REVIEW: The Structure of Argument: Conclusions
and Premises
• 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
• 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
• 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
• 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
• 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
• 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
•Since 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.
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.
Example:
Every dog is an animal.
• Whoever is an S is a P.
Whoever is a bachelor is a male.
• Any S is a P.
Any triangle is a geometrical figure.
• Each S is a P.
Each eagle is a bird.
• Only P are S.
Only Catholics are popes.
• Only if something is a
P is it an S.
Only if something is a dog is it a cocker spaniel.
• The only S are P.
The only tickets available are tickets for 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.
Example:
Not all politicians are liars.
Not everyone who is a politician is a liar
• Some S are non-P.
Some philosophers are non Aristotelians.
• Most S are not P.
Most students are not binge drinkers.
Paraphrasing
• The process of casting sentences that we find in at ext 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 logic exams,”
you’ll see it’s a claim about times. It’s about getting
nervous and about logic exams indirectly, of course, but it
pertains directly to times or occasions. The proper
translation of the example is “All times I take logic 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.
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
◦ 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.)
Exercises
• No certainty should be rejected. So, no self-evident
propositions should be rejected.
• Some beliefs about aliens are not rational, for all rational
beliefs are proportional to the available evidence.
• John is a member of the police force and all policemen
carry guns.
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.