To assert a belief is simple; defending it is far more difficult. Yet if a belief is not defended adequately, why accept it?
Saying something is true does not make it true. Suppose Smith says that Charles Darwin, who developed the theory of evolution, and Abraham Lincoln were both born on February 12, 1809. Jones denies this claim. If saying something is true proves it true, then what Smith says is true and what Jones says is also true—which is impossible, since one of them denies exactly what the other affirms. Their statements are contradictory, and asserting them both amounts to saying nothing at all. (Incidentally, Smith is correct.)
To reason effectively, we need to avoid contradiction and accept beliefs that are adequately defended. But what are the appropriate standards by which we can determine if our beliefs are consistent with each other and well-confirmed by the available evidence? Logic is the subject that offers answers to these questions, and the scope of logic is explained in the following essay by Wesley C. Salmon, Professor of Philosophy at the University of Pittsburgh, who served as President of the American Philosophical Association.
The remainder of my remarks should be read after
Salmon's article. So please proceed now to the selection, and return to
this point after finishing it.
-------
In his last paragraph Salmon refers to deductive correctness as "validity." If you have followed his account to that point, you will realize that a valid argument may have false premises and a false conclusion, false premises and a true conclusion, or true premises and a true conclusion. What is not possible is for a valid argument to have true premises and a false conclusion, for a valid argument is one in which if the premises are true, then so is the conclusion. For purposes of review, consider the following arguments:
Example (1) illustrates a valid argument with false premises and a false conclusion. Example (2) illustrates a valid argument with false premises and a true conclusion. Example (3) illustrates a valid argument with true premises and a true conclusion.
A valid argument with true premises is referred to
by philosophers as a "sound" argument. Since a sound argument has true
premises and its conclusion follows from its premises, the conclusion
of a sound argument is sure to be true. No wonder philosophers prize
sound arguments.
[Editors note, taken from Exploring Philosophy: An Introductory Anthology
by Stephen M. Cahn. Oxford University Press, 2005. Pages 43-56]
The Scope of Logic
Wesley C. Salmon
(Logic, 2d edition, by Salmon, © 1983. Reprinted by permission of Prentice-Hall, Inc., Upper Saddle River, NJ.)
In one of his celebrated adventures, Sherlock Holmes comes into possession of an old felt hat. Although Holmes is not acquainted with the owner of the hat, he tells Dr. Watson many things about the man—among them, that he is highly intellectual. This assertion, as it stands, is unsupported. Holmes may have evidence for his statement, but so far he has not given it.
Dr. Watson, as usual, fails to see any basis for Holmes's statement, so he asks for substantiation. "For answer Holmes clapped the hat upon his head. It came right over the forehead and settled upon the bridge of his nose. 'It is a question of cubic capacity/ said he; 'a man with so large a brain must have something in it.'"Now, the statement that the owner of the hat is highly intellectual is no longer an unsupported assertion. Holmes has given the evidence, so his statement is supported. It is the conclusion of an argument....
An argument consists of one statement which is the conclusion and one or more statements of supporting evidence. The statements of evidence are called "premises." There is no set number of premises which every argument must have, but there must be at least one.
When Watson requested a justification for the statement about the owner of the hat, Holmes gave an indication of an argument. Although he did not spell out his argument in complete detail, he did say enough to show what it would be. We can reconstruct it as follows:
a]
1. This is a large hat.
2. Someone is the owner of this hat.
3. The owners of large hats are people with large heads.
4. People with large heads have large brains.
5. People with large brains are highly intellectual.
6. The owner of this hat is highly intellectual.
This is an argument; it consists of six statements. The first five statements are the premises; the sixth statement is the conclusion.
The premises of an argument are supposed to present
evidence for the conclusion. Presenting evidence in premises involves
two aspects. First, the premises are statements of fact. Second, these
facts are offered as evidence for the conclusion. There are,
consequently, two ways in which the premises may fail to present
evidence for the conclusion. First, one or more of the premises may be
false, in this case, the alleged facts are not facts at all; the
alleged evidence does not exist. . . .
If an argument is offered as a justification of its
conclusion, two questions arise. First, are the premises true? Second,
are the premises properly related to the conclusion? If either question
has a negative answer, the justification is unsatisfactory. It is
absolutely essential, however, to avoid confusing these two questions.
In logic we are concerned with the second question only. When an
argument is subjected to logical analysis, the question of relevance is
at issue. Logic
deals with the relation between premises and
conclusion, not with the truth of the premises. (emphasis added, Slinker)
One of our basic purposes is to provide methods of distinguishing between logically correct and incorrect arguments. The logical correctness or incorrectness of an argument depends solely upon the relation between premises and conclusion. In a logically correct argument, the premises have the following relation to the conclusion: If the premises were true, this fact would constitute good grounds for accepting the conclusion as true. If the facts alleged by the premises of a logically correct argument are, indeed, facts, then they do constitute good evidence for the conclusion. That is what we shall mean by saying that the premises of a logically correct argument support the conclusion. The premises of an argument support the conclusion if the truth of the premises would constitute good reason for asserting that the conclusion is true. When we say that the premises of an argument support the conclusion, we are not saying that the premises are true; we are saying that there would be good evidence for the conclusion if the premises were true.
The premises of a logically incorrect argument may seem to support the conclusion, but actually they do not. Logically incorrect arguments are called "fallacious." Even if the premises of a logically incorrect argument were true, this would not constitute good grounds for accepting the conclusion. The premises of a logically incorrect argument do not have the proper relevance to the conclusion.
Since the logical correctness or incorrectness of an argument depends solely upon the relation between premises and conclusion, logical correctness or incorrectness is completely independent of the truth of the premises. In particular, it is wrong to call an argument "fallacious" just because it has one or more false premises. Consider the argument concerning the hat in example A. You may already have recognized that there is something wrong with the argument from the size of the hat to the intellectuality of the owner; you might have been inclined to reject it on grounds of faulty logic. It would have been a mistake to do so. The argument is logically correct—it is not fallacious—but it does have at least one false premise. As a matter of fact, not everyone who has a large brain is highly intellectual. However, you should be able to see that the conclusion of this argument would have to be true if all of the premises were true. It is not the business of logic to find out whether people with large brains are intellectual; this matter can be decided only by scientific investigation. Logic can determine whether these premises support their conclusion.
As we have just seen, a logically correct argument may have one or more false premises. A logically incorrect or fallacious argument may have true premises; indeed, it may have a true conclusion as well.
b] Premises: All mammals are mortal.
All dogs are mortal. Conclusion: All dogs are
mammals.
This argument is obviously fallacious. The fact that the premises and the conclusion are all true statements does not mean that the premises support the conclusion. They do not.... It happens that the conclusion, "All dogs are mammals," is true, but there is nothing in the premises which provides any basis for it.
Since the logical correctness or incorrectness of an argument depends solely upon the relation between the premises and the conclusion and is completely independent of the truth of the premises, we can analyze arguments without knowing whether the premises are true—indeed, we can do so even when they are known to be false. This is a desirable feature of the situation. It is often useful to know what conclusions can be drawn from false or doubtful premises. For example, intelligent deliberation involves the consideration of the consequences of various alternatives. We may construct arguments with various premises in order to see what the consequences are. In so doing, we do not pretend that the premises are true; rather, we can examine the arguments without even raising the question of the truth of the premises. Up to this point we have proceeded as if the only function of arguments is to provide justifications for conclusions. We see now that this is only one among several uses for arguments. In general, arguments serve to show the conclusions that can be drawn from given premises, whether these premises are known to be true, known to be false, or are merely doubtful.
For purposes of logical analysis it is convenient to present arguments in standard form. We shall adopt the practice of writing the premises first and identifying the conclusion by a triplet of dots.
c] Everyone who served on the jury was a registered voter.
Jones served on the jury . . . Jones was a registered voter.
This argument is logically correct. Outside of logic books, we should not expect to find arguments expressed in this neat form. We must learn to recognize arguments when they occur in ordinary prose, for they are not usually set off in the middle of the page and labeled. Furthermore, we have to identify the premises and the conclusion, for they are not usually explicitly labeled. It is not necessary for the premises to precede the conclusion. Sometimes the conclusion comes last, sometimes first, and sometimes in the middle of the argument. For stylistic reasons arguments may be given in a variety of ways; for example, any of the following variations of c] would be quite proper:
d] Everyone who served on the jury was a registered voter and Jones served on the jury; therefore, Jones was a registered voter.
e] Jones was a registered voter because Jones served on the jury, and everyone who served on the jury was a registered voter.
f] Since everyone who served on the jury was a registered voter, Jones must have been a registered voter, for Jones served on the jury-
The fact that an argument is being given is usually conveyed by certain words or phrases which indicate that a statement is functioning as a premise or as a conclusion. Terms like "therefore," "hence," "consequently," "so," and "it follows that" indicate that what comes immediately after is a conclusion. The premises from which it follows should be stated nearby. Also, certain verb forms which suggest necessity, such as "must have been," indicate that the statement in which they occur is a conclusion. They indicate that this statement follows necessarily (i.e., deductively) from stated premises. Other terms indicate that a statement is a premise: "since," "for," and "because" are examples. The statement which follows such a word is a premise. The conclusions based upon this premise should be found nearby. Terms which indicate parts of arguments should be used if, and only if, arguments are being presented. If no argument occurs, it is misleading to use these terms. For instance, if a statement is prefaced by the word "therefore," the reader has every right to expect that it follows from something which has already been said. When arguments are given, it is important to indicate that fact, and to indicate exactly which statements are intended as premises and which as conclusions. It is up to the reader to be sure he understands which statements are premises and which are conclusions before he proceeds to subject arguments to analysis.
There is another respect in which arguments encountered in most contexts fail to have the standard logical form. When we subject arguments to logical analysis, all of the premises must be given explicitly. Many arguments, however, involve premises which are so obvious that it would be sheer pedantry to state them in ordinary speech and writing. We have already seen an example of an argument with missing premises. Holmes's argument about the hat was incomplete; we attempted to complete it in example A. Outside a logic book, example c] might appear in either of the following forms, depending on which premise is considered more obvious:
g] Jones must have been a registered voter, for he served on the jury.
h] Jones was a registered voter, because everyone who served on the jury was a registered voter.
In neither case would there be any difficulty in finding the missing premise.
It would be unreasonable to insist that arguments always be presented in complete form without missing premises. Nevertheless, the missing premise can be a great pitfall. Although a missing premise is often a statement too obvious to bother making, sometimes a missing premise can represent a crucial hidden assumption. When we attempt to complete the arguments we encounter, we bring to light the assumptions which would be required to make them logically correct. This step is often the most illuminating aspect of logical analysis. It sometimes turns out that the required premises are extremely dubious or obviously false.
Logical analysis of discourse involves three preliminary steps which we have discussed.
1. Arguments must be recognized; in particular, unsupported statements must be distinguished from conclusions of arguments.
2. When an argument has been found, the premises and conclusions must be identified.
3. If the argument is incomplete, the missing premises must be supplied.
When an argument has been set out in complete and explicit form, logical standards can be applied to determine whether it is logically correct or fallacious. ...
What we have said so far applies to all types of arguments. The time has come to distinguish two major types: deductive and inductive. There are logically correct and incorrect forms of each. Here are correct examples.
a] Deductive: Every mammal has a heart.
All horses are mammals. . . . Every horse has a heart.
b] Inductive: Every horse that has ever been observed has had a heart.
. . . Every horse has a heart.
It is not difficult to see that the two examples satisfy these conditions.
Characteristic I.
The only way in which the conclusion of a deductive arguments could be false— that is, the only possible circumstance under which it could fail to be true that every horse has a heart—is that either not all horses are mammals or not all mammals have hearts. In other words, for the conclusion of a deductive argument to be false, one or both of the premises must be false. If both premises are true, the conclusion must be true. On the other hand, in b, it is quite possible for the premise to be true and the conclusion false. This would happen if at some future time, a horse is observed which does not have a heart. The fact that no horse without a heart has yet been observed is some evidence that none ever will be. In this argument, the premise does not necessitate the conclusion, but it does lend some weight to it.
Characteristic II.
When the conclusion of a] says that all horses have hearts, it says something which has already been said, in effect, by the premises. The first premise says that all mammals have hearts, and that includes all horses according to the second premise. In this argument, as in all other correct deductive arguments, the conclusion states explicitly or reformulates information already given in the premises. It is for this reason that deductive arguments also have characteristic I. The conclusion must be true if the premises are true, because the conclusion says nothing which was not already stated by the premises. On the other hand, the premise of our inductive argument b refers only to horses that have been observed up to the present, while the conclusion refers to horses that have not yet been observed. Thus, the conclusion makes a statement which goes beyond the information given in the premise. It is because the conclusion says something not given in the premise that the conclusion might be false even though the premise is true. The additional content of the conclusion might be false, rendering the conclusion as a whole false. Deductive and inductive arguments fulfill different functions. The deductive argument is designed to make explicit the content of the premises; the inductive argument is designed to extend the range of our knowledge.
We may summarize by saying that the inductive argument expands the content of premises by sacrificing necessity, whereas the deductive argument achieves necessity by sacrificing any expansion of content.
It follows immediately from these characteristics that deductive correctness (known as validity . . .) is an all or nothing affair. An argument either qualifies fully as a correct deduction or it fails completely; there are no degrees of deductive validity. The premises either completely necessitate the conclusion or they fail entirely to do so. Correct inductive arguments, in contrast, admit of degrees of strength, depending upon the amount of support the premises furnish for the conclusion. There are degrees of probability which the premises of an inductive argument can supply to a conclusion, but the logical necessity which relates premises to conclusion in a deductive argument is never a matter of degree.
NOTE
1. A. Conan Doyle, "The Adventure of the Blue Carbuncle," Adventures of Sherlock Holmes (New York and London: Harper & Row, n.d.), p. 157. Direct quotation and use of literary material from this story by permission of the Estate of Sir Arthur Conan Doyle.
Improving Your Thinking
Stephen F. Barker
(From The Elements of Logic, 5th edition, by Stephen F. Barker. Copyright © 1989 by McGraw-Hill, Inc. Reprinted by permission of The McGraw-Hill Companies.)
Effective reasoning calls for avoiding fallacious arguments and clarifying ambiguous terms. Our next selection, by Stephen F. Barker, Professor of Philosophy at Johns Hopkins University, addresses both these issues.
You can strengthen your own thinking by being alert to some commonly used words that are so notoriously vague that their appearance in any argument signals trouble. Here are some examples: subjective, natural, relative, pragmatic, diverse. Next time you hear someone use one of these terms, ask what it means. Everyone will benefit from the clarification.
1. Fallacies
If we want to become more skillful at playing chess, or football, or any other game, it is a good idea to study not only the shrewd moves that experts make, but also the poor moves that less experienced players make—we can learn from their mistakes. Similarly, as we try to improve our ability to reason logically, we should not confine our attention to specimens of good reasoning; we should also consider plenty of tempting examples of bad reasoning. By becoming more aware of how these bad arguments are bad, we strengthen our ability to distinguish between good and bad reasoning.
In ordinary talk the term "fallacy" is often loosely applied to any sort of mistaken belief or untrue sentence. "It's a fallacy to believe that handling a toad causes warts," people say. Here the thing being called a fallacy is just a belief, not a piece of reasoning. But in logic the term "fallacy" is restricted to mistakes in reasoning: a fallacy is a logical mistake in reasoning, especially one that it is tempting to make. There is a logical fallacy only when there are premises and a conclusion which is erroneously thought to be proved by them.
Many types of fallacies have been given special names, especially those types that are rather tempting and likely to deceive people. ...
An argument is called a petitio principii (or
begging of the question) if the argument fails to prove anything
because it somehow takes for granted what it is supposed to prove.
Suppose a man says "Jones is insane, you know," and we reply "Really?
Are you sure?" and he responds, "Certainly, I can prove it. Jones is
demented; therefore he is insane." This is a valid argument in the
sense that if the premise is true, the conclusion must be true too; but
the argument is unsatisfactory, for it does not really prove anything.
The premise is merely another statement of the conclusion, so that
practically anyone who doubts the truth of the conclusion ought to be
equally doubtful about the truth of the premise, and the argument is
useless for the purpose of convincing us of the truth of the
conclusion. Thus the argument takes for granted just what it is
supposed to prove; it begs the question.
[Another example
of begging the question commonly arises in Ethics classes, when the
statement is asked, "When is killing wrong?"
The most common answer students
give is, "When it is murder" - but murder is defined as wrongful
killing - so in answer to the first question, "When is killing wrong?"
the response turns out to be a trivial re-statement of the question,
""Killing is wrong when it is [replace "murder" with its
definition] wrongful killing" - Obviously what the Ethical
question asks is when is killing equal to murder? - Slinker]
Consider a longer chain of reasoning:
"We must not drink liquor."
"Why do you say that?"
"Drinking is against the will of Allah."
"How do you know?"
"The Koran says so."
"But how do you know that the Koran is right?"
"Everything said in the Koran is right."
"How do you know that?"
"Why, it's all divinely inspired."
"But how do you know that?"
"Why, the Koran itself declares that it is divinely inspired."
"But why believe that?"
"You've got to believe the Koran, because everything in the Koran is right."
This chain of reasoning is a more extended case of begging the question; the speaker is reasoning in a large circle, taking for granted one of the things that is supposed to be proved.
One specific form of petitio principii, or begging of the question, has a special name of its own: the fallacy of complex question. This is the fallacy of framing a question so as to take for granted something controversial that ought to be proved.
Suppose Mr. White is trying to prove that Mr. Green
has a bad character, and White asks Green the famous question "Have you
stopped beating your wife yet?" If Green answers "Yes" to this
question, White will argue that Green is admitting to having been a
wife-beater; if he answers "No," then White will argue that Green is
admitting to still being a wife-beater. The questioner has framed his
question in such a way as to take for granted that Green has a wife
whom he has been beating. The fallacy is that this is a controversial
proposition that is at least as doubtful as is the conclusion (that
Green has a bad character) supposedly being established. It is not
proper in this debate to take for granted this controversial
proposition; it needs to be proved if White is to make use of it at
all....
{Challenge to
students: What would be the appropriate response to this seemingly
catch-22 type question? - Slinker)
One important type of fallacy ... is the ad hominem fallacy. An argument is ad hominem (Latin: "to the man") if it is directed at an opponent in a controversy rather than being directly relevant to proving the conclusion under discussion. Such arguments are often, but not always, fallacious. For example, suppose someone argues: "Of course Karl Marx must have been mistaken in maintaining that capitalism is an evil form of economic and social organization. Why, he was a miserable failure of a man who couldn't even earn enough money to support his family." This is an ad hominem argument, for it attacks Marx the man instead of offering direct reasons why his views are incorrect. . ..
Another quite different fallacy of irrelevance is the appeal to unsuitable authority.. . . We commit this fallacy when we appeal to some admired or famous person as if that person were an authority on the matter being discussed—but when we have no good reason for thinking that the person is a genuine authority on it. Of course it is not always fallacious to appeal to authorities, but we are not entitled to appeal to persons as authorities unless there are good reasons for believing them to be authorities, and we should not trust an authority outside his or her special proven field of competence. A famous guitarist may be an expert on one type of music, but this does not make her an authority on philosophy of life. A movie star may be an authority on how to look attractive to the opposite sex, but is not likely to be an authority on which pain reliever is most healthful or which toothpaste tastes best....
We conclude with ... the fallacy of black-and-white
thinking. A wife may say to her husband "So you think the soup is too
cold, do you? Well, I suppose you would like to have had it scalding
hot then, instead." The second remark is presented as if it followed
logically from the first, and yet there is no logical connection
whatever. But people find it very easy to fall into this sort of
thinking in extremes, especially in the heat of controversy.
[A
more common type of the black-white fallacy is the All-Nothing Fallacy.
Suppose that I state that, "All
snakes are venomous". If this statement is false (which indeed it is)
the conclusion is NOT that "No snakes are venomous" but rather, "Some
snake are not venomous" - If I conclude that some statement which
asserts All (or the entire set) of a certain group have a certain
quality (In this case, that all snakes have the quality of being
venomous) is FALSE, then the proper conclusion is not that NO members
of the group have that quality (that no snakes are venomous) but only
that SOME members of that group do not have the property (Some
snakes are not venomous) - The only exception would be if there were
only one member of a group, so if only one snake existed in the
universe, then either it would be venomous (all snakes would be) or it
would not be venomous (no snakes would be) - This exception is rare and
often ignored by Logicians - Slinker]
2. Definitions
When we encounter words that cause confusion because their meanings are ambiguous, it is often helpful to define them.. ..
Definitions that are useful in preventing ambiguity may be subdivided into two types. Some of them serve the purpose of describing the meaning that a word already has in language. We might call these analytical definitions. In giving this kind of definition of a word, the speaker does not aim to change its meaning; he aims only to characterize the meaning it already has. Dictionary definitions are of this type. When a definition has this purpose, we can properly ask whether the definition is correct or incorrect.
In order to be correct in its description of the meaning of a word, an analytical definition must not be too broad; that is, it must not embrace things that do not really belong. (To define "pneumonia" as "disease of the lungs" would be too broad, for there are many lung diseases besides pneumonia.) Also, in order to be correct in its description of the meaning of a word, an analytical definition must not be too narrow; that is, it must not exclude things that really belong. (To define "psychosis" as "schizophrenia" would be too narrow, for there are other kinds of psychoses....)
Finally, a definition cannot serve much useful purpose if it is circular.... For example, to define "straight line" as "the line along which a ray of light travels when it goes straight" is circular and uninformative....
A second type of definition useful in preventing ambiguity is the stipulative definition, whose purpose is to declare how a speaker intends that a certain word, phrase, or symbol shall be understood ("Let "S' mean 'Samoans'"; "Let 'heavy truck' mean 'truck that can carry a load of 5 tons or more'"; etc.). Perhaps the expression being defined is one that previously had no meaning, or perhaps it had a different or a vaguer meaning. At any rate, the point of the stipulative definition is that the expression now is deliberately endowed with a particular meaning. Obviously, a stipulative definition cannot be of much use if it is unclear or circular. However, we do not have to worry about whether it is too broad or too narrow, for that sort of correctness cannot pertain to stipulative definitions. A stipulative definition is arbitrary, in that it expresses only the speaker's intention to use the word in the stipulated manner, and the speaker is, after all, entitled to use it in any desired way, so long as it does not cause confusion.
In order to avoid causing confusion, however, a stipulative definition should not assign to a word that already has an established meaning some new meaning that is likely to be confused with it. Consider the following dialogue:
SMITH: General Green is insane, you know. He ought to be dismissed.
JONES: He is? I agree that we should not have insane persons serving in the Army. But how do you know he's insane?
SMITH: It's obvious. He says he believes in extrasensory perception, and according to my definition—surely I'm entitled to use words as I please— anyone who does that is insane.
Here the stipulative definition is used to promote ambiguity rather than to prevent it. In the ordinary sense of the term "insane," Jones agrees with Smith that insane persons ought not to be generals. But Smith offers no evidence that General Green is insane in this sense. All that Smith shows is that the general is "insane" in a special, idiosyncratic sense of the word. From that, nothing follows about whether he ought to be dismissed. Smith is causing confusion by failing to keep distinct these two very different senses of the word; this happens because he fails to recognize the difference here between a stipulative and an analytical definition....
The two kinds of definitions mentioned so far both aim to inform us about verbal usage. ... It would be a mistake, however, to suppose that everything called a definition belongs to one of these two kinds. In fact, the profoundest and most valuable definitions usually do not fit tidily into either kind. When Newton defined force as the product of mass times acceleration, when Einstein defined simultaneity of distant events in terms of the transmission of light rays . . . [w]hat these definitions did was to propose new verbal usages growing out of the previously established usages. It was felt that these new usages perfected tendencies of thought implicit in the old usages and offered more insight into the subject matter being treated.
We might give the name revelatory definitions to definitions like these, which do not fit into either of the two categories of stipulative and analytical. Revelatory definitions constitute a third category. Further examples of revelatory definitions can be found in other, diverse fields. For example, when a nineteenth-century writer defined architecture as frozen music, he was not trying to describe how the word "architecture" is used in our language. (He took it for granted that his readers would know what kinds of constructions are considered architecture.) Nor was he proposing some arbitrary new usage. We should not censure his definition on the ground that it is unhelpful for the purpose of preventing ambiguity; that is not the purpose of this kind of definition. This definition is a metaphor, and it suggests a new way of looking at architecture, comparing the structural organization of the parts of a building with the structural organization of the parts of a musical composition. In trying to decide whether the definition is a good one or not, we must reflect about the extent and validity of this comparison between music and buildings; the definition is a good one if and only if the comparison is revealing....
How frequently are definitions needed? People sometimes think that one always should define one's terms at the beginning of any discussion. But this idea becomes absurd if carried too far. Suppose that we as speakers did undertake to define all our terms in noncircular ways. However far we proceeded, we would always still have ... undefined terms; therefore this task is an impossible one to complete. Moreover, we do have a fairly adequate understanding of the meanings of many words that we have never bothered to define and also of many words that we would not know how to define satisfactorily even if we tried. Thus, it would be foolish to try indiscriminately to define all or even most of our terms before proceeding with our thinking. What we should do at the beginning of a discussion is seek definitions of those particular words which are especially likely to make trouble in the discussion because they are harmfully ambiguous, obscure, or vague.
This is especially true with regard to discussions in which confusion is caused by failure to notice the different meanings of a term. A verbal dispute is a dispute arising solely from the fact that some word is being used with different meanings; this kind of dispute can be settled merely by giving the definitions that clarify the situation (though to say this is not to say that such disputes always are easy to settle).
The American philosopher William James gives a classic example of such a verbal dispute. . .. Suppose there is a squirrel on the trunk of a tree, and a man walks around the tree. The squirrel moves around the tree trunk so as to stay out of sight, always facing the man but keeping the tree between them. Has the man gone around the squirrel or not? Some of James's friends disputed hotly for a long time about this question. Here is a purely verbal dispute; it can be settled by pointing out that in one sense the man has gone "around" the squirrel, for he has moved from the north to the west and then to the south and east of the squirrel's location, but in another sense the man has not gone "around" the squirrel, for the squirrel has always been facing him. Once we have pointed out these two different senses of the word, we have done all that can reasonably be done; there is nothing more worth discussing (though this does not ensure that discussion will cease). With a verbal dispute like this, giving definitions is the way to resolve the dispute. But it would be utterly wrong to assume that all disputes are verbal in this way .
There are many serious problems for the settling of which definitions are not needed, and there are many other problems where if definitions help, they mark only the beginning of the thinking needed to resolve the issue.