. Consider the example below. Warm beer is better than nothing. Nothing is better than true love. Therefore, warm beer is better than true love. Although this looks like a valid syllogism of the kind we have seen before, the conclusion is not true. What went wrong? Notice that “better than nothing” (無いよりまし) in the first premise does not mean the same thing as “nothing is better” (最高) in the second premise. Those two different meanings add up to a fallacy of four terms. Affirmative conclusion from negative premises or negative conclusion from affirmative premises. Two negative premises cannot entail an affirmative conclusion. Likewise, it is not valid to add negative meaning to an affirmative syllogism. NOT VALID SYLLOGISMS No P is M. Some P is M. No M is Q. All M is Q Therefore, all P is Q. Therefore some P is not Q. As an example of the first pattern consider this invalid syllogism: “No rabbits are horses; no horses are birds. Therefore, all rabbits are birds.” It is not valid to draw an affirmative conclusion from negative premises. Likewise, negative conclusions cannot be drawn from premises that contain no negative statement. Maybe you can think of examples that seem to be true; for example: “Some people are doctors; all doctors are university graduates. Therefore, some people are not university graduates”. But the truth of that conclusion is only accidental. It is not a valid conclusion from the syllogism. Consider this example, which uses the same logic: “Some army officers are generals; all generals are soldiers. Therefore, some army officers are not soldiers.” That’s not valid and it’s not true. Remember: a valid syllogism allows us to deduce that the conclusion is true, but truth (matching the world) is not the same as validity (entailment from argument). Rhetorical (informal) fallacies Writers sometimes argue, meaning they try to convince the reader that what they say is right, without a logical argument in the sense of “a set of premises that imply the truth of, or support the likelihood of their conclusion”. Here are some examples of rhetorical fallacy. Appeal to authority. Writers may imply, or readers may assume, that something is true because a famous, smart, or respected person said it. There is, however, no necessary link between the authority of a speaker and the truth of what s/he says. Similarly a bandwagon argument suggests that if many people believe the same thing, that belief must be true. Again, there is no necessary link between popularity or fame and truth. Ad hominem. When two people or groups disagree, an ad hominem argument may appear: arguing that the person saying something is bad, so what s/he says must not be true. Just as the goodness of a speaker does not entail the truth of what s/he says, the badness of a speaker does not entail falseness. Straw man argument consists of misrepresenting either a conclusion or a logical argument in order to counter it. A scholar may reject another scholar’s conclusion by showing either that an argument was invalid or its premises are not true. If instead the scholar creates an invalid argument that reaches the same conclusion in order to reject that conclusion, he has created a straw man argument. Begging the question or circular reasoning involve making the conclusion one of the premises. Consider this argument: “Fundamentals of academic writing is a popular class. Most students like popular classes. Therefore, most students like fundamentals of academic writing.” The conclusion and the first premise mean basically the same thing, even though the words are slightly different. Therefore, it is not actually an argument; it just states what the teacher hopes is true. (Note that in everyday English the phrase beg the question is sometimes used to mean “cause to ask a question”. That is not related to this fallacy.) Appeal to ignorance refers to the assumption that something not proved to be true must be false, or that something not proved to be false must be true. Neither of these is a valid assumption; something not proved might be true or false, but it’s currently unknown. For example, there is no clear evidence that life exists on other planets, but that is not proof that no such life exists. It might not exist, or it might exist but be unknown to humans. (Note, however, that some kinds of absence can be used to support some kinds of inferences. For example if a doctor tests me for cancer cells and doesn’t find any then it is likely, though not certain, that I do not have cancer.) And although it’s not exactly a fallacy I will also share a warning from my former professor Lise Menn: “Beware Procrustes bearing Occam’s razor”. Occam’s razor is the valid suggestion (not a fallacy) that when two theories can account for the same data, it is best to assume the simpler of the two theories. But simple theories are not always correct. Procrustes is a character from a Greek myth who made everyone fit into the same bed by either stretching them or cutting off their legs. Scholars sometimes commit an error by “cutting off” some data in order to make it fit with a simple theory. For example, there is a simple theory that explains the evolution of large human brains, but this theory cannot explain variation in the size of other human-like species’ brains.