Download The Structure of Argument: Conclusions and Premises (Claims and

The Structure of Argument: Conclusions and
Premises (Claims and Warrants)
• An argument consists of a conclusion (the claim that the
speaker or writer is arguing for) and premises (the claims
that he or she offers in support of the conclusion). Here is
an example of an argument:
– [Premise] Every officer on the force has been certified, and
[premise] nobody can be certified without scoring above 70
percent on the firing range. Therefore [conclusion] every officer
on the force must have scored above 70 percent on the firing
range.
The Structure of Argument: Conclusions
and Premises (Claims and Warrants)II
• When we analyze an argument, we need to first separate
the conclusion from the grounds for the conclusion
which are called premises. Stating it another way, in
arguments we need to distinguish the claim that is being
made from the warrants that are offered for it. The claim
is the position that is maintained, while the warrants are
the reasons given to justify the claim.
• It is sometimes difficult to make this distinction, but it is
important to see the difference between a conclusion and
a premise, a claim and its warrant, differentiating
between what is claimed and the basis for claiming it.
The Structure of Argument: Conclusions
and Premises (Claims and Warrants)III
• We might make a claim in a formal argument. For
example, we might claim that teenage pregnancy can be
reduced through sex education in the schools.
• To justify our claim we might try to show the number of
pregnancies in a school before and after sex education
classes.
• In writing an argumentative essay we must decide on the
point we want to make and the reasons we will offer to
prove it, the conclusion and the premises.
The Structure of Argument: Conclusions
and Premises (Claims and Warrants)IV
• The same distinction must be made in reading
argumentative essays, namely, what is the writer claiming
and the warrant is offered for the claim, what is being
asserted and why. Take the following complete argument:
– Television presents a continuous display of violence in graphically
explicit and extreme forms. It also depicts sexuality not as a
physical expression of internal love but in its most lewd and
obscene manifestations. We must conclude, therefore, that
television contributes to the moral corruption of individuals
exposed to it.
The Structure of Argument: Conclusions
and Premises (Claims and Warrants)V
• Whether we agree with this position or not, we must first
identify the logic of the argument to test its soundness. In
this example the conclusion is “television contributes to
the moral corruption of individuals exposed to it.” The
premises appear in the beginning sentences: “Television
presents a continuous display of violence in graphic and
extreme forms,” and “(television) depicts sexuality…in its
most lewd and obscene manifestations.” Once we have
separated the premises and the claim then we need to
evaluate whether the case has been made for the
conclusion.
The Structure of Argument: Conclusions
and Premises (Claims and Warrants)VI
• Has the writer shown that television does corrupt society?
Has a causal link been shown between the depiction of
lewd and obscene sex and the moral corruption of society?
Does TV reflect violence in our society or does it promote
it?
Conclusion Indicators
•Dissection is sometimes difficult because we
cannot always see the skeleton of the
argument. In such cases we can find help by
looking for “indicator” words. When the
words in the following list are used in
arguments, they usually indicate a premise has
just been offered and that a conclusion is about
to be presented.
•
•
•
•
•
•
Consequently
Therefore
Thus
So
Hence
accordingly
•
•
•
•
•
•
We can conclude that
It follows that
We may infer that
This means that
It leads us to believe that
This bears out the point that
Conclusion Indicators II
• Example:
– Sarah drives a Dodge Viper. This means that either she is rich or
her parents are.
• The conclusion is:
– Either she is rich or her parents are.
• The premise is:
– Sarah drives a Dodge Viper.
Premise Indicators
When the words in the following list are used in
arguments, they generally introduce premises. They
often occur just after a conclusion has been given.
•
•
•
•
Since
Because
For
whereas
•
•
•
•
In as much as
For the reasons that
In view of the fact
As evidenced by
Premise Indicators II
• Example:
– Either Sarah is rich or her parents are, since she drives a
Dodge Viper.
• The premise is the claim that Sarah drives a
Dodge Viper; the conclusion is the claim that
either Sarah is rich or her parents are.
• Indicator words can tell us when the theses and the
supports appear, even in complex arguments that are
embedded in paragraphs. We can see whether the person
has good reasons for making the claim, or whether the
argument is weak. We should keep this in mind when
presenting our own case.
• An argument that presents a clear structure of premises
and conclusions, without narrative digressions,
metaphorical flights, or other embellishments, is much
easier for people to follow.
Exercises
•
1.
•
Identify the premises and conclusions in the following
passages, each of which contain only one arguments.
A well regulated militia being necessary to the security
of a free state, the right of the people to keep and bear
arms shall not be infringed.
ANSWER:
PREMISE: A well regulated militia is necessary for the
security of a free state.
CONCLUSION: The right of the people to keep and
bear arms shall not be infringed.
Categorical Propositions
• To help us make sense of our experience, we humans
constantly group things into classes or categories. These
classifications are reflected in our everyday language. In
formal reasoning the statements that contain our premises and
conclusions have to be rendered in a strict form so that we
know exactly what is being claimed. These logical forms
were first formulated by Aristotle (384-322 B.C.). They are
four in number, carrying the designations A, E, I, O, as
follows:
–
–
–
–
All S is P (A).
No S is P (E).
Some S is P (I).
Some S is not P (O).
Categorical Propositions II
•
Aside from these four logical types, there is no other
way of stating the relationship between the subject and
the predicate of statements. They can be illustrated by
the four following propositions:
1.
2.
3.
4.
All politicians are liars.
No politicians are liars.
Some politicians are liars.
Some politicians are not liars.
Universal Affirmative Propositions
• The first is a universal affirmative proposition. It is about
two classes, the class of all politicians and the class of all
liars, saying that the first class is included or contained in
the second class. A universal affirmative proposition says
that every member of the first class is also a member of the
second class. In the present example, the subject term
“politicians” designates the class of all politicians, and the
predicate term “liars” designates the class of all liars. Any
universal affirmative proposition may be written
schematically as
All S is P.
where the terms S and P represent the subject and
predicate terms, respectively.
Universal Affirmative Propositions II
• The name “universal affirmative” is appropriate because
the position affirms that the relationship of class inclusion
holds between the two classes and says that the inclusion is
complete or universal: All members of S are said to be
members of P also.
Universal negative propositions
• The second example
– No politicians are liars.
Is a universal negative proposition. It denies of politicians
universally that they are liars. Concerned with two classes,
a universal negative proposition says that the first class is
wholly excluded from the second, which is to say that there
is no member of the first class that is also a member of the
second. Any universal proposition may be written
schematically as
No S is P
Where, again, the letters S and P represent the subject and
predicate terms.
Universal negative propositions II
• The name “universal negative” is appropriate because the
proposition denies that the relation of class inclusion holds
between the two classes – and denies it universally: No
members at all of S are members of P.
Particular affirmative propositions II
• The word “some” is indefinite. Does it mean “at least one,”
or “at least two,” or “at least one hundred?” In this type of
proposition, it is customary to regard the word “some” as
meaning “at least one.” Thus a particular affirmative
proposition, written schematically as
– Some S is P
says that at least one member of the class designated by the
subject term S is also a member of the class designated by the
predicate term P. The name “particular affirmative” is
appropriate because the proposition affirms that the
relationship of class inclusion holds, but does not affirm it of
the first class universally, but only partially, of some
particular member or members of the first class.
Particular affirmative propositions
• The third example
– Some Politicians are liars.
is a particular affirmative proposition. Clearly, what the
present example affirms is that some members of the class
of all politicians are (also) members of the class of all liars.
But it does not affirm this of politicians universally: Not all
politicians universally, but, rather, some particular
politician or politicians, are said to be liars. This
proposition neither affirms nor denies that all politicians
are liars; it makes no pronouncement on the matter.
Particular negative propositions
• The fourth example
– Some politicians are not liars
is a particular negative proposition. This example, like the one
preceding it, does not refer to politicians universally but only to
some member or members of that class; it is particular. But
unlike the third example, it does not affirm that the particular
members of the first class referred to are included in the second
class; this is precisely what is denied. A particular negative
proposition, schematically written as
Some S is not P
says that at least one member of the class designated by the
subject term S is excluded from the whole of the class designated
by the predicate term P.
Exercises
• Translate the following sentences into standard form
categorical statements:
• Each insect is an animal.
• Not every sheep is white.
• A few holidays fall on Saturday.
• There are a few right – handed first basemen.
Venn Diagrams
Politicians
Liars
Anything in area 1 is a politician, but not a liar.
Anything in area 2 is both a politician and a liar.
Anything in area 3 is a liar but not a politician. And
anything in area 4, the area outside the two circles is
neither a politician or a liar.
Venn Diagrams II
Politicians
Liars
The shading means that the part of the politicians
circle that does not overlap with the liars circle is
empty; that is, it contains no members. The
diagram thus asserts that there are no politicians
who are are not liars. All politicians are liars.
Venn Diagrams III
Politicians
Liars
To say that no politicians are liars is to say
that no members of the class of politicians
are members of the class of liars – that is,
that there is no overlap between the two
classes. To represent this claim, we shade
the portion of the two circles that overlaps as
shown above. No politicians are liars.
Venn Diagrams IV
Politicians
Liars
In logic, the statement “Some politicians are
lairs” means “There exists at least one
politician and that politician is a liar.” To
diagram this statement, we place an X in that
part of the politicians circle that overlaps with
the liars circle.
Venn Diagrams IV
Politicians
Liars
A similar strategy is used with statements of the
form “Some S are not P.” In logic, the statement
“Some politicians are not liars” means “At least one
politician is not a liar.” To diagram this statement
we place an X in that part of the politicians circle
that lies outside the liars circle.
Claims about single individuals
• Claims about single individuals, such as “Aristotle is a
logician,” can be tricky to translate into standard form. It’s
clear that this claim specifies a class, “logicians,” and
places Aristotle as a member of that class. The problem is
that categorical claims are always about two classes, and
Aristotle isn’t a class. (We couldn’t talk about some of
Aristotle being a logician.) What we want to do is treat
such claims as if they were about classes with exactly one
member.
Claims about single individuals II
• One way to do this is to use the term “people who are
identical with Aristotle,” which of course has only
Aristotle as a member.
• Claims about single individuals should be treated as Aclaims or E-claims.
• “Aristotle is a logician” can be translated into “All people
identical with Aristotle are logicians.”
• Individual claims do not only involve people. For
example, “Fort Wayne is in Indiana” is “All cities identical
with Fort Wayne are cities in Indiana.”
Two important things to remember
about “Some” Statements
1.
2.
In categorical logic, “some” always means “at least one.”
“Some” statements are understood to assert that something
actually exists. Thus, “some mammals are cats” is
understood to assert that at least one mammal exists and
that that mammal is a cat. By contrast, “all” or “no”
statements are not interpreted as asserting the existence of
anything. Instead, they are treated as purely conditional
statements. Thus, “All snakes are reptiles” asserts that if
anything is a snake, then it is a reptile, not that there are
snakes and that all of them are reptiles.
Exercises
• Draw Venn diagrams of the following statements.
In some cases, you may need to rephrase the
statements slightly to put them in one of the four
standard forms.
• No apples are fruits.
• Some apples are not fruits.
• All fruits are apples.
• Some apples are fruits.
Translating into standard categorical form
• Do people really go around saying things like “some
fruits are not apples”? Not very often. But
although relatively few of our everyday statements
are explicitly in standard categorical form, a
surprisingly large number of those statements can
be translated into standard categorical form.
Common Stylistic Variants of “All S are P”
• Every S is P.
• Whoever is an S is a P.
• Any S is a P.
• Each S is a P.
• Only P are S.
• Only if something is a
P is it an S.
• The only S are P.
Example:
Every dog is an animal.
Whoever is a bachelor is
a male.
Any triangle is a
geometrical figure.
Each eagle is a bird.
Only Catholics are popes.
Only if something is a dog
is it a cocker spaniel.
The only tickets available are
tickets for the cheap seats.
ONLY
• Pay special attention to the phrases containing the word
“only” in that list. (“Only” is one of the trickiest words in
the English language.) Note, in particular, that as a rule the
subject and the predicate terms must be reversed if the
statement begins with the words “only” or “only if.” Thus,
“Only citizens are voters” must be rewritten as “All voters
are citizens,” not “All citizens are voters.” And, “Only if a
thing is an insect is it a bee” must be rewritten as “All bees
are insects,” not “All insects are bees.”
Common Stylistic Variants of “No S are P”
• No S are P.
• S are not P.
• Nothing that is an S
is a P.
• No one who is an S
is a P.
• All S are non-P.
Example:
No cows are reptiles.
Cows are not reptiles.
Nothing that is a known
fact is a mere opinion.
No one who is a Republican
is a Democrat.
If anything is a plant, then
it is not a mineral.
Common Stylistic Variants of “Some S are
P”
• Some P are S.
• A few S are P.
• There are S that are P.
• Several S are P.
• Many S are P.
• Most S are P.
Example:
Some students are men.
A few mathematicians are
poets.
There are monkeys that are
carnivores.
Several planets in the solar
system are gas giants.
Many students are hard
workers.
Most Americans are
carnivores.
Common Stylistic Variants of “Some S are not P”
• Not all S are P.
• Not everyone who is
an S is a P.
• Some S are non-P.
• Most S are not P.
• Nearly all S are
not P.
Example:
Not all politicians are men.
Not everyone who is a
politician is a liar.
Some philosophers are not
Aristotelians.
Most students are not binge
drinkers.
Nearly all students are not
cheaters.
Paraphrasing
• The process of casting sentences that we find into one of
these four forms is technically called paraphrasing, and
the ability to paraphrase must be acquired in order to deal
with statements logically.
• In the processing of paraphrasing we designate the
affirmative or negative quality of a statement principally
by using the words “no” or “not.” We indicate quantity,
meaning whether we are referring to the entire class or
only a portion of it, by using words “all” or “some.” In
addition, we must render the subject and the predicate as
classes of objects with the verb “is” or “are” as the copula
joining the halves.
Paraphrasing II
• We must pay attention to the grammar, diagramming the
sentences if need be, to determine the parts of the sentence,
the group that is meant, and even what noun is being
modified.
• The kind of thing a claim directly concerns is not always
obvious. For example, if you think for a moment about the
claim “I always get nervous when I take critical thinking
exams,” you’ll see it’s a claim about times. It’s about
getting nervous and about critical thinking exams
indirectly,of course, but it pertains directly to times or
occasions. The proper translation of the example is “All
times I take critical thinking exams are times that I get
nervous.”
• Once our statement is translated into proper form, we can
see it implications to other forms of the statement. For
example, if we claim “All scientists are gifted writers,” that
certainly implies that “Some scientists are gifted writers,”
but we cannot logically transpose the proposition to “All
gifted writers are scientists.” In other words, some
statements would follow, others would not.
• To help determine when we can infer one statement from
another and when there is disagreement, logicians have
devised tables that we can refer to if we get confused.
Table of Inferences
• The table of inferences can be found on page 139 of the text book.
• If true:
A
All men are wicked creatures.
If false:
false
E
No men are wicked creatures
undetermined
true
I
Some men are wicked creatures.
undetermined
false
O
Some men are not wicked creatures. true
• If true:
false
false
true
E
A
I
O
No men are wicked creatures.
All men are wicked creatures
Some men are wicked creatures.
Some men are not wicked creatures.
If false:
undetermined
true
undetermined
Table of Inferences II
If true:
undetermined
False
undetermined
If true:
false
undetermined
undetermined
I
A
E
O
Some men are wicked creatures.
If false:
All men are wicked creatures
false
No men are wicked creatures.
true
Some men are not wicked creatures. true
O
A
E
I
Some men are not wicked creatures. If false:
All men are wicked creatures
true
No men are wicked creatures.
false
Some men are wicked creatures.
true
Conversion Table
Does not convert to
A
A
All men are wicked creatures.
All wicked creatures are men.
Does convert to
E
E
No men are wicked creatures.
No wicked creatures are men.
Does convert to
I
I
Some wicked men are creatures.
Some wicked creatures are men.
Does not convert to
O
O
Some men are not wicked creatures.
Some wicked creatures are not men.
Syllogisms
• Syllogism – a deductive argument in which a conclusion is
inferred from two premises.
• In a syllogism we lay out our train of reasoning in an explicit
way, identifying the major premise of the argument, the minor
premise, and the conclusion.
• The major premise consists of the chief reason for the
conclusion, or more technically, it is the premise that contains
the term in the predicate of the conclusion.
• The minor premise supports the conclusion in an auxiliary
way, or more precisely, it contains the term that appears in the
subject of the conclusion.
• The conclusion is the point of the argument, the outcome, or
necessary consequence of the premise.
Syllogisms II
• Example in an argumentative essay (page 144 of
the text):
– In determining who has committed war crimes we must
ask ourselves who has slaughtered unarmed civilians,
whether as reprisal, “ethnic cleansing,” terrorism”, or
outright genocide. For along with pillaging, rape, and
other atrocities, this is what war crimes consist of . In
the civil war in the former Yugoslavia, soldiers in the
Bosnian Serb army committed hundreds of murders of
this kind. They must therefore be judged guilty of war
crimes along with the other awful groups in our
century, most notably the Nazis.
Syllogisms III
• The conclusion to this argument is that soldiers in the Bosnian
Serb army are guilty of war crimes. The premises supporting the
conclusion are that slaughtering unarmed civilians is a war crime,
and soldiers in the Bosnian Serb army have slaughtered unarmed
civilians. The following syllogism will diagram this argument.
All soldiers who slaughter unarmed civilians are guilty of war
crimes.
Some Bosnian Serb soldiers are soldiers who slaughter unarmed
civilians
Some Bosnian Serb soldiers are guilty of war crimes.
Enthymeme
• Enthymeme - An argument that is stated incompletely, the
unstated part of it being taken for granted. An enthymeme
may be the first, second, or third order, depending on
whether the unstated proposition is the major premise, the
minor premise, or the conclusion of the argument.
• Enthymemes traditionally have been divided into different
orders, according to which part of the syllogism is left
unexpressed.
Enthymeme II
• A first order enthymeme is one in which the syllogism’s
major premise is not stated.
• For example, suppose someone said, “We must expect to
find needles on all pine trees; they are conifers after all.”
Once we recognize this as an enthymeme we must provide
the unstated (major) premise, namely, “All conifers have
needles.” Then we need to paraphrase the statements and
arrange them in a syllogism, indicating by parentheses
which one we added was not in the text:
(All conifers are trees that have needles.)
All pine trees are conifers.
All pine trees are trees that have needles.
Enthymeme III
• A second - order enthymeme is one in which only the
major premise and the conclusion are stated, the minor
premise being suppressed.
• For example, “Of course tennis players aren’t weak, in
fact, no athletes are weak.” Obviously, the missing
premise is “Tennis players are athletes,” so the syllogism
would appear this way.
No athletes are weak.
(All tennis players are athletes.)
No tennis players are weak.
Enthymeme IV
• A third – order enthymeme is one in which both premises are
sated, but the conclusion is left unexpressed.
• For example, “All true democrats believe in freedom of
speech, but there are some Americans who would impose
censorship on free expression.” The reader is left to draw the
conclusion that some Americans are not true democrats. The
syllogism:
All true democrats are people who believe in freedom of speech.
Some Americans are not people who believe in freedom of speech.
(Some Americans are not true democrats.)
Validity and Truth
• No matter how diligent we are in constructing our
argument in proper form, our conclusion can still be
mistaken if the conclusion does not strictly follow from the
premises, that is, if the logic is not sound.
• For example,
All fish are gilled creatures.
All tuna are fish.
All tuna are gilled creatures.
• This seems correct.
Validity and Truth II
• But suppose we want to claim that all tuna are fish for the
simple reason that they have gills and all fish have gills.
Our syllogism would then appear in the following form:
All fish are gilled creatures.
All tuna are gilled creatures.
All tuna are fish.
• Of course, this syllogism is problematic. The mistake
seems to lie in the structure itself. From the fact that tuna
have gills we cannot conclude that tuna must be fish,
because we do not know that only fish have gills.
Validity and Truth III
• Another example:
• John is pro-choice, therefore John is a Democrat. Some
Republicans or Libertarians are pro-choice. Just because
John is pro-choice does not mean that he is necessarily a
Democrat. An argument of this kind, where the conclusion
fails to follow from the premises, is considered invalid.
That is, the form of the argument is flawed so that the
reasons that are given do not support the claim that is
made.
Validity and Truth III
Suppose we were to argue the following:
All trees are reptiles.
All rocks are trees.
All rocks are reptiles.
• It is true that if all trees are reptiles, and all rocks are trees,
then it logically follows that all rocks are reptiles. The
obvious problem is that trees are not reptiles and rocks are
not trees. The logical structure of an argument can be
sound. Given the premises, the conclusion follows
necessarily from them, but the premises are untrue.
Validity and Truth IV
• Truth is correspondence with reality. A statement is true if
it describes things as they are. Validity, on the other hand,
applies to the structure of an argument, not to the
statements that make up its content. As we have seen, an
argument is valid if, given the premises, the conclusion is
unavoidable.