- Equivocation is use of the same word in subtly different senses; due to ambiguity of word meaning, fallacious logic appears to be structurally valid. Particularly subject to this fallacy are arguments that repeatedly use qualitative descriptions such as large and small, or good and bad:
“The hypothesis is slightly incorrect, because there is a slight difference between predictions and observations.” The first use of ‘slight’ means ‘small but definitely significant,’ whereas the second ‘slight’ may mean ‘small and statistically insignificant.’
Proof that -1 is the largest integer [Spencer, 1983]: Listing all the integers . . . -4, -3, -2, -1, 1, 2, 3, 4, . . . where ‘. . .’ extends to infinity, we see that nothing has been omitted. But we also know that the largest integer (n) is the only integer for which there is no n+1; the only such number is -1.
- Straw man is a fallacious strategy for refuting an argument: misinterpret it, refute the misinterpreted version, and then conclude that you have refuted the original argument successfully. The term is a takeoff on the concepts of scarecrows and burning in effigy: imagine that you set up a straw man and easily knock it down, claiming that you have knocked down the real man. The term ‘straw man’ is sometimes used in a different sense than used here; it can be a ‘trial balloon’, an idea that is proposed knowing that it will be knocked down but expecting that it will be a productive starting point for further discussions.
Frequently, hypothesis refutations are of the following form: “Let’s examine the truth of your hypothesis by seeing how well it fits the following example: . . .” If the argument or hypothesis really should apply to the example, then this technique is compelling. The refutation or confirmation is valid, and any refuted argument must be abandoned or modified. With a straw man, in contrast, the original hypothesis was not intended to encompass the example, so the argument is fallacious although the entire logic of the analysis is just as valid. Thus one should evaluate the appropriateness of the example before applying it, lest the refutation act as a smoke-screen.
Case-dependent Relationship Between Parts and Whole
Cholesterol seems to have surpassed sex as the number-one source of guilt in modern America. Much of this cholesterol consciousness stems from the 1985 National Cholesterol Education Program. All Americans were urged to reduce cholesterol in order to avoid heart disease. Surprisingly, however, there was virtually no direct scientific evidence that cholesterol reduction prevents heart disease in either women or in the elderly, although 75% of heart attacks are in people older than 60 years.
The key studies were all on middle-aged men with high cholesterol. These studies conclusively found that: (1) higher cholesterol level is associated with higher risk of heart disease, and (2) giving cholesterol-lowering drugs to high-cholesterol subjects reduced their risk of heart disease. The first finding established a correlation, and the second result demonstrated causality. Generalization of this pattern to middle-aged women and to the elderly of both sexes is plausible, but neither data nor deduction implies it. [Kolata, 1992b].
The conclusion that everyone should reduce cholesterol is a hasty generalization, the extrapolation to an entire population from a possibly nonrepresentative sample. The conclusion may be correct -- indeed, it has been demonstrated by subsequent experiments to be correct -- but it does not follow compellingly from these data. This inductive fallacy and several deductive fallacies go astray
