Logical
Theory can be inductive or deductive but usually is both. You are using inductive logic if you buy a book on the advice of a friend whom experience suggests shares your tastes. The conclusion probably is correct but is never certain: this time you might not like the book.
Inductive arguments predict a conclusion from general premises, extending information to a specific situation. Scientists use inductive reasoning when they develop a theory from experiments and observations. The basic form is “every set of events A has been followed by event B so the next time the set of events A occur B probably will follow again. That is, it assumes nature acts uniformly, but this is not always true. When we have the green light, we conclude inductively that the other driver has a red light and will stop, but it does not always happen. Inductive reasoning may be good evidence, but never is certain. Evaluation of an inductive argument requires determining its reliability, completeness, relevance, and probability.You are using deductive logic if you conclude that Ed is good swimmer because Ed is a SEAL and all SEALs are good swimmers. Deductive arguments draw general conclusions from specific premises. The basic form, called a syllogism, consists of two or more premises leading to a logical conclusion: All X’s are Y (all SEALS are good swimmers) and Z is a Y (Ed is a SEAL). Therefore, Z is an X (Ed is a good swimmer). Premises can be true, false, or debatable. If you can disprove a premise, then conclusions drawn from it are illogical, although they might still be true! Evaluation of a deductive argument requires determining the truth of each premise and the logic of the conclusion.
The latter is tricky because there are so many types of logical error. Here we give one example from each of eight major classes of logical error, providing a more complete list with brief definitions in the Appendix.
Consider a driver convicted of going through a red light because a witness swore that the light was not green. The jury made two mistakes in logic. First, it accepted a false dichotomy, one of a class of fallacies in question framing. The light could have been yellow, or red and green (some systems use both instead of a yellow light), or not functioning. If anyone tries to limit you to two choices, always determine if there are other possibilities. Second, the jury accepted a negative proof, one of a class of fallacies of factual verification. Saying what the light was no t does not say what it was. The bumper sticker reading “War is not the answer” does not tell you what the answer is. Worse, it does not even tell you what the question is.Third are fallacies of significance, such as judging politicians of your own and the opposing party by different standards. It is common to hear corporate CEOs condemned as greedy for salaries that are large multiples of their lowest paid workers. A recent study showed the median income of major corporate CEOs to be about $8 million a year. Oprah Winfrey earns about thirty times more. But few denounce her or other entertainers and sport stars. Nazi Admiral Karl Doenitz was spared trial for war crimes on this principle when it was pointed out that the US submarine campaign in the Pacific was little different from that of the Germans except for being more successful.6 Fourth are fallacies of generalization, such as the self-refuting question the Greeks asked long ago: “What is one to believe when a Cretan tells you that all Cretans are liars?”
Correlation often is mistaken for proof of causation. The correlation observed during the 1920s and 1930s between fashionable hem height and the Dow-Jones average led to the advice, “Do not sell until you see the whites of their thighs,” which probably is not a reliable guide to managing one’s investments. Fallacies of substantive distraction shift attention from reasoned argument to the irrelevant and irrational.
The most common undoubtedly is the ad hominem, but the most dangerous probably is the appeal to authority, including pedantic words, obscure sources, and fallacious mathematics. We can legitimately begin by defining “a” as equal to “b” then perform a number of perfectly normal algebraic manipulations, always doing the same thing on both sides to keep the equation equal on both sides:| Multiply both sides by a: | a2 = ab |
| Subtract b2 from both sides: | a2 - b2 = ab - b2 |
| Factor: | (a + b)(a - b) = b(a - b) |
| Divide both sides by (a - b) | a + b = b |
| Substitute b for a, as the two are equal | 2b = b |
| Thus, any number is half itself | 2 = 1, 3 = 6, etc.7 |
Fallacies of narration include anachronisms such as the crossbows, domed buildings and bell towers in the film Gladiator, the Lewis guns in Lawrence of Arabia, the boxes labeled “Product of Israel” (founded in 1948) in The Sound of Music (set in the 1930s), and mention of Freud’s Pleasure Principle (published 1920) in Titanic (sunk 1912). Freud’s psychoanalysis, which extrapolated normal behavior from the study of neurotics, commits a fallacy of motivation. You will encounter semantic distortions such as equivocation, such as the claim that women do not need to worry about man-eating sharks.
Logic alone is insufficient to establish a theory. It is perfectly possible to construct a logical argument that is absolute nonsense, as Lewis Carroll did for fun in Alice and Wonderland and Through the Looking Glass. Whately (1819), a renowned English logician and theologian, later the Anglican Archbishop of Dublin, “proved” in a 25-page pamphlet that Napoleon did not exist—at a time when Napoleon was alive on St. Helena. He claimed that Napoleon’s achievements were too far-fetched to believe, that there were discrepancies in the stories of his exploits, that different sources describe him differently, that Louis XVIII said he was the King of France at the time Napoleon claimed to rule, and that Britain created him to justify tax increases and increased military spending. There is much more in his pamphlet, written to satirize the arguments of those trying to prove Jesus had not existed. Those who asserted that 9/11 was a government conspiracy resurrected the techniques (Dunbar and Reagan 2006).