Uploaded by Manuj Kant

Sober- Ch. 2 v3.2

I ~ l l i o tSober,
Core Questions in Philosophy (6" e d . 2 0 1 2 ) .
Part One:
apter 2
Deductive Arguments
asstirnptions. Ln geometry yuu may have spent little or no lime askina whether the axioms
arc trilc. Not so [or the philonnphlcd arguments I discus in thir bwt. W'c'll want tn see
wlictlier the prcllltses are plausible. We'll also want to see whether the l>rr~nises,
if they
were true, would prwidc a nxson for thinltlng the conclusion is true as well. 1'11 pose these
two questions again and again.
Good Arguments
I now want to talk about different kinds of "good arguments? What does "good" mean?
A good argument Is iwtionaJIy persuasive it glves you a substantial reason to think the
conciusion is true, Adverfisers and politicians sametimes use arguments that trtck people
into believing what they say These arguments sometimes persuade people, but they don't
always pmnde gomi reasons.
A good argument should have true premises; if the premises are false, how could they
give you good reasons to believe the conclusion? Rut mom is required than this. In the
following argument, the premise is true, but it doesn't provide you R good reason to think
that the conclusion is true:
Chapter Outline
Good Arguments
Testing for Invalidity
Circularity, or Begglng the Question
Deductive Validity Defined
Is a Technical Term
"True for W
Logical Form
Wishful Thfnking
Self-TalflUing Prophesies
Philosophy involves constructing and evaluating arguments. In this respect, philosophy is
no different from any other rational activitp-mathemat~cims do this, as do economists,
physicists, and people in everyday hfe. The distincblve thing about philosophy isn't that
philosophers construct and evaluate arguments: what is distinctive is the k~ndsof questron.5 those arguments aim to answer. In the previotls chapter, I talked about what makes a
question philosophical. The goal in this chapter is to develop some techniques that can be
used to tell whether an argument Is good or bad.
Grass is green
Roses are red
What is wrong here is that the premises are irrelevant to the conclusian. A good argument
should contain true premises, but it should also cite premises that are related in the right
way to the conc~usion.The truth of the premises should give you a reason to think that the
conclusion is true. The thee types o f u g dargument" that I'll now describe differ in what
relationship their premises and wndusions have to each other.
Good arguments can be divided into two categories, and one of those categories can be
divided into two more:
Good Armrnents
/ - \
Not Deductivelv
/ \
An argument divides into two parts: the premises and the ~onclusion.The premlses and
the conclusion are statements; each is expresed by a declarative sentence. Each is either
true or false. When people argue that a given statement i s true, they try toprwide reasons
for th~nkingthis. The reasons are the premises of their arpment; premises are assumptions. The statement to be established is the argument's conclusion.
In high school geometry, you talked about axioms and theorems. Axioms are assumptlans (prcrnises); the theorem (the canclus>on)is what 1s supposed to follow from those
I'll treat the three categories (deductivelyd i d , inductivelystrong, and abductively strong)
as mueudIy actusiw. Jf an w e n t belongs to one category, it can't belong to any of the
others. At the end of Chapter 3, I'11 modlfy this dassification slightly.
Y w may have heard some of this hrmino!ogy before. Deduction i s what you do in
a mathematical proof. Induction involves sampling from a pop~~latton
to decide what
its characteristics are. "Abduction" may be a less familiar term. It has nothing lo do wlth
' . . . l . . . * . . . , . , "
.......+ . . . ,
Chaptar +: Deductlv* Argumsntr
. . . . . . . . . . . . . . . . . . . . . . .
Wdnapping. The word was invented by the great dneteenth-centuryAmerican philosopher Charla Sanders P e w Philosopherssometimes use the longer lab4 "inference to the
best explanation'' to describe what Pe~rwmeant by abduction.
fI consider deduction in this chapter, induction and abduction in the next The god
in ea&-casc is to describe some ofthe considerationsthat are rdwantto deciding whether
an argument is good or bad.
Deductive Validity Defined
The first type of good argument consists of ones that are *deductivety valid.? Here are two
eampIes of this type of argument:
AU fish swim.
AU shark are fish.
AU partid- have mass.
All electrons are particles.
M sharks swim.
All eIectmns haw mass.
In these arguments. the premises are the statements above the horizontal line; the condusion b the statement below. These arguments say that the premises are true and that,
M o r e , the conclusion also 18 true.
Hwe is what deductive validity means:
A deductive@valid argument is an argument that has the following property: IF in
Part One: ln!mduction
Logical Form
What makes an argument dcduct~vclyvalid? Tbe thmc example arguments described so
Iar have diflercnt suhject matters. Thc first is about fish, the second is about particles, and
the third ir about plants. Although they are ahout different things, they have the rnme
slnlctrm. The structural property [hat they have in common is called their 'logical lorrnP
Think of each argument as the result of substituting terms into the forlaving skeleton:
All Bs are O
All As are Bs
All As are Q
Thls is the logical form of the three arguments given. You can think of A, B, and C as
blanh into which terms may be substituted. Take a mlnute to see how the arguments
just stated can be obtained from the above skeleton by substitution-by *filling In
the blanks."
An argument is valid or invalid solely because of the logical form it has. The subject
matter of the argument Is irrelevant. Since the three example arguments have the same
logical form, they are all valid or 111 invalid. They have the same logcal form. ao thgr
are in the same boat. As already mentioned, they are valid Indeed, each and every one
of the millions of arguments you can construct by substitution into the above skeleton
is valid as well.
pmnises were true, its c~nctusionwould have to be true.
I've capitalized the word IF: I'd print it in bright colors ifI auld because it is important
not to forget thls wo-letter word. A valid argument need not how true premises. What Is
required is that the mndusion would have to be true IF the premises were true. Take a
minute to look at these two arguments Conrlnce yourself that they are deductively valid.
Validityn Is a Technical Term
What philosophers and logicians mean by 'Galid" doesn't have much in common with
what we mean by *validmin ordinary English. In everyday life, we say that a statement is
Palid* if it is plausible or true. The technical use of the term that 1just explained dfffers
f m ordinary usage la two ways. Flrst, wtnever say that a statement or an idea is valid or
invalid. Valldity is a property of arguments and of arguments only. Second, an argument
can be valid even if the statements it contains arewtldly implausible. Avalid argument can
have false premfses and a false conclusion.
Here is an example:
All pIants haw minds.
A1I ladders are plants,
All Iadders have minds.
The definition of validity tells you what a deductively invalid argument will be like, If there
is even t h e smallest possibflity that the conclusion could be false when the premies are
true, then the w p m h n t 1s deductiwly invalid
The ladder argument is valid, although all the statements it contains are false. L the
reverse situation possible? Can an argument be invaIid, even t h o u ~ haU the statements if
contains are true? The answer is yes. Here's an example:
Emeralds are gre@n.
Lemons we yellm
The premise is true, tord so Is the conduslon. Sa why isn't the argument deductiwly
valid? The definition ofvalidity says that the premises In a d i d argument must prwide an
nbsolwteguarantcc that the conclusion is tme. Rut the fact that emeralds are green doesn't
guarantee that lemons must be yellow. The color af lemons tsni' entalled by the fact that
emeralds are green. Validity conccrns the mlatronship of premises m conclusion, not the
queshon of whether the premises and the condusIon each happen to be true.
Sometimes it isn't so obvious that an argument is t d d . T f i e a h e example is prep
blatant-the premisehas nnthing to do with the conclusion. But what do yw thinkof the
following at.gumcnt? Is it valid or not?
Ckmpter n: D d u ~ I I v eArguments
IfJones stands In the heavy rain wlthout an umbrella, then Jones will get wet.
1011- Is wet.
Jones was standing In the heavy rdn without an umbrella.
Imagine that all t h m .of the statements in this argument are hue Ima@nethat rones is
now standing before you w d n g wet and that Jonesjust came in from the rain.
Even ifall the statements in this argument are true, this argument Is still Inrelid. It
is just l$c the argument about emeralds and lemons. Although the premises and the
conclusion happen to be true, the premises don't guarantee that the conclusion must
be true.
How can we see this more d d y ?I said before that all arguments that have the same
logical form are in the same boat Thtf means that if the argument about Jones is Invalid, so
is each and evwy argument that bas the same form. Let's begin by isolating the argument's
logical f m . Here it i s
Part One: lniroductiun
the conclusion is false. If you can find even one rottell apple of this we,you arc finished. If
there is evcn une argument with this property, thm every argument ofthat form is invalid
When an argument has true premiscs and a false co~~cIuslon,
it 1s quife ohlous that
the truth of the premises dwsn'tpmntee that the conclusion must be true. The premises
can't be guaranteeing this, as the conclus~onIS false. But this tells you something general.
It tells you that each and every argument of this form will be such that the prcmises don't
guarantee the truth nf the conclusion.
So Ear, I t e presented someexamples oiargumentr I'veexplained that a valid argument
needn't have true statements In it and that an argument composed solely of true statements needn't b e e h d . This should make you wonder whether tberc Is any connectron at
all between the question of whether an argument is valid and the question of whether the
premlses and conclusion are true
There is a connection. It is iilustrated by the following table. Ifan argument is valid, it
can exhibit three of the four following combinations in which the premises are either all
true or not all true and the conclusion is either true or false:
h i r e s
at do and Q stand for in thIs argument skeleton? You can subslltute any statement
(declarative sentence) you please for these letters to obtain an argument with this logfcal
form Notice that the letters in this skeleton differ in their function from the letters in the
previous skeleton. There, A, $ and C are blanks into which terms denoting kinds of thing5
[Wsh,'' "electmn%'etc.) can be suhsiituted Anyhow, we now have the loeicsl
form of the
argument about Jones.If it is invalld, so are all arguments that have the same logical f o m
This means that iffhere is even one a r m e n t that bas t h i s l .,o n i c a l h in which the ~ m iaes are true and the condusion false, then the argument form is i n d i d . This will mean
that the initial argument about Jones is itrvalid as well,
Here i s an argument that has the same lopica1 form as the argument about Jones that
settles the question:
If Sam Iives in Wiswnsin, then Sam lives in the United States.
Sam lives in the United States.
Sam Iives in Wisconsin.
The premises of this.argument are true, but the conclusion, J mure you, is false. The Sam
I'm talking about lives In Georgia
Ali true
Not all true
This table indicates that a d i d argument m ' t have ew premises and a false conclusion.
However, the faa that an argument is valid leaves open which of the other three cells the
argument occupies.
What can be said of an imlld a r p e n t ? If an argument is invalid, are any of the fmr
combinations Impossible? 1 leave thrs to you to figure out by consulting the definition of
When you find an invalid argument, you may want to ask if the argument can be
repaired Is there anything that can be done to an i n d i d argument to turn it into an argument that is valid? There ia By adding premises, p u can turn a deductijely i n d i d
argument into a valid one. Consider the following argument:
Smith liws in the United States.
Smith liws in Wwnsin.
Thls is invalid, but it can be made valid by adding a premise:
Testing for Invalidity
So here's a strategyto we if you want to knowwhether an argument it invalid Fint, ignore the
Smith Iives in the United StatEveryone who lives In the United States lives in 1Visconsin.
argument'ssubject matter and isolate 'the logical form (the "skeletonn)of the argument. Second,
see if you can invent an argument that has this logicdl form in which the premises are true and
Smith lives in Wisconsin.
Chapter I:
Osductlve Ar(umnts
.................................................................. . . . .
Notice that the conclusion now follows from the premises. The trouble is that the second
premise is false.
In the preceding pair of arguments, r i n g the defect of invalidity just substitutes one
problem for another; instead of having to criticize an argument for being invalid you now
have m d t i d z e an argument for having a premise that isn't true. The following argument
pair is different. Here you can repair the defect of invalidity and obtain a perfectly fine
argument. Notice first that the following argument isn't deductiwly valid:
Smith lives in Wisconsin.
Smith lives inthe United States.
The argument can be repaired, however, by adding a premise:
Smith lives in Wisconsin.
Everyone who l i e s in Wisconsin lives in the United State.
Smith lives in the United States.
Thfs argument is valid and has true premises as well. You can see from these two pain
of arguments that invalidity is easy to fix. Just add premises. What is harder is to add
premises that not only make the argument valid, but that are true as well.
Thls idea will come up repeatedly when I discuss various philosophical arguments.
I will sometimes claim an argument is invalid. When this happens, you should ask yourself whether the argument can be repaired. Often the price of making the argument valid
(by adding a premise) is that you have to supply a new premise that you thirik is false. In
making this addition, you are trading one defect (invalidity) for another (false premises).
If you can't repair the argument so that it is both valid and has all m e premises, then
you should consider the possibility that there is something fundamentally flawed about
the whole line of argument On the other hand, sometimes an invalid argument can be
replaced by a vahd one merely by supplying a true premise that maybe you neglected to
mention because it is so obvious. In this case, the defect in the original argument isn't
So far I've emphasized two questions that we will want to ask about arguments:
Is the argument deductivelyvalid?
Are all the premises true?
If the answer to both questions is p the conclusion of the argument must be true.
Arguments are tools We use them to do things. When the goal is rational persuasion.
a good argument will provide a good reason to think that the conclusion is m e , If an argumem is deductively valid and has true premises, is that sufficient to make the argument
good?To see why validity and true premises aren't enough, consider the followingargument:
Lemons are yellow.
Lemons are yellmv.
Here the conclusion merely repeats what the premise asserts. This argument is valid and
the premise is true. But there is something defective about this argument. What is it?
part one: Introduction
If/then statements are called conditionals. Cond~tionalstatements have other state.
ments as components. For example, the statement "If pigs fly, then grass IS green"
is a statement ofthe form "If P, then Q," whcre P and Q are themselves statements.
In the statement "If P, then Q," P is called the antecedent and Q ir called the
consequent. A conditional doesn't say that its antecedent is true; the statement "If Joe
drinks arsenic, then )oe will die" does not say that Joe drinks arsenic. And a condltional doesn't say that i!s consequent is true; "If there is a nuclear war, then Wash~ngton will be attacked" doesn't say that Washington will be attacked.
Conditionals can be rewritten without changing what they Say. Consider the state
ment "Ifyou l ~ v eiq Wisconsin, then you live in the United States." Th~si s equ~valent
in meaiing to "If you don't live in the United States, then you don't l~wein Wisconsin."
The conditional 'If P, then Q is equivalent to "If not-Q, then not-P," no matter what
P and Q happen to be. Here's a piece of terminology: The statement "If not.Q, then
not-P' is the contrapositive ofthe conditional "ICP, then Q." A conditional and its contrapositive are equivalent.
Consider the following two conditionals: "If P, then Q and "If Q, then P" Are they
equivalent? That is, do they mean the same thing? The answer is no. 'If you live in
Wisconsin,then you live in the United States" is true, but "Ifyou live in the United States,
then you live in Wisconsin" is false. These two iflthen statements can't mean the same
thing, because one is true while the other is false. "If Q, then P* is termed the converse of
the conditional "If P,then Q." A conditional and its converse are not equivalent.
Circularity, or Begging the Question
The previous argument is circular: it begs the question. Supposc you didn't already have an
opinion as to whether lemons are yellow. The above argument wouldn't help you resole
your uncertainty. The argument would he useless in this regard.
Good arguments are tools that help answer questions about whether their conclusions
are true. A good argument should give you a reason to accept the conclusion if you dodt
already believe the conclusion is true. So h i d e s che&ng to see if an argument is deductively valid and has true premises, you should also see if the argument begs the question.
You'll notice in what I've just said that I am using the exprewion "beggmg the question"
to name a defect in an argument. Unfortunately, the phrase is often used now to simply
mean that a question is betng asked You'll hear this usage on the evening news-- ?he recession has not i m p d . This begs the question of whcther guvetnment action can make
things better." As with the term "validity:' the term " b a i n g the question" is used by philosopherswith a special, technical meaning one that doesn't coincide with ordinary usage.
One other idea needs clearing up before I leave the topic of deductive validity, You'll notice
that the ddmition of validity makes use ofthe concept of truth. What is truth?
Deductive Rrgumsnts
Part One: Introdudian
There are deep philosophical questions here, most of which I'll skirt. My goal is to
describe the concept of truth I use in this book It is beyond the scope of this book to defend this choice or to fully develop its implications. To begin with, whether a statement is
true is an entirely diierent question from whether you or anybody happens to believe it.
Whether someone believes the statement *The Rocky Mountalna are in North America"
is a psychoPOgica1 question. If beings with minds had never popdated the earth, no one
would have thought about the location of this mountain range. But this dwsn't affect the
question of whether the statement is true. There can be truths that no one believes. Symrnetrjcally, there can be propositions that everyone thinks are m e , but that aren't. Them
can be beliefs that aren't tnre.
To understand what makes an argument questron.begglng, it rs useful to exarnlne
some examples.
Suppose you were trylng to convlnce someone that God exlsts. The argument
you give for th~nkingthat t h ~ sIS true is that the h b l e says that there IS a God.
Would t h ~ argument
connnce someone who d~dn'talready believe that there rs a
God? Probably not Anyone who doubts that there IS a God probably doesn't th~nk
that everythng the Bible says 1 5true
Here's a second example Someone IS very susp~c~ows
about the rel~abll~ty
consumer magazines You try to convlnce h ~ mthat Consumer Reports is rel~ableby
panting out that Consumer Repolas ranks ~tselfvery highly In an art~cleevaluating the
rellab~lityof consumer magazines. Probably your argument wlll fa11to convlnce.
In these two examples, 1dent1Sythe prernlses and conclusion In each argument
Then descrrbe what ~tIS about the argument that makes it question-begg~ng.
When I say that a certain sentence has the property of being true, what am I saying?
For example, when E say that the English sentence *TheRocky Mountains ate in North
A m e r i d is true, am I attributing some mysterious property to the sentence? Not really.
All I'm saying is that the world is the way the scntence says It is. When I say that the sentence is true, all I'm saying is that the Rocky Mountains are in North America. So in a
way,the concept of truth 1s often 'redundant? Sometimes when I use the concept of truth,
I could say the same thing without using that concept.
In high school English, your teacher might have t d d you to avoid redundancy. If you
hand In an essay containing the sentence "Osmr is an unmarried bachel~r,"the essay
might come back with "unmarried crossed out and the marginal comment "avoid redundancy* The word "unmarried" is redundant because "Oscnr is an unmarried bachelor"
means exactly the same thing as "Oscar~sa ba~helor.~
Adding the word *unmarrieC 1s to
spill useless ink. The Redundancy Theory of Truth claims that the word "truemIS redundant rn just this sense. "lt is true that the Rockies are in North America" says exactly what
the sehtence "The Rockies are in North America" asserts. This helps show why truth isn't
a mysteriom property If you believe a statement FI you also belleve that P is true. So,if
you have any belle5 about rhe world at all, you should be qulkc cornfortable applying the
concept of truth to those beliefs.
U T r ~for
e Me"
You'll see from these remarks that the expression "It is true for me" can be dangerously
rnislead~ng.Sometimes sayng that astatemen? istrue4for you" just means that you bdieve
it. If that rs what you want to say, just use the ward *belief" and leave truth out of it. Howwer, there is a more controvers~alIdea that might be involved here. Sometimespeople use
tlie ewpresqlon "true for me*to express the Idea that each of us makes our own reality and
that the beliefs we have Eonstitute rhat reality. I'll asrume this is a mistake. My concept of
truth assumes a fundamental division between the way things mlly are and the way they
may seem to be m this or that indiuidual. Thia is whst I meant in Chapter I bydistinyishing the objective realm and the subjective realm.
Wishful Thinking
Closely relatcd to this distinction behueen objective and subjectiw is a piece of advice:
We should m i d wtrhful thznking. Most of the things we believe arenl made true by our
believing them. That the Rockies are m North America is a fact that is rndependent of w r
thought and language. We don't bring this geographic fact into being by thfnldng or talking in the way we dn.
Self-Fulfilling Prophesies
In saying hi$,I'm not denyingthat the thoughts we haw often affect the world outside the
mind. If I think to myseII, =I can't hit a basebalr this may have the effect that I do badly
in the batter's box; here my believlng something has the effect that t h bellef is made m e .
This is the idea of a "self-hlfillingprophesjr Notice how this causalchain works:
I believr that
1won't hit
the baseball.
I swing toe high.
1 don't hit
the basehall.
My believing a proposition causes m action, which has the effect of makingthe proposition trw.
I have no problem mth the idea that various statements may be caused to be true by
individuals thinkingthoughts to themselves. What I deny s that the mere act of thlnldng,
unconnected with action or some other causal pathway, can make statements true in the
world outside the mind. I'm rejecting the idea that the world Is arranged so that it spontaneously conforms to the ideas we happen to entertain.
Part On@:Iniroduction
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Later in thh book 111 investigate whether there are any exceptions to this principle
that says that we should avoid wishful thinking. Maybe there are some statements that
become true just because we think they are. Here are some philosophical claim we'll
Mathematical statements and ddinitlons are made true by our regarding them as
snch: for example, "a + 3 = 5" 1s true just because we choose to deflne our termhology ('a: "+: &.I in the waywe do (Chapter4).
S:me statements about the contents of my own mind (for example, 1am in pain")
are made true just by
believing they are true (Chapter 13).
Ethical statements are true Justbecause God,sadety, or some individual agent thinks
they are [Chapter 31).
I'm mentioning these philosophical claims here without tlpping
hand as t o whether
Ithink any of them is plausible. If any of them were correct, they would be exceptions to
the pattern I've just described. For the moment, though, I'm merev noting that belief and
truth are generallyvery separate questions.
7. What doe5 ~tmean to 5ay that an argument IS "ctrcular,"that ~t"begs the question') Conrtrvct
an example ofan arp;urnent o f t h ~ type
r dlllerent Corn the ones pres~ntedIn tha~chapter
8 What does i t mean to r a y that truth
oblectlv?, not sublcct~veJ
Problems for Further Thought
The R~dundancyThew of Truth may seem plausible as an account of what the following sentence means:
is true that the 'Rockies are in North America.
Does it work as well as an explanation ofwhat the lollowing sentence means?
Some statements that are [rue have not been formulated yet
Consider the following argument:
I release an otherwise unsupporled apple fmm my hand a few feet from the earth's surface.
The apple falls to earth.
Is thrs argument dedudlvely val1d3What is the logical form oftha argumenl'
3. (Here 1s a problem that was drawn to my attemt~onby R~chardBehllng ) In this chapker, I sa~dthat
each argument has a rrngte logical form This IS the skeleton Into wh~chterms can be subst~tuted
ta obtaln the argument What I s a d is an oversirnplAcation.A g~ve"argument can be obtained
from many logical forms For example, consider the follow~ngargument
When is a statement or idea valid) (a tnck question)
Define what it means to say that an argument is deductively valid.
3, Invent an example ofa valid argument that has false premises and a true conclusion. Invent an
example of an invalid argument that has true premises and a true conclusion.
4. Can a statement be a premise in one argument and a conclusion in another? If-youthink so, give
an example.
5. Which of the following argument forms is valid? Which is invalid? For each of the invalid ones,
construct an example of an argument with that form in which the premises are true and the con-
Fred l i e s In California.
If Fred l~vesin tal~fornia,then Fred lives In the United Stales
Fred lives m the Un~tedYates
This argument can be obtained from both ofthe Followingskeletons by subst~tut~on:
clwsion false,
IFP, then Q
IFP, then Q
Argument form (a) is valld, but (b) is mvalid The argument about Fred 1s valid
If P, then Q
If P, then Q
Here's the problem: Use the concept of log~calform to define when an argument isualld, and
when it Is inual~d,w~thoutfall~ngInto the trap of thlnklng that each argument has eractly one
logical lorm.
Not. P
4. In this chapter, E claimed that there are "objective truths." Do you agree? Construct an argument
in which you try to demonstrate that such things exist, or that they do not
IId )
For the argument forms you th~nkare Yallac~ous,
Invent names 'or these fallacres by using the
vocabula7 about cond1:lonals presented In the box on page 18.
6 A sign on a store says, "No shws, no senrice " Does t h ~ smean that
will be served'
you wear shoes, then you
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Listen W h
the Natlon
: A H w t o Gulden-fPlk d
. m this interview with
NPR, Profirsor
Simon BIatkbum dis~urserthe dcbatt Between objdctivlsts and rubJcGlivirts about
trutkthmughout history and t h y . Who1
dour Blackbrrm think a wrong w ~ t hths
subjenivisr porition? Do you tkrnk that
here is alirolutc truth or that eoch pfion
detcmines who: ir "truefor him or hcr"7
Research deductive vatldity
Research oblwtive truth