THE NORMAL, AND THE PERILS OF THE SYLLEPTIC ARGUMENT EDMOND A. MURPHY, M.D., ScD* The basic notion of syllepsis can be simply represented. Two attributes separately predicated of two quantities may be confused and make it appear that the two quantities have an attribute in common . Algebraically we might say that A is predicated of B and A* of B*; confusion of the quantities A and A* may make it appear that B and B* have the attribute A in common. Syllepsis is widely used for literary effect. For example in Mrs. Packletide's Tiger the heroine wishes to shoot a tiger so that she can give a party to gloat over her friends with the "tiger-skin rug occupying most of the background and all of the conversation" [I]. Here the word "occupied" is being applied to the words "background" and "conversation"—in the former in a literal sense, in the latter as a metaphor. Syllepsis may be carried over into the field of argumentation. In Molière's Le bourgeois gentilhomme (act 1, sc. 2) the dancing master argues that the diplomat should learn dancing because the errors of diplomacy are false steps, and that the best prophylactic against taking false steps is to know how to dance. There is little danger of error from such transparent cases. But this kind of absurdity is often perpetrated quite unconsciously with words which have many meanings. A brief classification of such words is given in table 1. A typical misuse in an argument, which it seems appropriate to call the "sylleptic syllogism," is provided at the top of table 1. Here the same word, "fitness," is used in two different senses in the two premises: in a medical sense in the first, in a genetic sense in the second. The attendant problems are admirably illustrated in the use of the word "normal." Doubtless many different meanings can be attached to the word, but at least seven are sufficiently different to involve some peril of syllepsis (table 2). From top to bottom of table 2 * Division of Medical Genetics, Department of Medicine, The Johns Hopkins University School of Medicine, Baltimore, Maryland 21205. 566 j Edmond A. Murphy · Perils of Sylleptic Argument TABLE 1 Proper and Sylleptic Syllogisms Proper Syllogism Sylleptic Syllogism* A implies B ........ A is true .......... Therefore B is true . A implies B. A* is true. Therefore B is true. Examples All men are mortal ......... Socrates is a man ........... Therefore Socrates is mortal . Fitness is always desirable. Fitness implies having many healthy children. Therefore it is always desirable to have many healthy children. * Some classes of words which lead to sylleptic arguments: (1) Words which refer tointrinsically human acts (love, responsibility, consent, faith). (2) Words involving value judgment (good, true, beautiful, scientific, democratic). (3) Common words inadequately focused (normal, gene, lawful, the ether, democracy). (4) Words with a common meaning adopted in a specialized sense (random, fit, measurable, probability) or in a generalized sense (bias, myth, disease). (5) Technical words misappropriated by the laity (hysteria, allergic, fractured, tumor, abortion, assault, libel, replica). (6) Euphemisms (malnutrition, promiscuous, privilege). (7) Words which have been watered down, perhaps deliberately (libido, homosexual, education, freedom, home). TABLE 2 Seven Meanings of the Word "Normal" Paraphrase Domains of Use Preferable Term 1. Having probability density function '<^-K(^)'] (predicated of a metrical character) . 2. Most representative of its class. 3.Commonly encountered in its class. 4.Most suited to survival and reproduction .................... 5. Carrying no penalty 6.Commonly aspired to. . . 7.Most perfect of its class. Statistics Descriptive science (biology, etc.) Descriptive science Genetics, operations research , quality control, etc. Clinical medicine Politics, sociology, etc. Metaphysics, esthetics, morals, etc. Gaussian Average, median, modal Habitual Optimal or "fittest" Innocuous or harmless Conventional Ideal there is increasing loss of simplicity and objectivity and increase in complexity and subjectivity. For each sense there are spheres of study in which the term is so used, and for each an alternative term is suggested which is preferable because it is less ambiguous. 1. The word "normal" may mean that it is a metrical variate with Perspectives in Biology and Medicine · Summer 1972 | 567 a particular probability density function which is better described by some such term as "Gaussian." Why the term "normal" ever became applied to it is not clear, but there is no reason for thinking that it has anything whatsoever to do with the word normal in any other sense. There is no reason at all why an attribute of "normal" people should have this distribution: indeed it is usually impossible for it to do so, since this distribution has no limits, and most variables in man (height, weight, blood sugar, etc.) cannot assume negative values. Nevertheless this use of "normal" is a constant source of confusion. The statistician commonly asks, "Is it reasonable to suppose that the data are normally distributed?" The investigator often mistakes the sense, and because he has examined these people himself and considered them normal, he is liable to say that it is a reasonable assumption. In fact, the use of methods based on at least approximate normality must be justified either by serious mathematical theory or by analysis of empirical data. There are several other uses of "normal" in mathematics (for example, in geometry and in measure theory) which are of little interest to the biologist and will be ignored. 2.Then normality may be used in the sense of simple descriptive statistics. The man in the street asked what the normal height of a giraffe is might reply, "Ten feet." This figure may be wrong, but at least what he is trying to do is to give the most representative height of a giraffe from his own knowledge. The most...