introduction to logic (chapter 1)

8/13/2019 Introduction to Logic (Chapter 1)

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Recognizing Arguments

Not all passages contain arguments. Because logic deals with arguments, it is important

to be able to distinguish passages that contain arguments from those that do not.

In general, a passage contains an argument if it purports to prove something; if it does

not do so, it does not contain an argument. Two conditions must be fulfilled for apassage to purport to prove something: (1 !t least one of the statements must claim

to present evidence or reasons. (" There must be a claim that the alleged evidence or

reasons supports or implies something#that is, a claim that something follows from

the alleged evidence. !s we have seen, the statements that claim to present the

evidence or reasons are the premises, and the statement that the evidence is claimed to

support or impl$ is the conclusion. It is not necessar$ that the premises present actual

evidence or true reasons nor that the premises actuall$ support the conclusion. But at

least the premises must claim to present evidence or reasons, and there must be aclaim that the evidence or reasons support or impl$ something.

The first condition e%presses a factual claim, and deciding whether it is fulfilled

usuall$ presents few problems. Thus, most of our attention will be concentrated on

whether the second condition is fulfilled. This second condition e%presses what is

called an inferential claim. The inferential claim is simpl$ the claim that the passage

e%presses a certain &ind of reasoning process#that something supports or implies

something or that something follows from something. 'uch a claim can be either

e%plicit or implicit. !n explicit inferential claim is usuall$ asserted b$ premise or conclusion indicator

words ( thus,)) since,)) because,)) hence,)) therefore,)) and so on . *%ample:

The human e$e can see a source of light that is as faint as an ordinar$ candle from

a distance of "+ &ilometers, through a nonabsorbing atmosphere. Thus, a powerful

searchlight directed from a new moon should be visible on earth with the

na&ed e$e.

( iane *. -apalia and 'all$ end&os /lds, Psychology

The word thus)) e%presses the claim that something is being inferred, so the passageis an argument.

!n implicit inferential claim e%ists if there is an inferential relationship between the

statements in a passage. *%ample:

The price reduction 0seen with the electronic calculator is the result of a technological

revolution. The calculator of the 1234s used integrated electronic circuits


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that contained about a do5en transistors or similar components on a single

chip. Toda$, mass6produced chips, onl$ a few millimeters s7uare, contain several

thousand such components.

(8obert '. Boi&ess and *dward *delson, Chemical Principles

The inferential relationship between the first statement and the other two constitutesan implicit claim that evidence supports something, so we are 9ustified in calling the

passage an argument. The first statement is the conclusion, and the other two are the

premises.

In deciding whether there is a claim that evidence supports or implies something,

&eep an e$e out for (1 indicator words and (" the presence of an inferential relationship

between the statements. In connection with these points, however, a word of

caution is in order. irst, the mere occurrence of an indicator word b$ no means

guarantees the presence of an argument. or e%ample, consider the following passages:'ince *dison invented the phonograph, there have been man$ technological

developments.

'ince *dison invented the phonograph, he deserves credit for a ma9or technological

development.

In the first passage the word since)) is used in a temporal sense. It means from the

time that.)) Thus, the first passage is not an argument. In the second passage since)) is

used in a logical sense, and so the passage is an argument.

The second cautionar$ point is that it is not alwa$s eas$ to detect the occurrenceof an inferential relationship between the statements in a passage, and the reader

ma$ have to review a passage several times before ma&ing a decision. In reaching

such a decision, it sometimes helps to mentall$ insert the word therefore)) before the

various statements to see whether it ma&es sense to interpret one of them as following

from the others. *ven with this mental aid, however, the decision whether a passage

contains an inferential relationship (as well as the decision about indicator words

often involves a heav$ dose of interpretation. !s a result, not ever$one will agree

about ever$ passage. 'ometimes the onl$ answer possible is a conditional one: If thispassage contains an argument, then these are the premises and that is the conclusion.))

To assist in distinguishing passages that contain arguments from those that do not,

let us now investigate some t$pical &inds of nonarguments. These include simple

noninferential passages, e%positor$ passages, illustrations, e%planations, and conditional

statements.


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Simple Noninferential Passages

'imple noninferential passages are unproblematic passages that lac& a claim that

an$thing is being proved. 'uch passages contain statements that could be premises or

conclusions (or both , but what is missing is a claim that an$ potential premise supports

a conclusion or that an$ potential conclusion is supported b$ premises. -assagesof this sort include warnings, pieces of advice, statements of belief or opinion, loosel$

associated statements, and reports.

! warning is a form of e%pression that is intended to put someone on guard

against a dangerous or detrimental situation. *%amples:

atch out that $ou don)t slip on the ice.

hatever $ou do, never confide personal secrets to Blabbermouth Bob.

If no evidence is given to prove that such statements are true, then there is no argument.

! piece of advice is a form of e%pression that ma&es a recommendation aboutsome future decision or course of conduct. *%amples:

ou should &eep a few things in mind before bu$ing a used car. Test drive the car

at var$ing speeds and conditions, e%amine the oil in the cran&case, as& to see

service records, and, if possible, have the engine and power train chec&ed b$

a mechanic.

Before accepting a 9ob after class hours, I would suggest that $ou give careful

consideration to $our course load. ill $ou have sufficient time to prepare for

classes and tests, and will the 9ob produce an e%cessive drain on $our energies< !s with warnings, if there is no evidence that is intended to prove an$thing, then there

is no argument.

! statement of belief or opinion is an e%pression about what someone happens

to believe or thin& at a certain time. *%amples:

e believe that our compan$ must develop and produce outstanding products

that will perform a great service or fulfill a need for our customers. e believe

that our business must be run at an ade7uate profit and that the services and

products we offer must be better than those offered b$ competitors.(8obert . =a$ and *dmund 8. >ra$, Introduction to 'ocial 8esponsibilit$))

I thin& a nation such as ours, with its high moral traditions and commitments, has

a further responsibilit$ to &now how we became drawn into this conflict, and

to learn the lessons it has to teach us for the future.

(!lfred =assler, Saigon, U.S.A.


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Because neither of these authors ma&es an$ claim that his belief or opinion is supported

b$ evidence, or that it supports some conclusion, there is no argument.

Loosely associated statements ma$ be about the same general sub9ect, but the$

lac& a claim that one of them is proved b$ the others. *%ample:

Not to honor men of worth will &eep the people from contention; not to valuegoods that are hard to come b$ will &eep them from theft; not to displa$ what

is desirable will &eep them from being unsettled of mind.

(?ao6T5u, Thoughts from the Tao Te Ching

Because there is no claim that an$ of these statements provides evidence or reasons

for believing another, there is no argument.

! report consists of a group of statements that conve$ information about some

topic or event. *%ample:

*ven though more of the world is immuni5ed than ever before, man$ old diseaseshave proven 7uite resilient in the face of changing population and environmental

conditions, especiall$ in the developing world. New diseases, such as !I ',

have ta&en their toll in both the North and the 'outh.

('teven ?. 'piegel, World Politics in a Ne !ra

These statements could serve as the premises of an argument; but because the author

ma&es no claim that the$ support or impl$ an$thing, there is no argument. !nother

t$pe of report is the news report:

! powerful car bomb blew up outside the regional telephone compan$ head7uartersin @edellin, in9uring "A people and causing millions of dollars of damage to

nearb$ buildings, police said. ! police statement said the 12 6pound bomb was

pac&ed into a mil& churn hidden in the bac& of a stolen car.

(Newspaper clipping

!gain, because the reporter ma&es no claim that these statements impl$ an$thing,

there is no argument.

/ne must be careful, though, with reports a"out arguments:

The !ir orce faces a serious shortage of e%perienced pilots in the $ears ahead,because repeated overseas tours and the allure of high pa$ing 9obs with commercial

airlines are winning out over lucrative bonuses to sta$ in the service,))

sa$s a prominent !ir orce official.

(Newspaper clipping

-roperl$ spea&ing, this passage is not an argument, because the author of the passage


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does not claim that an$thing is supported b$ evidence. 8ather, the author reports the

claim b$ the !ir orce official that something is supported b$ evidence. If such passages

are interpreted as containing)) arguments, it must be made clear that the argument

is not the author)s but one made b$ someone about whom the author is

reporting.E pository Passages

!n e pository passage is a &ind of discourse that begins with a topic sentence

followed b$ one or more sentences that develop the topic sentence. If the ob9ective is

not to prove the topic sentence but onl$ to e%pand it or elaborate it, then there is no

argument. *%amples:

There are three familiar states of matter: solid, li7uid, and gas. 'olid ob9ects ordinaril$

maintain their shape and volume regardless of their location. ! li7uid

occupies a definite volume, but assumes the shape of the occupied portion of its container. ! gas maintains neither shape nor volume. It e%pands to fill completel$

whatever container it is in.

(Cohn . =ill and oris D. Dolb, Chemistry for Changing Times, +th ed.

There is a st$li5ed relation of artist to mass audience in the sports, especiall$ in

baseball. *ach pla$er develops a st$le of his own#the swagger as he steps to

the plate, the uni7ue windup a pitcher has, the clean6swinging and hard6driving

hits, the precision 7uic&ness and grace of infield and outfield, the sense of surplus

power behind whatever is done.(@a% ?erner, America as a Ci#ili$ation

In each passage the topic sentence is stated first, and the remaining sentences merel$

develop and flesh out this topic sentence. These passages are not arguments because

the$ lac& an inferential claim. =owever, e%positor$ passages differ from simple

noninferential

passages (such as warnings and pieces of advice in that man$ of them can

also be ta&en as arguments. If the purpose of the subse7uent sentences in the passage

is not onl$ to flesh out the topic sentence but also to prove it, then the passage is anargument. *%ample:

'&in and the mucous membrane lining the respirator$ and digestive tracts serve as

mechanical barriers to entr$ b$ microbes. /il gland secretions contain chemicals

that wea&en or &ill bacteria on s&in. The respirator$ tract is lined b$ cells that

sweep mucus and trapped particles up into the throat, where the$ can be swallowed.


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The stomach has an acidic p=, which inhibits the growth of man$ t$pes

of bacteria.

('$lvia '. @ader. %uman &iology, Eth ed.

In this passage the topic sentence is stated first, and the purpose of the remaining

sentences is not onl$ to sho ho the s&in and mucous membranes serve as barriersto microbes but to pro#e that the$ do this. Thus, the passage can be ta&en as both an

e%positor$ passage and an argument.

In deciding whether an e%positor$ passage should be interpreted as an argument,

tr$ to determine whether the purpose of the subse7uent sentences in the passage is

merel$ to develop the topic sentence or also to prove it. In borderline cases, as&

$ourself whether the topic sentence ma&es a claim that ever$one accepts or agrees

with. If it does, the passage is probabl$ not an argument. In real life situations authors

rarel$ tr$ to prove something that ever$one alread$ accepts. =owever, if the topicsentence ma&es a claim that man$ people do not accept or have never thought about,

then the purpose of the remaining sentences ma$ be both to prove the topic sentence

as well as to develop it. If this be so, the passage is an argument.

inall$, if even this procedure $ields no definite answer, the onl$ alternative ma$

be to sa$ that if the passage is ta&en as an argument, then the first statement is the

conclusion and the others are the premises.

!llustrations

!n illustration consists of a statement about a certain sub9ect combined with areference

to one or more specific instances intended to e%emplif$ that statement. Illustrations

are often confused with arguments because man$ of them contain indicator

words such as thus.)) *%amples:

Fhemical elements, as well as compounds, can be represented b$ molecular formulas.

Thus, o%$gen is represented b$ /",)) water b$ ="/,)) and sodium

chloride b$ NaFl.))

henever a force is e%erted on an ob9ect, the shape of the ob9ect can change. or e%ample, when $ou s7uee5e a rubber ball or stri&e a punching bag with $our

fist, the ob9ects are deformed to some e%tent.

(8a$mond !. 'erwa$, Physics 'or Scientists and !ngineers, Eth ed.

These selections are not arguments because the$ ma&e no claim that an$thing is being

proved. In the first selection, the word thus)) indicates how something is done#


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namel$, how chemical elements and compounds can be represented b$ formulas. In

the second selection, the e%ample cited is intended to give concrete meaning to the

notion of a force changing the shape of something. It is not intended primaril$ to

prove that a force can change the shape of something.

=owever, as with e%positor$ passages, man$ illustrations can be ta&en as arguments.'uch arguments are often called arguments from e ample. =ere is an instance

of one:

ater is an e%cellent solvent. It can dissolve a wide range of materials that will not

dissolve in other li7uids. or e%ample, salts do not dissolve in most common

solvents, such as gasoline, &erosene, turpentine and cleaning fluids. But man$

salts dissolve readil$ in water. 'o do a variet$ of nonionic organic substances,

such as sugars and alcohols of low molecular weight.

(8obert '. Boi&ess and *dward *delson, Chemical PrinciplesIn this passage the e%amples that are cited can be interpreted as providing evidence

that water can dissolve a wide range of materials that will not dissolve in other li7uids.

Thus, the passage can be ta&en as both an illustration and an argument, with the

second sentence being the conclusion.

In deciding whether an illustration should be interpreted as an argument one must

determine whether the passage merel$ shows how something is done or what

something

means, or whether it also purports to prove something. In borderline cases ithelps to note whether the claim being illustrated is one that practicall$ ever$one

accepts or agrees with. If it is, the passage is probabl$ not an argument. !s we have

alread$ noted, in real life situations authors rarel$ attempt to prove what ever$one

alread$ accepts. But if the claim being illustrated is one that man$ people do not

accept or have never thought about, then the passage ma$ be interpreted as both an

illustration and an argument.

Thus, in reference to the first two e%amples we considered, most people are aware

that elements and compounds can be e%pressed b$ formulas#practicall$ ever$one&nows that water is ="/#and most people &now that forces distort things#that

running into a tree can cause a dent in the car bumper. But people ma$ not be aware

of the fact that water dissolves man$ things that other solvents will not dissolve. This

is one of the reasons for evaluating the first two e%amples as mere illustrations and the

last one as an argument.


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E planations

/ne of the most important &inds of nonargument is the e%planation. !n e planation

is a group of statements that purports to shed light on some event or phenomenon.

The event or phenomenon in 7uestion is usuall$ accepted as a matter of fact.

*%amples:The Challenger spacecraft e%ploded after liftoff because an /6ring failed in one of

the booster roc&ets.

The s&$ appears blue from the earth)s surface because light ra$s from the sun are

scattered b$ particles in the atmosphere.

Fows can digest grass, while humans cannot, because their digestive s$stems contain

en5$mes not found in humans.

*ver$ e%planation is composed of two distinct components: the e%planandum and

e%planans. The e planandum is the statement that describes the event or phenomenonto be e%plained, and the e planans is the statement or group of statements that

purports to do the e%plaining. In the first e%ample above, the e%planandum is the

statement The Challenger spacecraft e%ploded after liftoff,)) and the e%planans is !n

/6ring failed in one of the booster roc&ets.))

*%planations are sometimes mista&en for arguments because the$ often contain the

indicator word because.)) et e%planations are not arguments because in an

e%planation the purpose of the e%planans is to shed light on, or to ma&e sense of, the

e%planandum event#not to prove that it occurred. In other words, the purpose of thee%planans is to show hy something is the case, while in an argument, the purpose of

the premises is to prove that something is the case.

In the first e%ample above, the fact that the Challenger e%ploded is &nown to

ever$one. The statement that an /6ring failed in one of the booster roc&ets is not

intended to prove that the spacecraft e%ploded but rather to show hy it e%ploded. In

the second e%ample, the fact that the s&$ is blue is readil$ apparent. The intention of

the passage is to e%plain hy it appears blue#not to prove that it appears blue.

'imilarl$, in the third e%ample, virtuall$ ever$one &nows that people cannot digestgrass. The intention of the passage is to e%plain hy this is true.

Thus, to distinguish e%planations from arguments, identif$ the statement that is

either the e%planandum or the conclusion (usuall$ this is the statement that precedes

the word because)) . If this statement describes an accepted matter of fact, and if the

remaining statements purport to shed light on this statement, then the passage is an


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e%planation.

This method wor&s for practicall$ all passages that are either e%planations or arguments

(but not both . =owever, as with e%positor$ passages and illustrations, there

are some passages that can be interpreted as both e%planations and arguments.

*%ample:omen become into%icated b$ drin&ing a smaller amount of alcohol than men

because men metaboli5e part of the alcohol before it reaches the bloodstream

whereas women do not.

The purpose of this passage could be to prove the first statement to those people who

do not accept it as fact, and to shed light on that fact to those people who do accept

it. !lternatel$, the passage could be intended to prove the first statement to a single

person who accepts its truth on blind faith or incomplete e%perience, and simultaneousl$

to shed light on this truth. Thus, the passage can be correctl$ interpreted as bothan e%planation and an argument.

-erhaps the greatest problem confronting the effort to distinguish e%planations

from arguments lies in determining whether something is an accepted matter of fact.

/bviousl$ what is accepted b$ one person ma$ not be accepted b$ another. Thus, the

effort often involves determining which person or group of people the passage is

directed to#the intended audience. 'ometimes the source of the passage (te%tboo&,

newspaper, technical 9ournal, etc. will decide the issue. But when the passage is ta&en

totall$ out of conte%t, this ma$ prove impossible. In those circumstances the onl$possible answer ma$ be to sa$ that if the passage is an argument, then such6and6such

is the conclusion and such6and6such are the premises.

"onditional Statements

! conditional statement is an if . . . then . . .)) statement; for e%ample:

If air is removed from a solid closed container, then the container will weigh less

than it did.

*ver$ conditional statement is made up of two component statements. The component

statement immediatel$ following the if)) is called the antecedent, and the onefollowing the then)) is called the conse#uent. (/ccasionall$, the word then)) is left

out, and occasionall$ the order of antecedent and conse7uent is reversed. In the

above e%ample the antecedent is !ir is removed from a solid closed container,)) and

the conse7uent is The container will weigh less than it did.)) This e%ample asserts a

causal connection between the air being removed and the container weighing less.


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=owever, not all conditional statements e%press causal connections. The statement If

$ellow fever is an infectious disease, then the allas Fowbo$s are a football team)) is

9ust as much a conditional statement as the one about the closed container.

Fonditional statements are not arguments, because the$ fail to meet the criteria

given earlier. In an argument, at least one statement must claim to present evidence,and there must be a claim that this evidence implies something. In a conditional

statement, there is no claim that either the antecedent or the conse7uent presents

evidence. In other words, there is no assertion that either the antecedent or the

conse7uent is true. 8ather, there is onl$ the assertion that if the antecedent is true, then

so is the conse7uent. /f course, a conditional statement as a whole ma$ present

evidence because it asserts a relationship between statements. et when conditional

statements are ta&en in this sense, there is still no argument, because there is then no

separate claim that this evidence implies an$thing.'ome conditional statements are similar to arguments, however, in that the$ e%press

the outcome of a reasoning process. !s such, the$ ma$ be said to have a certain

inferential content. Fonsider the following:

If both 'aturn and Granus have rings, then 'aturn has rings.

If iron is less dense than mercur$, then it will float in mercur$.

The lin& between the antecedent and conse7uent of these conditional statements

resembles the inferential lin& between the premises and conclusion of an argument.

et there is a difference because the premises of an argument are claimed to be true,whereas no such claim is made for the antecedent of a conditional statement.

!ccordingl$, these conditional statements are not arguments.H et their inferential

content ma$ be ree%pressed to form arguments:

Both 'aturn and Granus have rings.

Therefore, 'aturn has rings.

Iron is less dense than mercur$.

Therefore, iron will float in mercur$.

inall$, while no single conditional statement is an argument, a conditional statementma$ serve as either the premise or the conclusion (or both of an argument, as

the following e%amples illustrate:

If cigarette companies publish warning labels, then smo&ers assume the ris& of

smo&ing.

Figarette companies do publish warning labels.


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Therefore, smo&ers assume the ris& of smo&ing.

HIn sa$ing this we are temporaril$ ignoring the possibilit$ of these statements being

enthymemes. !s we will see in Fhapter A, an enth$meme is an argument in which a

premise or conclusion (or both is implied but not stated. If, to the second e%ample, we

add the premise Iron is less dense than mercur$)) and the conclusion Therefore, ironwill float in mercur$,)) we have a complete argument. To decide whether a conditional

statement is an enth$meme, we must be familiar with the conte%t in which it occurs.

If ban&s ma&e bad loans, then the$ will be threatened with collapse.

If ban&s are threatened with collapse, then the ta%pa$er will come to the rescue.

Therefore, if ban&s ma&e bad loans, then the ta%pa$er will come to the rescue.

The relation between conditional statements and arguments ma$ now be summari5ed

as follows:

1. ! single conditional statement is not an argument.". ! conditional statement ma$ serve as either the premise or the conclusion (or both

of an argument.

. The inferential content of a conditional statement ma$ be ree%pressed to form an

argument.

The first two rules are especiall$ pertinent to the recognition of arguments. !ccording

to the first rule, if a passage consists of a single conditional statement, it is not an

argument. But if it consists of a conditional statement together with some other

statement, then, b$ the second rule, it may be an argument, depending on such factorsas the presence of indicator words and an inferential relationship between the

statements.

Fonditional statements are especiall$ important in logic because the$ e%press the

relationship between necessar$ and sufficient conditions. A is said to be a sufficient

condition for & whenever the occurrence of A is all that is needed for the occurrence

of &. or e%ample, being a dog is a sufficient condition for being an animal. /n the

other hand, & is said to be a necessar$ condition for A whenever A cannot occur

without the occurrence of &. Thus, being an animal is a necessar$ condition for beinga dog. These relationships are e%pressed in the following conditional statements:

If ( is a dog, then ( is an animal.

If ( is not an animal, then ( is not a dog.

The first statement sa$s that being a dog is a sufficient condition for being an animal

and the second that being an animal is a necessar$ condition for being a dog. =owever,


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a little reflection reveals that these two statements sa$ e%actl$ the same thing.

Thus each e%presses in one wa$ a necessar$ condition and in another wa$ a sufficient

condition. The terminolog$ of sufficient and necessar$ conditions will be used in later

chapters to e%press definitions and causal connections.

SummaryIn deciding whether a passage contains an argument, one should loo& for three things:

(1 indicator words such as therefore,)) since,)) because,)) and so on; (" an inferential

relationship between the statements; and ( t$pical &inds of nonarguments. But

remember that the mere occurrence of an indicator word does not guarantee the

presence of an argument. /ne must chec& to see that the statement identified as the

conclusion is intended to be supported b$ one or more of the other statements. !lso

&eep in mind that in man$ arguments that lac& indicator words, the conclusion is

the first statement. urthermore it helps to mentall$ insert the word therefore))before the various statements before deciding that a statement should be interpreted

as a conclusion. The t$pical &inds of nonarguments that we have surve$ed are as

follows:

warnings

pieces of advice

statements of belief

statements of opinion

loosel$ associated statementsreports

e%positor$ passages

illustrations

e%planations

conditional statements

Deep in mind that these &inds of nonargument are not mutuall$ e%clusive, and that,

for e%ample, one and the same passage can sometimes be interpreted as both a report

and a statement of opinion, or as both an e%positor$ passage and an illustration. Theprecise &ind of nonargument a passage might be is nowhere near as important as

correctl$ deciding whether or not it is an argument.

!fter wor&ing the e%ercises in this section, $ou ma$, if $ou wish, proceed directl$

to 'ection 1.3 ( *%tended !rguments)) .

E$ER"!SE %.&


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I. etermine which of the following passages are arguments. or those that are,

identif$ the conclusion. or those that are not, attempt to determine the &ind of

nonarguments.

J1. omen tend to have higher pitched voices than men because the$ have

shorter vocal chords. 'horter vocal chords vibrate at a higher fre7uenc$ thanlonger ones.

". If public education fails to improve the 7ualit$ of instruction in both primar$

and secondar$ schools, then it is li&el$ that it will lose additional students to

the private sector in the $ears ahead.

. reedom of the press is the most important of our constitutionall$ guaranteed

freedoms. ithout it, our other freedoms would be immediatel$ threatened.

urthermore, it provides the fulcrum for the advancement of new freedoms.

JE. ater is a good solvent for man$ different substances, and it pic&s them upas it moves through the environment. Thus, rain water flowing over and

under the ground dissolves minerals such as limestone.

(>ilbert Fastellan et al., The World of Chemistry

A. It is strongl$ recommended that $ou have $our house inspected for termite

damage at the earliest possible opportunit$.

3. 'hut the cage door, $ou foolK The lions are escaping into the streetsK

J+. If the earth)s magnetic field disappears, then the Lan !llen radiation belt will

be destro$ed. If the Lan !llen radiation belt is destro$ed, then intense cosmicra$s will bombard the earth. Therefore, if the earth)s magnetic field disappears,

then intense cosmic ra$s will bombard the earth.

. ictional characters behave according to the same ps$chological probabilities

as real people. But the characters of fiction are found in e%otic dilemmas that

real people hardl$ encounter. Fonse7uentl$, fiction provides us with the opportunit$

to ponder how people react in uncommon situations, and to deduce

moral lessons, ps$chological principles, and philosophical insights from their

behavior.( C.8. @cFuen and !.F. in&ler, )eadings for Writers, Eth edition

2. I believe that it must be the polic$ of the Gnited 'tates to support free peoples

who are resisting attempted sub9ugation b$ armed minorities or b$ outside

pressures. I believe that we must assist free peoples to wor& out their own

destinies in their own wa$. I believe that our help should be primaril$ through


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economic and financial aid, which is essential to economic stabilit$ and orderl$

political processes.

(-resident Truman, !ddress to Fongress, 12E+

J14. ive college students who were accused of snea&ing into the Fincinnati Moo

and tr$ing to ride the camels pleaded no contest to criminal trespass $esterda$.The students scaled a fence to get into the 5oo and then climbed another

fence to get into the camel pit before securit$ officials caught them, 5oo

officials said.

(Newspaper clipping

11. @ortalit$ rates for women undergoing earl$ abortions, where the procedure

is legal, appear to be as low as or lower than the rates for normal childbirth.

Fonse7uentl$, an$ interest of the state in protecting the woman from an

inherentl$ ha5ardous procedure, e%cept when it would be e7uall$ dangerousfor her to forgo it, has largel$ disappeared.

( Custice Blac&mun, )oe #. Wade

1". The pace of reading, clearl$, depends entirel$ upon the reader. =e ma$ read

as slowl$ or as rapidl$ as he can or wishes to read. If he does not understand

something, he ma$ stop and reread it, or go in search of elucidation before

continuing. The reader can accelerate his pace when the material is eas$ or

less than interesting, and can slow down when it is difficult or enthralling. If

what he reads is moving he can put down the boo& for a few moments andcope with his emotions without fear of losing an$thing.

(@arie inn, The Plug*In +rug

J1 . Fancer is not one disease, but man$. 'ome forms are particularl$ susceptible

to radiation therap$. 8adiation is carefull$ aimed at the cancerous tissue, and

e%posure of normal cells is minimi5ed. If the cancer cells are &illed b$ the

destructive effects of the radiation, the malignanc$ is halted.

(Cohn . =ill and oris D. Dolb, Chemistry for Changing Times, +th edition

1E. ?ions at Druger National -ar& in 'outh !frica are d$ing of tuberculosis. !ll of the lions in the par& ma$ be dead within ten $ears because the disease is

incurable, and the lions have no natural resistance,)) said the deput$ director

of the epartment of !griculture.

(Newspaper clipping

1A. *conomics is of practical value in business. !n understanding of the overall


15/75

operation of the economic s$stem puts the business e%ecutive in a better

position to formulate policies. The e%ecutive who understands the causes

and conse7uences of inflation is better e7uipped during inflationar$ periods

to ma&e more intelligent decisions than otherwise.

(Fampbell 8. @cFonnell, !conomics, th edition J13. Bear one thing in mind before $ou begin to write $our paper: amous literar$

wor&s, especiall$ wor&s regarded as classics, have been thoroughl$ studied

to the point where prevailing opinion on them has assumed the character of

orthodo%$.

(C.8. @cFuen and !.F. in&ler, )eadings for Writers, Eth edition

1+. oung people at universities stud$ to achieve &nowledge and not to learn a

trade. e must all learn how to support ourselves, but we must also learn

how to live. e need a lot of engineers in the modern world, but we do notwant a world of modern engineers.

( inston Fhurchill, A Churchill )eader, ed. Folin 8. Foote

1 . No business concern wants to sell on credit to a customer who will prove

unable or unwilling to pa$ his or her account. Fonse7uentl$, most business

organi5ations include a credit department which must reach a decision on the

credit worthiness of each prospective customer.

( alter B. @eigs and 8obert . @eigs, Accounting

J12. or organisms at the sea surface, sin&ing into deep water usuall$ meansdeath. -lant cells cannot photos$nthesi5e in the dar& depths. ishes and other

animals that descend lose contact with the main surface food suppl$ and

themselves become food for strange deep6living predators.

( avid =. @ilne, arine -ife and the Sea

"4. 'ince the 12A4s a malad$ called whirling disease has invaded G.'. fishing

streams, fre7uentl$ attac&ing rainbow trout. ! parasite deforms $oung fish,

which often chase their tails before d$ing, hence the name.

( Trout isease#! Turn for the orse,)) National eographic "1. achshunds are ideal dogs for small children, as the$ are alread$ stretched

and pulled to such a length that the child cannot do much harm one wa$ or

the other.

(8obert Benchle$, 7uoted in Cold Noses and Warm %earts

J"". !toms are the basic building bloc&s of all matter. The$ can combine to form


16/75

molecules, whose properties are generall$ ver$ different from those of the

constituent atoms. Table salt, for e%ample, a simple chemical compound

formed from chlorine and sodium, resembles neither the poisonous gas nor

the highl$ reactive metal.

( ran& C. Blatt, Principles of Physics, "nd edition" . The coarsest t$pe of humor is the practical /o0e1 pulling awa$ the chair from

the dignitar$)s lowered bottom. The victim is perceived first as a person of

conse7uence, then suddenl$ as an inert bod$ sub9ect to the laws of ph$sics:

authorit$ is debun&ed b$ gravit$, mind b$ matter; man is degraded to a

mechanism.

(!rthur Doestler, 2anus1 A Summing Up

"E. If a man holding a belief which he was taught in childhood or persuaded of

afterwards &eeps down and pushes awa$ an$ doubts which arise about it inhis mind, purposel$ avoids the reading of boo&s and the compan$ of men

that call in 7uestion or discuss it, and regards as impious those 7uestions

which cannot easil$ be as&ed without disturbing it#the life of that man is

one long sin against man&ind.

( . D. Flifford, The *thics of Belief))

J"A. It is usuall$ eas$ to decide whether or not something is alive. This is because

living things share man$ common attributes, such as the capacit$ to e%tract

energ$ from nutrients to drive their various functions, the power to activel$respond to changes in their environment, and the abilit$ to grow, to differentiate,

and to reproduce.

( onald Loet and Cudith >. Loet, &iochemistry, "nd edition

"3. ords are slipper$ customers. The full meaning of a word does not appear

until it is placed in its conte%t. . . . !nd even then the meaning will depend

upon the listener, upon the spea&er, upon their entire e%perience of the language,

upon their &nowledge of one another, and upon the whole situation.

(F. Fherr$, 3n %uman Communication"+. =a$dn developed the string 7uartet from the eighteenth centur$ di#ertimento,

giving more substance to the light, popular form and scoring it for

two violins, a viola, and a cello. =is eight$6three 7uartets, written over the

course of his creative lifetime, evolved slowl$ into a sophisticated form. Together

the$ constitute one of the most important bodies of chamber music


17/75

literature.

(8obert =ic&o&, !xploring usic

J" . ! person never becomes trul$ self6reliant. *ven though he deals effectivel$

with things, he is necessaril$ dependent upon those who have taught him to

do so. The$ have selected the things he is dependent upon and determinedthe &inds and degrees of dependencies.

(B. . '&inner, &eyond 'reedom and +ignity

"2. There is no doubt that some businessmen conspire to shorten the useful life

of their products in order to guarantee replacement sales. There is, similarl$,

no doubt that man$ of the annual model changes with which !merican

(and other consumers are increasingl$ familiar are not technologicall$

substantive.

(!lvin Toffler, 'uture Shoc0 4. If one &nows the plant life of an area, certain assumptions can be made about

the climate and the animals that will be found there. or e%ample, in grasslands

the animal life t$picall$ includes large mammalian herbivores, insects,

and birds.

(Ding, 'aunders, and allace, &iology1 The Science of -ife

J 1. In areas where rats are a problem, it is ver$ difficult to e%terminate themwith

bait poison. That)s because some rats eat enough poison to die but others eat

onl$ enough to become sic& and then learn to avoid that particular poisontaste in the future.

(8od -lotni&, Introduction to Psychology, Eth edition

". @en are less li&el$ to develop osteoporosis until later in life than women and

seldom suffer as severel$ because the$ have 4 percent more bone mass on

the average and don)t undergo the sudden drop in estrogen that occurs with

menopause.

(@att Flar&, The Falcium Fra5e,)) Ne s ee0

. Newspapers, radio, and television are essential for a democrac$. The$ are thecritical lin& between the people and their government. The$ provide information

and anal$sis about polic$ issues, and the$ also sensiti5e polic$ma&ers

to public opinion#which enables them to respond to the needs and desires

of the population. inall$, the media pla$ a critical role in reporting and

evaluating the decisions of government.


18/75

('tephen C. a$ne et al., The Politics of American o#ernment

J E. Nations are made in two wa$s, b$ the slow wor&ing of histor$ or the galvanic

force of ideas. @ost nations are made the former wa$, emerging slowl$ from

the mist of the past, graduall$ coalescing within concentric circles of shared

s$mpathies, with an accretion of consensual institutions. But a few nationsare formed and defined b$ the citi5ens) assent to a shared philosoph$.

(>eorge ill, ?ithuania and 'outh Farolina))

A. !lthough the plane mirror is perhaps the oldest optical instrument &nown to

man, it remains an important element in the modern arsenal of sophisticated

optical devices. or e%ample, the earth6moon laser6ranging e%periments, initiated

in 1232, rel$ on high67ualit$ reflectors.

( ran& C. Blatt, Principles of Physics, "nd edition

II. The following selections were originall$ submitted as letters to the editor ofnewspapers

and maga5ines. etermine which of them can, with good reason, be considered

arguments. In those that can, identif$ the conclusion.

J1. hat this countr$ needs is a return to the concept of swift and certain 9ustice.

If we need more courts, 9udges and prisons, then so be it. !nd as for capital

punishment, I sa$ let the punishment fit the crime. hen criminals behave

more li&e humans, then we can start to treat them more humanel$. In the

meantime, I would li&e to see the Night 'tal&ers of our societ$ swiftl$ e%ecutedrather than coddled b$ our courts and prisons.

( Cohn -earson

". The big problem with computers in elementar$ schools isn)t their minimal

educational value but the fact that the$ often replace science in the budget and

curriculum. /ur local -arent Teachers !ssociation is throwing awa$ science

e7uipment as ferventl$ as it raises mone$ for more computers. I use computers

e%tensivel$ in the college ph$sics classes I teach, so I appreciate their value in

communications and advanced computation. But in elementar$ schools, toomuch is being sacrificed so that children can have all those price$ beige bo%es.

(8oger >. Tobin

. Is there an$ countr$ in the world that worries more about its &ids having fun

in school, ma&ing lessons e%citing and relevant, and then is more disappointed

with the result than the Gnited 'tates< e thin& learning is li&e bu$ing


19/75

a car or smo&ing a cigarette. Cust get into the thing or draw a breath and $ou

will be effortlessl$ transported to lands of pleasure and e%citement.

(Fharles @. Breinin

JE. !fter reading $our cover stor$, I find that cable TL has simpl$ flooded our

airwaves with more se%, violence and teen6age pun& 9un&. Now our childrencan spend even less time stud$ing and we can spend more time in blan&space

stares at the idiot bo%. Fable would be fine with more educational

channels#and fewer cheap thrills aimed at narrow6minded bubble brains.

( Cac7ueline @urra$

A. In opposing obligator$ pra$er in the public schools, I am not deserting m$ god

(and I would li&e to thin& of m$self as a Fhristian . /n the contrar$, it is perfectl$

possible that I am thus serving m$ god, who I believe wants his children

to pra$ to him of their own free will and not because some legislator, who ma$or ma$ not be motivated b$ trul$ religious considerations, forces them to.

(-hilip . al&er

3. @$ own son returned from his public elementar$ school with a boo& on

dinosaurs loaned to him b$ his first6grade science)) teacher. It depicted the

beasts as fire6breathing dragons and said the Bible informs us the$ were this

wa$. >od help us to achieve an educated and scientificall$ literate societ$,

because these narrow6minded cretins won)t.

(Bruce 'trathdee J+. The poor 7ualit$ of parenting and the lac& in continuit$ of adult care provided

to man$ G.'. children contribute to a passivit$ and a sense of helplessness

that hobbles individuals for the remainder of their lives. Their subse7uent

unemplo$ment, lac& of education, and inabilit$ to ma&e necessar$ life6st$le

changes such as 7uitting an addiction can be attributed, in large part, to the

helplessness the$ learned from childhood.

( illiam C. @cFarth$

. ort$6one million !mericans cannot afford health insurance in this time of global capitalism. !t the same time, nine insurance e%ecutives earned more

than 14 million last $ear, according to a recent stud$. If this is the celebrated

triumph of capitalism over other forms of economic organi5ation, what e%actl$

did we win< =ave we gained the world at the cost of our soulsreece, or it originated in *g$pt. Flassical

culture did not originate in *g$pt. Therefore, classical culture originated in

>reece.

J1 . orld6renowned ph$sicist 'tephen =aw&ing sa$s that the condition of the

universe at the instant of the Big Bang was more highl$ ordered than it istoda$. In view of =aw&ing)s stature in the scientific communit$, we should

conclude that this description of the universe is correct.

1E. If !le%ander the >reat died from t$phoid fever, then he became infected in

India. !le%ander the >reat did die from t$phoid fever. Therefore, he became

infected in India.


31/75

1A. It seems li&el$ that $oung people will be at war with old people in another 1A

or "4 $ears. ou can see it coming in the numbers. In 1244 onl$ 1 percent of the

population was older than +A. Toda$ E percent of all !mericans are more than

+A $ears old, and in a few $ears it)s going to be A percent . . . 1 million people.

(Newspaper editorial J13. *ach element, such as h$drogen and iron, has a set of gaps#wavelengths that

it absorbs rather than radiates. 'o if those wavelengths are missing from the

spectrum, $ou &now that that element is present in the star $ou are observing.

(8ic& >ore, *$es of 'cience))

1+. Because the apparent dail$ movement which is common to both the planets

and the fi%ed stars is seen to travel from the east to the west, but the far slower

single movements of the single planets travel in the opposite direction from

west to east, it is therefore certain that these movements cannot depend onthe common movement of the world but should be assigned to the planets

themselves.

( Cohannes Depler, !pitomy of Copernican Astronomy

1 . 8eserves of coal in the Gnited 'tates have an energ$ e7uivalent times that

of oil and natural gas. /n a worldwide basis the multiple is about 14. B$

shifting to a coal6based econom$, we could satisf$ our energ$ re7uirements

for at least a centur$, probabl$ longer.

( illiam ?. @asterson and *mil C. 'lowins&i, Principles of Chemistry J12. hen the 8omans occupied *ngland, coal was burned. 'ince coal produces

7uite a bit of soot and sulfur dio%ide, there must have been da$s almost "444

$ears ago when the air in the larger towns was badl$ polluted.

('tanle$ >ed5elman, The Science and Wonders of the Atmosphere

"4. The graphical method for solving a s$stem of e7uations is an appro%imation,

since reading the point of intersection depends on the accurac$ with which

the lines are drawn and on the abilit$ to interpret the coordinates of the point.

(Darl C. 'mith and -atric& C. Bo$le, Intermediate Alge"ra for College Students"1. That 0the moons of Cupiter revolve in une7ual circles is manifestl$ deduced

from the fact that at the longest elongation from Cupiter it is never possible to

see two of these moons in con9unction, whereas in the vicinit$ of Cupiter the$

are found united two, three, and sometimes all four together.

(>alileo >alilei, The Starry essenger


32/75

J"". ?enses function b$ refracting light at their surfaces. Fonse7uentl$, their action

depends not onl$ on the shape of the lens surfaces, but also on the indices of

refraction of the lens material and the surrounding medium.

( ran& C. Blatt, Principles of Physics, "nd edition

" . >iven present growth rates in underdeveloped countries, the limited practiceof birth control, and the difficult$ of slowing the current growth momentum,

it can be said with virtual certaint$ that none of the people now reading this

boo& will ever live in a world where the population is not growing.

( C. Cohn -alen, Social Pro"lems

"E. The interpretation of the laws is the proper and peculiar province of the

courts. ! constitution is, in fact, and must be regarded b$ the 9udges, as a

fundamental law. It therefore belongs to them to ascertain its meaning, as

well as the meaning of an$ particular act proceeding from the legislative bod$.(!le%ander =amilton, 'ederalist Papers, No. +

J"A. The 'impson incident had shown me that a dog was &ept in the stables, and

$et, though someone had been in and had fetched out a horse, he had not

bar&ed enough to arouse the two lads in the loft. /bviousl$ the midnight

visitor was someone whom the dog &new well.

(!. Fonan o$le, emoirs of Sherloc0 %olmes

"3. *ternit$ is simultaneousl$ whole. But time has a before and an after. Therefore

time and eternit$ are not the same thing.(Thomas !7uinas, Summa Theologica

"+. /rdinar$ things that we encounter ever$ da$ are electricall$ neutral. Therefore,

since negativel$ charged electrons are a part of ever$thing, positivel$

charged particles must also e%ist in all matter.

( Cames *. Brad$ and >erard *. =umiston, eneral Chemistry

J" . !nimals that live on plant foods must eat large 7uantities of vegetation, and

this consumes much of their time. @eat eaters, b$ contrast, have no need to

eat so much or so often. Fonse7uentl$, meat6eating hominines 0earl$ humansma$ have had more leisure time available to e%plore and manipulate their

environment; li&e lions and leopards, the$ would have time to spend l$ing

around and pla$ing.

( illiam !. =aviland, Cultural Anthropology, th edition

"2. 0-s$chologists irtshafter and avis noted that the gl$cerol content of the


33/75

blood is related to the si5e of the fat cells 0in the bod$ . 'ince the si5e of the

fat cells would indicate something about the amount of stored fats, increases

in blood gl$cerol should indicate increases in bod$ weight.

(=erbert ?. -etri, oti#ation1 Theory and )esearch, "nd edition

4. Because the moon moves relative to the earth so that it returns to the sameposition overhead after about "A hours, there are two high and two low tides

at an$ point ever$ "A hours.

( ouglas F. >iancoli, The Ideas of Physics, rd edition

II. efine the following terms:

deductive argument

inductive argument

argument based on

mathematicsargument from definition

categorical s$llogism

h$pothetical s$llogism

dis9unctive s$llogism

argument from analog$

inductive generali5ation

prediction

argument from authorit$argument based on signs

causal inference

particular statement

general statement

III. !nswer true)) or false)) to the following statements:

1. In an inductive argument, it is intended that the conclusion contain more

information than the premises.

". In a deductive argument, the conclusion is not supposed to contain moreinformation than the premises.

. The form of argumentation the arguer uses ma$ allow one to determine

whether an argument is inductive or deductive.

E. The actual strength of the lin& between premises and conclusion ma$ allow

one to determine whether an argument is inductive or deductive.


34/75

A. ! geometrical proof is an e%ample of an inductive argument.

3. @ost arguments based on statistical reasoning are deductive.

+. If the conclusion of an argument follows merel$ from the definition of a word

used in a premise, the argument is deductive.

. !n argument that draws a conclusion about a thing based on that thing)ssimilarit$ to something else is a deductive argument.

2. !n argument that draws a conclusion that something is true because someone

has said that it is, is a deductive argument.

14. !n argument that presents two alternatives and eliminates one, leaving the

other as the conclusion, is an inductive argument.

11. !n argument that proceeds from &nowledge of a cause to &nowledge of an

effect is an inductive argument.

1". If an argument contains the phrase it definitel$ follows that,)) then we &nowfor certain that the argument is deductive.

1 . !n argument that predicts what will happen in the future, based upon what

has happened in the past, is an inductive argument.

1E. Inductive arguments alwa$s proceed from the particular to the general.

1A. eductive arguments alwa$s proceed from the general to the particular.

IL. -age through a boo&, maga5ine, or newspaper and find two arguments, one

inductive and the other deductive. Fop$ the arguments as written, giving the

appropriate reference. Then identif$ the premises and conclusion of each.%.- alidity, /rut(, Soundness,

Strengt(, "ogency

This section introduces the central ideas and terminolog$ re7uired to evaluate

arguments.

e have seen that ever$ argument ma&es two basic claims: a claim that evidence

or reasons e%ist and a claim that the alleged evidence or reasons support

something (or that something follows from the alleged evidence or reasons . The first

is a factual claim, the second an inferential claim. The evaluation of ever$ argumentcenters on the evaluation of these two claims. The most important of the two is the

inferential claim, because if the premises fail to support the conclusion (that is, if the

reasoning is bad , an argument is worthless. Thus we will alwa$s test the inferential

claim first, and onl$ if the premises do support the conclusion will we test the factual

claim (that is, the claim that the premises present genuine evidence, or are true . The


35/75

material that follows considers first deductive arguments and then inductive.

+eductive Arguments

The previous section defined a deductive argument as one in which the premises are

claimed to support the conclusion in such a wa$ that it is impossible for the premises

to be true and the conclusion false. If the premises do in fact support the conclusionin this wa$, the argument is said to be valid. Thus, a valid deductive argument is an

argument such that it is impossible for the premises to be true and the conclusion

false. In these arguments the conclusion follows with strict necessit$ from the premises.

Fonversel$, an invalid deductive argument is a deductive argument such that

it is possible for the premises to be true and the conclusion false. In invalid arguments

the conclusion does not follow with strict necessit$ from the premises, even though it

is claimed to.

!n immediate conse7uence of these definitions is that there is no middle groundbetween valid and invalid. There are no arguments that are almost)) valid and almost))

invalid. If the conclusion follows with strict necessit$ from the premises, the

argument is valid; if not, it is invalid.

To test an argument for validit$ we begin b$ assuming that all premises are true,

and then we determine if it is possible, in light of that assumption, for the conclusion

to be false. =ere is an e%ample:

!ll television networ&s are media companies.

NBF is a television networ&.Therefore, NBF is a media compan$.

In this argument both premises are actuall$ true, so it is eas$ to assume that the$ are

true. Ne%t we determine, in light of this assumption, if it is possible for the conclusion

to be false. Flearl$ this is not possible. If NBF is included in the group of television

networ&s (second premise and if the group of television networ&s is included in the

group of media companies (first premise , it necessaril$ follows that NBF is included

in the group of media companies (conclusion . In other words, assuming the premises

true and the conclusion false entails a strict contradiction. Thus the argument is valid.=ere is another e%ample:

!ll automa&ers are computer manufacturers.

Gnited !irlines is an automa&er.

Therefore, Gnited !irlines is a computer manufacturer.

In this argument, both premises are actuall$ false, but it is eas$ to assume that the$ are


36/75

true. *ver$ automa&er could have a corporate division that manufactures computers.

!lso, in addition to fl$ing airplanes, Gnited !irlines could ma&e cars. Ne%t, in light of

these assumptions, we determine if it is possible for the conclusion to be false. !gain,

we see that this is not possible, b$ the same reasoning as the previous e%ample.

!ssuming the premises true and the conclusion false entails a contradiction. Thus, theargument is valid.

!nother e%ample:

!ll ban&s are financial institutions.

ells argo is a financial institution.

Therefore, ells argo is a ban&.

!s in the first e%ample, both premises of this argument are true, so it is eas$ to assume

the$ are true. Ne%t we determine, in light of this assumption, if it is possible

for the conclusion to be false. In this case it is possible. If ban&s were included in onepart of the group of financial institutions and ells argo were included in another

part, then ells argo would not be a ban&. In other words, assuming the premises

true and the conclusion false does not involve an$ contradiction, and so the argument

is invalid.

In addition to illustrating the basic idea of validit$, these e%amples suggest an

important point about validit$ and truth. In general, validit$ is not something that is

determined b$ the actual truth or falsit$ of the premises and conclusion. Both the NBF

e%ample and the ells argo e%ample have actuall$ true premises and an actuall$ trueconclusion, $et one is valid and the other invalid. The Gnited !irlines e%ample has

actuall$ false premises and an actuall$ false conclusion, $et the argument is valid.

8ather, validit$ is something that is determined b$ the relationship between premises

and conclusion. The 7uestion is not whether premises and conclusion are true or

false, but whether the premises support the conclusion. In the e%amples of valid

arguments the premises do support the conclusion, and in the invalid case the$ do not.

Nevertheless, there is one arrangement of truth and falsit$ in the premises and

conclusion that does determine the issue of validit$. !n$ deductive argument havingactuall$ true premises and an actuall$ false conclusion is invalid. The reasoning behind

this fact is fairl$ obvious. If the premises are actuall$ true and the conclusion is

actuall$ false, then it certainl$ is possi"le for the premises to be true and the conclusion

false. Thus, b$ the definition of invalidit$, the argument is invalid.

The idea that an$ deductive argument having actuall$ true premises and a false


37/75

conclusion is invalid ma$ be the most important point in all of deductive logic. The

entire s$stem of deductive logic would be 7uite useless if it accepted as valid an$

inferential process b$ which a person could start with truth in the premises and arrive

at falsit$ in the conclusion.

Table 1.1 presents e%amples of deductive arguments that illustrate the variouscombinations of truth and falsit$ in the premises and conclusion. In the e%amples having

false premises, both premises are false, but it is eas$ to construct other e%amples

having onl$ one false premise. hen e%amining this table, note that the onl$

combination of truth and falsit$ that does not allow for "oth valid and invalid arguments is

!ll wines are beverages.

Fhardonna$ is a wine.

Therefore, chardonna$ is

a beverage.0sound


Fhardonna$ is a beverage.

Therefore, chardonna$ is a wine.

(unsound

/rue

premises

0alseconclusion

None e%ist


>inger ale is a beverage.

Therefore, ginger ale is a wine.

0unsound

0alse

premises/rue

conclusion

!ll wines are soft drin&s.

>inger ale is a wine.

Therefore, ginger ale is a


38/75

soft drin&.

0unsound

!ll wines are whis&e$s.

Fhardonna$ is a whis&e$.

Therefore, chardonna$ is a wine.0unsound

0alse

premises

0alse

conclusion


>inger ale is a wine.

Therefore, ginger ale isa whis&e$.

0unsound


>inger ale is a whis&e$.

Therefore, ginger ale is a wine.

0unsound

true premises and false conclusion. !s we have 9ust seen, an$ argument having this

combination is necessaril$ invalid.The relationship between the validit$ of a deductive argument and the truth or

falsit$ of its premises and conclusion, as illustrated in Table 1.1, is summari5ed as

follows:

Premises "onclusion alidity

TT

T T

eorge ashington was beheaded, then >eorge ashington died. >eorge

ashington died. Therefore, >eorge ashington was beheaded.

4& "(apter %) *asic "oncepts JE. The longest river in 'outh !merica is the !ma5on, and the !ma5on flows

through Bra5il. Therefore, the longest river in 'outh !frica flows through Bra5il.

A. 'ince the 'panish !merican ar occurred before the !merican Fivil ar, and

the !merican Fivil ar occurred after the Dorean ar, it follows that the

'panish !merican ar occurred before the Dorean ar.

3. The *mpire 'tate Building is taller than the 'tatue of ?ibert$, and the 'tatue of

?ibert$ is taller than the *iffel Tower. Therefore, the *mpire 'tate Building is

taller than the *iffel Tower. J+. !ll leopards with lungs are carnivores. Therefore, all leopards are carnivores.

. Fhicago is a cit$ in @ichigan and @ichigan is part of the Gnited 'tates. Therefore,

Fhicago is a cit$ in the Gnited 'tates.

2. If >alileo invented 7uantum mechanics, then he was familiar with ph$sics in

the twentieth centur$. >alileo was not familiar with ph$sics in the twentieth

centur$. Therefore, >alileo did not invent 7uantum mechanics.

J14. *ver$ province in Fanada has e%actl$ one cit$ as its capital. Therefore, since

there are thirt$ provinces in Fanada, there are thirt$ provincial capitals.11. 'ince the epartment of efense Building in ashington, .F. has the shape

of a he%agon, it follows that it has seven sides.

1". 'ince inston Fhurchill was *nglish, and inston Fhurchill was a famous statesman,

we ma$ conclude that at least one *nglishman was a famous statesman.

J1 . 'ince some fruits are green, and some fruits are apples, it follows that some


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fruits are green apples.

1E. !ll ph$sicians are individuals who have earned degrees in political science,

and some law$ers are ph$sicians. Therefore, some law$ers are persons who

have earned degrees in political science.

1A. The Gnited 'tates Fongress has more members than there are da$s in the$ear. Therefore, at least two members of Fongress have the same birthda$.

II. The following arguments are inductive. etermine whether each is strong or

wea&, and note the relationship between $our answer and the truth or falsit$ of

the premise(s and conclusion. Then determine whether each argument is cogent

or uncogent.

J1. The grave mar&er at !rlington National Femeter$ sa$s that Cohn . Denned$ is

buried there. It must be the case that Denned$ reall$ is buried in that cemeter$.

". The ebb and flow of the tides has been occurring ever$ da$ for millions of $ears. But nothing lasts forever. Therefore, probabl$ the motion of the tides

will die out within a few $ears.

. The vast ma9orit$ of 8ose Bowl games (in -asadena, F! have been pla$ed in

free5ing cold weather. Therefore, probabl$ the ne%t 8ose Bowl game will be

pla$ed in free5ing cold weather.

JE. ran&lin elano 8oosevelt said that we have nothing to fear but fear itself.

Therefore, women have no reason to fear serial rapists.

A. @ost famous movie stars are millionaires. ?eonardo i Faprio is a famousmovie star. Therefore, probabl$ i Faprio is a millionaire.

3. Fonstructing the great p$ramid at >i5a re7uired lifting massive stone bloc&s

to great heights. -robabl$ the ancient *g$ptians had some antigravit$ device

to accomplish this feat.

J+. -eople have been listening to roc& and roll music for over a hundred $ears.

-robabl$ people will still be listening to it a $ear from now.

. -aleontologists have unearthed the fossili5ed bones of huge reptiles, which

we have named dinosaurs. Tests indicate that these creatures roamed theearth more than A4 million $ears ago. Therefore, probabl$ dinosaurs reall$

did roam the earth at that time.

2. The eclaration of Independence sa$s that all men are endowed b$ their

creator with certain unalienable rights. Therefore it probabl$ follows that a

creator e%ists.


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J14. Foca6Fola is an e%tremel$ popular soft drin&. Therefore, probabl$ someone,

somewhere, is drin&ing a Fo&e right this minute.

11. *ver$ map of the Gnited 'tates shows that !labama is situated on the -acific

coast. Therefore, !labama must be a western state.

1". hen Neil !rmstrong landed on the moon, he left behind a gold plated'chwinn bic$cle, which he used to ride around on the moon)s surface. -robabl$

that bic$cle is still up there on the moon.

J1 . !frican !merican athlete Cerome Bettis is able to withstand tremendous impacts

on the football field. =owever, Lenus illiams, li&e Cerome Bettis, is a

great !frican !merican athlete. Therefore, Lenus illiams should be able to

withstand tremendous impacts on the football field.

1E. Gnli&e mon&e$s, toda$)s humans have feet that are not suited for grasping

ob9ects. Therefore, a thousand $ears from now, probabl$ humans will stillhave feet that are not suited for grasping ob9ects.

1A. ! random sample of twent$6five famous countr$ and western singers, including

>arth Broo&s and oll$ -arton, revealed that ever$ single one of them

studied music in !fghanistan. Therefore, probabl$ the ma9orit$ of famous

countr$ and western singers studied in !fghanistan.

III. etermine whether the following arguments are inductive or deductive. If an

argument is inductive, determine whether it is strong or wea&. If it is deductive,

determine whether it is valid or invalid. J1. 'ince !gatha is the mother of 8a7uel and the sister of Tom, it follows that Tom

is the uncle of 8a7uel.

". hen a coo& can)t recall the ingredients in a recipe, it is appropriate that she

refresh her memor$ b$ consulting the recipe boo&. 'imilarl$, when a student

can)t recall the answers during a final e%am, it is appropriate that she refresh

her memor$ b$ consulting the te%tboo&.

. The sign on the highwa$ leading into enver, Folorado sa$s that the cit$)s

elevation is A" 4 feet. It must be the case that enver is 1 mile high. JE. 'ince Fhristmas is alwa$s on a Thursda$, it follows that the da$ after Fhristmas

is alwa$s a rida$.

A. This figure is a *uclidean triangle. Therefore, the sum of its angles is e7ual to

two right angles.

3. B$ accident Daren ba&ed her brownies two hours longer than she should


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have. Therefore, the$ have probabl$ been ruined.

J+. !fter ta&ing ?' , !lice said she saw a fl$ing saucer land in the shopping

center par&ing lot. 'ince !lice has a reputation for alwa$s telling the truth, we

must conclude that a fl$ing saucer reall$ did land there.

. 'ince -h$llis is the cousin of enise, and enise is the cousin of =arriet, itfollows necessaril$ that =arriet is the cousin of -h$llis.

2. The picnic scheduled in the par& for tomorrow will most li&el$ be cancelled.

It)s been snowing for si% da$s straight.

J14. Fircle ! has e%actl$ twice the diameter of circle B. romthiswema$ conclude

that circle ! has e%actl$ twice the area of circle B.

11. 8obert has lost consistentl$ at blac&9ac& ever$ da$ for the past several da$s.

Therefore, it is ver$ li&el$ that he will win toda$.

1". 'ince Cohn loves Nanc$ and Nanc$ loves -eter, it follows necessaril$ that Cohnloves -eter.

J1 . This cash register drawer contains over 144 coins. Three coins selected at

random were found to have dates earlier than 12EA. Therefore, probabl$ all

of the coins in the drawer have dates earlier than 12EA.

1E. The Capanese attac& on -earl =arbor happened in either 12E1 or 12A1. But it

didn)t happen in 12E1. Therefore, it happened in 12A1.

1A. =arr$ will never be able to solve that difficult problem in advanced calculus

in the limited time allowed. =e has never studied an$thing be$ond algebra,and in that he earned onl$ a FJ.

J13. 'ince x J y J 14, and x J +, it follows that y J E.

1+. If acupuncture is hocus pocus, then acupuncture cannot relieve chronic pain.

But acupuncture can relieve chronic pain. Therefore, acupuncture is not

hocus pocus.

1 . If inflation heats up, then interest rates will rise. If interest rates rise, then

bond prices will decline. Therefore, if inflation heats up, then bond prices

will decline. J12. 'tatistics reveal that 3 percent of those who receive flu shots do not get the

flu. Cac& received a flu shot one month ago. Therefore, he should be immune,

even though the flu is going around now.

"4. 'ince @ichael is a -isces, it necessaril$ follows that he was born in @arch.

IL. efine the following terms:


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valid argument

invalid argument

sound argument

unsound argument

strong argumentwea& argument

cogent argument

uncogent argument

L. !nswer true)) or false)) to the following statements:

1. 'ome arguments, while not completel$ valid, are almost valid.

". Inductive arguments admit of var$ing degrees of strength and wea&ness.

. Invalid deductive arguments are basicall$ the same as inductive arguments.

E. If a deductive argument has true premises and a false conclusion, it is necessaril$invalid.

A. ! valid argument ma$ have a false premise and a false conclusion.

3. ! valid argument ma$ have a false premise and a true conclusion.

+. ! sound argument ma$ be invalid.

. ! sound argument ma$ have a false conclusion.

2. ! strong argument ma$ have false premises and a probabl$ false conclusion.

14. ! strong argument ma$ have true premises and a probabl$ false conclusion.

11. ! cogent argument ma$ have a probabl$ false conclusion.1". ! cogent argument must be inductivel$ strong.

1 . If an argument has true premises and a true conclusion, we &now that it is a

perfectl$ good argument.

1E. ! statement ma$ legitimatel$ be spo&en of as valid)) or invalid.))

1A. !n argument ma$ legitimatel$ be spo&en of as true)) or false.))

%.4

Argument 0orms) Proving !nvalidity

The previous section showed that validit$ is determined b$ the truth of a deductiveargument)s inferential claim. If the inferential claim is true, then the conclusion follows

with strict necessit$ from the premises, and the argument is valid. or such an argument,

it is impossible for the premises to be true and the conclusion false.

This section shows that the truth of a deductive argument)s inferential claim (that

is, the correctness of the argument)s reasoning is determined b$ the form of the


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argument. In other words, validit$ is determined b$ form. or these purposes, consider

the following argument:

!ll adlers are bob&ins.

!ll bob&ins are croc&ers.

Therefore, all adlers are croc&ers.Because the words adlers,)) bob&ins,)) and croc&ers)) are nonsensical, we do not

&now whether an$ of the statements in this argument are true or false. et, we do

&now that if we assume that the premises are true, it is impossible for the conclusion

to be false. That is, if we assume that the adlers, whatever the$ might be, are included

in the bob&ins and the bob&ins in the croc&ers, then we must accept the conclusion

that the adlers are included in the croc&ers. !ccording to the definition of validit$,

therefore, the argument is valid.

This fact is important for understanding the nature of validit$ because it shows thatthe validit$ of an argument has nothing to do with its specific sub9ect matter. *ven

though we &now nothing about adlers, bob&ins, and croc&ers, we still &now that the

argument is valid. The validit$ of the argument arises from the wa$ the terms adlers,))

bob&ins,)) and croc&ers)) are arranged in the statements. If we represent these terms

b$ their first letters, we obtain the following argument form. e use a line to separate

the premises from the conclusion.

!ll A are &.

!ll & are C. !ll A are C.

This is a valid argument form. Its validit$ rests purel$ upon the arrangement of the

letters within the statements, and it has nothing to do with what the letters might stand

for. In light of this fact, we can substitute an$ terms we choose in place of A, &, and C,

and as long as we are consistent, we will obtain a valid argument. or e%ample, we

might substitute daisies)) for A, flowers)) for &, and plants)) for C and obtain the

following valid argument:

!ll daisies are flowers. !ll flowers are plants.

Therefore, all daisies are plants.

!n$ argument, such as this, that is produced b$ uniforml$ substituting terms or

statements in place of the letters in an argument form is called a substitution instance

of that form.


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?et us turn now to the concept of invalidit$. Fonsider the following argument:

!ll adlers are bob&ins.

!ll croc&ers are bob&ins.

Therefore, all adlers are croc&ers.

!s with the previous argument, we do not &now whether the premises and conclusionof this argument are true or false. But if we assume that the premises are true, it is

possi"le for the conclusion to be false. It might be the case, for e%ample, that the adlers

ma&e up one part of the bob&ins, that the croc&ers ma&e up another part, and that the

adlers and the croc&ers are completel$ separate from each other. In this case the

premises would be true and the conclusion false. The argument is therefore invalid. If

we represent the terms in this argument b$ their first letters, we obtain the following

argument form:

!ll A are &. !ll C are &.

!ll A are C.

This is an invalid form, and an$ argument that has this form is an invalid argument.

!n argument is said to ha#e a certain form if it is a substitution instance of that form.

In the case of invalid forms, we must add the proviso that an argument has an invalid

form onl$ if it is not a substitution instance of an$ valid form.H The following argument

is a substitution instance of the invalid form 9ust discussed and it is not a substitution

instance of an$ valid form. Thus, the following argument has the invalid form 9ustdiscussed:

!ll cats are animals.

!ll dogs are animals.

Therefore, all cats are dogs.

HThe reason for this proviso is that some substitution instances of invalid forms are

actuall$ valid.

*%ample:

!ll bachelors are persons. !ll unmarried men are persons.

Therefore, all bachelors are unmarried men.

This argument is a substitution instance of the invalid form discussed above, but the

argument is valid because its conclusion is true b$ definition. =owever, because


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bachelors)) is e7uivalent in meaning to unmarried men,)) the argument is also a

substitution instance of the valid form

!ll A are &.

!ll A are &.

!ll A are A.Thus, b$ the stated proviso, the bachelors argument does not have the invalid form in

7uestion but rather has this valid form. The e%ercises in this boo& avoid e%amples of this

sort, where the form of the argument is obscured b$ the meaning of the terms.

Notice that this substitution instance has true premises and a false conclusion. It is

therefore clearl$ invalid, and it constitutes proof that the original argument is invalid.

The reasoning behind this proof is as follows. The substitution instance is invalid

because it has true premises and a false conclusion. Therefore, the substitution instance

has an invalid form. But the form of the substitution instance is identical to theform of the (second adler6bob&in argument. Therefore, the adler6bob&in argument is

invalid.

! substitution instance having true premises and a false conclusion is called a

countere%ample, and the method we have 9ust used to prove the adler6bob&in argument

invalid is called the countere ample met(od. The countere%ample method

can be used to establish the invalidit$ of an$ invalid argument, but it cannot establish

the validit$ of an$ valid argument. Thus, before the method is applied to an argument,

the argument must be &nown or suspected to be invalid in the first place. Thecountere%ample method consists in isolating the form of the argument and then

constructing a substitution instance having true premises and a false conclusion. ?et us

appl$ it to the following invalid categorical s$llogism: 'ince some emplo$ees are not

social climbers and all vice6presidents are emplo$ees, we ma$ conclude that some vice6

presidents are not social climbers. This argument is invalid because the emplo$ees who

are not social climbers might not be vice6presidents. !ccordingl$, we can pro#e the

argument invalid b$ constructing a substitution instance having true premises and a false

conclusion. e begin b$ isolating the form of the argument:'ome ! are not S .

!ll 5 are ! .

'ome 5 are not S .

Ne%t, we select three terms to substitute in place of the letters that will ma&e the

premises true and the conclusion false. The following selection will wor&:


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! J animals

S J mammals

5 J dogs

The resulting substitution instance is:

'ome animals are not mammals. !ll dogs are animals.

Therefore, some dogs are not mammals.

The substitution instance has true premises and a false conclusion and is therefore, b$

definition, invalid. 'ince it has the same form as the original argument, it constitutes

proof that the original argument is invalid.

In appl$ing the countere%ample method to categorical s$llogisms, it is useful to

&eep in mind the following set of terms: cats,)) dogs,)) mammals,)) fish,)) and

animals.))@ost invalid s$llogisms can be proven invalid b$ strategicall$ selecting three of

these terms and using them to construct a countere%ample. Because ever$one agrees

about these terms, ever$one will agree about the truth or falsit$ of the premises and

conclusion of the countere%ample. !lso, in constructing the countere%ample, it often

helps to begin with the conclusion. irst, select two terms that $ield a false conclusion,

and then select a third term that $ields true premises. !nother point to &eep in mind

is that the word some)) in logic alwa$s means at least one.)) or e%ample, the

statement'ome dogs are animals)) means !t least one dog is an animal))#which is true.

!lso note that this statement does not impl$ that some dogs are not animals.

Not all deductive arguments, of course, are categorical s$llogisms. Fonsider, for

e%ample, the following h$pothetical s$llogism:

If the government imposes import restrictions, the price of automobiles will rise.

Therefore, since the government will not impose import restrictions, it follows

that the price of automobiles will not rise.

This argument is invalid because the price of automobiles might rise even thoughimport restrictions are not imposed. It has the following form:

If , then P.

Not .

Not P.

This form differs from the previous one in that its letters stand for complete statements.


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, for e%ample, stands for The government imposes import restrictions.)) If we ma&e

the substitution

J !braham ?incoln committed suicide.

P J !braham ?incoln is dead.

we obtain the following substitution instance:If !braham ?incoln committed suicide, then !braham ?incoln is dead.

!braham ?incoln did not commit suicide.

Therefore, !braham ?incoln is not dead.

'ince the premises are true and the conclusion false, the substitution instance is clearl$

invalid. Thus, it constitutes proof that the original argument is invalid.

hen appl$ing the countere%ample method to an argument having a conditional

statement as a premise (such as the one above , it is recommended that the statement

substituted in place of the conditional statement e%press some &ind of necessar$connection. In the ?incoln e%ample, the first premise asserts the necessar$ connection

between suicide and death. There can be no doubt about the truth of such a statement.

urthermore, if it should turn out that the conclusion is a conditional statement, note

that one sure wa$ of producing a false conditional statement is b$ 9oining a true

antecedent with a false conse7uent. or e%ample, the conditional statement If ?assie

is a dog, then ?assie is a cat)) is clearl$ false.

Being able to identif$ the form of an argument with ease re7uires a familiarit$ with

the basic deductive argument forms. The first tas& consists in distinguishing thepremises from the conclusion. !lwa$s write the premises first and the conclusion last.

The second tas& involves distinguishing what we ma$ call form words)) from content

words.)) To reduce an argument to its form, leave the form words as the$ are, and

replace the content words with letters. or categorical s$llogisms, the words all,))

no,)) some,)) are,)) and not)) are form words, and for h$pothetical s$llogisms the

words if,)) then,)) and not)) are form words. !dditional form words for other t$pes

of arguments are either,)) or,)) both,)) and and.)) or various &inds of h$brid

arguments,a more intuitive approach ma$ be needed. =ere is an e%ample:

!ll movie stars are actors who are famous, because all movie stars who are famous

are actors.

If we replace movie stars,)) actors,)) and famous)) with the letters , A, and ', this

argument has the following form:


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!ll who are ' are A.

!ll are A who are '.

=ere is one possible substitution instance for this form:

!ll humans who are fathers are men.

Therefore, all humans are men who are fathers.Because the premise is true and the conclusion false, the argument is invalid.

Gsing the countere%ample method to prove arguments invalid re7uires a little ingenuit$

because there is no rule that will automaticall$ produce the re7uired term or

statement to be substituted. !n$ term

introduction to logic (chapter 1)

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