Fallacy

10 Unnecessary Vagueness (Rule 4)
The fourth rule of adequate classification (see p. 36) requires that the divisions must be precise enough to avoid serious marginal cases. Let us briefly resume the account of the model of a scientific law (see pp. 5ff.) to see how classifications are set up in science. What needs to be added to the previous discussion is that science characteristically defines the divisions between the categories in terms of measurable properties.
One of the first things that impresses the young student or science is the difference between scientific and ordinary vocabularies. When he now uses such terms as "mass," "force," "energy," "velocity," he must use them exactly. The student finds that they are precisely defined; in fact, they are specified in mathematical equations. All the categories to which the student is introduced turn out to be almost perfectly determined. The laws and observations are expressed in terms as free from vagueness as it is possible to make them, the language of measurement and precise definition. Compared to the language of ordinary affairs, that vapor of vagueness, scientists use a language that seems a relatively perfect instrument of communication.
The precise determination of the categories becomes possible in science because the phenomena dealt with are concrete: they can be measured. This means that the laws are so formulated as to be open to test by procedures of the laboratory and of the trained observer. It means, moreover, that the definitions can in all typical cases be stated so clearly (since they are given in measurable units) that these definitions make explicit the necessary and sufficient conditions for the application of the terms: a given thing or event is an instance of a particular category if and only if such and such. The characteristics, as they are measurable, provide criteria for classifications that are unmistakable and final. The lines between the categories are cleanly drawn, so that a marginal case is a great rarity, calling for a redefinition of the terms involved.
To anyone acquainted with the clarity of scientific classifications, further description will be unnecessary; to anyone without scientific experience, unintelligible. What can be said about the clarity of nonscientific classification? Surprisingly, the case is not always desperate. Mr. Richards in lamenting the imprecision of "the sphere of random belief and hopeful guesses" (see p. 8) allows that there are "rules of thumb" in "the concrete affairs of commerce, law, organization and police work," and speaks of "generally accepted convention" being helpful there. He is not interested in these fields, but let us see what these conventions and rules of Jhumb are like.
If your bank sends you a statement reading, "Your account is overdrawn," you know exactly what evidence will render this sentence true or false. You know the conditions of the category of overdraft: subtract your withdrawals, plus charges, from your deposits; if the figure you get is minus, the sentence is true; if plus, false -- supposing neither you nor the bank keep inaccurate records. Thus the category "overdraft," like scientific categories, is defined in terms of necessary and sufficient conditions: you are overdrawn if and only if the figure determined as above is minus. Many commercial expressions are far from vague.
Mr. Richards also exempts the law. It is true that the legislatures and the courts make a great effort to define legal categories so that the characteristics of all the basic classes can be accurately determined. "The people of the State of N. charge that on or about 7:00 P.M. EST, October 5, 1957, at 100 First Street, City of X, County of Y, the accused committed an act of burglary, to wit . . ." The dates and times, the names of the people and places, are of course almost always unmistakable. What of the category of burglary? This is determined exactly enough for all but rare cases. A court applying common law will instruct the jury to find the accused guilty if and only if the prosecution has proved that at the times and places specified the accused did in fact

break and enter
the dwelling of another
in the nighttime
with intent to commit a felony (not necessarily theft).

All these four elements are, in turn, defined to make each concept as precise as possible. To "break and enter" refers to any entrance without authority even though no door or window is moved and even though the accused only reaches in with an arm or hook; "dwelling" refers to any place of abode and its immediate outbuildings; "nighttime" receives a statutory definition as so many minutes after sunset; while felony is generally defined by statute as applying to any act punishable by a certain penalty, commonly over one year imprisonment. The trial will involve attempting to prove that the accused committed certain acts (as specified in the dots following "to wit" above) which fall within the legal category of burglary.
But legal categories, since crime and other social relations can be exceedingly various, are sometimes unfortunately vague. Many problems do not lend themselves to crisp definitions even though jurists might be willing, as with the case of separating day from night, to adopt an arbitrary definition for the sake of clarity. Sometimes it is not helpful to press for arbitrary definitions, since they would not be useful in solving the problems. For instance, "negligence" or the establishment of guilt "beyond a reasonable doubt" cannot profitably be defined in an arbitrary way. In law as in less rigorous fields there are categories that resist either reduction to particular cases (precedents) or precise definition.
Let us turn from the fields of law and commerce to Mr. Richards' area of "random belief and hopeful guesses." It must be admitted at once that many important constructions are relatively very vague. Particular instances may be instructive.
1. Peter is bald.
The construction bald is vague. Let us see just in what the vagueness consists. It is possible to construct a scale from one extreme condition of a man's head to the other:

bald ____ ____ | ? | ____ ____ hairy-on-top
x₁ x₂ x₃ | x₄ | x₅ x₆ x₇

In the every-day situation represented here, people use the term "bald" without knowing at precisely what point they would be unwilling to call a man "bald." For x₁ there is no doubt, and his dome shines afar. For x₂ and x₃ only very charitable persons would hesitate to employ the description, though there may be a fringe and a combed-across wisp. As to x₅, there is a good thatching over, albeit a little thinning in front. But x₇! His hair springs up, it seems, from every possible minute spot: you feel there is not room for another hair, and nobody would call him bald. What about the wide range where x₄ is? Well, people may say that x₄ is balding, getting bald, losing his hair. Some actually say that he is bald.
If "Peter is bald" is a case of x₄, then there is a broad range of possibilities concerning the condition of Peter's scalp. Moreover, the borders, so sharply drawn on the scale, are in doubt. Some users of the term might not distinguish between x₃ and x₄. Other users might not distinguish between x₄ and x₅, as we have.
Is this vagueness an insurmountable disadvantage? If it were to become important to know for every man whether or not he is bald, scientists could certainly set up one arbitrary line in the middle of the scale somewhere. Tliey could say: "bald if fewer than 5000 hairs on the head." But note, if it were important, the importance would surely lie in a tie-in with something else, artistic ability, say, or mathematical genius. In such a case, the arbitrary number of 5000 hairs might be no help at all. The definition of baldness would depend in part on the proved relationships to the tie-in, and scientists would draw the line only where evidence of connection with genius or the like warranted doing so. Again, that evidence might not prevent a rather vague border.
The possibility of precisely setting limits is not the important thing about the usage represented by (1). Though at the present time nothing much would be gained by setting such strict limits, it is still possible to use the term "bald" in a very definite way. In the case of x₁, as contrasted with x₇, the difference is striking. Avoiding, then, the vague range and staying well to the extremes, a careful speaker can say "Peter is bald" and communicate very effectively to those who know Peter. At the same time, the speaker does not exclude the possibility that Paul, who may have quite a number of hairs compared to Peter, perhaps is also bald. The speaker leaves Paul's case open. Obviously, it would be a very narrow view of the function of the categories of description to deny the right to say that Peter is bald just because one cannot say whether or not Paul is bald (but see #11).
This consideration enables us to give a sufficient condition for deciding when a term is too vague for reasonable communication. We shall say that when there is no clear case, no x₁ on a scale, then the term should be rejected for vagueness. It will be evident that many constructions of the language pass this test. In spite of areas of vagueness, there are cases where nearly perfect communication is possible. "Child" and "redness" are quite precise enough for the needs of ordinary communication. Other constructions are becoming more clearly defined day by day. With the application of statistical analysis, the refinement of observational techniques, the discovery of linguistic and semantical principles, informed speakers today are in a position to make many judgments with a degree of intelligibility that would have been impossible only a few years ago. Despite its conceded limitations, I.Q. measurement provides a more exact description of mental ability than vague terms such as "capable" or "bright." Let us take another instance for the purpose of exploring the application of the rule for excluding vague terms.
2. Chivalry implies the ideal of womanhood.
There are here two constructions, chivalry and ideal of womanhood. Certainly these constructions are vague to the point of being diaphanous. The borders of the concept are almost hopelessly fuzzy. Can such constructions be excluded by the rule? One feels that (2) is saying something; it is not mere nonsensical mouthings. In fact, sentence (2) itself provides some help: any likely elements the speaker includes in the construction of chivalry apparently will be related in some sense ("implies" is a very vague term in common usage) to elements in ideal of womanhood. But the latter is no less vague than chivalry. Still something is gained.
What of the technique of reduction? Clearly this technique will not work unless there are some clear-cut particular instances. What particulars would all users agree upon? In the case of bald there would be no reasonable doubt about x₁, though the term does not reduce as readily as other abstractions, such as "redness" -- it passes the test. Would informed users of "chivalry" unanimously regard this deed of Sir Lancelot as germane? What of this decree by King Arthur? Or, more generally, this practice of wearing a lady's colors in tournament? This body of amorous song? This search for the Grail?
Probably not unanimously. Nevertheless, a conscientious historian could specify certain feelings, beliefs, attitudes, as they reflect themselves in various language samples and cultural practices and weave themselves in and out of medieval institutions, such as courtly love, and thus roughly specify the development of chivalry in the history of the Middle Ages. The historian's difficulties are legion in such an enterprise, but they are in degree surmountable.
As the term exists in the common language, it is to be ruled out by the condition for excluding vague usages. But this is not to say that it is entirely meaningless. What happens when the speaker of (2) intends an observation about behavior of today? When this is the case, how is (2) to be interpreted? Presumably the speaker can refer to feelings, beliefs, attitudes, and the like, which resemble the historian's construction called "chivalry." In the common usage, as opposed to the careful historical usage, it would seem that such terms as "chivalry" merely point in a direction. It is as if one gestured casually to the north when asked where Nome is. Even a general direction is something, and there is no occasion to condemn the common usage of terms represented by "chivalry." But in responsible discussion, one can expect something more. In the case of the speaker of (2) referring to today, he can be reasonably held responsible for a knowledge of some historical specifications and, moreover, for a list of contemporary developments which he has in mind when speaking of chivalry.
One thing remains to be noted about sentences of the type represented by (2). This is the danger of reification (see pp. 41 ff.-J. Language encourages its users to suppose that there exists a structure corresponding to the constructions named, that there is a kind of Platonic entity in the nature of things. A term like "chivalry" names, of course, the construction of the users, but people feel that their construction more or less corresponds to strands of reality. Instead of saying that speakers and writers construct a class by relating one cultural or social phenomenon to another and calling it, for convenience, "chivalry," some speakers tend to suppose that strands or structures of in-themselves-related phenomena, however poorly realized in any actual place at any actual time, have a basic reality which men perforce notice and name. It is natural to assume that the way to achieve a sensible notion of such a term is to study, yes, the actualizations of the ideal in its poor embodiments in France and England, say, but at the same time to hold in view the pure concept itself.
Yet chivalry can be used by conscientious writers and speakers. They do not have to suggest a reified perfection crudely embodied in some Medieval institutions. They can realize that they are exploring a construction-for-convenience of cultural attitudes or practices, and the like. As to the vagueness of such terms, what is required is that one designates the particular instances intended. Presumably these will lie in the "direction" of the common use. If this is done carefully, the speaker can be as clear as he needs be for communication. Finally, there remains to be discussed a class of usages which have been called vague from the earliest times.
3. Man pursues the good.
Value terms are an instance of terms that resist reduction, in spite of heroic efforts on the part of recent writers. (They may have been the instance that led Plato to his theory of ideas.) "Man pursues the good" illustrates a use of "good" *^nfar impossible fn analyze. There are indeed many uses of "good" tnat can be reliably reduced or that can be translated, without loss, into a group of sentences not employing "good" or its synonyms. "That is a good design" translates into a sum of sentences about the adequacy of the- rlf-sifrn its economy, qualities it has that many people find pleasing. If the condition is added that "good," as well as describing such things, also expresses the approval of the speaker and invites an appropriate attitude on the part of the listener, then the result is a sort of translation for "good" in "That is a good design," that few will object to. Like many other abstractions, it turns out to be a short-hand expression for something complicated, but not impossible, to spell out. Similarly, if one says, "Money is a good," it is possible to reduce this meaning of "good" (as in "goods") to things desired by people. If one should say, with Aristotle, "It is a good to have a good," restatement would yield, without much loss of content, something like "People feel a satisfaction in the having of something they desire as well as in the thing itself." A great many usages of value terms can be analyzed in this way, but almost certainly not all of them. Dewey and his school seem in error when they suggest that all usages can be so analyzed because most can. There still remain uses of (3) in ethics and religion that do not yield to reduction.
Can we say of these cases that they are so vague as to be useless? Well, we shall not say so, in spite of the condition of exclusion. Let extreme positivisms legislate as they choose, few will obey them. For our part, we prefer to hope that analysis in years to come will teach us the secrets of these terms.
In conclusion, we can draw together the tentative findings of this section. People are always making new classifications, tinkering with old ones. The best we are able to suggest is a few rough and ready rules to follow in making or testing classifications, rules which a careful arguer employs. As we saw (pp. 36ff.), a classification must be able to separate elements of the situation, The rules of classification can be observed only if the characteristics are given, at least implicitly, in a way clear enough for others to apply them and come up with the same results. This will not be possible unless there are at least some indisputable applications of the construction, as with the case of baldness, or unless the user of the term gives it such applications himself by pointing to unmistakable examples of what he has in mind. Let us summarize these observations.
1. Peter is bald. The unmistakably bald person is called "bald" by all users of the conventional term. Despite some borderline cases, the construction is useful. If Peter's case is marginal, it can be dealt with by further description: "getting bald," "thinning at the temples."
2. Chivalry implies the ideal of womanhood. The sentence points in the general direction of certain (or uncertain) feelings, beliefs, and attitudes. The terms can be employed where a mere indication of such general meaning is sufficient, that is, where the notions are not crucial for the discussion, as when the speaker is merely blocking in a background. Otherwise the speaker must show by citing instances some clear applications.
3. Man pursues the good. The meaning of such statements is beyond our analysis. However, note that other uses are serviceably clear: the speaker of "That is a good design" considers that the instance before him carries out effectively the principles of design. (These principles and their application to the given case can be explained on demand.) This use of "good" is not hopelessly vague, though there may be an ambiguity with ethical and other uses of "good."
Apparently the vague usages in question are approved for argument? Not exactly. The qualifications are important. Let us gather them together:

a merely directional use of such terms as "chivalry" is permissible only when nothing central to the argument hangs on it.
vague terms in argument may be employed in a crucial place only when there are clear applications and these are the cases under discussion. If a marginal case becomes important, then a satisfactory decision must be made for this case.

When arguers make up new constructions and give them new names, they often specify the application with care and clarity. If they neglect to do so, someone will sooner or later find a counter instance and explode their balloon. But when arguers use the old abstractions, like "chivalry," which designate constructions very vague indeed, being merely general directions of use, then they are in danger of getting into such trouble that even finding a clear counter instance would be a real help. They do not know the borders of the construction, but fail to observe that they do not know them -- after all, "chivalry" occurs in the language and is defined in the dictionary. They cannot disentangle the various characteristics; they have notions of two or more unrelated strands of phenomena floating in their constructions, like letters in alphabet soup. These vague abstractions can be illustrated from almost every conversation, every popular non-fiction book, every student paper or speech, many a lecture on literature, history, social science.
EXAMPLE COMMENT
Dialogue overheard in the Forum: First Citizen: I don't want war, but I do want our lost territory back.
Second Citizen: Well, friend, do you want the lost territory back even if it's going to take a war to get it?
First Citizen: I don't want war, as I say. But if it's going to take a war to regain the lost province, then we will have to beat our plowshares into swords.
Second Citizen: I see what you mean. You don't regard war as a good thing, but you want to regain the lost province even more than you want to avoid war."
First Citizen; I guess that's right.
Second Citizen has pressed this dialogue to clear up the vagueness of First Citizen's assertion; the reply reveals the relative intensity of his "wants." Vagueness in the common language is nowhere more pronounced than in the case of words designating choices: "want," "desire," "hope for," "like." These can range from the slightest predilection to the most intense. Consider the range of meaning possible in the simple assertion "I like ice cream." I might be affirming my preference for ice cream over any other food, or I might mean that only cream pie and tapioca pudding stand lower in my order of desserts. Vagueness arises from failure to limit the range of choice-words: "I like ice cream best of all."
A grocery company was indicted under a statute making it unlawful to charge "unjust or unreasonable" prices. The attorneys for the defendant argued that the statute violated the constitutional provision, "In all criminal prosecutions, the accused shall ... be informed of the nature and cause of the accusation." The court upheld the defendent's contention since the term "unjust and unreasonable" did not reduce to clearcut acts so that an individual would know in every case whether or not his contemplated act would be a violation of the law. (Example founded on United States vs. L. Cohen Grocery Co., 1921.) Barring vague descriptions of crime is one of the protections for individual liberty enjoyed where a rule of law prevails. Fairness to individuals requires that the terms of the criminal law be so phrased that there can be no doubt as to whether or not an act is illegal.
A literary quarterly publishes an article arguing that "responsiveness to the Zeitgeist" is the chief mark "of genius of the true poet." This is in the first paragraph. On the second page we read "Artistic sensibility always reveals itself in a fresh wonder at language." None of these constructions is intelligible, and the sentences are nonsense. Terms like "Zeitgeist" and the dogmatically positive use of "reveal themselves" suggest, moreover, a strong leaning toward Word Magic (#12).
Professor Peter lectures his class in sociology: "The matrix of cultural usage provides for the necessary safety valve of a few non-conformists. The deviates, however, must conform at least to an accepted-rejected pattern of non-conformity. They may be non-conformists only in a prescribed way: not all patterns of nonconformity are open to them." Professor Peter is probably trying to say something, maybe something interesting. But there is a difference between paradox and open contradiction, and the difference often reveals almost at sight the difference between intelligible constructions and the kind of vague thinking that leads to the verbiage of the pseudo-scientists. One would like to bang Professor Peter's heads together and make him talk sense.
"Give to the Midgets' Rest Home. You can take it off your income tax."
"Relax your tired blood. Take Elixir of Ambrosia."
"Panty Waists are tighter."
Without such vagueness modern advertising would be impossible; it's of the essence. "Take it off your income tax" can, in law, mean only "take it off your income before computing the tax, if you use the long form and not the standard deduction for charity, local taxes, etc.," but you are not supposed to think of that. "Tired" is so vague in everyday usage that it seems hardly a metaphor to apply the adjective to blood, but what can it mean? "Tighter," "better," "smoother," "longer lasting," "less fattening" -- than what? "Better," perhaps, than the worst in the field?
"-ism"
"-ist," "-ite"
"-er"
It is superfluous to illustrate the tiresome exploitation of these vague formations. In political controversy, a "communist" can be anybody from a card holding Communist Party member to a patriotic clergyman who twenty years ago foolishly allowed his name to appear on the letterhead of the American League for Peace and Freedom. "Peter is a Morrisite," "Peter is a deceiver." Do these mean that Peter once deceived or habitually deceives? that he agrees with Morris on some particular, or that he follows him around day and night like a disciple? The use of these formations in argument brands the speaker as naive or vicious. Look back to the previous sections. Do such terms as "relativism" or "reifier" offend against this principle?

bald	____	____	\| ? \|	____	____	hairy-on-top
x₁	x₂	x₃	\| x₄ \|	x₅	x₆	x₇

EXAMPLE	COMMENT
Dialogue overheard in the Forum: First Citizen: I don't want war, but I do want our lost territory back. Second Citizen: Well, friend, do you want the lost territory back even if it's going to take a war to get it? First Citizen: I don't want war, as I say. But if it's going to take a war to regain the lost province, then we will have to beat our plowshares into swords. Second Citizen: I see what you mean. You don't regard war as a good thing, but you want to regain the lost province even more than you want to avoid war." First Citizen; I guess that's right.	Second Citizen has pressed this dialogue to clear up the vagueness of First Citizen's assertion; the reply reveals the relative intensity of his "wants." Vagueness in the common language is nowhere more pronounced than in the case of words designating choices: "want," "desire," "hope for," "like." These can range from the slightest predilection to the most intense. Consider the range of meaning possible in the simple assertion "I like ice cream." I might be affirming my preference for ice cream over any other food, or I might mean that only cream pie and tapioca pudding stand lower in my order of desserts. Vagueness arises from failure to limit the range of choice-words: "I like ice cream best of all."
A grocery company was indicted under a statute making it unlawful to charge "unjust or unreasonable" prices. The attorneys for the defendant argued that the statute violated the constitutional provision, "In all criminal prosecutions, the accused shall ... be informed of the nature and cause of the accusation." The court upheld the defendent's contention since the term "unjust and unreasonable" did not reduce to clearcut acts so that an individual would know in every case whether or not his contemplated act would be a violation of the law. (Example founded on United States vs. L. Cohen Grocery Co., 1921.)	Barring vague descriptions of crime is one of the protections for individual liberty enjoyed where a rule of law prevails. Fairness to individuals requires that the terms of the criminal law be so phrased that there can be no doubt as to whether or not an act is illegal.
A literary quarterly publishes an article arguing that "responsiveness to the Zeitgeist" is the chief mark "of genius of the true poet." This is in the first paragraph. On the second page we read "Artistic sensibility always reveals itself in a fresh wonder at language."	None of these constructions is intelligible, and the sentences are nonsense. Terms like "Zeitgeist" and the dogmatically positive use of "reveal themselves" suggest, moreover, a strong leaning toward Word Magic (#12).
Professor Peter lectures his class in sociology: "The matrix of cultural usage provides for the necessary safety valve of a few non-conformists. The deviates, however, must conform at least to an accepted-rejected pattern of non-conformity. They may be non-conformists only in a prescribed way: not all patterns of nonconformity are open to them."	Professor Peter is probably trying to say something, maybe something interesting. But there is a difference between paradox and open contradiction, and the difference often reveals almost at sight the difference between intelligible constructions and the kind of vague thinking that leads to the verbiage of the pseudo-scientists. One would like to bang Professor Peter's heads together and make him talk sense.
"Give to the Midgets' Rest Home. You can take it off your income tax." "Relax your tired blood. Take Elixir of Ambrosia." "Panty Waists are tighter."	Without such vagueness modern advertising would be impossible; it's of the essence. "Take it off your income tax" can, in law, mean only "take it off your income before computing the tax, if you use the long form and not the standard deduction for charity, local taxes, etc.," but you are not supposed to think of that. "Tired" is so vague in everyday usage that it seems hardly a metaphor to apply the adjective to blood, but what can it mean? "Tighter," "better," "smoother," "longer lasting," "less fattening" -- than what? "Better," perhaps, than the worst in the field?
"-ism" "-ist," "-ite" "-er"	It is superfluous to illustrate the tiresome exploitation of these vague formations. In political controversy, a "communist" can be anybody from a card holding Communist Party member to a patriotic clergyman who twenty years ago foolishly allowed his name to appear on the letterhead of the American League for Peace and Freedom. "Peter is a Morrisite," "Peter is a deceiver." Do these mean that Peter once deceived or habitually deceives? that he agrees with Morris on some particular, or that he follows him around day and night like a disciple? The use of these formations in argument brands the speaker as naive or vicious. Look back to the previous sections. Do such terms as "relativism" or "reifier" offend against this principle?