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Cash Value

■ It is not possible that the argument’s premises are true and its conclusion false.
■ The conclusion could be false, if at least one of the premises is false.
■ It is contradictory to accept a valid argument’s premises and reject its conclusion.

SOUNDNESS

Definition

An argument is sound if and on!)> if it is valid and all its premises are true.

Cash Value

■ The argument’s conclusion is true: to deny it is to say something false.
■ A logical thinker who recognizes an argument as sound must accept its conclusion.

COGENCY

Definition

An argument is cogent if and on!)> if it is recognizab!J valid and has acceptable premises which
are more acceptable than the conclusion they attempt to support.

Cash Value

■ Any argument that satisfies these conditions is rationally compelling, in the sense that
it would move the thinker to accept its conclusion (provided she accepts its premises
and works out the entailment).

■ It would be irrational for the thinker to reject the conclusion of that argument.

■ Key Words

Validity

Entailment

Truth-preserving argument

Argument form

Propositional argument

Categorical argument

Soundness

Counterexample

Substitution instance

Cogency

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BOX 3 ■ THREE MEANINGS OF 'CAUSE'

1. Sufficient cause: C is a sufficient cause of E if and only if C always produces E.
2. Necessary cause: C is a necessary cause of E if and only if E cannot occur in the absence of C.
3. Necessary and sufficient cause: C is a necessary and sufficient cause of E if and only if C always

is the sole cause of E.

The methods of agreement and difference, and of concomitant variation. In his System of
Logic (1843), John Stuart Mill (1806-1873) made use of ordinary intuitions in an attempt to
establish generalizations about cause-and-effect relations. According to those intuitions,
whenever something occurs, it is often possible to narrow the range of acceptable hypotheses
about its likely cause-or about its effect-by eliminating plainly irrelevant factors until at
last we find the hypothesis most likely to be the actual cause (or effect) of the occurrence. Of
the five methods to establish generalizations about causal relationships proposed by Mill,
we'll here consider two: the so-called method of agreement and difference and the method of

concomitant variation.

The method of agreement and difference The method of agreement and difference rests on
the following basic principles:

1. Agreement: What different occurrences of a certain phenomenon have in common is
probably its cause.

2. Difference: Factors that are present only when some observed phenomenon occurs are
probably its cause.

Suppose a coach wants to find out why Mick, Jim, and Ted, three of his best players, often
perform poorly on Friday afternoons. After collecting some data about what each player does
before the game, the coach reasons along these lines:

35 1. Mick,Jim, and Ted have been performing poorly on Friday afternoons.
2. Going to late parties on Thursday is the one and only thing that all three do when

and only when they perform poorly.
3. Going to late parties on Thursday likely causes their poor game performance.

The coach's reasoning here illustrates 'agreement,' since it runs roughly alone these lines:

36 1. X has occurred several times.
2. Y is the one and only other thing that precedes all occurrences of X.
3. Y causes X.

But to make a more precise cause-effect claim, the coach should also use the method of
difference: first, he should compare the players' performance when they've been going to late
parties and when they haven't, and then, if they perform poorly only in the former cases, he
should conclude that that difference also points to late-evening party-going as the likely

cause of their poor performance. In fact, although the methods of agreement and difference
are independent, they are usually employed jointly for the sake of greater precision.

The method of concomitant variation The method of concomitant variation rests on the
following principles:

1. When variations of one sort are highly correlated with variations of another, one is likely
to be the cause of the other, or they may both be caused by something else.

2. When variations in one phenomenon are highly correlated with variations in another
phenomenon, one of the two is likely to be the cause of the other, or they may both be
caused by some third factor.

Suppose now someone asks the coach why being fit matters for the members of a team. He
may safely invoke empirical evidence to argue that there is a causal relationship between a
player's being fit and his or her performance:

37 1. The more fit the players are, the better their performance.
2. Probably, being fit causes their better performance, or their better performance

causes their being fit, or something else causes both their better performance and
their being fit.

The underlying reasoning is roughly

38 1. X varies in a certain way if and only if Yvaries in a certain way.
2. Y causes X, or X causes Y, or some Z causes both X and Y.

Analogy

Analogy is a type of inductive argument whereby a certain conclusion about individuals,
qualities, or classes is drawn on the basis of some similarities with other individuals, qualities,
or classes. Here is an example of an analogy whose conclusion about a certain vehicle rests on
this vehicle having some things in common with other similar vehicles:

39 1. Mary's vehicle, a 2007 SUV, is expensive to run.
2. Jane's vehicle is a 2007 SUV and is expensive to run.
3. Simon's vehicle is a 2007 SUV and is expensive to run.
4. Peter's vehicle is a 2007 SUV.
5. Peter's vehicle is expensive to run.

In (39), the arguer attempts to make her conclusion reasonable by analogy: Peter's vehicle
shares two features with Mary's, Jane's, and Simon's: being a 2007 model and an SUV. This
provides some reason to think that it may also have in common a third feature, that of being
expensive to run. Let 'm,' 'j,' 's,' and 'p' stand, respectively, for Mary's vehicle, Jane's vehicle,
Simon's vehicle, and Peter's vehicle; and A, B, and C for the ascribed features: being a 2007

model, being an SUV, and being expensive to run. Then (39)'s pattern is

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When an inductive argument is reliable, it has a form that makes its conclusion plausible

provided that its premises are true. Consider

41 1. 99 percent of guitar players also play other musical instruments.
2. Phong is a guitar player.
3. Phong also plays other musical instruments.

This inductive argument seems pretty reliable: its form is such that, if its premises were true,
its conclusion would be plausible. Compare (42), which is itself less reliable than (41) but more
reliable than (43):

42 1. 59 percent of guitar players also play other musical instruments.
2. Phong is a guitar player.
3. Phong also plays other musical instruments.

43 1. 39 percent of guitar players also play other musical instruments.
2. Phong is a guitar player.
3. Phong also plays other musical instruments.

Inductive reliability is, then, a matter of degree. An inductive argument of (44)’s form is more
reliable than (45):

44 1. 59 percent of A are B
2. p is an A
3. p is a B

45 1. 39 percent of A are B
2. p is an A

3. p is a B

The cash value of inductive reliability for logical thinkers can be better appreciated by comparing
it to the cash value of deductive validity. Each of these concerns argument form, as well as the sup­
port an argument’s premises may give its conclusion, provided they are true. In the case of a valid
argument, if its premises are true, its conclusion must be true. In that of a reliable argument, if its
premises are true, its conclusion is likely to be true. As we saw in Chapter 5, a valid deductive
argument is truth-preserving. By contrast, a reliable inductive argument is not. Even so, inductive
reliability is one of the two desirable features that ordinary and scientific arguments should have.

Inductive Strength

Strength is another desirable feature for inductive arguments; thus we may use it to
evaluate such arguments. An inductive argument is strong just in case it meets the
conditions listed in Box 5.

BOX 5 ■ STRONG INDUCTIVE ARGUMENT

An inductive argument is strong if and only if

1. It is reliable.
2. It has all true premises.

When an inductive argument is strong, it is reasonable to accept its conclusion. That is, it
is reasonable to think that the conclusion is true. We may think of this standard in terms of
competition: given the structure of an inductive argument, rival conclusions are always
logically possible. Imagine a case where a professor in Biology 100 has just received an email
from one of her new students, whose name is Robin Mackenzie. She is trying to decide
whether she should begin her reply, ‘Dear Mr. Mackenzie’ or ‘Dear Ms. Mackenzie.’ Let’s
assume that it is true that 80 percent of the students in Biology 100 are women and reason
through the steps of this inductive argument:

46 1. 80 percent of the students in Biology 100 are women.
2. Robin is a student in Biology 100.

3. Robin is a woman.

Since (46) is an inductive argument, the conclusion, statement 3, may in fact fail to be true,
even if both premises are true. After all, a person named ‘Robin’ could be a man. Even so, given
the evidence provided by the premises, it seems that conclusion 3 is more plausible than the
other competing hypothesis (i.e., that Robin is a man). But imagine a different scenario:
suppose that we knew that 80 percent of the students in Biology 100 were men. Then, among
then the competing hypotheses, the conclusion that is most likely to be true on the basis of
that information is that Robin is a man. The argument now is

47 1. 80 percent of the students in Biology 100 are men.
2. Robin is a student in Biology 100.

3. Robin is a man.

We may alternatively define inductive strength in this way:

An inductive argument is strong if and only if its hypothesis is the one that has the greatest
probability of being true on the basis of the evidence.

In the same way that inductive reliability can be contrasted with deductive validity,
inductive strength can be contrasted with deductive soundness. For one thing, the latter does
not come in degrees, since it depends on validity and truth, neither of which is itself a matter
of degree (there’s no such thing as a ‘sort of true’ premise or a ‘sort of valid’ argument). Hence,
just as any given deductive argument is either valid or invalid, so, too, it’s either sound or
unsound. On the other hand, inductive strength does come in degrees, for it depends in part
on reliability, which is a matter of degree. What about the cash value of these standards? When
an argument is deductively sound, its conclusion is true-and must be accepted by any logical
thinker who recognizes the argument’s soundness. But the conclusion of any inductively
strong argument can be, at most, probably true-and thus reasonable to accept by a logical

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■ Key Words

Induction

Evidence

Hypothesis

Analogy

Enumerative induction

Statistical syllogism

Inductive generalization

Causal argument

Inductive reliability

Inductive strength

Non-universal generalization

Universal generalization

Method of agreement and difference

Method of concomitant variation

Pa rt

Informal Fallacies

Some Ways
an Argument
Can Fail

CHAPTER

This chapter introduces the notion of fallacy as illustrated in common patterns of
defective argument and proposes a way of classifying twenty of the so-called

informal fallacies. It then considers how inductive arguments can fail in at least
five different ways, each of which illustrates one of the fallacies of the abuse of
induction. Here you'll find:

■ A classification of twenty informal fallacies.

■ Discussion of the fallacy of hasty generalization.

■ Discussion of the fallacy of weak analogy.

■ Discussion of the fallacy of false cause and three of its common variations.

Discussion of the fallacy of appeal to ignorance.

■ Discussion of the fallacy of appeal to unqualified authority.

Discussion of arguments that appeal to authority but are not fallacious.

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7.1 What Is a Fallacy?

We've seen that arguments sometimes go wrong by failing to meet deductive standards, such

as validity and soundness, or inductive ones, such as reliability and strength. We'll now look

more closely at other types of defect that arguments may have. We can learn a lot about what

good reasoning is by paying close attention to some clear examples of how reasoning can go

wrong. Here we begin the study of fallacies, which are recurrent types of mistake in reasoning,

affecting especially arguments and other relations among beliefs and concepts. In logical

thinking, a fallacy is not simply an erroneous belief or a mistaken opinion-as, for example,

when in an ordinary conversation someone speaks of the "fallacy that animals do not feel

pain." Rather,

A fallacy is a pattern of failed relation among concepts or beliefs. It affects any reasoning
that exemplifies that pattern.

Fallacies are worth studying, not only because arguments that exemplify them fail to

support their conclusions, but also because they could be misleading. They may affect an

argument in subtle ways, so that it will seem okay when we first read or hear it. But the

more we think about it, the more we will come to suspect that something has gone wrong.

Fallacies are standardly classified as either formal or informal. A formal fallacy is a type of

mistake made in arguments that may appear to be instances of a valid argument form but

are in fact invalid in virtue of their form. As there are many types of such mistakes, there

are many formal fallacies. They all have in common that they affect only deductive arguments

whose forms superficially resemble valid forms of a logical system, such as propositional or

categorical logic, but are actually invalid. When one such type of mistake is recurrent, it's

usually given a name-we'll discuss some of these in Part IV. The informal fallacies, on

the other hand, involve defects that arguments may have in virtue of instantiating some

patterns of error in form or content. They may affect either deductive or inductive

arguments, in all cases rendering them ill-suited to support their conclusions. For example,

an argument committing an informal fallacy may show a pattern of failed relation between

premises and conclusion that's not related to any specific argument form. It may also be

affected by confusion in expression or content. Since there are many types of informal

fallacy, our first step must be to provide some assistance in site navigation by offering a

tentative classification.

BOX 1 ■ THE CASH VALUE OF AVOIDING FALLACIES

Logical thinking requires knowing how to detect and avoid fallacies-that is, knowing

■ how to recognize when someone else's argument commits a fallacy (so as not to be fooled), and

■ how to keep one's own arguments from committing them (so that they can support their
conclusions).

7.2 Classification of Informal Fallacies

There is more than one way to classify the informal fallacies. But some fallacies are more
important than others. In this book, you'll find a fairly standard list, which includes the
following.

Fallacies of Failed Induction

1 hasty generalization

2 weak analogy

3 false cause

4 appeal to ignorance

5 appeal to unqualified authority

Fallacies of Presumption

6 begging the question

7 begging the question against

8 complex question

9 false alternatives

10 accident

Fallacies of Unclear Language

11 slippery slope

12 equivocation

13 amphiboly

14 confused predication

Fallacies of Relevance

15 appeal to pity

16 appeal to force

17 appeal to emotion

18 ad hominem

19 beside the point

20 straw man

We'll consider each of these subcategories one by one, looking carefully at each of the

informal fallacies grouped under them. Since we've just finished (in Chapter 6) discussing

inductive reasoning, let's look first at fallacies that may arise through the abuse of
induttion.

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7 .3 When Inductive Arguments Go Wrong

In this chapter, we consider five informal fallacies associated with the misuse of inductive
reasoning, grouped as follows:

BOX 2 ■ FALLACIES OF FAILED INDUCTION

FALLACIES OF

FAILED

INDUCTION

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APPEAL TO
APPEAL TO

HASTY WEAK FALSE
UNQUALIFIED

GENERALIZATION ANALOGY CAUSE IGNORANCE
AUTHORITY

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NON CAUSA 0vERSIMPLIFIED

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Hasty Generalization

The fallacy of hasty generalization may affect enumerative induction. Earlier we saw that an
enumerative induction typically starts out with premises asserting that certain things have
(or lack) some feature, and then draws a general conclusion about all things of that kind, to the
effect that they have (or lack) that feature. The conclusion of the argument is a universal gener­

alization, such as 'All leopards are carnivorous' and 'No leopard is carnivorous'. Thus an

enumerative induction might go like this:

1 1. All leopards so far observed have been carnivorous
2. All leopards are carnivorous

When a representative sample of leopards has been observed to be carnivorous, the conclusion
of this inductive argument is well supported. Similarly, if we've observed a representative
sample of leopards and found them all to be wild animals, we would be justified in drawing
the general conclusion that leopards are wild animals on the basis of those observations. Our
inductive argument would be,

2 1. Every leopard observed so far has been a wild animal
2. All leopards are wild animals

But for any such inductive conclusion to be justified, the conditions listed in Box 3 must be
met. If either of those two conditions, or both, is unfulfilled, then the argument commits

the fallacy of hasty generalization and therefore fails.

Hasty generalization is the mistake of trying to draw a conclusion about all things of a certain

kind having a certain feature on the basis of having observed too small a sample of the things
that allegedly have it, or a sample that is neither comprehensive nor randomly selected.

Suppose a team of naturalists were to observe 500,000 leopards, which all turn out to be
wild animals. Yet they were all observed in India, during the first week of August, at a time
when these animals were about to eat. The sample seems large enough, and the observers
might therefore draw the conclusion that

3 All leopards are wild animals.

But they would be committing a hasty generalization, since leopards are also found in other parts
of the world. And they are found at other times of the year, and in other situations. Clearly, the
sample lacks comprehensiveness and randomness. In this case, argument (2) would fail to provide
a good reason for its conclusion. On the other hand, suppose the naturalists directly observed
patterns of wild behavior among leopards in all parts of the world where such animals are found,
at different times of the year, and in many different situations. Yet the sample now consists of
only thirty-seven leopards. Do the naturalists have better grounds for concluding (3) above? No,
because although the comprehensiveness and randomness criteria are now met, the sample is
too small. The charge of hasty generalization would similarly apply in this scenario.

It is, however, not only naturalists and other scientists who will need to beware of this
sort of blunder. Logical thinkers will want to be on guard for hasty generalization in many
everyday situations. Among these is the familiar mistake of stereotyping people. Suppose
someone from the Midwest visits California for the first time. He becomes acquainted with
three native Californians, and it happens that all three practice yoga. Imagine that, on his
return home after his vacation, he tells his friends,

4 All Californians practice yoga.

If challenged, he would offer this argument:

5 1. I met Margaret Evans, who is Californian and practices yoga.
2. I met Alisa Mendoza, who is Californian and practices yoga.
3. I met Michael Yoshikawa, who is Californian and practices yoga.
4. All Californians practice yoga.

The reasoning in (s) is again an instance of hasty generalization. Furthermore, it stereotypes
Californians: on the basis of the sample described by the premises, the conclusion is simply
unwarranted.

Now imagine a different scenario: suppose that an anthropologist visited California with the
intention of studying the folkways of modern Californians. Suppose she went to southern
California, northern California, the San Joaquin Valley, the Bay Area, all regions of the state, and
met Californians from all walks of life, all social groups, all religions, all ethnic groups-from
cities, suburbs, small towns, and rural areas. Suppose she talked to thousands, and suppose she
discovered that all of these people practiced yoga! (This is unlikely, but suppose it happened.)
Then it would not be a fallacy to draw conclusion 4: assuming the thoroughness and breadth of
the study, this conclusion would be a reasonable outcome of a strong enumerative induction.

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But notice how different this argument is from the earlier (s) above! A conclusion about
all Californians based only on three instances is plainly unreasonable. It is a mockery of enumer­
ative induction, and an offensive stereotype, to boot. To avoid stereotyping, together with the
fallacy of hasty generalization that always underlies it, logical thinkers should keep in mind that

No conclusion about a class or group could gather support from a sample that is either

■ too small, or
■ insufficiently comprehensive and random, or both.

BOX 3 ■ HOW TO AVOID HASTY GENERALIZATION

In evaluating an enumerative induction, keep in mind that it would avoid hasty generalization only if

■ The sample on which its conclusion is based is large enough. In examples (1) and (2) above,
the arguer has to have observed quite a few leopards.

■ The sample is both comprehensive and randomly selected among the target group.
In (1) and (2), the arguer has to have observed typical leopards, under a variety of different
circumstances, from all the regions of the world where leopards are found.

Weak Analogy

Weak analogy is another way an inductive argument could fail to support its conclusion.
The underlying pattern of reasoning in analogy is something like this:

6 1. f and j are alike in that both have features n.

2. f also has feature n + 1.

3. j has also feature n + 1.

But whether an argument of this form can succeed depends very much on whether it passes
the test outlined in Box 4. If the test shows that n + 1 may be features that only fhas, then the
things thought to be analogous would actually be disanalogous and the argument would
commit the fallacy of weak analogy, which we may summarize as follows:

To succeed, an analogy must make reasonable that the things alleged to be alike in the
premises are in fact analogous in ways relevant to its conclusion. Any failure to do so
would count as a fallacy of weak analogy.

Imagine this scenario: there are two siblings, a boy five years old and his sister, who is thirteen.
One evening it's little Johnny's bedtime, and his mother says to him, "Johnny, it's nine o'clock.
Time for bed!" But Johnny replies, "You let Susie stay up late." Could Johnny rightfully claim
unfair treatment here? His argument may be reconstructed as follows:

7 1. Susie and I are alike in a number of ways.
2. Susie is not supposed to go to bed at 9:00 p.m.
3. I'm not supposed to go to bed at 9:00 p.m.

This, however, is a weak analogy, since it takes for granted that Susie's situation and Johnny's are

relevantly similar. Yet they are not. Although they live in the same house, attend the same school,

and have the same parents, there is a feature relevant to this argument that they don't share: the

same age. Johnny is only five years old, while Susie is thirteen. When it comes to staying up late,

the mother may reasonably respond: What I allow for a thirteen-year-old differs from what I

allow for a five-year-old. In this respect, the two cases are relevantly dissimilar; thus Johnny's

argument is too weak an analogy to support its conclusion.

Of course, not all cases of weak analogy are as clear-cut as this, and often there is room for

disagreement about whether a certain analogy is a fallacy at all. Some analogies are weak, but

others are strong. Still others are borderline cases whose degree of strength or weakness is

hard to assess. Moreover, analogy is one of the most common forms of argument in everyday

reasoning. It's a form widely used in political rhetoric. Logical thinkers are advised to beware
of attempts by politicians to treat certain analogies as obviously strong, when in fact they are

debatable. Was the threat from Saddam Hussein's Iraq really analogous to that of Hitler's

Germany? Is the Afghan War really analogous to the Vietnam War? When we think logically

about current affairs, we will want to do careful research into the facts of the matter before we

decide that an analogy is strong or weak. And obviously, this is the kind of argument on which

much may depend in real-life decisions. When presented with an argument to the effect thatj

has feature D because j and fare similar in having some other features A, B, and C in common,

and because f also has feature D, we should

Accept the analogy's conclusion only if

■ having A, B, and C is relevant to also having D; and
■ no available evidence suggests that f and j differ in some important respect relevant to

whether or not both have D.

BOX 4 ■ HOW TO AVOID THE FALLACY OF WEAK ANALOGY

In evaluating an argument of (6)'s form, ask these questions:

■ How large is number n? And are these n features relevant to the analogy's conclusion? (Here
we want to know whether the premises provide an exhaustive account of the features relevant
to the claim being made in the analogy's conclusion.)

■ Are the things alleged, in the premises, to be alike really alike, in that they all have features n?
(Here we want to know whether the similarities alleged in the premises are in fact present.)

False Cause

We saw earlier that a causal argument occurs when, on the basis of having observed two

constantly conjoined events, it is inferred that they are causally related to each other or to

some other event. Some such arguments can be inductively strong. If little Emily comes down

with the chicken pox only a week after her sisters, Penelope and Bernice, had chicken pox, and

if Emily has been in contact with Penelope and Bernice during that time, we may reasonably

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infer that she caught the chicken pox from her sisters. Given what we know about how
infectious diseases are transmitted, this inductive conclusion seems supported. But not all
causal arguments are strong. When either of the two types of error listed in Box s occurs, a
fallacy of false cause has been committed.

False cause is the mistake of arguing that there is a significant causal connection between
two phenomena, when in fact the connection is either minimal or nonexistent.

BOX 5 ■ HOW TO AVOID THE FALLACY OF FALSE CAUSE

Causal arguments can fail in two basic ways:

■ The argument concludes that there is a cause-effect connection between two phenomena
where there is none at all.

■ The argument mistakenly identifies some phenomenon as a sufficient (or determining) cause,
when in fact it's only a contributory cause (i.e., one among many) of some observed effect.

Let's consider three different ways the fallacy of false cause may occur. One is:

Post hoc ergo propter hoc ('after this, therefore because of this'):
The fallacy of concluding that some earlier event is the cause of some later event, when

the two are in fact not causally related.

The inclination to commit this fallacy in everyday life rests on the fact that, when we see two
events constantly conjoined-so that they are always observed to occur together, first the one,
then the other-it may eventually seem natural to assume that the earlier is the cause of the latter.
But it is not difficult to imagine cases of precisely this sort where an imputation of causal connec­
tion would be absurd. Suppose we saw a bus passing the courthouse in the square just before the
clock in the tower struck 9:00 a.m., and we then continued to see the exact same sequence of
events day after day. Do we at last want to say that it's the bus's passing the courthouse that causes

the clock to strike 9:00 a.m.? Of course not! And yet, in our experience, the two events have been
constantly conjoined: the clock's striking has always been preceded by the bus's passing.

Clearly it would be preposterous to argue, in that case, that, from the evidence of constant
conjunction between the bus's passing and the clock's striking 9:00, it follows that the former
causes the latter. But equally absurd arguments are in fact sometimes heard in everyday life.
Suppose that Hector and Barbara are not getting along, and one of their friends ventures to
explain the source of the problem:

8 1. Hector was born under the sign of Capricorn.
2. Barbara was born under Pisces.
3. Capricorns and Pisces are not compatible.
4. Their recent difficulties are owing to their having incompatible zodiac signs.

Argument (8) fails to support its conclusion, since it claims a causal connection for which the
argument gives no good evidence-nor, in this case, should we expect good evidence to be
forthcoming. After all, there's no good reason to think that configurations of stars and other
celestial events really do affect the courses of our lives, and whatever the cause of this couple's
troubles may be, it's probably traceable to something else. Argument (8) is a fallacy of post hoc

ergo propter hoc, a form of false cause, for it assumes a cause-effect relation between being born
on a day when celestial bodies have a certain configuration (which determines a certain zodiac
sign) and subsequently growing up to develop certain personality traits. But there is no reason
to think that these two sequential events are in fact causally related.

Another way false cause may occur is

Non causa pro causa (roughly, what is not the cause is mistaken for the cause):
A fallacy in which the error is not an imputation of causality in a temporal sequence of

events (as in post hoc ergo propter hoc, where an earlier event is wrongly thought to be
the cause of a later one), but rather the simple mistake of misidentifying some event
contemporaneous with another as its cause, when in reality it's not.

One form of this error occurs when cause and effect are confused. An early nineteenth-century
study of British agriculture noted that, of farmers surveyed, all the hard-working and industri­
ous ones owned at least one cow, while all the lazy ones owned no cows. This led the
researchers to conclude that productivity could be improved overall and habits of industry
encouraged in the lazy farmers by simply giving them each of those farmers a cow!

Now, plainly there is something wrong in this reasoning. But what? It seems to rest on an
extended argument along these lines:

9 1. All of the observed industrious farmers are cow owners.
2. None of the observed lazy farmers is a cow owner.
3. All and only cow-owning farmers are industrious.
4. There is a positive correlation between cow-owning and industriousness.
5. It's cow-owning that causes industrious farmers to be industrious.

If we grant, for the sake of discussion, that the sample of British farmers in the study was large
enough, and that it was also comprehensive and randomly selected, then premises 1 and 2

support conclusion 3, and its restatement, conclusion 4. But s's claim about cause and effect
fails to be supported! It's industriousness that is probably the cause of cow-owning, and not the
other way around. By confusing cause with effect, (9) commits non causa pro causa.

Finally, there is a version of false cause in which the source of the mistake is something
rather different from what we've seen so far:

Oversimplified cause:

The fallacy of overstating the causal connection between two events that do have some
causal link.

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Suppose a vice president, campaigning for reelection, says,

10 1. At the beginning of this administration's term, the national economy was sluggish.
2. At the end of this administration's term, the national economy is booming.
3. White House economic policies do have an effect on the nation's economy.
4. The improvement in the economy is due to this administration's policies.

(10) fails to support its conclusion. Let's assume that the premises are true. Even then, the
causal relation asserted in premise 3 is merely one of contributory cause-in effect, one causal
factor among others-which amounts to a rather weak sense of 'cause.' But 4 grandly asserts as
the conclusion something much more than that: namely, that the actions taken by the incum­
bent administration are a sufficient cause of the improvement in the economy. Now, surely
this is an exaggeration. The campaigning vice president commits a fallacy of oversimplified
cause by taking full credit for the nation's economic turnaround, thereby overstating the sense
in which his administration's policies 'caused' it. Of course, many politicians are quite prepared
to take credit for anything good that happens while they're in office. But proving that it was
due entirely to their efforts is something else again. The logical thinker should be on guard for
this and any of the other versions of false cause as representing different ways in which a

causal argument may fail.

BOX 6 ■ THREE TYPES OF CAUSAL FALLACY

Post Hoc Ergo
Propter Hoc

Appeal to Ignorance

FALLACY OF FALSE

CAUSE

Non Causa Pro
Causa

Oversimplified
Cause

Another fallacy of failed induction is the appeal to ignorance (or ad ignorantiam): an argu­
ment that commits this fallacy concludes either that some statement is true because it has
never been proved false, or that it is false because it has never been proved true. More

generally,

The fallacy of appeal to ignorance is committed by any argument in which the conclusion
that something is (or isn't) the case is supposedly supported by appeal to the lack of
evidence to the contrary.

Suppose someone reasons,

11 1. It has never been proved that God doesn't exist.
2. We can confidently assert that God exists.

(11) commits the fallacy of appeal to ignorance, but so does (12):

12 1. It has never been proved that God exists.
2. We can confidently assert that God doesn't exist.

Similarly, a believer in 'extrasensory perception' might argue,

13 1. No one has ever been able to prove that ESP doesn't exist.
2. It's reasonable to believe that there is ESP.

Clearly, the only reason offered by (13) to support its conclusion is the absence of contrary evi­
dence. But from that premise, all that can be supported is that we don't know what to say about
ESP! The conclusion given-that "it's reasonable to believe that there is ESP"-is far too strong
to be supported by such a flimsy premise. Reasoning along similar lines could also be used to
demonstrate the failure of (11) and (12).

BOX 7 ■ HOW TO AVOID THE FALLACY OF APPEAL

TO IGNORANCE

■ An argument whose premises merely invoke the lack of evidence against a certain conclusion
commits the fallacy of appeal to ignorance. Such premises are bad reasons for the conclusion
they attempt to support, and the argument therefore fails.

■ Why? Because the mere lack of negative evidence does not in itself constitute positive evidence
for anything! It justifies nothing more than an attitude of non belief (i.e., neutrality) toward
the conclusion.

We must, however, add a note of caution. Suppose that the attempt to prove some claim
has occasioned rigorous scientific investigation, and that these efforts have repeatedly turned
up no evidence in support of the claim. Furthermore, suppose that the claim doesn't serve the
purpose of explaining anything. In that case, it is not a fallacy to reject that claim out of hand.
Here we have to proceed case by case. Consider the claim,

14 There are witches.

Although there is of course a long history of claims that witches exist, all efforts to prove those

claims have so far failed for lack of evidence. Furthermore, the concept of a witch has no serious
explanatory function in any scientific theory: the existence of witches doesn't explain anything that
happens in the natural world. These considerations suggest that it is not a fallacy to conclude,

15 Probably there are no witches.

Inductive conclusions of this sort are rendered plausible by the absence of reliable empirical
evidence after thorough investigation, and must not be confused with the fallacy of appeal to
ignorance.

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attempt to support the conclusion by invoking an alleged authority that in fact either has
no expertise relevant to the claim that's being made or presents a point of view at odds
with the consensus of expert opinion on the topic.

When CNN talk-show host Larry King, the well-known television personality, proclaimed the
health benefits of 'Ester-C,' a brand of vitamin C pills, King's many fans might well have been
influenced in their beliefs about the nutritional properties of this vitamin supplement.
Suppose that a viewer, inspired by King's message, argued,

16 Ester-C will help me to be healthier, because Larry King said so.

(16) is an appeal to unqualified authority. King, though undoubtedly an expert on popular
celebrities in entertainment, sports, and politics, has no special expertise in the field of
nutrition. He was merely exploiting his own immense popularity by serving as a television
pitch man for a product. But note that in this case, it's not King committing the fallacy-it's
the TV viewer speaking in (16), who wrongly thinks that the television personality's testi­
mony supports the claim that a regimen of Ester-C pills will be conducive to health. The
argument would not have committed this fallacy if she had instead cited a view for which
there is consensus among experts on the topic of the commercial in support of the claim.
Experts on this topic would be respected nutritionists and biomedical researchers. But
whether such real-life experts would actually have shared King's on-camera enthusiasm for
the product is not clear.

Now, notice another important point: not all appeals to authority are fallacious. Consider,

17 1. To prevent tooth decay, the American Dental Association recommends daily flossing.
2. Daily flossing is a good way to prevent tooth decay.

Although (17) appeals to an authority, the American Dental Association, in support of its claim
about the benefits of daily flossing, it does not commit the fallacy under discussion. Since the ADA
is a qualified authority on the topic of the conclusion (namely, dental health), that conclusion is
supported by (17)'s premise. There are, then, perfectly legitimate uses of appeal to authority.
When the expert opinion being cited is that of a person, group, or organization that is truly well
informed on the topic of discussion, and therefore in a position to render an authoritative judg­
ment about it, an argument from authority citing that source commits no fallacy. Indeed, most of

what we know is known on the basis of testimony from sources we trust (certainly most of what
we know about science, and near(y all of what we know about history, is known in this way). And
although this trust is usually justified, it sometimes is not, for even the most respected experts are
occasionally wrong. The truth of the conclusions of arguments that appeal to authority, then, is at
best probable in some degree, never certain. Since expertise is itself something had by degree
(some experts are bigger experts than others), the degree of support provided by premises
appealing to authority is never conclusive. Such arguments are plainly inductive.

Even so, it is beyond denying that there are cases of uncontroversially bogus claims made
by mountebanks and crackpots who present themselves as 'experts' when they are nothing of
the kind. And it is the appeal to the testimony of such pseudo-authorities on behalf of a claim
that is perhaps the most egregious form of the fallacy of appeal to unqualified authority. But
an equally misleading form of the fallacy occurs when one cites, on behalf of a claim, the tes­
timony of a genuine expert on one side of a question disputed among the experts themselves.
That is, on a topic on which there is presently no consensus among experts, to treat on(y one

side's view as ultimately authoritative by citing it in support of one's conclusion amounts to an
appeal to unqualified authority. That Sir Arthur Eddington, an eminent physicist, believed
'paranormal' psychic phenomena deserved to be taken seriously as a topic of research gives us
no good reason to believe it too, for Eddington's view on this subject does not represent the
consensus of expert opinion among physicists, either in his day or in ours.

Yet another version of this fallacy occurs when we draw a conclusion based on the testi­
mony of sources that are biased by virtue of self-interested involvement in the issue at hand.
In a study reported recently in the New York Times, researchers attempted to determine
whether the use of paper towels or air dryers was more efficient in drying hands quickly. But
the research was sponsored by a paper company! Unsurprisingly, the researchers discovered
that drying with paper towels was quicker. Now, imagine using that conclusion as the basis of
a knowledge claim about the quickest way to dry your hands. It would plainly be an appeal to
unqualified authority.

Thus appeals to authority are sometimes open to dispute-and may be fallacious-only
when the invoked source is not authoritative on the subject of the claim an argument makes,
or when a genuine authority's views are presented as representing expert consensus when in
fact they do not. Consider

18 State University Law School is a great place to study law, because Uncle Jack says so.

This appeal would be fallacious unless Uncle Jack is an authority expressing a view well repre­
sented among experts on law schools. By contrast, the appeal to authority is not fallacious in

19 Many eminent jurists and law professors hold State University Law School in high regard.
State University Law School is a great place to study law.

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Argument (19) appeals to the view of experts on the topic of the conclusion, which is
supported-provided that the premise is true. Since an appeal to authority is often needed for
the justification of many claims, it is crucial that we distinguish between legitimate authorities

who have expertise relevant to the claim being made and those who don't. The rule is:

In evaluating an argument of the form, A says P, therefore P, check whether A is a
genuine authority expressing a view on P that is well represented among the experts on
P. If A is not, then the argument fails to support its conclusion and must be rejected.

For example, beliefs about history are more reasonable when based on the writings of
reputable professional historians than when proposed by amateur ones. If we want to have
well-founded beliefs about the French Revolution, the Ming Dynasty, or the presidency of

Theodore Roosevelt, we should look to writers whose books are not "self-published" or
published by vanity presses (where the authors pay to get their books into print). We should

look for historians who are held in high regard by peers in their fields and whose work has

been favorably reviewed. Although none of these criteria guarantee expertise, they make it

vastly more likely. Similarly, for beliefs about nature, it goes without saying that respected

journals in the natural sciences are generally dependable sources of information, unlike
supermarket tabloids that describe miracle cures for cancer and 'evidence' of mental telepathy.

For scientists, too, being the author of respected, mainstream scholarship and having the

favorable regard of fellow scholars are usually the marks of credibility as genuine experts. For
logical thinkers, then, an important competence is the ability to tell the difference between

real experts and bogus ones, since it is often on that distinction that the difference between
legitimate appeals to authority and the fallacy of appeal to unqualified authority turns.

BOX 9 ■ HOW TO AVOID FALLACIOUS APPEALS TO

AUTHORITY

To avoid fallacious appeal to authority, keep in mind the way it differs from appeals to authority
that aren't fallacious. The difference hinges on whether the authority cited in support of a claim

■ does indeed have sufficient expertise in the relevant field; and

■ is expressing a view well represented (perhaps the prevailing one) among experts on the topic.

Exercises

1 . What is a fallacy?

2. What's the point of studying fallacies, as far as logical thinking is concerned?

3. What is the fallacy of hasty generalization?

4. Are all generalizations to be avoided?

5. What is stereotyping? And how is this related to hasty generalization?

6. What is the fallacy of weak analogy?

7. The fallacy of false cause has at least three different forms. Identify the kind of mistake each makes,

and explain why they are all mistakes in causal reasoning.

8. What is the fallacy of appeal to ignorance?

9. When a fallacy of appeal to unqualified authority is committed, who commits it? Is it the arguer or

the bogus authority?

1 o. What is the difference between the legitimate use of appeal to authority and the fallacy of appeal to

unqualified authority?

II. Each of the following arguments commits one of the fallacies of failed induction

discussed in this chapter. Identify the fallacy.

1. I'm an Aquarius, so I love doing lots of projects at once.

SAMPLE ANSWER: False cause

2. Some people can cure heart disease by meditation. I know because the coach of my son's soccer

team told me.

*3. Wage and price controls will not work as a means of controlling the rate of inflation. After all, no econ­

omist has ever been able to give conclusive proof that such controls are effective against inflation.

4. Most HIV patients are young. Thus youth causes HIV.

5. Yogi Berra, an Italian American, was one of the greatest baseball players of all time. Other all-time

greats of baseball include Joe DiMaggio, Mike Piazza, and Roy Campanella. So, no doubt about it,

Italian Americans are great baseball players.

*6. Last week, when Notre Dame won the game, the coach was wearing his green tie. So their victory

must have been due to the coach's choice of necktie, since this nearly always happens when he

wears that tie.

*7. Foreign wars are good for a nation, just as exercise is good for the body. In the same way that

exercise keeps the body fit, foreign wars keep a nation fit as a society.

8. According to recent polls of registered voters, the state of Massachusetts has a large percentage of

voters who are political liberals. This suggests that all states have a large percentage of voters who

are political liberals.

*9. The chances for stability in the Middle East will continue to improve. Popular singer Britney Spears

has recently said that that is what she expects to happen.

10. Dallas and Houston are North American cities, and one can drive from the one to the other in only a

few hours. Montreal and Los Angeles are also North American cities. Thus one can drive from

Montreal to Los Angeles in only a few hours.

11. Some years ago, after not having seen my best friend from Duckwood High School for several years,

we met for lunch and were surprised to find that our clothes and hairstyles were the same! The only

possible explanation for this is that we both went to Duckwood High.

*12. Some regular churchgoers believe that taxpayers' dollars should not be used to fund laboratories

that carry out tests on animals for medical research. Hence, it is wrong to go on spending taxpayers'

dollars for that purpose.

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13. I think you're giving up on advanced calculus too easily. Calculus and simple arithmetic are both

parts of math. Since you can do simple arithmetic, you can also do advanced calculus.

14. Every rainy day I have a pain in my elbow; so it must be the damp weather we're having that's solely

responsible for this pain.

*15. Sandra Day O'Connor, the first woman to serve on the United States Supreme Court, did not do a

good job. This suggests that women are not fit to serve as Supreme Court justices.

16. There is no extraterrestrial life. After all, no one has ever found observable data to support the claim

that such life exists.

17. The Internet is a great technological advance and is available to many people. Space travel is another

great technological advance. Thus space travel is available to many people.

*18. Off-shore oil drilling is an environmental hazard, for there is no conclusive evidence to prove that it

is safe.

*19. Several television personalities on the David Letterman Show the other night said that they had

decided to invest in gold. So, it's probably a good idea to buy gold now.

20. Local radio station KNSR provides lively reporting on local and national news. So probably all local

radio stations provide lively reporting on local and national news.

Ill. Each of the following arguments commits one or two of the fallacies of failed

induction discussed in this chapter. Identify the fallacies.

1. There is no evidence linking industrial waste in our rivers with the higher incidence of birth defects in

this area. Thus industrial waste in our rivers is not responsible for such defects. So it must be the

mothers' carelessness that is responsible for them.

SAMPLE ANSWER: Appeal to ignorance/false cause

2. The reason why the band U2 hasn't had a hit in the Top 40 for nearly a year is simply that they have

been touring for too long, which follows from what a fan of the band told a local TV news reporter

today: "U2 toured New Zealand, Australia, Japan, and Hawaii this year. Now they don't have any hit

in the Top 40. This failure is no doubt the result of being on the road too long."

*3. Irving Berlin ate beet soup every day, and he lived to be 101. Therefore, regular consumption of beet

soup leads to longevity.

4. The attorneys for the prosecution were not able to establish beyond a doubt that Hinckley was sane

when he fired at President Reagan. We know this because Hinckley's own lawyers declared that at

the end of the trial. So we have no choice but to conclude that he was insane.

*5. Bats not only harbor Ebola virus, but also are the hidden cause of mental illnesses among humans.

Each of these long-standing suspicions has been proved true on the Austin American-Statesman

website by Alicia Smith, professor of ancient Greek at Texas A&M.

6. To achieve something good, we sometimes have to break things. A famous twentieth-century politi­

cal leader once observed, "In order to make an omelet, it is necessary to break some eggs." So, in

exactly the same way, in a revolution to make a better world, some civilian enemies of the revolution

will have to be shot."

*7. Drinking and smoking are not harmful for anyone. In fact, they promote longevity. After all, Winston

Churchill and Ulysses S. Grant both smoked cigars and drank whiskey every day, and they did not

die young.

8. I ought to wait before deciding whether or not to take that job in California, because my friend Mack,

who is a professional astrologer, told me to wait.

*9. Bud had a stomachache before he was to take the LSAT exam to qualify for law school. He failed the

exam and went on to become a taxi driver. Thus a stomachache caused Bud to become a taxi driver.

10. My grandfather never went to a doctor in his life. He went to a healer who practiced folk medicine.

As a result, granddad lived to be ninety-four. So folk remedies always work.

*11. When I'm really hungry, the best thing for me is a double cheeseburger. I know this because the ad

for Burger King says, "Double cheeseburger: what you really need when you're really hungry!"

*12. All the stories in the newspaper about Zheng's resignation are false. For one thing, some interested

parties tried to prove them true and did not succeed.

13. When Professor Digby began studying philosophy as a young man, he also began losing his hair. The

more philosophy he read, the balder he became. After years of study, he was completely bald. We

may infer that Digby could have avoided baldness if he hadn' t studied philosophy.

14. The top ten biggest earners in music include Aerosmith, Coldplay, and Sir Paul McCartney, and they

all play popular music. Since Aerosmith and Coldplay are bands, we may infer that Sir Paul

McCartney is a band.

*15. Toyota Corollas are fuel-efficient Japanese cars recently found to have defective accelerators that

made them dangerous. Subaru Foresters are also fuel-efficient Japanese cars. So Subaru Foresters

are likely to have defective accelerators that make them dangerous. This also suggests that all

Japanese-made cars are dangerous.

IV. For each of the above arguments, explain how it commits one or more fallacies.

V. Assuming that the premises of the following arguments are true, determine which

commits a fallacy of appeal to unqualified authority and which doesn't.

1. We must accept that Landis was the best American rider in the last Tour de France, since that's

precisely what tour director Jean-Marie Leblanc reported as an opinion shared by all the judges of

this important event.

SAMPLE ANSWER: Not a fallacy

*2. Leonardo DiCaprio is the best American actor this year. We may be sure of this because it is the

unanimous decision of the worldwide Leonardo DiCaprio Fan Club.

3. The most recent National Census shows that Latinos are the fastest-growing ethnic group,

representing the largest minority in the country. Therefore, Latinos are the fastest-growing ethnic

group, representing the largest minority in the country.

*4. There is reason to suspect that Mel Gibson may have been involved in drunk driving, since a

spokesman for the sheriff's department confirmed that Gibson has been charged with driving while

intoxicated. His bail was set at $5,000.

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CHAPTER

Avoiding Ungrounded
Assumptions

In this chapter you’ll learn about the fallacies of presumption and some related
logical and philosophical issues. The topics include

■ Circular reasoning: When is it vicious? When is it benign?

■ The fallacies of begging the question and begging the question against.

The concept of burden of proof.

■ The fallacy of complex question.

■ The fallacy of false alternatives.

■ The fallacy of accident.

166

8.1 Fallacies of Presumption

Now we’re ready to look at some fallacies that can be grouped together because arguments

committing them take for granted something that is in fact debatable. Such arguments rest on
presumptions, which are strong assumptions or background beliefs taken for granted.

Generally, there is nothing wrong with presumptions: arguments commonly rest on implicit

beliefs that create no fallacy of presumption at all. But when an argument takes for granted a

belief that is in fact debatable, it commits a fallacy of presumption. The unsupported belief at

work in such fallacious arguments may at first seem innocent or even acceptable, though in

reality it is neither. The patterns of mistake illustrated by arguments that rest on debatable
presumptions include the five types of fallacy listed in Box 1.

BOX 1 ■ SOME FALLACIES OF PRESUMPTION

I FALLACIES OF I PRESUMPTION

BEGGING THE BEGGING THE

I
COMPLEX

I
FALSE I ACCIDENT I QUESTION QUESTION QUESTION ALTERNATIVES

AGAINST

8.2 Begging the Question

In Chapter s we saw that the premises of valid arguments could be true yet fall short of count­

ing as persuasive reasons for their conclusion. That would be the case with any sound argument

that failed to be cogent. As a result, no such argument can move a rational thinker to accept its

conclusion, even when the validity of the argument may be obvious to the thinker. Why?

Imagine that we intend to convince you rationally to accept a certain claim-say, that

1 We care about logical thinking.

We offer you this reason as a premise:

2 It is not the case that we don’t care about logical thinking.

The argument is

3 1. It is not the case that we don’t care about logical thinking.
2. We care about logical thinking.

(3) is valid, and we may assume that it has a true premise. Yet it lacks cogency, since it doesn’t

offer reasons that could persuade a logical thinker of the truth of its conclusion if that thinker

is skeptical about that very conclusion. Philosophers call this ‘circular reasoning.’ (3) is affected

by a degree of circularity that may be considered ‘vicious,’ since it would make any argument

that has it fail-by contrast with ‘benign circularity,’ which, as we’ll see, is the tolerable degree

of circularity that affects many deductive arguments.

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Although in (16) there is some conceptual circularity between the concepts 'satellite' and 'large
celestial body that orbits a planet,' this does not make the argument question-begging. For a
logical thinker who lacked some basic astronomical knowledge and initially doubted claim 4
could be persuaded to accept it on the basis of deducing it from 1, 2, and 3, provided that she
were led to recognize the acceptability of those premises and the validity of the argument.

An important point to keep in mind is that

Logical circularity, whether formal or conceptual, comes in degrees. Some valid arguments
have more circularity than others. The more logically circular an argument is, the more its
conclusion follows trivially from its premises and is likely to beg the question.

The Burden of Proof

It is not uncommon to find the expression 'burden of proof' in dialectical contexts, which are
situations involving deliberation among two or more parties, such as a debate, controversy, or
deliberation on a disputed question between opposing sides defending incompatible claims.

'Burden of proof' refers to the obligation to take a turn in offering reasons, which, at any given
stage of the deliberation, is on one side or the other (except for the paradoxical situations
discussed below). A deliberation commonly follows this pattern: one party, C, makes a claim.

The other party, 0, replies by raising some objections to it. If these objections are adequate,
the burden of proof is now on C, who must get rid of (or 'discharge') it by offering reasons for
her claim. If she comes up with a sound or strong argument that outweighs O's argument, the
burden of proof then switches to 0, who must try to discharge it by offering the appropriate
arguments.

It may happen, however, that the reasons on both sides appear equally strong. As a result,
there would then be a dialectical impasse, or standoff in the deliberation. No progress can be
made until new reasons are offered to resolve the conflict. Except for these situations,
however, we may expect that the burden of proof will, at any given stage of a deliberation, be
on either the one side or the other. As the deliberation progresses, it will likely switch from the
one side to the other more than once, always falling on the participant whose claim is more in
need of support.

BOX 4 ■ WHERE IS THE BURDEN OF PROOF?

In the following debate,® shows the burden of proof andQan impasse.

1. A rejects a claim made by!!, which is a commonly held belie£®A
2. A defends her rejection with an argument that begs the question against!!-® A
3. A recasts her argument so that it now seems cogent.®!!
4. !! offers an argument that turns out to be clearly invalid.®!!
5. !!'s argument is modified and now seems as cogent as A's.Q
6. A provides further strong evidence in support of her view.®!!
7. !! replies by offering weak evidence for his view.®!!
8. !! offers further evidence which is equally strong as A's.Q

Commonsense beliefs, which are ordinary beliefs based on observation, memory, and

inference, enjoy a privileged standing with respect to the burden of proof. Whoever

challenges them has, at least initially, the burden of proof. For example, the belief that the
Earth has existed for more than five minutes belongs to common sense. If someone
challenges it, the burden of proof is on the challenger, who must now offer adequate

reasons against that commonsense belief. But that advantage can be overridden by a strong
argument if available.

Knowing where the burden of proof is at any given stage of a debate has this cash value:

■ If you know that the burden of proof is on you, you know you must discharge it by
offering an adequate argument in support of your claim.

■ If you know that the burden of proof is on the other side, you can rest until a sound
objection to your view has been offered.

■ If you know that you are defending a claim that is part of common sense, then you also
know that the burden of proof is on any challenger.

Finally, note that some deliberation goes on 'internally'-for example, when a person
reflects upon which of two opposite theories is correct. If, in the course of inner delibera­

tion, a thinker is fair-minded, then the burden of proof will tend to shift from one position

she is considering to an opposite view, following the same general considerations outlined

above.

BOX 5 ■ RATIONAL DELIBERATION

EITHER ON ONE SIDE

THE BURDEN OF

PROOF IS

ON THE OTHER

SIDE, OR

8.3 Begging the Question Against

THERE IS AN IMPASSE

A common mistake that undermines argument is committed by failing to discharge the

burden of proof. Suppose that we assert 'Not P' (i.e., that Pis false), but someone else, Melinda,
has just offered us some good reason for thinking that P is true.

BOX 6 ■ HOW TO AVOID BEGGING THE QUESTION AGAINST

Don't include any controversial statement among your premises without first offering adequate
reasons for it.

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The burden of proof is now on us, and we must discharge it by offering an adequate
argument against P. The failure to do so-by assuming that P is false, without offering a reason
for this-commits the fallacy of begging the question against Melinda. For it amounts to
implicitly reasoning in either of these viciously circular forms:

17 1. P is false
2. P is false

Or similarly,

18 1. NotP
2. Not P

The fallacy of begging the question against (your opponent) is often committed in everyday
arguments on controversial topics. For example, when someone maintains

19 1. In abortion, the fetus is intentionally killed.
2. A fetus is an innocent person.
3. Intentionally killing an innocent person is always murder.
4. Abortion is always murder.

Although 1 seems unobjectionable, 2 and 3 are controversial premises that cannot be
employed unless good reasons have already been offered to back them up. Premise 2 begs
the question against the view that a fetus is not a person-a view that can be supported in a
number of ways (as most parties to the current popular debate over the morality of abortion
now recognize).

Begging the question against can be difficult to detect, for it involves presupposing the
truth of premises that, although controversial, are sometimes inadvertently taken for granted.
To avoid this fallacy, always abide by the rule in Box 6 above.

BOX 7 ■ SECTION SUMMARY

1. When an argument begs the question, at least one premise assumes the conclusion being
argued for.

2. When an argument begs the question against, at least one premise assumes something that
is in need of support.

Exercises

1 . What do all fallacies of presumption have in common?

2. What does it mean for an argument to be 'circular'? Is all circularity bad?

2. Define non-cogency in relation to begging the question.

3. What's wrong with a question begging argument?

4. What is the fallacy of begging the question against? How does it differ from begging the

question?

5. Against whom is the question begged in any argument that begs the question against?

6. Could the conclusion of a question-begging argument be true? Explain.

7. What is meant by burden of proof? How do commonsense beliefs matter to it?

8. Where is the burden of proof at each stage of a deliberation?

II. Each of the following arguments begs the question. Explain why.

1. Dylan is a brother. Therefore, Dylan has a sibling.

SAMPLE ANSWER: The logical thinker who rejects the conclusion would reject that Dylan is a brother.

2. Capital punishment is cruel, for it is cruel and unusual punishment. And it's demeaning to the society

that inflicts it.

*3. The mind is different from the body. Hence, the mind and the body are not the same.

4. Mount Aconcagua and Mount Whitney are both tall mountains. But Mount Aconcagua is taller than

Mount Whitney. Consequently, Mount Whitney is shorter than Mount Aconcagua.

*5. Demons are supernatural beings. Supernatural beings are only fictional. Therefore, demons do not exist.

6. Dorothy is a historian. For, she is a historian and art collector.

*7. Since Aaron is a hunter, he is someone who hunts.

8. The U.S. president and the British prime minister both oppose the treaty. Hence, it's false that both

leaders do not oppose the treaty.

*9. If a plane figure is a circle, then it is not a rectangle. Therefore, if the figure is a rectangle, then it is not

a circle.

10. The first witness is not trustworthy, since he is not reliable.

Ill. [Note: This exercise is somewhat more challenging.] For each of the above

arguments, determine whether the circularity is formal, conceptual, or both.

IV. For each of the following arguments, determine whether it would, under normal

circumstances, beg the question, beg the question against, or do both.

1. Whoever is less productive should have lower wages. Women are less productive than men. Hence,

women should have lower wages.

SAMPLE ANSWER: Begs the question against

2. Euthanasia is murder and is wrong. So, euthanasia is wrong.

*3. Fido is a puppy. Therefore, Fido is a young dog.

4. A woman has an absolute right to control her own body. And if a woman has an absolute right to

control her own body, then abortion is morally permissible. Therefore, abortion is morally permissible.

*5. Since the Democrats won the '08 presidential election, it is simply false that they didn't win.

6. Derek Jeter has an insurance policy on his cars, for it is not the case that his cars lack such a policy.

*7. The fetus is an unborn baby. Therefore, it is not the case that the fetus is not an unborn baby.

8. Anyone who is an idealist is also a loser. Thus idealists are losers.

9. Vladimir is a bachelor. Therefore, Vladimir is unmarried.

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*10. Infanticide is always morally wrong. So, infanticide is never morally right.

11. If there is intelligent life elsewhere in the universe, then life on Earth is not unique. But life on Earth is

unique. Hence, there is no intelligent life elsewhere in the universe.

12. The right to life is God's will. Therefore, the right to life is the will of Divine Providence.

*13. Given atheism, God doesn't exist. But it is not the case that He doesn't exist, so atheism is mistaken.

14. Priscilla got a B on her philosophy paper this semester. Therefore, she turned in a philosophy paper

this semester.

15. There is life after death. Therefore, there is an afterlife.

*16. Since no person should be denied freedom, and Bruno is a person, it follows that Bruno is entitled to

freedom.

17. Magdalene is a sister. Therefore, she is a female.

18. Since capital punishment is murder, capital punishment is wrongful killing.

*19. Northfield is not far from Minneapolis. Thus Northfield is close to Minneapolis.

20. Socialism is an unjust system of government. Unjust systems of government must be abolished.

Therefore, socialism must be abolished.

V. Determine whether the following arguments are possible or impossible.

1. An argument that is cogent for a logical thinker but not rationally compelling.

SAMPLE ANSWER: Impossible

2. A valid argument that is non-cogent.

3. A sound argument that is non-cogent.

*4. A question-begging argument that is not circular.

5. A circular argument that is not fallacious.

*6. A cogent argument that begs the question against.

7. A sound argument that is cogent.

*8. A question-begging argument that is sound.

9. A question-begging argument that is rationally compelling.

*1 0. The burden of proof being on the side that has offered the most cogent argument.

VI. In the deliberation described below, determine where the burden of proof lies at

each stage: if on Carolyn, write 'C'; if on Karl, write 'K'; and if there is a dialectical

impasse, write 'I.'

1. C rejects a commonsense belief held by K.

SAMPLE ANSWER: C

2. C defends her rejection with an argument that begs the question against K.

3. C recasts her argument in a way that makes it clearly unsound.

*4. C offers a new argument that turns out be invalid.

5. C's argument undergoes another recast that makes it cogent.

*6. K advances a valid yet question-begging argument against C.

7. K offers a non-question-begging argument with clearly false premises.

*8. K recasts his argument so that it is now as cogent as C's.

VII. In the following deliberation, either Sor O has the burden of proof. Identify which

has it at any given stage in the deliberation, and mark dialectical impasses.

Explain your choice.

1. S makes a claim that challenges a commonly held belief.

SAMPLE ANSWER: Burden of proof on S. When commonsense beliefs are at issue, the burden of proof is

on the challenger.

2. S attempts to support her claim by offering an inductively weak argument.

*3. S recasts her argument so that it is now clearly valid but unsound.

4. S recasts her argument again so that it is now sound but question-begging.

*5. S's argument undergoes another recast that makes it deductively cogent.

6. 0 responds with a valid argument that begs the question against S.

*7. 0 recasts her argument so that it is now non-question-begging but plainly unsound.

8. 0 recasts her argument once more so that it is now as cogent as S's argument.

VIII. YOUR OWN THINKING LAB

*1. Consider the following argument: "Marriage can be only between two persons of different sexes.

Therefore, gay couples cannot be married." What's the matter with this argument?

2. Provide an argument that both begs the question and begs the question against.

3. Provide an argument that begs the question without begging the question against.

4. Provide an argument that begs the question against without begging the question.

*5. Discuss the conditions an argument must meet to be deductively cogent.

*6. An argument that is invalid always falls short of being rationally compelling, but could such an

argument be cogent? Must its conclusion be rejected? Explain your answers.

7. Imagine a debate in which two rival claims are equally well supported by observational data. Of the

two, one agrees with common sense, the other doesn't. Does this make a difference? Where is the

burden of proof? Explain.

8. Discuss what's wrong with an argument that begs the question.

9. Discuss what's wrong with an argument that begs the question against.

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This has the form

26' Either P or Q(or both).

That is, (26) presupposes that any apple that is both too small and too ripe is also discarded.
Another thing to notice about these disjunctions is that they present the alternatives as being
exhaustive-that is, they are the on/y possible alternatives. For example, (25) presupposes that
hibernation (or suspended animation) and animation are the only two possible states a
groundhog could enter in winter.

An argument commits the fallacy of false alternatives if and only if it offers in its premises
a disjunction presenting two extreme alternatives as the only ones possible, when in reality
there are one or more others equally plausible.

When an arguer offers a disjunctive premise as presenting exhaustive, exclusive alterna­
tives, we must determine whether this is really so. This involves checking premises of (24)'s
form, to be sure that P and Qexhaust all the alternatives and could not both be true-provided
that the disjunction is intended to be exhaustive and exclusive. A fallacy of false alternatives
would be committed, for example, by this argument:

27 There are only two possibilities: either our country abandons its involvement in
foreign wars or it continues to interfere in other nations' affairs. If it does the former,
then it will become neutral like Switzerland, but if it does the latter, it'll get deeper in
debt to China. So our country will either become neutral like Switzerland or get
deeper in debt to China.

Although this argument is valid, it is also unsound, since its first premise is false in virtue of
treating as exhaustive, exclusive alternatives what are in reality only two among plausible
scenarios. In fact there are more alternatives than the two expressed in that premise! Much
the same problem affects

28 1. Either all U.S. universities will convert their programs entirely into online
courses, or they'll all soon go bankrupt.

2. U.S. universities will not convert their programs entirely to online courses.
3. They'll all soon go bankrupt.

This argument, too, is plainly valid, but unsound owing to the falsity of premise 1, which causes
the argument to commit false alternatives.

Let's consider one more example. Suppose that a political activist is trying to convince us
to agree with her. She appeals to our sense of civic duty and says,

29 You must join my party, the only one that offers a solution to the problem of
homelessness. For you're either part of the solution or part of the problem.

But these options seem unduly restrictive. Why are just those the only choices? Perhaps we are
neither part of the problem (since we did not really contribute to causing it) nor part of the

solution (since our participation might not make any difference). Or perhaps we are both part
of the problem and also (potentially) part of its solution-isn't that equally possible? So, in this
example, the activist commits the fallacy of false alternatives. Once all missing premises are
stated, her extended argument is:

29' 1. There is a problem of homelessness.
2. Either you are part of this problem or part of its solution.
3. It is wrong for you to be part of the problem.
4. You must be part of the solution to the problem of homelessness.
5. To be part of the solution to that problem, you must join my party.
6. You must join my party.

Assuming that other premises are true, premise 2 rests on an inaccurate assumption: namely,
that our choice is limited to either the one or the other of the two mutually exclusive alterna­
tives offered there-that is, to being either part of the solution or part of the problem. Since
that is false, the argument should be rejected on the ground that it commits the fallacy of false
alternatives.

Yet not all arguments featuring exhaustive, exclusive disjunctions commit this fallacy, for
there are situations that do appear to present us with such a choice. It is plausible to say that
citizens of France in 1940 really did have to make a decision between only two mutually
exclusive alternatives: either collaborate with the puppet government imposed by Hitler's
invading armies, or resist it in some way. And a southerner in the United States in 1961 really
did have to choose whether or not to support the integration of schools, churches, and lunch
counters-a movement that was then challenging racially discriminatory laws. But most every­
day situations are not likely to be as dramatic as these. Therefore, for the most part, one is well
advised to be skeptical when someone claims that there is a choice of only two extreme alter­
natives. (It may be so, but probably not.)

BOX 9 ■ HOW TO AVOID FALSE ALTERNATIVES

In evaluating an argument with a disjunctive premise, check that premise to see if
1. It claims that the two extreme alternatives offered are the only possible ones.
2. The alternatives are assumed to be incompatible.
3. In reality, both (1) and (2) are false.

If these conditions are met, then the argument commits the fallacy of false alternatives.

8.6 Accident

Accident is another fallacy of presumption that can undermine arguments: it is committed
when some 'accidental' or exceptional feature of the case at hand is overlooked.

The fallacy of accident is committed by an argument that treats a certain case as falling
under a general rule or principle when in fact the case counts as an exception to it.

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Suppose someone reasons as follows:

30 1. Dogs are friendly animals.
2. My Rottweiler, Otto, is a dog.
3. Otto is a friendly animal.

But suppose it's also true that Otto has recently bitten six of my friends and two hapless
bystanders. What, then, shall we say about the above argument? Although it's true in general
that "dogs are friendly animals," that rule does not apply to Otto. Thus (30) commits the fallacy
of accident. As in other arguments committing this fallacy, here the arguer fails to notice that
some principle that is generally true may not be always true, so that he fails to allow for an
exception to the rule in a case where an exception is warranted.

Now imagine that Smith invites Adkins to lunch one day. "Come on, let's go to lunch," he
says. "We can go to the corner delicatessen, and I'll treat you." Adkins is about to accept but then
thinks to himself, "Wait a minute! There's no such thing as a free lunch!" Now, this judgment
results from the fallacious reasoning involved in accident. Although part of the problem is that
a familiar cliche is being taken too literally, the larger mistake is that some principle that is

generally true is being misapplied. Of course, for the most part, it is true that "there's no such
thing as a free lunch" (meaning that things ostensibly free of charge ordinarily come with
hidden costs we must pay), but if Smith is inviting Adkins to lunch, then this is an exception.
Usual!}, there's no free lunch, But today there is. Adkins is simply being obtuse.

BOX 10 ■ HOW TO AVOID ACCIDENT

Logical thinkers must bear in mind that even the best principles usually have exceptions, and that
if a principle is applied inappropriately-that is, to a case that is rightly an exception-then a fallacy
of accident has been committed.

Or again, suppose Jones believes that one should always tell the truth. In general, this is of
course a good rule to follow. One day Jones meets his next-door neighbor in the supermarket. She
says, "How do you like my new hat?" Jones looks at the hat and thinks to himself, "Always tell the
truth, no matter what." So he says, "I think it looks ridiculous," thereby hurting her feelings and
contributing slightly toward increasing the unhappiness in the world. Now, wouldn't we say here
that Jones is simply being too fanatical about truth telling? Yes, one should usually tell the truth. But
surely this was a case in which a small lie was called for! No one would have been treated unfairly
or otherwise wronged by doing so, and a small degree of happiness would thereby have been

produced. By not recognizing this, Jones has committed a fallacy of accident. He has failed to
understand that, although the rule prescribing veracity is in general a good one, there are justifiable
exceptions; and here he has not allowed for an exception where an exception was warranted.

Exercises

1 . What sort of questions may commit the fallacy of complex question?

2. In which sense may complex questions be considered arguments?

3. Are all questions with presuppositions instances of complex question?

4. How does complex question differ from begging the question? And how do both count as fallacies

of presumption?

5. What is the fallacy of accident?

6. Consider: 'All arguments featuring an either/or statement commit the fallacy of false alternatives.'

Is this claim true? Explain.

X. The following arguments are instances of complex question, false alternatives,

and accident. Determine which is which.

1. Are you still in agreement with the senator's unpatriotic view that tax cuts will help the economy?

SAMPLE ANSWER: Complex question

2. Jorge plans to apply to the University of Texas, where one can major in biology or in history. But since

he cannot stand history, he'll major in biology.

*3. Since people generally survive influenza, you shouldn't worry about your eighty-eight-year-old grand­

father's catching it.

4. Have you stopped cheating on your taxes?

5. One can be either a Roman Catholic or a Protestant. But since both religions are too demanding for

me, it's clear that there is no religion suitable for me.

*6. I'm sure that Jane avoids eating at night. For she has been losing weight without dieting. And to lose

weight, one either diets or avoids eating at night.

7. Professor Wilson almost never gives F's in her classes. So I'm sure I won't get an F this time, even

though I've missed all but one of her class sessions and failed all three exams.

8. Midwesterners vacation in either Florida or the Rocky Mountains. The Gustafsons are Midwesterners

but don't like the Rocky Mountains. Therefore, the Gustafsons vacation in Florida.

*9. Does the defendant wish to deny his past connections to terrorist organizations?

10. Since successful people usually come from a background of wealth and privilege, and Pele, the

soccer player born in a shantytown in Brazil, was a successful person, he must have come from a

background of wealth and privilege.

11. How long will we permit taxpayer dollars to be used as a welfare program for rich farmers?

*12. There can be no such thing as the "politics of happiness" for America. For either we'll have a

Republican president who'll get us into more wars, or we'll have a Democrat who'll get us into a

recession.

*13. People with long-lived parents and grandparents often can expect to be long-lived them­

selves, so I'll be long-lived. Of course, I've smoked cigarettes, a pack a day, for the last thirty

years. But because of my long-lived parents and grandparents, I'm sure I'll live to be at least

ninety-five.

14. Is Aunt Betty still wasting her days watching soap operas on television?

*15. Cancer is a deadly disease, so Isabel should resign herself to her breast cancer and simplify her life

by refusing treatment for it-even when it was detected early in her case.

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3. Complex Question. The question either has an unsupported assumption built into it or is

a conflation of two or more different questions.

4. False Alternatives. The argument features a premise with a disjunction, mistakenly taking

it to be either exclusive, when in fact both disjuncts could be true, or exhaustive, when in

fact there is a third alternative.

5. Accident. The argument assumes that some principle generally applicable is applicable

also in the anomalous case, when in fact it isn't.

■ Key Words

Presumption

Begging the question

Begging the question against

Burden of proof

Commonsense belief

Vicious circularity

Formal circularity

Conceptual circularity

Complex question

False alternatives

Accident

Benign circularity

CHAPTER

From Unclear
Language to Unclear
Reasoning

This chapter considers some common forms of unclarity in language, and the ways
in which they lead to unclarity in reasoning. Its topics will include

Three types of linguistic unclarity that may lead to fallacies: vagueness, ambiguity, and

confused predication.

■ The heap paradox.

■ The fallacy of slippery slope.

The fallacy of equivocation.

■ The fallacy of amphiboly.

■ The fallacy of composition.

The fallacy of division.

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9.1 Unclear Language and Argument Failure

Vagueness, ambiguity, and confused predication are three different sources of unclear
language. Each may lead to argument failure, and we shall find, rooted in these defects, several
types of informal fallacy as well as a type of puzzling argument. When an expression is vague
to a significant degree, it is unclear whether it applies to certain things. For instance, it’s
unclear whether ‘rich’ applies to Betty, who has $900,000 in her bank account. She’s certainly
doing well, but she’s not even a millionaire, much less a billionaire! The problem is that ‘rich’ is
a vague word: for some cases, it’s not clear what (or who) counts as being ‘rich.’ By contrast,
when an expression is ambiguous to a significant degree, it has more than one meaning and
reference, and it is unclear which one is intended by its user. For example, it is unclear whether
“challenging arguments” means either the act of disputing some arguments or complex
arguments that are difficult to follow. Roughly, the reference of an expression is what the
expression applies to, while its meaning is its content. Consider

1 The sum of 1+1

2 The smallest even number.

Both (1) and (2) may be used to refer to the same thing, since they both apply to the same
number-namely, the number 2. Yet (1) and (2) don’t have the same content, which is equivalent
to saying that they don’t have the same meaning, for

MEANING = CONTENT

Since reference and meaning belong to the semantic dimension of a language, vagueness and
ambiguity are two different forms of semantic unclarity. Each may undermine an argument by
affecting some of the terms or concepts that make up its premises and conclusion.

Confused predication, on the other hand, also amounts to semantic unclarity, but it can
arise only at the level of relations between statements in an argument. That is, confused predi­
cation is a fallacy involving a certain error committed in using some predicate, or expression
that attributes some feature or quality to a thing- for example, ‘occupying 60 percent of the
surface of the Earth’ in the conclusion of this argument:

3 Since oceans occupy 60 percent of the surface of the Earth and the Mediterranean is
an ocean, therefore the Mediterranean occupies 60 percent of the surface of the
Earth.

While ‘occupying 60 percent of the surface of the Earth’ might be truly predicated of all oceans
taken collectively, it obviously fails to be true of the Mediterranean Sea. The confusion in (3) is
a common type of mistake that stems from an erroneous inference involving a predicate (we’ll
have more to say about predicates later in this chapter).

Linguistic unclarity rooted in any of these phenomena (confused predication, vagueness,
or ambiguity) can render an argument fallacious. Yet before we examine common ways
in which this may happen, we must ask why such mistakes matter to logical thinking at all.

BOX 1 ■ SOME FALLACIES OF UNCLEAR LANGUAGE AND

A PARADOX

I
Heap

I paradox
Vagueness

Slippery

Slope

Equivocation
UNCLEAR

Ambiguity
LANGUAGE

Amphiboly

Composition
Confused

Predication
Division

Two millennia ago, Greek philosophers pointed out that unclarity in language is a sign of
unclarity in reasoning. Today we’d say much the same. Assuming that speakers are sincere,

what they say is what they believe. And since beliefs are the building blocks of their reasoning,
it is then quite likely that any unclarity in what they say results from unclarity in how they rea­

son (for more on this topic, see Chapters 2. and 3).

9.2 Semantic Unclarity

Vagueness and ambiguity are forms of semantic unclarity that may affect linguistic expressions
of different kinds, as well as the logical relations between them. When an expression is vague, it
is unclear whether or not certain cases fall within its reference. When an expression is ambiguous,

it is unclear which of its possible meanings is the one intended by the speaker. Suppose some­

one says

4 She got the cup.

Furthermore, this is said in a room where there are several women, without pointing to any­
one in particular. In this context, it is unclear to whom the word ‘she’ applies. At the same time,
the term ‘cup’ is ambiguous, since it may equally mean and refer to either ‘bowl-shaped drink­

ing vessel’ or ‘sports trophy.’ Furthermore, if we assume that it is used to refer to a drinking
vessel, it is unclear just how wide the range of its application may be. Does it apply, for exam­

ple, to coffee mugs? What about beer tankards? These seem borderline cases about which ‘cup’
neither definitely applies nor definitely fails to apply. Hence, ‘cup’ is not only ambiguous, but
also to some degree vague.

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BOX 2 ■ VAGUENESS AND AMBIGUITY

■ When an expression is vague, there are borderline cases where it is unclear whether the
expression applies.

■ When an expression is ambiguous, it has more than one meaning and sometimes more than
one reference.

Vagueness and ambiguity are, however, also found at a higher level in the statements that

make up arguments. Here the worst-case scenario is one where a defect of either type renders

an argument misleading. In any such argument, although its conclusion might at first appear

acceptable on the basis of the argument’s premises, a closer look could show that in fact it’s

not. The premises actually provide no support for it.

Logical thinkers should be alert for misleading arguments and try, through careful, case­

by-case scrutiny, to unmask fallacies lurking behind vague or ambiguous language.

These two forms of semantic unclarity are unavoidable features of many everyday

arguments. Such arguments are, after all, cast in a natural language, which, unlike a formal

language, is rich in semantic connotations. For example, suppose that a college instructor, on

the day of an examination, receives this phone message on her answering machine:

5 This is Mary. I was at the bank during the test, so I’d like to take the makeup.

Unable to recognize the voice, and aware of several financial institutions as well as a river

nearby, the instructor cannot make much of (5). For one thing, of the several students

named ‘Mary’ who missed the exam, it is unclear who the caller in (s) is. Furthermore, of the

two meanings of ‘bank’ possible in (5), either ‘financial institution’ or ‘side of a river,’ it is

unclear which one is intended. Suppose the student who left the message later sends a note

from the local Citibank branch attesting that, on the date of the exam, she, Mary McDonald,

had to go there to refinance her mortgage. Putting two and two together, the instructor

reasons that

6 Mary McDonald was the student who reported her absence. She can prove she was at

the local Citibank branch the day of the exam. Thus she qualifies for the makeup.

No ambiguity remains now: a look at contextual information has eliminated the semantic

unclarity in (s) above.

Yet sometimes semantic unclarity bearing on the soundness or strength of an argument

persists even after we have engaged in a charitable and faithful reconstruction of the argu­

ment. In that case, we must reject the argument on the ground that its premises provide no

support for its conclusion, even though they might at first appear to support it. As we shall

presently see in detail, each of these two types of semantic unclarity can render an argument

misleading.

BOX 3 ■ HOW TO AVOID AMBIGUITY AND VAGUENESS

Ambiguity and vagueness are a matter of degree. Although they affect most expressions in
natural languages (which is in part why symbolic logic has developed formal languages to study
logical relations such as inference), the fog they raise can often be thinned by looking at the context

that is, other linguistic expressions surrounding the affected ones, and factors in the arguer’s
environment. When we are engaged in argument reconstruction, the principles of charity and
faithfulness recommend that we check the context, when available, to gain semantic clarity.

9.3 Vagueness

Vagueness is at the root of some philosophically interesting puzzling arguments and also of
many fallacious ones. Later in this section, we’ll examine some cases of each. But first, let’s
consider a shortcoming common to all arguments affected by vagueness: indeterminacy.

When either the premise or conclusion of an argument is significantly vague, that

statement is indeterminate: neither determinately true nor determinately false. Such

indeterminacy undermines the argument as a whole.

This is because, as you may recall, to be deductively sound or inductively strong, an argu­
ment must have premises that are determinately true. Without that, it counts as neither.
Consider this argument:

7 1. Tall buildings in Chicago are in danger of terrorist attacks.
2. The 30-story Nussbaum Building in Chicago is a tall building.
3. The 30-story Nussbaum Building in Chicago is in danger of terrorist attacks.

This argument seems valid, since if its premises are true, its conclusion cannot be false. At the
same time, it also seems unsound, for soundness requires determinately true premises, and
premise 2 suffers from a significant degree of vagueness: putting aside the problem that tall­
ness is relative, although a 100-story building is clearly tall (even by Chicago standards) and a

2-story building clearly not tall, it is unclear whether a 30-story building is tall in Chicago. No
contextual information is available to reduce the vagueness of premise 2, which results from
the two facts described in Box 4. The problem is that there is no determinate point or cutoff
between tall Chicago buildings and Chicago buildings that are not tall.

BOX 4 ■ WHAT’S WRONG WITH ARGUMENT 7?

1. It uses the expression ‘tall,’ which has no clear cutoff point between the cases to which it
determinately applies and those to which it determinately does not apply.

2. The 30-story Nussbaum Building is among the borderline cases of things about which it is
indeterminate whether that word applies or not. It is neither determinately tall nor
determinately not tall.

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When a statement has a vague term applied to a borderline case, that statement is neither
determinately true nor determinately false. Try this yourself: run another series with, for
example, 'cold,' beginning with the determinately true statement, 'A temperature of zero degrees
Fahrenheit is cold,' and continuing to a point where you 'cannot draw the line.' Is it 47 degrees?
48 degrees? 50? Again, any cutoff point in the series would be rather arbitrary.

Keep in mind, however, that vague terms may have non-vague occurrences. Compare

8 The 30-story Nussbaum Building is tall.
9 The 100-story John Hancock Building is tall.

10 The one-story Exxon Station on Route 10 is tall.

While (8) is indeterminate, (9) seems determinately true and (10) determinately false.

BOX 5 ■ SUMMARY OF VAGUENESS

When a term is vague,

■ It is indeterminate whether it applies or not to certain borderline cases.
■ There is no cutoff between the cases to which it determinately applies and those to

which it determinately does not.

When a statement is vague, it is neither determinately true nor determinately false.

The Heap Paradox

Every bit as puzzling to us today as it was to the philosophers of ancient Greece who discov­
ered it is the heap paradox, also called 'argument from the heap' or 'sorites' (from the Greek,
soros, 'a heap'). The argument begins with obviously true premises, but, because they contain a
vague term, ends with an obviously false conclusion:

11 1. One grain of sand is not a heap.
2. If 1 grain of sand is not a heap, then 2 grains of sand are not a heap.
3. If 2 grains of sand are not a heap, then 3 grains of sand are not a heap.
4. If 3 grains of sand are not a heap, then 4 grains of sand are not a heap.
5. If 4 grains of sand are not a heap, then …
6. A large number (say, a million) grains of sand are not a heap.

Given (u), no matter how many grains of sand there are, they never make up a heap.
Something has gone wrong in (u), but since it is difficult to tell what, (11) is a puzzle or para­
dox. After all, it seems that,

A. The argument is valid.
B. Its premises are true.
C. Its conclusion is false.
D. But a valid argument can't have true premises and a false conclusion.

Like other heap arguments, (11) then creates a paradox, for D is true by definition of 'valid
argument.' Therefore, A, B, and C cannot all be true, but it is difficult to say which of them
is false.

A paradox is a puzzle without apparent solution involving claims that cannot

all be true at once, even though each seems independently true. Standardly,

a paradox may be dealt with in one or the other of two ways: it may be solved

or it may be dissolved. To solve a paradox, at least one of its claims must be

shown false. To dissolve it, it has to be shown that the claims are not really

inconsistent.

Until we do either the one or the other, the paradox remains. Since antiquity, the heap
paradox has resisted many attempts of both kinds, all of which have turned out to be flawed in
one way or another.

Let's now use another vague word, 'child,' to run a simplified heap paradox.

12 1. A 3-year-old is a child.
2. If a 3-year-old is a child, then a 4-year-old is a child.
3. If a 4-year-old is a child, then …
4. A 90-year-old is a child.

Again, the argument seems valid, its premises true, and its conclusion false. Premise 2 suggest
a chain of premises such as

13 If a 4-year-old is a child, then a 5-year-old is a child.

14 If a 5-year-old is a child, then a 6-year-old is a child.

The series eventually reaches borderline cases such as a 14-year-old or a 15-year-old, about
whom to the term 'child' neither clearly applies nor doesn't apply. There is no cutoff point
between these and the previous cases, to which the word clearly applies. Or between these and
the following case, to which the word clearly doesn't apply:

15 A no-year-old person is a child.

The unclarity affecting (12), then, is owing to the vagueness of the word 'child.'
More needs to be said about what goes wrong in the heap argument, but on the basis of

its puzzling aspects, it has all the marks of a paradox.

The above arguments run into the heap paradox because they feature words such as

'heap' and 'child,' which are affected by vagueness.

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We smile when we read or hear amphibolous sentences like the patient's, where a clumsy word
order causes it to have a double meaning. Of course, the sentence by itself is not an argument,
but if its ambiguity leads the 'doctor' to draw the wrong conclusion from it, then the dialogue
contains an implicit argument. How, then, does that argument commit the fallacy of amphiboly?
Plainly, it is defective by virtue of ambiguity caused by word order. The argument runs,

23 1. Your arm hurts in two places.
2. Pain is to be avoided.

3. You shouldn't go to those places where your arm hurts.

Assuming that premise 2 is true, even so, since premise 1 is amphibolous, (23) fails to support
statement 3. Fortunately for those who want to be alert for this fallacy, there is a distinguishing
characteristic that may help in recognizing it: in all cases of amphiboly, the ambiguity can
be eliminated by recasting the sentence. For example, in (22), the patient's complaint is not
amphibolous if recast as

24 There are two places on my arm that hurt.

Although not all amphibolies are humorous, the amphiboly that makes us laugh is fairly typical
of this fallacy. Here is another example:

25 The Chase Manhattan Bank once ran an advertisement that said, Talk to one of

Chase's small business advisers today. "So," one potential customer wondered, "what
is the average height of business advisers at Chase?"

In this argument, the conclusion (signaled by 'so') is phrased as a question, but really it's a
sarcastic reaction to the advertisement, better rendered as, 'So Chase bankers who specialize in
business loans are all short!' The semantic confusion that generates this miscommunication is
in the amphibolous phrase 'small business advisers.' Is it the businesses that are small? Or is it
the advisers? Let's look at one more example, this time from Moses Hadas, the distinguished
classical scholar. An author who had sent his book to Hadas hoping for a favorable review
received Hadas's acerbic reply,

26 I have read your book and much like it.

If, from this sentence, the author had drawn the conclusion, "Therefore, Hadas liked my book!" he
would have been too hasty, since it's not clear that that's what Hadas meant. (26) is ambiguous,
owing to its grammar: in this case, 'like' could be either a verb expressing Hadas's favorable assess­
ment of the book, or a modifier of 'it.' In the latter case, the statement would have meant, "I have
read your book and many other things very similar to it" (i.e., "this work lacks originality!'').

The lesson we can take from all of these examples is that we must be on guard for
language that carries a double meaning. To detect (and avoid) the fallacy of amphiboly, the
rule is to inspect an argument's premises as directed in Box 8. If you find ambiguity caused
by awkward grammar, word order, excessive concision, or mere carelessness in the wording
of a premise, recast that premise, when possible, in a way that removes the ambiguity. In
doing so, be sure to follow the principles of charity and faithfulness for argument
reconstruction.

BOX 8 ■ HOW TO AVOID AMPHIBOLY

When evaluating an argument, be alert for ambiguous word order in the premises that leaves
uncertain whether they do in fact support the argument's conclusion.

9.5· Confused Predication

We must now turn our attention to two types of informal fallacy that are rooted in a confusion
involving predication. First, let's explain terminology. What, exactly, is 'predication'? Consider,
for example,

27 Mount Whitney is tall.

BOX 9 ■ WHAT IS A PREDICATE?

The smallest meaningful components of statements are terms or concepts, which divide into two
categories: singular, used to talk about individual things, and general, used to attribute properties
or qualities, such as being tall, amused, or a philosopher. General terms have the logical role of
predicates. To assign a predicate is, in many cases, to describe something.

Of the two terms in (27), 'tall' and 'Mount Whitney,' only the former is uncontroversially a

predicate-in this case, one that attributes the property of being tall to Mount Whitney.
Predicates are often used to describe individual entities as being in certain ways. But they

may also be used to attribute properties to complex entities such as classes, groups, and
wholes. Those entities may involve a class of things (e.g., yellow cars), a collective group

(e.g., the Cleveland Orchestra), or a whole made up of parts (e.g., a computer). Classes and
collective groups have members, while wholes have parts. Predicates are used to attribute

properties and relations to individual things or persons and also to such complex entities.
Consider the following:

28 Yellow cars are fashionable.

29 The Cleveland Orchestra is first-rate.

30 My new computer is well designed.

Here being fashionable, being.first-rate, and being well designed are the properties attributed by

the predicates. There is, of course, nothing wrong with using predicates in these ways to

describe individual things or classes, collectives, and wholes. We couldn't do without these
types of descriptions.

But sometimes a confusion in predication leads to defects in reasoning that happen when
the arguer fails to notice either of these:

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1. Some properties that apply to a whole, a class of things, or a collective group, as stated

in an argument's premises, do not apply to each part of the whole or to each individual

member of the class or group as stated in its conclusion.
2. Conversely, some properties that apply to a part of a whole, or an individual member of

a class or a group as stated in an argument's premises, do not apply to the entire whole,

class, or group as stated in its conclusion.

Whether it is an individual thing that is said to have a property or a class of things (or a collective
group or a whole) matters for clarity in reasoning. When this important distinction is ignored, an
argument may, for example, fallaciously attribute a certain property to a class of things in the
premises and to a member of that class in the conclusion, as in argument (3) at the beginning of
this chapter:

3 Since oceans occupy 60 percent of the surface of the Earth and the Mediterranean is
an ocean, therefore the Mediterranean occupies 60 percent of the surf ace of the
Earth.

Let's now look closely at two informal fallacies of confused predication, known as composition

and division.

Composition

Confused predication underlies the informal fallacy known as 'composition.'

Composition rests on the mistake of thinking that, since each of the parts of some

whole, or each of the members of a class or group, has a certain property, therefore

the whole, class, or group itself also has that same property.

For example, consider this argument:

31 1. Each player for the Chicago Cubs is an excellent player.
2. The Chicago Cubs are an excellent team.

It is very likely that (31)'s premise is true (in baseball, one has to be very good to get into the
major leagues). Yet even if each player for the Cubs is excellent, that wouldn't support the
claim that the team as a group is excellent. For an excellent team is more than just a
collection of excellent individual athletes. It's a team that functions well as a coordinated
group. Argument (31), then, is defective, even if the premise and conclusion are both true.
Why? Because it commits the fallacy of composition through overlooking the crucial dis­
tinction in Box 10.

BOX 10 ■ HOW TO AVOID THE FALLACY OF COMPOSITION

■ It is one thing to predicate a property of each individual member of a team, class, and so on,
but quite another to predicate it of the team itself What may be true in the one case might
not be so in the other.

■ If an argument concludes that a whole itself has a certain property on the basis of its parts
each having that property individually, it commits the fallacy of composition and should be

rejected.

Similarly, consider

32 1. Each part of a computer consumes very little energy.
2. A computer consumes very little energy.

Argument (32) falls short of being deductively valid, or even inductively strong. A research-lab
supercomputer would make its premise true and its conclusion false. Again, the root of the
problem is in thinking that because each of the parts individually has a certain property
(namely, that of running with little energy), therefore the whole made up of all of those parts
must have it, too. Here's another argument with the same sort of problem:

33 Advertisement: "At Global Gobel Airlines, we've got the best-maintained fleet of
planes in the air. We have more than 500 state-of-the-art jets, and each plane is
expertly operated. Therefore, our airline is expelrtly operated."

To predicate the property 'expertly operated' of the aiirPlane is one thing. To predicate that
same property of the airline is something else. So it doesn't follow that Global Gobel is 'expertly
operated' just because each of its planes is. Argument (33) commits the fallacy of composition.

Bear in mind the advice in Box 10.

Division

Another fallacy of confused predication is division.

Division rests on the mistake of thinking that because the whole has a certain property,

therefore each of the parts or members that make it up has that same property.

Unlike composition, division makes the mistake of thinking that what can be truly
predicated of the whole can likewise be truly predicated of the parts that make it up. Suppose
someone argues,

34 1. The U.S. Congress represents every state in the Union.
2. Each member of the U.S. Congress represents every state in the Union.

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state in the Union is taken to support the conclusion that that person individually represents
every state in the Union. And, of course, that does not follow. What is true of the Congress
may well not be true of each member of Congress. Thus the argument commits the fallacy
of division.

While we're on the subject of Washington, here is another argument that commits the
fallacy of division:

35 1. The taxicabs in Washington, D.C., are numerous.
2. Each taxicab in Washington, D.C., is numerous.

(35) makes an inferential move from a predicate being true of a class of things (i.e., Washington
taxicabs) in the premise, to that predicate's being true of each individual Washington taxi in
the conclusion. Thus this is an instance of division. It is only classes of things that can (collec­
tively) be numerous. Individuals can't be, so the conclusion in (35) is just nonsense! As we've
seen, the fact that some collective entity has an attribute does not provide a good reason
to conclude that the same attribute can rightly be ascribed to any part of it. Let's look at one
more argument:

36 The annual National Spelling Bee contest has grown popular over the years, partly as
a result of the Academy Award-nominated documentary Spellbound. Therefore, the
fourteen-year-old girl from Ohio who has won the spelling bee has grown popular
over the years.

Again, the problem is that a property rightly attributed to a complex whole is being wrongly
attributed to the part. In this case, the complex whole is the National Spelling Bee, and the
part is the current winner of the contest, the girl from Ohio. The property in question is
that of having 'grown popular over the years.' From the fact that that is true of the spelling
bee, it doesn't follow that it's true of the girl. A fallacy of division has been committed.

Logical thinkers, then, should beware of the informal fallacies that can arise through con­
fusion in predication and be able to distinguish the two different types of confusion that
underlie division, on the one hand, and composition, on the other. To detect and avoid these
fallacies, follow the rules in Boxes 11 and 12.

BOX 11 ■ HOW TO AVOID THE FALLACY OF DIVISION

In evaluating an argument, ask whether it concludes that each part of a whole has a certain
property on the basis of the whole's having that property. If it does, the argument commits the
fallacy of division and should be rejected.

BOX 12 ■ SUMMARY OF CONFUSED PREDICATION

In evaluating an argument, check whether

■ It concludes that each part of a whole has a certain property because the whole has that

property, or

■ It concludes that a whole itself has a certain property because each of its parts has that
property individually.

If either of these is the case, then the argument commits one of the fallacies of confused
predication and must therefore be rejected.

Exercises

Review auestjons

1 . What is the difference between meaning and reference?

2. Explain the difference between vagueness and ambiguity.

3. What is a predicate? Provide examples of sentences, identifying their predicates.

4. What is the heap argument? And why is it a paradox?

5. Explain what a slippery-slope fallacy is. Why should such arguments be rejected?

6. What is the fallacy of equivocation?

7. Name three sources of confusion that might lead to the fallacy of amphiboly.

8. Why are composition and division fallacies of confused predication?

II. Some of the following are plainly vague and some are not. Determine which is

which.

1. Hot day

SAMPLE ANSWER: Plainly vague

2. Young

*3. Equilateral triangle

4. Leopard

*5. Bachelor

6. U.S. District Attorney

*7. Poor

8. Populous

*9. Parallel lines

10. Odd number

11 . The United Nations

*12. Person

13. Human being

14. Gold

*15. Bald

Ill. For each of the above terms that are plainly vague, show its vagueness by

constructing a heap paradox involving that term.

IV. For each of the following expressions, show that it can be used ambiguously by

constructing a sentence where the expression could have different meanings. If

necessary, provide a context.

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1. Sub

SAMPLE ANSWER: 'My recent experience with subs has been a disaster.' In one context, 'sub'

may mean a type of naval vessel; in another, a type of sandwich; in still another, a substitute

worker.

2. Snake in the grass 6. Desert

3. Fraternity 7. Pirate

4. Siren 9. Honey

5. Birthday 10. Plateau

The following are instances of the heap paradox, slippery slope, equivocation,

amphiboly, composition, or division. For each argument, indicate which of these

it exemplifies.

1 . The one who testified against Tony Soprano was a rat. A rat is a rodent of the genus Rattus. It follows

that the one who testified against Tony Soprano was a rodent of the genus Rattus.

SAMPLE ANSWER: Equivocation

2. Donors to the Philharmonic's fund-raising campaign have given the orchestra millions of dollars this

year. My neighbor Mrs. Martinez was one of those donors. We may infer that Mrs. Martinez gave the

orchestra millions of dollars.

*3. Phil is taking six courses this semester, and they're all three-credit courses. But each course is easy,

so Phil will have an easy semester.

4. Leon Kass, a prominent bioethicist. argues for a ban or moratorium on human cloning. Permitting

such cloning, he insists, can only lead to abuse. "Today, cloned blastocysts for research; tomorrow,

cloned blastocysts for baby-making"-New York Times, February 17, 2004.

5. Perhaps you think that twelve is an even number? Well, I can prove that it is odd. Consider my uncle

Horace. He was born with five toes on one foot and seven toes on the other, which gives him twelve

toes. Now, I'm sure you'll agree that twelve toes is an odd number of toes for a man. Therefore,

twelve is an odd number.

6. If we continue to permit abortion, then we'll soon be allowing euthanasia on demand. This line of rea­

soning leads straight to justifying mass exterminations of any 'unwanted' people. At last we'll be led

to death camps and outright genocide. Therefore, abortion should not be permitted.

*7. Sue says: "The Department of Traffic Control announced last month that in Boston a pedestrian is hit

by a car once every thirty-seven minutes." Sam replies: "Wow! That guy must be in bad shape!"

8. The manager told me she would lose no time in looking at my resume. So I'm sure she will read it

immediately.

9. Young people are independent minded. Ryan Seacrest is young, so he is independent minded.

*1 O. Some people think that all citizens should have to carry national identity cards, just as people do in

most other countries. But it's clear that this is a bad idea. Once we begin registering our identities

with the government, that can lead only to more government control over individual lives. Eventually,

all our precious freedoms will be gone, and we'll have a dictatorship.

11 . The Rolling Stones were at their best in the first half of the year. It follows that their guitarist Keith

Richards was at his best in the first half of the year.

12. If a man has one hair on his head, he is bald, isn't he? Suppose he has two hairs: he is also bald. This

seems to suggest that a man with one million hairs on his head is also bald.

*13. The Brooklyn Bridge is made up entirely of atoms. Science has proved that atoms are invisible.

Therefore, the Brooklyn Bridge is invisible.

14. Mother says Uncle Ryan is a couch potato. Since potatoes are vegetables, it follows that Uncle Ryan

is a vegetable.

15. Dissenters must be suppressed at once, to ensure that they do not undermine presidential authority.

One dissenter today means millions of dissenters tomorrow. If even a single person is allowed to dis­

sent, this will be the first step that will lead ultimately to anarchy.

16. Private universities are not particularly expensive. For they are charging about $48,000 per year for

tuition plus room and board. If that's expensive, then $47,999 is expensive, too. But if $47,999 is

expensive, then $47,998 is expensive. It follows that any amount, even $1, is expensive.

*17. You can eat that chocolate chip cookie if you want, but I say you're asking for trouble. Next you'll be

eating ice cream, then hot fudge sundaes. Soon it'll be double cheeseburgers, fried chicken, and

layer cakes! Stroke and a heart attack are waiting for you, without a doubt.

18. The chemical designation for common table salt is sodium chloride (NaCl). Salt is a compound of

sodium and chlorine. And since salt is, of course, edible and not at all poisonous, it follows that

sodium and chlorine are each edible and not at all poisonous.

19. A "cybersquatter" misused a web address containing Tom Cruise's name, which must be returned to

the actor, since the arbitrators have determined that the actor owns it.

*20. Ice cream is enjoyable. Beer is enjoyable, too. Therefore, ice cream and beer for lunch would be

enjoyable.

21. Colleges should not consider cheerleading a competitive sport, for that will lead to their hav­

ing to consider tai chi a competitive sport. That will lead to considering hotdog eating, stilt

walking, and many other activities as competitive sports. The concept of sport would then lose

its meaning.

22. In the ancient world, Persia was a mighty kingdom. But Croesus, the Greek king, also ruled a mighty

kingdom in Lydia. When Croesus asked the Delphic Oracle for advice, she told him, "If Croesus

crossed the river Halys (i.e., invaded Persia) he would destroy a mighty kingdom." Croesus was

delighted with this news and concluded that he should immediately invade Persia, which he did. As

a result, Lydia was destroyed.

23. Some who read the New York Times headline 'ON DRUGS, BUSH AIMS FOR A MEETING OF THE

MINDS AT LEAST,' concluded that the president was on drugs!

*24. Residents of San Francisco come from every country in the world. Ms. Solomon is a resident of San

Francisco. It follows that Ms. Solomon comes from every country in the world.

25. A candidate for Congress introduces himself as follows: "My name is Henry G. Honest, and I

believe you should vote for me. I'm the only candidate in this election who can truly call himself

honest."

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Amphiboly, committed by any argument in which an awkward grammatical con­

struction, word order, or phrasing of the premise creates ambiguity and makes it pos­

sible to draw the wrong conclusion.

Composition, committed by any argument that concludes that a whole (class, group)

itself has a certain property, given that each of its parts or members has that property

individually.

Division, committed by any argument that concludes that each part of a whole (class,

group) has a certain property, given that the whole has that property.

■ Key Words
Semantic unclarity

Vagueness

Borderline case

Indeterminacy

Slippery-slope fallacy

Ambiguity

Equivocation

Amphiboly

Predicate

Meaning

Confused predication

Composition

Paradox

Division

Reference

Heap paradox

CHAPTER

Avoiding Irrelevant
Premises

This chapter is devoted to the fallacies of relevance. You'll learn about six different
ways in which premises may be irrelevant to the conclusion they're supposedly
supporting. There is also a discussion of how logical thinkers can take account of

emotion in reasoning. The topics include

Appeal to pity.

Appeal to force.

Appeal to emotion.

Ad hominem.

Beside the point.

Straw-man arguments.

Non-fallacious appeals to emotion in everyday reasoning.

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10.1 Fallacies of Relevance

Another source of error in reasoning that can cause an argument to be misleading is the
failure of premises to be relevant to the conclusion they are offered to support. Even if a
premise is plainly true, if it is also irrelevant to the conclusion it is supposedly backing up, then
it cannot count as a reason for it, and the argument fails. Arguments that are fallacious by
virtue of having irrelevant premises often rely on distractions that draw attention away from
what truly matters for the conclusions at hand, and thus are sometimes employed as rhetorical
tricks by artful persuaders who aim to influence us by psychologically effective but logically
defective means. There are several types of informal fallacy that manifest this form of error,
often known as 'fallacies of relevance.' We'll consider six of them here.

BOX 1 ■ FALLACIES OF RELEVANCE

I FALLACIES OF
I

. RELEVANCE .
APPEAL TO APPEAL TO

PITY FORCE
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AD HOMINEM
BESIDE THE jsTRA� MANI POINT .

10.2 Appeal to Pity

One type of fallacy of relevance is the appeal to pity (also called ad misericordiam).

An argument commits the fallacy of appeal to pity if and only if its premises attempt

to arouse feelings of sympathy as a means of supporting its conclusion.

Consider, for example, an argument that was once made on behalf of clemency for Rudolf
Hess, a close associate of Hitler arrested in Britain during World War II and later sentenced to
life imprisonment for war crimes. In 1982, when Hess was old and in poor health, some people
argued that he should be freed from prison. The argument went this way:

1 1. Hess has already spent more than forty years in prison.
2. He is in his eighties now and his health is failing.
3. This elderly man should be permitted to spend his last years with his family.
4. Hess should be granted clemency.

But Hess's age and failing health were irrelevant to the real issue: his guilt as one of the
founders of a regime that had terrorized Europe. Many Russians, whose country had suffered
millions of deaths at the hands of the German invaders, recognized this argument as an
appeal to pity and objected vigorously. As a result, Hess's sentence was never commuted and
he died in prison.

A similar argument was offered recently by the mother of a sea pirate, who begged the
president of the United States for leniency in her son's case on the grounds that he was "lured
into piracy by older friends." According to a report in the Associated Press, the pirate himself
expressed contrition. "I am very, very sorry about what we did," he said through an
interpreter. "All of this was about the problems in Somalia." But even if we do feel sorry for
him, in view of his wretched existence in a war-torn, lawless land, that is hardly enough to
justify the murder of innocent merchant seamen on foreign-flag ships. The argument is
plainly an appeal to pity.

It's worth noting, however, that it's not only on behalf of scoundrels and criminals that
people resort to the appeal to pity. We find it in everyday life in many guises, including some
uses we may (wrongly) think free of this fallacy-for example, when a student argues,

2 You gave me a B in this course, but . . . can't you give me an A? If I don't have an A,
then it'll mean that my grade average will fall, and I won't be able to get into law
school! And I've been working hard all semester.

The argument in fact is:

2' 1. I've been working hard in this course.

2. Any grade below an A would adversely affect my chances for law school.

3. I should get an A in this course.

This argument commits the fallacy of appeal to pity. But not because of premise 1: plainly, how
hard the student has been working is not relevant to its conclusion, but that is the fallacy
known as 'beside the point' (more on this later). What's making the argument count as an
appeal to pity is premise 2: that premise shows that the argument attempts to support its
conclusion by making the professor feel sorry for the student. It might succeed in doing that,
but it fails to make its conclusion rationally acceptable.

More generally, an appeal to pity is a fallacious argument trading on the fact that feeling
sorry for someone is often psychologically motivating. Yet that is not a good reason for the
argument's conclusion. Logical thinkers would want to be able to recognize and avoid this
fallacy. For some tips on this, see Box 2.

, BOX 2 ■ HOW TO AVOID APPEAL TO PITY

1. An argument whose premises attempt to provoke feelings of sympathy that might move an
audience to accept its conclusion commits the fallacy of appeal to pity.

2. Any such argument should be rejected, since it provides no reason relevant to its conclusion­
that is, it provides no rational support for it.

10.3 Appeal to Force

Another informal fallacy trading on feelings, though in an entirely different way, is the appeal
to force (sometimes called ad baculum, literally, 'to the stick').

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An argument commits the fallacy of appeal to force if and only if it resorts to a threat

as a means of supporting its conclusion.

In any argument that commits this fallacy, the arguer attempts to arouse feelings of fear in
someone as a way of getting her to accept a conclusion (it's as if he were saying, 'Agree with me
or else!'). At the end of World War II, when Allied leaders met at Potsdam, Germany, to decide
how Europe would be divided, Stalin's armored divisions already held Eastern Europe in an
iron grip guaranteeing Soviet influence there. Told that the Pope had suggested a political
settlement less accommodating to Soviet aims, Stalin harrumphed, "How many divisions does
the Pope have?"

Of course, the threat voiced in an appeal to force need not be a physical threat. It might
merely hint darkly of unfortunate consequences awaiting those who disagree with the arguer.
To detect (and avoid) the fallacy of appeal to force in arguments, the rule is to check their
premises as suggested in Box 3.

When Richard J. Daley was mayor of Chicago, from 1955 until his death in 1976, he
exercised near-autocratic control over the Cook County Democratic Party organization.
Public officials were well aware that they served at the pleasure of Mayor Daley and that
any evidence of their disloyalty could have adverse consequences. Every time Daley would
run for reelection, the word would go out to senior public officials serving in his
administration:

3 We think it might be a good idea for you to get out and campaign for Mayor Daley in
this election, Mr. Parks Commissioner [Street Commissioner, Fire Commissioner,
etc.], because if you don't, and Mayor Daley wins … well … you might be out of a
job! And … you know … we'd hate to see you lose your job! So, really, we're just
giving you a little bit of friendly advice here … that's all. We're looking out for you!

This may sound innocuous, but it's really a thinly veiled threat:

3' 1. If you don't campaign for Mayor Daley's reelection, you'll lose your job.

2. You ought to campaign for Mayor Daley's reelection.

(3') qualifies as an appeal to force. After all, the reason it offers (what'll happen to the addressee
if she or he doesn't campaign for Mayor Daley), although no doubt psychologically powerful as
a motivator of enthusiastic campaigning, is not relevant to the conclusion that the addressee
should campaign for Mayor Daley. In itself, it gives no reason why Daley deserves to be re­
elected, so that people can campaign for him with a good conscience. Notice that it would
have been possible to give an entirely different argument for the same conclusion that would
commit no fallacy: campaigners could simply have said,

4 You ought to get out and campaign for Mayor Daley in this election because of all
the great things the Daley administration has done for the city of Chicago,

and then listed the accomplishments of the Daley administration. (In fact, there were many.) Thus
completed, (4)'s premises would be relevant to the argument's conclusion and might very well
support it. By contrast, (3')'s premise is completely irrelevant to the argument's conclusion.

BOX 3 ■ HOW TO AVOID APPEAL TO FORCE

1. An argument whose premises merely express a threat of unpleasant consequences for thos1e
who refuse to accept the argument's conclusion commits the fallacy of appeal to force.

2. Any such argument should be rejected, since its premises provide only a "reason" that is
irrelevant to the argument's conclusion-thus falling short of rationally supporting it.

10.4 Appeal to Emotion

So far, we've seen two ways in which fallacies of relevance might be committed by arguments

that offer premises appealing to our emotions in ways utterly irrelevant to supporting their
conclusions. A third variation on this common sort of mistake is found in the fallacy of appeal
to emotion.

An argument commits the fallacy of appeal to emotion if and only if it attempts to

support its conclusions by appealing to people's feelings rather than to their reason.

This fallacy is sometimes called ad populum-literally, 'to the people.' In any argument

that commits it, emotively charged language is used to try to persuade someone to accept a
certain conclusion. In some cases, the language employed for this purpose may include

images that carry emotive force, as can be seen from the immense popularity of this fallacy in

television commercials and other advertising media. But often appeals to emotion are made
by using words carefully chosen for maximum emotional impact. To detect and avoid this

fallacy, follow the rules in Box 4.

Appeal to emotion is, of course, a medium much beloved by stem-winding political

orators. In 1896, populist Democrat William Jennings Bryan drew upon biblical allusions to

argue that the gold standard in U.S. monetary policy was bad for working people:

5 You shall not press down upon the brow of labor this crown of thorns; you shall not

crucify mankind upon a cross of gold.

And forty years later, in the depths of the Great Depression, President Franklin D. Roosevelt
attempted to rally support for his reforms with emotive language of stirring intensity:

6 This generation of Americans has a rendezvous with destiny.

Notice that each of these examples amounts to a premise offered in support of a conclusion
to the effect: 'Therefore you should support my programs!' They are both arguments with

implicit conclusions. And both try to move their audiences through the psychological
power of emotively charged phrases such as 'crucify mankind,' 'crown of thorns,'

'rendezvous,' 'cross,' and 'destiny.' As these examples show, the fallacy of appeal to emotion

is as likely to be committed by mainstream politicians as it is by demagogues and despots

(such as Adolf Hitler, who used it constantly). But it is a fallacious form of argument,

whoever indulges in it.

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Sometimes reasoning that commits the fallacy of appeal to emotion rests on a clever use
of images that provoke a strong emotional response. When President Lyndon Johnson was

running for reelection in 1964, his campaign sought to capitalize on prevalent voter fears about

the alleged recklessness of his opponent, Senator Barry Goldwater. In a charged, Cold War era,

some feared that Goldwater might be too quick to resort to nuclear weapons, and Johnson's

campaigners wanted to exploit this uneasiness. So the Democratic Party ran a television

commercial that opened with a view a of sunny meadow and a little girl picking flowers, then

cut to a dark screen with the fiery mushroom cloud of a nuclear explosion billowing up into

the night sky. Across a black screen the message then flashed: 'VOTE FOR PRESIDENT
JOHNSON.' One of the most notorious examples of emotively charged images in the history

of political advertising, the commercial was widely denounced as tasteless, prompting

Democrats to withdraw it.

BOX 4 ■ HOW TO AVOID APPEAL TO EMOTION

1. Be on guard for arguments that attempt, through the use of emotively charged words or
images, to elicit a strong psychological response conducive to the acceptance of its
conclusion.

2. Any such argument commits the fallacy of appeal to emotion and should be rejected. Why?
Because its premises offer only "reasons" that are irrelevant, in the way suggested in (1), to the
argument's conclusion. No such argument can provide rational support for its conclusion.

The Bandwagon Appeal

Some forms of emotional appeal are intended to take advantage of common feelings that

seem to be part of human nature, such as the desire not to miss out on the latest trends-for

example, when books are marketed as 'best sellers' or a film is touted as 'the Number One Hit

Movie of the Summer!' This so-called bandwagon appeal exploits our desire to join in with the

common experiences of others and not be left out. But the reasons offered for buying the book

or seeing the movie merely note their popular appeal, not their quality. A best seller might be

only a shallow entertainment, a hit movie little more than a television sitcom. That they're

widely sought does nothing to support the claim that they're worth seeking.

Appeal to Vanity

Appeal to vanity (sometimes called 'snob appeal') is another of the varieties of ad populum­

this time trying to exploit people's unspoken fears about self-esteem. When a car is advertised

as in (7), the advertiser attempts to persuade prospective buyers to buy the car by making an

appeal to their vanity.

7 Not for everyone-this is the car that tells the world who you are!

In another example of this argumentation tactic, Virgin Atlantic Airways has decided to attract

customers to its premium-class service by calling it, not 'first class,' but 'Upper Class.' Can you

see what is going on here?

10.5 Ad Hominem

Another way arguments can fail because of irrelevant premises is the very common fallacy of
ad hominem (literally, 'to the man'), which has less to do with emotion than with personal
attack. It is sometimes called 'argument against the person,' but we'll call it by its Latin name,
since that has now come to be familiar in everyday usage.

An argument commits the fallacy of ad hominem if and only if it attempts to discredit

someone's-or some group's-argument, point of view, or achievement by means of

personal attack.

That is, the fallacious ad hominem rests on some personal consideration strictly irrelevant
to the matter at hand, which is intended to undermine someone's credibility, as a means of
indirectly attacking the person's position or argument. The problem with such an ad hominem,

of course, is that in this way the question of the real merit of that person's position is evaded.
Instead, the ad hominem offers only a cheap shot aimed at the person herself. Before turning to
some specific arguments of this sort, notice that they all fail to support their conclusions-yet
they can be recognized easily and avoided in the way suggested in Box 5.

Examples of ad hominem are, unfortunately, easy to find-sometimes committed by
people you'd not expect to be committing fallacies. Planned Parenthood recently ran a series of
advertisements on buses and subways that featured a photo of several grumpy-looking men in
suits. Across the photo was mounted the ad copy, which read, "79% of abortion opponents are
men. 100% of them will never be pregnant." We may smile at this rhetorically clever
juxtaposition of image and slogan, but, make no mistake, this is an ad hominem against male
opponents of abortion. Instead of focusing on what those men's objections to abortion may be,

the effect of the ad is simply to dismiss the objections as men's views. But the views of men­
on abortion or any other topic-cannot be legitimately rejected solely on the basis of their
provenance (that they are "men's views"). Rather, the question is: Are these views well
supported? It's not whose views they are that matters, but do the proponents have good or bad
arguments for their claims?

Suppose a new political scandal erupts in Washington. Senator Dunster has been caught
using public funds to pay for expensive luxury vacations for himself and his family, and
another legislator, Senator Brewster, has taken to the Senate floor to denounce this
impropriety. But Dunster is a Harvard man and cannot resist pointing out that Brewster's
college days were spent at Yale. In a speech, Dunster loudly responds,

8 These charges are all false! And these unfounded accusations are coming from
exactly the place we would expect. Apparently Senator Brewster, like all Yalies, cannot
resist the temptation to besmirch the reputation of a Harvard man!

Here Senator Dunster's argument is an ad hominem that attempts to discredit Brewster's
statements, not by speaking to their content (the accusations of impropriety), but by pointing

to Brewster's personal background-the fact that he is a Yale graduate. Its clear assumptions
are that all Yalies are naturally prejudiced against Harvard graduates, and that that is why

Brewster is saying these things! But Dunster's argument simply engages in personal attack:

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it introduces an irrelevant consideration that has no power to actually discredit the opponent's
claim (though it may appear to do so).

The thing to keep in mind, again, is that it's not who says it that makes a claim well
supported or not, but rather whether there are in fact good reasons to back it up. Those reasons
should be judged on their own merits: either they provide some support for the claim, or they
don't. In our example, we would of course need to hear Senator Brewster 's argument­

presumably citing facts in support of the conclusion that Dunster had behaved
inappropriately-in order to determine this.

BOX 5 ■ HOW TO AVOID A FALLACIOUS AD HOMINEM

1. Beware of any argument that appeals to some personal facts (or alleged facts) that are
irrelevant to its conclusion.

2. Any such argument commits the fallacy of ad hominem and should be rejected, for its

premises are irrelevant to its conclusion-that is, they are offered as a means of attempting
to discredit an argument or point of view by discrediting the person who presents it.

The Abusive Ad Hominem

Sometimes ad hominem arguments attack a person's character. Suppose a moviegoer announces,

9 I have no desire to see Woody Allen's latest movie. I'm sure it's worthless, and I wouldn't

waste my money on it-not after what I know about him now! He betrayed Mia Farrow
and broke her heart when he became romantically involved with Mia's adopted daughter,

Soon-Yi Previn. So his movies are without artistic merit, as far as I'm concerned.

Now, (9) plainly commits the fallacy of ad hominem, since it seeks to discredit Woody Allen as a
film director not by invoking evidence that his movies are artistically questionable, but by a

personal attack that refers to his relationship to Soon-Yi Previn (whom he later married). But
this ad hominem is of a more abusive sort, since it attacks Allen's character-he is denounced
on moral grounds as a 'betrayer,' which is, of course, a term of contempt. But, whatever we may

think of Allen's personal qualities, does any of that prove that his films are bad? Isn't all of that

simply irrelevant to an assessment of his art?

Tu Quoque

Finally, the fallacy of ad hominem is also committed when one tries to refute someone's point
of view by calling attention to the person's hypocrisy regarding that very point of view. This is

sometimes called 'tu quoque' (literally, 'you also'). For example, consider how Thomas

Jefferson's writings must have sounded to the British in his day. Jefferson famously wrote, in
the Declaration of Independence, "We hold these truths to be self-evident, that all men are
created equal, that they are endowed by their Creator with certain unalienable Rights, that

among these are Life, Liberty, and the pursuit of Happiness." But one can easily imagine how
this must have been received in conservative circles in Britain in 1776. Tories certainly
regarded this lofty language as risible political rhetoric, since they knew very well that

Jefferson was himself a prominent slave holder. In London, Dr. Samuel Johnson scoffed,

"How is it that we hear the loudest yelps for 'liberty' among the drivers of Negroes?" Johnson's
remark could be expanded into an extended argument that looks like this:

10 1. Jefferson claims that all men are created equal and have rights to liberty.

2. But Jefferson himself is a slave owner.

3. He preaches lofty principles for others that he does not practice himself.

4. Jefferson's claims about liberty and equality are false.

Yet if any did actually offer such an argument, it would have committed the fallacy of tu quoque, a
form of ad hominem. The imagined argument, after all, tries to bring a personal matter-Jefferson's
real-life hypocrisy about race and human nature-into the discussion to cast doubt on his
assertions about human equality and rights. Now, it is of course true that the Sage of Monticello
did not permit his own black slaves to enjoy the very liberty and equality he so forcefully advocated
for himself and his fellow white men. But did that personal failure go any way at all toward
showing that Jefferson's claims about liberty and equality were false? Naturally, we all think that
people should not be hypocrites. People should practice what they preach. Yet if someone fails to

heed this moral maxim, and we point out his hypocrisy, we have not thereby proved that what he
preaches is false. In fact, we are only indulging in a form of ad hominem, a tu quoque.

Nonfallacious Ad Hominem

Before we leave the discussion of ad hominem, there remains one important clarification that
should be added. Some uses of argument against the person are not fallacious, for there are
contexts in which such an argument may be in order. In public life, for instance, the moral
character of a politician may be a highly relevant issue to raise during a campaign, since we do
very reasonably expect our elected leaders to be trustworthy. In the second example given
above, Senator Brewster's speech calling Senator Dunster's personal rectitude into question
amounts to a kind of personal attack, but it commits no fallacy (as does Dunster's reply), since
conduct that is unethical (or illegal!) would not be irrelevant to an assessment of a person's
fitness to serve as a senator. Brewster's remarks, then, could justifiably be seen as an ad hominem

argument but not a fallacious one, for they commit no fallacy of irrelevant premises.
Similarly, in the Anglo-American system of justice, which employs an adversarial model in

court-with attorneys on opposing sides each presenting an argument for their client's case
and trying to undermine their opponent's position-some of what happens in the courtroom
may appear to be ad hominem. Here, after all, attorneys might try to discredit a witness by

presenting evidence about his personal life.
But in fact this does not amount to a fallacious ad hominem at all, since in the courtroom,

the reliability of a witness is not irrelevant. Given that the purpose of a witness just is to give
testimony, it is highly relevant to know whether the person can be believed or not. Thus an
attorney does not commit a fallacy of ad hominem when she appeals to relevant personal
matters in an attempt to discredit the claims made by a witness. An attorney's job is to defend
her client's interest by aggressively pressing his case, and part of that may include presenting
facts about a witness's background and personal life in an effort to undermine his credibility.
This is a kind of personal attack, but it commits no fallacy.

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Logical thinkers must bear in mind that courtroom procedure is a specialized subject in

the law, and that we're not attempting here to venture into its complexities. When one is called

to serve on a jury, one should follow the instructions of the judge. The important thing to

notice now, however, is simply that there can be some uses of ad hominem that are not

fallacious, and that it is the context that determines when this is so.

10.6 Beside the Point

An argument might commit a fallacy of relevance by offering premises that simply have little

or nothing to do with its conclusion. Maybe they support some conclusion, but they don't

support the one given by the argument. When this happens, the argument commits a beside­

the-point fallacy (also known as ignoratio elenchi).

An argument commits the fallacy of beside the point if and only if its premises fail to

support its conclusion by failing to be logically related to its conclusion, though they

may support some other conclusion.

Faced with an argument of this sort, we may at first find ourselves unable to identify the

source of the confusion. For example, imagine that opponents of cruelty to animals introduce

legislation to ban the mistreatment of chickens, pigs, and cows in certain 'factory farms.' But

suppose the corporations who own the farms respond,

11 These farms are not cruel to animals. After all, the farms provide the food that most

consumers want, and they do so in a manner that is cost-effective; moreover, these

poultry, pork, and beef products are nourishing and contribute to the overall health

of American families.

The odd thing about (11) is that nothing in its premises contributes toward providing support

for the conclusion, 'These farms are not cruel to animals.' Perhaps the premises support some

conclusion. But they don't support that one, since they offer no reason to think that the factory

farms in question are not cruel. As a result, (11) commits the beside the point fallacy.

Here's another example that does so as well. Early in Barack Obama's administration, a

state dinner at the White House was attended by a local couple who had not been invited and

had no authorization to enter the White House. They were, in effect, party crashers.

Threatened with prosecution under federal law for having breached White House security,

they responded that they should not be prosecuted because they had "made a sacrifice in time

BOX 6 ■ HOW TO AVOID THE BESIDE-THE-POINT FALLACY

Logical thinkers should be on guard for

1. Arguments whose premises are simply irrelevant to proving the conclusion.
2. Any such argument is defective, even if nothing else is wrong with it; it commits a

beside-the-point fallacy and should be rejected.

and money to get ready for the party." Now, let us suppose that it's true that they had made
such a sacrifice. Even so, how is that relevant to their claim that they do not deserve

prosecution for breaking the law? The proposed "reason" why they should not be prosecuted
(namely, the alleged "sacrifice in time and money") is not a reason that supports the
conclusion. This argument is plainly an instance of the beside-the-point fallacy.

Yet another example of this type of mistake was inadvertently provided by a radio listener
who responded to a BBC program predicting a crisis of overpopulation in the United Kingdom
by 2051. "We can meet this challenge," the listener confidently asserted, "because we all stood
together as one people when we were fighting the Nazis." But there is more than one problem
in this argument, not least of them the fact that none of the Britons who fought the Germans
in World War II are likely to be alive in 2051. So, whatever the coping skills of those who
prevailed in Britain's Finest Hour, their application in the envisaged crisis to come at mid­
century seems unlikely. Moreover, it is not at all clear how a nation's possessing the military
skills necessary to defeat Hitler proves anything at all about their ability to overcome an

entirely different sort of problem in the foreseen population crisis. Thus the argument is only
a beside-the-point fallacy. Its premise, though manifestly true, provides no support for the

conclusion.

12 1. We all stood together as one people when we were fighting the Nazis.

2. We can meet the coming challenge of overpopulation.

10. 7 Straw Man

Finally, let us consider a type of informal fallacy committed by any argument where the view of

an opponent is misrepresented so that it becomes vulnerable to certain objections. The distorted
view may consist of a statement or a group of related statements (i.e., a position or a theory).
Typically ignored in such distortions are charity and faithfulness, the principles of argument
reconstruction discussed in Chapter 4. Given the principle of charity, interpreting someone else's
view requires that we maximize the truth of each of its parts (in the case of an argument,
premises and conclusion) and the strength of the logical relation between them. Given the
principle of faithfulness, such interpretation requires that we strive for maximum fidelity to the

author's intentions. It is precisely the lack of charity, faithfulness, or both, in the interpretation of
the views of others with whom the arguer disagrees that results in straw man.

An argument commits the fallacy of straw man if and only if its premises attempt to

undermine some view through misrepresenting what that view actually is.

Situations where this type of informal fallacy often occurs include deliberations, such as de­
bates and controversies. Straw man is (regrettably) a common tactic in public life, often heard
in the rhetoric of political campaigns. Typically, the straw-man argument ascribes to an oppo­

nent some views that are in fact a distortion of his actual views. These misrepresentations may
be extreme, irresponsible, or even silly views that are easy to defeat. The opponent's position,

then, becomes a 'straw figure' that can be easily blown away. But to refute that position is of

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BOX 7 ■ WHAT'S GOING ON IN A STRAW MAN ARGUMENT?

1. A straw-man argument attempts to raise an objection 0 against a certain view-call it 'V.'

2. But the argument misrepresents Vas being in fact W-where Wis vulnerable to the objection 0.
3. The argument concludes by rejecting Von the basis of 0.

But does 0 really undermine V? It seems not. After all, 0 is an objection only to w; a distorted
rendering of V, not to V itself

course not at all to disprove the person's actual position. This can be seen in Box 7, which out­
lines what's going on in straw-man arguments.

It is not difficult to find examples of this fallacy in political debates. Imagine two rival
political candidates who disagree about foreign policy: Barton declares that the nation should
not act unilaterally in using military force but do so only with the support of traditional allies.
But Burton tries to undermine Barton's credibility by arguing as follows:

13 1. My opponent's international policy is: Wait for foreign permission before acting.

2. Waiting for foreign permission before acting is inconsistent with promoting our
national security and our right to act in our own self-interest.

3. Both promoting our national security and our right to act in our own self-interest
are reasonable.

4. My opponent's international policy is unreasonable.

But suppose there is in fact no evidence that Barton does actually hold the view ascribed to her in
the first premise-then what? In that case, (13) is a straw-man argument. Seeking the support of
traditional allies before undertaking a potentially dangerous step is hardly the same thing as
"waiting for foreign permission before acting." Burton is misrepresenting Barton's argument.

Consider another example: some members of Congress announce that they favor trials in
civilian criminal courts for Guantanamo detainees. Their opponents then charge,

14 1. Those who favor such civilian trials are pro-terrorist.

2. To be pro-terrorist is to be against our country.

3. Those who favor such civilian trials are against our country.

To detect (and avoid) a fallacy of this sort, the rule is to check whether an argument's reasons
against a certain view can really count as reasons against that view. Always ask yourself whether
the target view has been reconstructed according to the principles of charity and faithfulness.

BOX 8 ■ HOW TO AVOID A STRAW-MAN ARGUMENT

When objecting to a view V, if the argument goes, "View Vis wrong because it faces objection 0,"
keep in mind that, whether or not 0 is actual!), an objection to V depends on whether V has been
construed in accordance with faithfulness and charity. An obviously false view may be a view

nobody holds!

10.8 Is the Appeal to Emotion Always Fallacious?

Earlier in this chapter, the appeal to emotion was identified as one of the Fallacies of
Relevance. But, it will be objected, it simply cannot be that a logical thinker's only appropriate
attitude toward emotion is a wary distrust. Given the large role of emotion in human life­
indeed, if we consider that life would surely be impoverished without it-philosophers can ill
afford to ignore emotion, and logical thinking ought to have a way of accommodating the
many benign manifestations of it that commit no fallacies.

What, then, are some of these? First, emotions plainly have an important role in motivating
our actions. Feelings, sentiments, desires, and ordinary inclinations and aversions of many sorts
all move us to act in everyday life in ways that involve no fallacious inferences. We need not go
so far as holding that reason "is and ought to be the slave of the passions" to recognize that our
feelings and desires motivate our actions. And actions motivated by feelings may be guided by
reason (e.g., "don't do to others what you'd not like done to you").

Second, being alert to the personal emotional commitments of our loved ones, friends,
and co-workers can give us reasons for action, or for forbearance. If we know what others care
about-especially what matters to them in deep and important ways-then we'll know how to

avoid saying things that will hurt their feelings. This is a concern about emotion (theirs!) that
commits no fallacy. Similarly, if we know that mentioning certain subjects will cause a certain
person to become enraged, then it's not fallacious to conclude that we should take his feelings
into account and try to avoid such talk in his presence unless it's necessary.

Third, emotions may appropriately move us to take action for the sake of strangers who
are suffering or in peril. When reports of famine, war, epidemics, and natural disasters moti­
vate us to contribute to relief programs, we are following our feelings of compassion for our
fellow human beings and commit no fallacy. Likewise, when our instincts of fairness move us
to speak out on behalf of minorities subjected to prejudice or discrimination, there is no
fallacy in acting on these feelings. And when we read of outrageous acts of brutality and
violence, or criminal acts of an especially nefarious sort, there is no fallacy in concluding that
such acts ought to be punished, or prevented if possible. Finally, we may, of course,
appropriately and rationally respond to emotion in our desire to aid needy individuals, as
when a doctor acts to relieve her patient's suffering, or when we give our pocket change to a
homeless person begging in the street.

What all of the above examples have in common is this: they are appeals to emotion that
are not irrelevant as reasons for our conclusions. That is, they represent types of situation in
which one may rationally be moved by emotion. In the fallacy of appeal to emotion (ad
populum), by contrast, the use of emotion always represents a diversion from the matter at

hand, often a subtle attempt at manipulating one's feelings for the sake of some strictly
irrelevant consideration that does not actually contribute to supporting the argument's
conclusion (though it may appear to do so). Logical thinkers are advised to beware of such
trickery, as it amounts to an abuse of reason.

But the purpose of logical thinking is not to turn people into coldly rational beings
without emotions, like Star Trek's Mr. Spock. (Of course, since Spock is half-Vulcan and only
half-human, he may be inclined to overestimate the value of rigidly rational behavior and to
underrate the value of ordinary affections.) There are, after all, many occasions in life when it

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*25. Mafioso to shopkeeper: 'You got a nice business here. It' d be a shame if somethin' were to

happen to it.'

26. Advertisement: 'You've always known that Mercedes-Benz was the car for you. It's not a car for

everybody. But then, you're not just anybody. When you've truly achieved a place of distinction in life,

you know you're ready. Mercedes-Benz.'

27. According to contemporary biology, species evolve over time. But I have never seen any animals

evolving. Have you? Has anyone ever seen animals evolving? So, contemporary biology is false.

*28. "Everything that today we admire on earth-science and art, technique and innovations-is only the

creative product of a few peoples and perhaps originally of one race. [Therefore, on the Germans]

now depends also the existence of this entire culture. If they perish, then the beauty of this earth

sinks into the grave with them . . . The man who misjudges and disdains the laws of race actually

forfeits the happiness that seems destined to be his. He prevents the victorious march of the best

race and with it also the presumption for all human progress . . . All that is not race in this world is

trash."-Adolf Hitler, Mein Kampf.

29. Dear State Senator: Our organization believes that protecting the environment is an issue of

paramount importance. Unless your legislature passes the Clean Air and Water Act, we will urge all

business meetings, conventions, and tourists to boycott your state indefinitely.

*30. Darwin's theory of evolution cannot be correct. It holds that we all evolved from monkeys! But

monkeys do not evolve into people. And we are too different to have evolved from them. Thus

Darwin's theory of evolution has to be false.

31. Los Angeles has twenty or thirty downtowns. There is no conventional pattern of people commuting

to work in one direction in the morning and the reverse in the evening. So it seems there is no central

authority in organizing the city or its government .

32. French actress Brigitte Bardot insists that cruelty to animals is a serious crime and that we should

treat our dogs and cats humanely. But we cannot take this seriously. She is well known for

expressions of bigotry toward ethnic and religious minority immigrants in France.

*33. We in the industrialized world would suffer terribly if our government imposed energy-restricting

policies. Thus the government should refrain from making energy restrictions in our country.

34. My opponent, Representative Smith, says she favors abolishing the death penalty. But what she is

really saying is that it's just fine for murderers to be housed and fed for years at taxpayer expense,

and that it's OK with her if they are ultimately released to prey on our citizens again.

*35. In the Gospel of St. John, Nathaniel expresses doubt, on first hearing of Jesus' teachings, that there

could be a truly wise man from such an obscure, small town: "Nazareth! Can anything good come

out of Nazareth?" -John 1 :46:

36. President Gerald Ford granted his predecessor, Richard Nixon, a presidential pardon that spared

Nixon from a possible prison sentence for his involvement in illegal activities in the Watergate scandal

of 1972-74. Ford's advisers argued, "The humiliation of having to resign the presidency in disgrace is

punishment enough for poor Nixon."

37. Liberal economic theories and the policies that have sprung from them cannot be good for this

nation's economy over the long run, for these very theories and policies are now opposed by the

great majority of Americans.

38. You'd better be careful not to mention the chairman Mr. Grace's friend Lulu around Mrs. Grace. If you

mention her, I'll see to it that you're never promoted!

*39. State College should require basic computer literacy of all its students, since colleges everywhere are

introducing a requirement of this kind into their curricula.

40. The UN should not sanction India for selling weapons to Myanmar. After all, India is still a developing

country with millions of poor people in need of humanitarian aid.

Ill. Some of the following arguments commit a fallacy of appeal to emotion, and

some don't. Determine which commits which.

1. Cousin Ed is always getting into scrapes with the law and can't seem to stay out of jail. But Aunt

Betty and Uncle Jake love him nonetheless. So I ought not to make jokes about Ed in their presence.

SAMPLE ANSWER: Not a fallacy of appeal to emotion

*2. As your representative in Congress, I have sworn upon the altar of God to uphold the sacred freedoms

of our mighty democracy! Despite the scurrilous attacks of my yelping-dog opponents who accuse me

of tax evasion, I have always defended the American way! Thus I ought to be reelected.

3. News reports from Zambia describe a nation devastated by an epidemic of AIDS. When I read of

people dying for lack medical care, I feel horrible about this. Therefore, I'm contributing to relief

efforts to send doctors to Zambia.

4. "I feel very bad for the couple next door," said Mary Ellen. "Jack and Harry have been told that gay

couples are not welcome at their church. So I'm going to invite them to mine."

*5. Jurors in the Enron case were infuriated by the lies and deceptions perpetrated by the company's

executives. "We were appalled," one juror said later, "and therefore we asked for the stiffest

sentences possible."

6. In a famous television advertisement for an aftershave lotion, a commercial aired during televised

sports events and aimed at men, a woman in a revealing dress purrs, "There's something about an

Aqua Velva man."

7. The Da Vinci Code is the number-one best-selling book in America. So I really ought to read it.

8. I know she misses me. I miss her, too. So I'm going to e-mail her some photos of me that were taken

just yesterday. I know she'll like that.

*9. Dear Membership Committee: When I heard that the Davis family's application for membership in the

Country Club was rejected because some members did not like their religion, I was shocked. I was

furious. So I have decided to resign from the Country Club as of today.

*10. Now all the guys at school are driving pickup trucks. The bigger the better! Everybody in our school

has got one, and I feel that I've got to be part of this. So I am going to buy a pickup truck.

IV. YOUR OWN THINKING LAB

1 . For each of the following claims, construct an argument that attempts to support it but fails by virtue

of committing at least one of the fallacies discussed in this chapter.

A. Members of the Board, I think it's time now for me to be promoted.

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11.1 Argument as a Relation between Propositions

In this chapter and the next, we’ll return to a topic briefly addressed in Chapter 5: propositional
arguments. Here we’ll have a close look at propositions, the building blocks of propositional
arguments. Consider

1 1. If the Earth is a planet, then it moves.
2. If the Earth does not move, then it is not a planet.

(1) is a propositional argument because it consists entirely in the relation between the proposi­
tions that make it up. Its premise and conclusion are compound propositions, which result
from logical connections established between two simple propositions: ‘The Earth is a planet’
and ‘The Earth moves.’ The connections ‘if … then … ‘ and ‘not’ are among the five types of
truth-functional connectives (or simply ‘connectives’) that we’ll study here-namely,

Truth-Functional Connectives

negation*
conjunction
disjunction
conditional
biconditional

Standard English Expression

notP
PandQ
either Por Q
if P,then Q
P if and only if Q

* As we’ll see, negation is called a ‘connective’ by courtesy.

Here we are using capital letters such as ‘P,’ •�• and ‘R’ as symbols or “dummies” for any propo­
sition. We’ll use other capital letters from ‘A’ to ‘O’ to translate propositions in English into
symbols, reserving P through W to represent non-specific propositions. Whenever possible,
we’ll pick the first letter of a word inside the proposition that we are to represent in symbols,
preferably a noun if available. For example, ‘If the Earth is a planet, then it moves’ may be
represented as ‘If E, then M’-where

E

M

The Earth is a planet
The Earth moves

We’ll resort to the same chosen symbol every time the proposition it symbolizes occurs again.
And if we have already used a certain letter to stand for a different proposition, then a letter of
another word, preferably a noun, in the proposition in question will serve. The argument form
of example (1) may now be represented by replacing each proposition occurring in its premise
and conclusion with a propositional symbol in this way, while momentarily retaining the con­
nective ‘if … then … ‘ in English. The resulting translation is

1 ‘ 1. If E, then M
2. If not M, then not E

Let’s now consider the following arguments with an eye toward translating their propositions
into symbols:

2 1. Ottawa is the capital of Canada.
2. It is not the case that Ottawa is not the capital of Canada.

3 1. Either Fido is in the house or he’s at the vet.
2. Fido is not in the house.
3. Fido is at the vet.

4 1. Jane works at the post office and Bob at the supermarket.
2. Bob works at the supermarket.

5 1. TV is amusing if and only if it features good comedies.
2. TV does not feature good comedies.
3. TV is not amusing.

Once we have translated the propositions into symbols, we obtain

2′ 1. 0

2. It is not the case that not 0

3′ 1. Either For E

2. NotF

3. E

4′ 1. J and B
2. B

5′ 1. A if and only if C
2. Not C
3. NotA

Although (2 1 ) through (s’) feature connectives, not all propositional argument forms do:
(6) doesn’t.

6 1. p

2. p

In ( 6), the propositional symbol ‘P’ stands for exactly the same proposition in the premise and in the

conclusion. Known as ‘identity,’ any argument with this form would of course be valid, since if its

premise were true, its conclusion could not be false. But this is not our present concern. Rather, in

this section we’ve considered propositional arguments and discovered that their premises and
conclusions often feature truth-functional connectives. So let’s now look more closely at these.

11.2 Simple and Compound Propositions

Any proposition that has at least one truth-functional connective is compound; otherwise, it is
simple. Consider

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7 Celine Dion is a singer and Russell Crowe is an actor.

This is a compound proposition, made up of the conjunction of two simple propositions,

8 Celine Dion is a singer.

9 Russell Crowe is an actor.

Conjunction is one of the five truth-functional connectives that we'll consider here-together

with negation, disjunction, material conditional, and material biconditional. For each connec­

tive, we'll introduce a symbol and provide a truth-value rule that will be used to determine the
truth value of whatever compound proposition is created by applying that connective. Since the

truth-value rule associated with each connective defines the connective, each of them is a
'truth-functional connective.' But for the most part, we'll refer to them simply as 'connectives.'

Here is the picture that will emerge:

BOX 1 ■ TRUTH-FUNCTIONAL CONNECTIVES

Connective In English In Symbols Symbol's Name

negation notP ~P tilde

conjunction PandQ P•Q dot

disjunction PorQ PvQ wedge

conditional if Pthen Q P:J Q horseshoe

bi conditional P if and only if Q P=Q triple bar

Before turning to each of these connectives, notice that there is always one connective

governing a compound proposition, called 'main connective.' By identifying the main connec­

tive, we determine what kind of compound proposition a given proposition is: a conjunction, a

negation, a disjunction, etc. Obviously, in cases where a compound proposition contains more

than one connective, it is crucial to be able to determine which connective is the main one.

Negation

Negation is a truth-functional connective standardly expressed in English by 'not,' and

symbolized by'-', the tilde. Negation can affect one proposition by itself. Even so, we'll refer to

it as a 'connective' by courtesy. In ordinary English, the expression for a negation may occur in

any part of a statement. When a negation is added to a simple proposition, that proposition

becomes compound. (10), which may be represented as (10') exemplifies this:

1 0 Russell Crowe is not an actor.

10' ~C

Here the simple proposition that has become compound by adding a negation is 'Russell Crow
is an actor.' In (10'), we've used the tilde to represent negation, and C for the simple proposition

affected by it. When possible, we'll use the first letter of an important word occurring in the

proposition we wish to represent in symbolic notation.

Propositions affected by negation could also be themselves compound. For example,

11 It is false that both Mars and Jupiter have water.

12 It is not the case that Mary is not at the library.

To represent propositions that are negations, the symbol for negation always precedes what is

negated. (12) is the negation of 'Mary is not at the library,' which is already a negation. So we

have a double negation: the negation of a proposition that's itself a negation, which we can

represent by the propositional formula

12'~ ~ L

Since the two negations cancel each other out, (12') is logically the same as

12" L

Any proposition or propositional formula affected by a negation is a compound proposition.

The 'truth-value rule' that defines negation, and can be used to determine the truth value of a

proposition (or propositional formula) that's affected by that connective, is:

A negation is true whenever the negated proposition is false.
A negation is false whenever the negated proposition is true.

When a proposition is the logical negation of another, the two could not both have the same

truth value: where 'P' is true,'~ P' is false; where 'P' is false,'~ P' is true. For example, (11) above,

which is true, is the negation of 'both Mars and Jupiter have water,' which is false. But (14)

below is not the negation of (13), since both propositions are false.

13 All orthodontists are tall.

14 No orthodontists are tall.

Now consider these:

15 Some orthodontists are not tall.

16 Some orthodontists are tall.

(15) is the negation of (13), and (16) is the negation of (14), for those pairs could not have the

same truth value. But propositions that are logically the same would have the same truth value.

For example, if (17) is true, (18) is also true.

17 Lincoln was assassinated.

18 It is not the case that Lincoln was not assassinated.

(18) is a case of double negation: it is the negation of 'Lincoln was not assassinated.'

Notice that propositions featuring expressions such as 'it is not true that,' 'it is false that,'

'it never happened that' are commonly negations-as are some propositions containing

prefixes such as 'in-,' 'un-,' and 'non-.' For example,

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19 My right to vote is inalienable.

Here 'inalienable' means 'not alienable.' (19) is logically the same as

19' My right to vote is not alienable.

Similarly, since 'unmarried' means 'not married,' (20) and (20') are also logically the same:

20 Condoleezza Rice is unmarried.

20' It is not the case that Condoleezza Rice is married.

But (21) is not a negation:

21 Unmarried couples are also eligible for the prize.

Here 'unmarried' is not being used to deny the whole proposition. It affects only the word

'couples.'
Finally, notice that although verbs such as 'miss,' 'violate,' 'fail,' and the like have a negative

meaning, they need not be taken to express negations.

Conjunction

Conjunction is a compound proposition created by a truth-functional connective standardly

expressed in English by 'and,' and in symbols by '• ', the dot. The connective for conjunction is

always placed between two propositions, each of which called a 'conjunct.' Conjuncts may

themselves be simple or compound propositions. Let's consider the conjunctions of some

simple propositions:

22 Mount Everest is in Tibet and Mont Blanc is in France.

23 Mars and Jupiter have water.

In symbols, these are

22' E • B

23' M •J

Recall (11) above:

11 It is false that both Mars and Jupiter have water.

The formula that represents this proposition is (11'), which has parentheses to indicate that

both M and J are under the scope of the negation.

11 '-(M • J)

We'll have more to say on the use of parentheses and other punctuation signs later. Now let's

consider why conjunction is a truth-functional connective: because it determines the truth
value of the compound proposition affected by it, given the values of its members and this

truth-value rule:

A conjunction is true if and only if its conjuncts are both true. Otherwise, a

conjunction is false.

(22) is true since both its conjuncts are in fact true. But if one conjunct is false and the other

true, or both are false, then a conjunction is false. Thus (23) is false, since for all we know, both

of its conjuncts are false. The following are also false:

24 Mount Everest is in Tibet and Mont Blanc is not in France.

25 Mount Everest is not in Tibet and Mont Blanc is not in France.

Since Mont Blanc is in France, the second disjunct in (24) is false, which makes the

conjunction false. In a conjunction, then, falsity is like an infection: if there's any at all, it
corrupts the whole compound. (Logical thinkers who are contemplating a career in politics

should keep this in mind!) In (25)1 both conjuncts are false, since each is the negation of a true

proposition. In symbols:

24'E•-B

25'-E •-B

Note also that, like (23), many conjunctions in ordinary language are abbreviated. For instance,

26 Rottweilers and Dobermans are fierce dogs.

This is just a shortened way of saying

27 Rottweilers are fierce dogs and Dobermans are fierce dogs.

Yet (28) is not short for a conjunction of two simple propositions, but is rather a single propo­

sition about a certain relation between some such dogs.

28 Some Rottweilers and Dobermans are barking at each other.

Another thing to notice is that conjunction, as a truth-functional connective, is commutative­

that is, the order of the conjuncts doesn't affect the truth value of the compound. Assuming that

(26) is true, the facts that make it true are exactly the same as those that make 'Dobermans are

fierce dogs and Rottweilers are fierce dogs' true, which are also the same that make (27) true.

However, we must be careful about this, since sometimes order matters. When it does, the

conjunction is not a truth-functional connective: for example,

29 He took off his shoes and got into bed.

The facts that make (29) true do not seem to be the same as those that make (30) true:

30 He got into bed and took off his shoes.

The order of events, and therefore of the conjuncts, does matter in these non-truth-functional

conjunctions-as it also does in (31) and (32).

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31 He saw her and said 'hello.'

32 He said 'hello' and saw her.

Finally, note that besides 'and,' there are a number of English expressions for conjunction,
including 'but,' 'however,' 'also', 'moreover,' 'yet,' 'while,' 'nevertheless,' 'even though,' and

'although.'

Disjunction

Disjunction, also a commutative connective, is a type of compound proposition created by the

truth-functional connective standardly expressed in English by 'or,' and in symbols by 'v', the
wedge. In representing a disjunction, the connective is placed between two propositions called
'disjuncts,' which may themselves be simple or compound propositions. Here are two disjunc­

tions, first in English and then in symbols:

33 Rome is in Italy or Rome is in Finland.

33' I v F

34 Rome is not in Italy or Paris is not in France.

34'-I v-F

(33) and (34) are disjunctions and thus compound propositions. Disjunction is a truth­
functional connective because it determines the truth value of the compound proposition it

creates on the basis of the values of its members and this truth-value rule:

A disjunction is false if and only if its disjuncts are both false. Otherwise, a

disjunction is true.

Given the above rule, at least one of the disjuncts must be true for the disjunction to be true.
So (33) is true, but (34) is false. (35) is also false, for both its disjuncts, both of them compound

propositions, are false:

35 Either snow tires are useful in the tropics and air conditioners are popular in Iceland,
or it is not the case that Penguins thrive in cold temperatures.

35' (S • A) v ~ P

Clearly, the conjunction (S • A) is false because both conjuncts are false, and – P is false because

it is the negation of P, which is true. Since both disjuncts in (35) are false, given the truth-value

rule for disjunction, (35) is false.

In addition to 'or,' disjunction can be expressed by 'either … or … ' and 'unless,' and other

locutions of our language. It is also sometimes found embedded in a negation in 'neither …

nor … '(where negation is the main connective). Thus these are also disjunctions:

36 She is the director of the project, unless the catalog is wrong.

36' Either she is the director of the project, or the catalog is wrong.

(37) is a shortened version of (37'):

37 Neither the CIA nor the FBI tolerates terrorists.

37' Neither the CIA tolerates terrorists nor the FBI tolerates terrorists.

Since 'neither … nor … ' is a common way to express the negation of a disjunction, (37) is log­

ically the same as (or equivalent to)

38 It is false that either the CIA tolerates terrorists or the FBI tolerates terrorists.

Thus both (37) and (38) may be symbolized as the negation of a disjunction:

38'-(CvF )

Note that here the main connective is negation, not disjunction. Furthermore, (37) and (38) are

logically equivalent to (39), which may be symbolized as

39 The CIA doesn't tolerate terrorists and the FBI doesn't tolerate terrorists.

39'- C • -F

Finally, a truth-functional disjunction may be inclusive, when both disjuncts could be true

('either P or Qor both'), or exclusive, when only one could be ('either P or Qbut not both'). This

book focuses on inclusive disjunction, whose truth-value rule is given above.

Material Conditional

Material conditional, a type of compound proposition also called 'material implication' or simply

'conditional,' is created by a truth-functional logical connective, standardly expressed in English

by 'if … then … ,' and in symbols by '::)', the horseshoe. For example,

40 If Maria is a practicing attorney, then she has passed the bar exam.

A conditional has two members: the proposition standardly preceded by 'if' is its antecedent,

and the one that follows 'then,' its consequent.

The conditional is a truth-functional connective because the value of the compound

proposition it creates is determined by the truth value of the antecedent and consequent,

together with this truth-value rule:

A material conditional is false if and only if its antecedent is true and its consequent
false. Otherwise, it is true.

Thus any conditional with a true consequent is true, and any conditional with a false

antecedent is true.

The two propositions in a conditional, which may themselves be either simple or

compound, stand in a hypothetical relationship, where neither antecedent nor consequent is

being asserted independently. Does (40) assert that Maria is a practicing attorney? No. Does it

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stand in a hypothetical relationship such that P's being true implies that Qis also true. To chal­

lenge a conditional, one has to show that its antecedent is true and its consequent false at once.

Notice that sometimes the 'then' that often introduces the consequent of a conditional sen­

tence may be left out. Moreover, besides 'if … then … ,' many other linguistic expressions can be

used in English to introduce one or the other part of a conditional sentence. Such expressions

may precede that sentence's consequent, its antecedent, or both-as shown in the examples

below, where double underlines mark the antecedent and single underlines the consequent:

Maria has passed the bar exam, provided she is a practicing attorney.
Supposing that Maria is a practicing attorney. she has passed the bar exam.
On the assumption that Maria is a practicing attorney. she has passed the bar exam.
Maria is a practicing attorney only if she has passed the bar exam.
That Maria is a practicing attorney implies that she has passed the bar exam.

We'll now translate these conditional sentences into our symbolic language, using 'M' to stand

for 'Maria is a practicing attorney' and 'E' for 'Maria has passed the bar exam.' Our formula rep­

resenting any of these propositions has 'M' for the antecedent and 'E' for the consequent. It

lists 'M' first, then the horseshoe symbol, and 'E' last:

40' M :J E

Here the rule is:

To translate a conditional sentence into the symbolic language, we must list its

antecedent first and its consequent last, whether or not these two parts occur in

the English sentence in that order.

Let's now translate the conditionals below into the symbolic language using this glossary:

N = The United States is a superpower
I = China is a superpower
C = China has agents operating in other countries
0 = The United States has agents operating in other countries

41 If China is a superpower, then China and the United States have agents operating in

other countries.

41' I :J (C • 0)

42 It is not the case that if the United States has agents operating in other countries,

then it is a superpower.

42' – (0 ::J N)

43 China has agents operating in other countries provided that the United States and
China are superpowers.

43'(N • I) ::JC

44 If the United States doesn't have agents operating in other countries, then it is not a
superpower.

44'- 0::J-N

45 That China has agents operating in other countries implies that either it is a super­
power or the United States is not a superpower.

45' C ::J (Iv -N)

46 If either the United States or China has agents operating in other countries, then
neither the United States nor China is a superpower.

46' (0 v C) ::J -(Nv I)

47 If the United States is not a superpower, then it either has or doesn't have agents
operating in other countries.

47' – N ::J (0 v -0)

Note that 'P unless Q'. could also be translated as 'if not P, then Q' Thus 'China is a member of
the UN unless it rejects the UN Charter' is equivalent to 'If China is not a member of the UN,
then it rejects the UN Charter.'

Necessary and Sufficient Conditions. In any material conditional, the antecedent expresses

a sufficient condition for the consequent, and the consequent a necessary condition for the
antecedent. Thus another way of saying 'If P, then Q'. is to say that P is sufficient for � and Q
is necessary for P. A necessary condition of some proposition P's being true is some state of
affairs without which P could not be true, but which is not enough all by itself to make P true.

In (40), Maria's having passed the bar exam is a necessary condition of her being a practicing
attorney (she could not be a practicing attorney if she had not passed it, though merely having
passed doesn't guarantee that she's practicing). A sufficient condition of some proposition Q'.s
being true is some state of affairs that is enough all by itself to make Q true, but which may not

be the only way to make Q true. In (40 ), Maria's being a practicing attorney is sufficient for her

having passed the bar exam (in the sense that the former guarantees the latter).

In a material conditional

■ Its consequent is a necessary (but not sufficient) condition for the truth of its antecedent.
■ Its antecedent is a sufficient (though not a necessary) condition for the truth of its

consequent.

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Material Biconditional

A material biconditional is a type of compound proposition, also called 'material equiva­

lence,' or simply 'biconditional,' created by the truth-functional connective standardly

expressed in English by 'if and only if,' and in symbols by '!!!!', the triple bar. Some other
English expressions for the biconditional connective are 'just in case,' 'is equivalent to,'

'when and only when,' and the abbreviation 'iff.' Each of the two members of a biconditional

could be either simple or compound. Here is a biconditional, in both English and symbols,

made up of simple propositions:

48 Dr. Baxter is the college's president if and only if she is the college's chief executive

officer.

48' B= 0

The truth value of the compound proposition the biconditional creates is determined by the

truth value of its members, together with this truth-value rule:

A material biconditional is true whenever its members have the same truth value­

that is, they are either both true or both false. Otherwise, a biconditional is false.

Given this rule, for a biconditional proposition to be true, the propositions making it up must

have the same truth value-that is, be both true or both false. When a biconditional's members

have different truth values, the biconditional is false. (49) through (51) are false, for each

features propositions with different truth values.

49 The Himalayas are a chain of mountains if and only if the Pope is the leader of the

Anglican Church.

50 London is in England just in case Boston is in Bosnia.

51 Parrots are mammals if and only if cats are mammals.

By contrast, the following biconditionals are all true because in each case its members have the

same truth value:

52 Lincoln was assassinated if and only if Kennedy was assassinated.

53 Beijing is the capital of France just in case Bill Gates is poor.

54 That oaks are trees and tigers are felines are logically equivalent.

In any biconditional, each member is both a necessary and a sufficient condition of the other.

Thus in (48), Baxter's being the college's CEO is both a necessary and sufficient condition for

her being the college's president, and her being the college's president is both a necessary and

sufficient condition for her being the college's CEO. So a biconditional can be understood as a
conjunction of two conditionals. Thus we can represent (52) in either of these ways:

52' L=K

52" (L :::l K) • (K :::l L)

(5211

) is the conjunction of two conditionals whose antecedent and consequent imply each

other. That is why the material equivalence relation is called a 'biconditional,' and, obviously,

this connective is commutative.

BOX 2 ■ SUMMARY: COMPOUND PROPOSITIONS

■ Any proposition that is affected by a truth-functional connective is compound. Otherwise, it is
simple.

■ The truth value of a compound proposition is determined by factoring in: (1) the truth values