Patterns of Deductive Thinking
• In deductive thinking we reason from a broad claim to some
specific conclusion that can be drawn from it.
•In inductive thinking we reason from specific instances to some
generalization based upon those instances.
•If the premises are general in nature (e.g., “All dogs bark”) and
the conclusion involves a particular item (e.g., “Dusty barks”),
the reasoning is deductive.
•If the premises are particular in nature (e.g., Dusty is a dog that
barks”) and the conclusion is a generalization (e.g., “All male
dogs bark.”), the reasoning is inductive.
Using Categorical Arguments
• They typically begin with “All” or “No,” make some
categorical claim, then reach some specific conclusion. For
example,
– All Planets are bodies that orbit the sun.
Venus is a planet.
Venus is a body that orbits the sun.
Upon examination of this syllogism, we can see that the
statements consist of three terms as subject and predicate,
that is, “planets,” “bodies that orbit the sun,” and “Venus.”
Planet is called the middle term, and it is recognizable
because it appears twice in the premises. The verbs “are”
and “is” are called copulas, and they function to connect the
terms.
Using Categorical Arguments II
• When we are uncertain whether a conclusion follows from
the premises we have to use strict procedures to test the
validity of the reasoning.
• The words “all,”, “no,” and “some” are called quantifiers
because they specify how much of the subject class is
included or excluded from the predicate class. The first
form above asserts that the whole subject class is included
in the predicate class, the second that the whole subject
class is excluded in the predicate class, and so on.
Inductive and Deductive Reasoning
• Both forms of reasoning have subclassifications.
Deductive thinking has three patterns: categorical,
hypothetical, and disjunctive. Inductive reasoning has four
types: analogy, causation, generalization, and hypothesis.
• When a deductive argument is not just broad based but
begins with a universal claim, it is referred to as
categorical in nature. The major premise is not
surrounded by qualifications, exceptions, or alternatives
but asserts that something is the case universally. The
deductive arguments we have discussed so far are mainly
of this pattern.
Universal, Particular, Affirmative or
Negative
Table 8.1 in the textbook, page 155
Sentence
Standard Form
Attribute
All snakes are slimy.
A All S is P.
Universal affirmative
No snakes are slimy.
E No S is P.
Universal negative
Some snakes are slimy.
I Some S is P.
Particular affirmative
Some snakes are not
slimy.
O Some S is not P.
Particular negative
Distribution
• Distribution is an attribute of the terms (subject and
predicate) of propositions. A term is said to be distributed
if the proposition makes an assertion about every member
of the class denoted by the term; otherwise, it is
undistributed. In other words, a term is distributed if and
only if the statement assigns (or distributes) an attribute to
every member of the class denoted by the term. Thus, if a
statement asserts something about every member of the S
class, then S is distributed; otherwise S and P are
undistributed.
All S are P
• Here is another way to look at All S are P.
The S circle is contained in the P circle, which represents
the fact that every member of S is a member of P.
Through reference to this diagram, it is clear that every
member of S is in the P class. But the statement does not
make a claim about every member of the P class, since
there may be some members of the P class that are outside
of S.
All S are P II
• Thus, by the definition of “distributed term”, S is
distributed and P is not. In other words for any (A)
proposition, the subject term, whatever it may be, is
distributed and the predicate term is undistributed.
No S are P
• “No S are P” states that the S and P class are separate, which
may be represented as follows:
This statement makes a claim about every member of S and
every member of P. It asserts that every member of S is separate
from every member of P, and also that every member of P is
separate from every member of S. Both the subject and the
predicate terms of universal negative (E) propositions are
distributed.
Some S are P
• The particular affirmative (I) proposition states that at least one
member of S is a member of P. If we represent this one member
of S that we are certain about by an asterisk, the resulting diagram
looks like this:
Since the asterisk is inside the P class, it represents something that
is simultaneously an S and a P; in other words, it represents a
member of the S class that is also a member of the P class. Thus,
the statement “Some S are P” makes a claim about one member (at
least) of S and also one member (at least) of P, but not about all
members of either class. Thus, neither S or P is distributed.
Some S are not P
• The particular negative (O) proposition asserts that at least one
member of S is not a member of P. If we once again represent
this one member of S by an asterisk, the resulting diagram is as
follows:
Since the other members of S may or may not be outside of P, it is
clear that the statement “Some S are not P” does not make a claim
about every member of S, so S is not distributed. But, as may be seen
from the diagram, the statement does assert that the entire P class is
separated from this one member of the S that is outside; that is, it does
make a claim about every member of P. Thus, in the particular
negative (O) proposition, P is distributed and S is undistributed.
Two mnemonic devices for
distribution
• “Unprepared Students Never Pass”
Universals distribute Subjects.
Negatives distribute Predicates.
• “Any Student Earning B’s Is Not On Probation”
–
–
–
–
A distributes Subject.
E distributes Both.
I distributes Neither.
O distributes Predicate.
Table 8.2 Distribution in Four Standard
Types of Statements, page 155 of the
text
Type of Sentence
Subject
Predicate
All parrots are birds. (A All S is
P.)
Distributed
Undistributed
No wars are profitable.
(E No S is P.)
Distributed
Distributed
Some diseases are tropical. ( I
Some S is P.)
Undistributed
Undistributed
Some New Englanders are not
friendly. (O Some S is not P.)
Undistributed
Distributed
•
1.
2.
3.
4.
Once we understand affirmative and negative and the
concept of distribution, we can apply the rules
governing the validity of deductive arguments of a
categorical type. There are four rules:
At least one of the premises must be affirmative.
If a premise is negative then the conclusion must be
negative, and if the conclusion is negative then a
premise must be negative.
The middle term must be distributed at least once.
Any term distributed in the conclusion must also be
distributed in a premise.
From page 156 in the textbook:
From these four rules we can judge that the following
syllogisms are invalid:
Violates Rule 1:
No Australians are poor swimmers.
Some poor swimmers are not sailors.
No sailors are Australians.
Violates Rule 2:
No fish is fattening food.
All fattening food is tasty.
Some fish is tasty.
• Violates Rule 3:
All feminists are pro-choice.
Some Communists are pro-choice.
Some feminists are Communists.
• Violates rule 4:
All stars are bright.
No planets are stars.
 No planets are bright.
•
•
1.
2.
3.
4.
5.
Having understood the summary parts of a syllogism and
how to judge the soundness of a formal argument, we can
now apply what we know to the arguments we meet and to
the ones we make.
The steps are:
Separate the conclusion from the premises (the claims from the
warrant).
Paraphrase the sentences into standard form A, E, I, O.
Arrange the statements into a categorical syllogism, completing any
enthymemes.
Judge the validity of the syllogism in terms of the four rules, using the
factors of affirmative or negative distribution.
Determine whether the premises and conclusion are true and the
argument sound.
Please turn to page 157 in the textbook.
We are going to read and analyze the
argument about feminists in the book.
•Please turn to page 161 of your textbook.
Hypotheticals: The If/Then Form
• Hypothetical arguments are usually more obvious than
categorical ones. A hypothetical argument has an “if/then”
pattern. It is conditional rather than making some absolute
claim. We say that, provided one thing is true, then
another thing would follow. For instance, if the ground is
wet then it must have rained; if the bells are chiming, then
I must be late for class; if he is the starting quarterback,
then he must be off the injured list. An assumption is made
at the start and the argument then carries out the
implications of that assumption.
Hypotheticals: The If/Then Form II
• The first part of the major premise, from “if” to “then” is
called the antecedent, and the second part, from “then” to
the end of the sentence, is called the consequent.
Antecedent and consequent mean nothing more than the
part that goes before and the part that goes afterward.
• Take the following as a typical example of a valid
hypothetical syllogism:
If Emily is a doctor, then she can cure bronchitis.
Emily is a doctor.
She can cure bronchitis.
Hypotheticals: The If/Then Form III
• The argument is perfectly valid because, in the minor
premise, we have affirmed the antecedent “Emily is a
doctor,” then drawn the conclusion that follows from it,
that “she can cure bronchitis.”
• Another valid form would be:
If Emily is a doctor, then she can cure bronchitis.
Emily can’t cure bronchitis.
Emily is not a doctor.
• Here we have denied the consequent, and although the
reasoning might be more difficult to see, it is also correct.
The assumption is that every doctor can cure bronchitis,
and if Emily is unable to do this then she cannot be a
doctor.
Hypotheticals: The If/Then Form IV
• These arguments are arranged in two different patterns but
in both cases the conclusion follows from the premises.
From this we can generalize that the two valid forms of
hypothetical thinking are affirming the antecedent and
denying the consequent.
• In contrast to these valid forms, take the following two
syllogisms:
• If Emily is a doctor, then she can cure bronchitis.
Emily is not a doctor.
 Emily can’t cure bronchitis.
Hypotheticals: The If/Then Form V
• Here the conclusion does not follow logically, for although
Emily is not a doctor, that does not mean she cannot cure
bronchitis. Although all doctors can cure bronchitis, we do
not know that only doctors (and no one else) can cure
bronchitis.
• In this process of reasoning, we have denied the
antecedent, which is an invalid form of a hypothetical
argument.
Hypotheticals: The If/Then Form VI
• Another invalid argument:
• If Emily is a doctor, then she can cure bronchitis.
Emily can cure bronchitis.
 Emily is a doctor.
• This thinking is also incorrect, for just because Emily can
cure bronchitis that does not make her a doctor. Although
all doctors can cure bronchitis, that does not mean only
doctors can cure bronchitis. This error is known as
affirming the consequent.
Hypotheticals: The If/Then Form VII
• Please turn to pages 166 and 167 in your
textbooks.
Disjunctives: Either/Or Alternatives
• In a disjunctive sentence two possibilities are presented, at
least one of which is true (although both might be). If we
say, for example, “Either we will stay at home or we will
go to the movies tonight,” that is a disjunct. So are the
sentences, “Either you are in class or you are absent,” and
“The man is either fat or skinny.”
• One of the disjuncts has to be true, so if we know one of
the alternatives to be false, we can declare the other to be
true and produce a valid argument. It does not matter
which disjunct we eliminate; the one remaining must be
true.
Disjunctives: Either/Or Alternatives II
• In diagram form, then a valid disjunctive argument would
appear this way:
• Either P or Q
not P.
Therefore Q
• Now we said that at least one alternative is true, but in fact
both could be. That means we would not get a valid
argument by affirming one part of the disjunct in a minor
premise and denying the other in our conclusion. Since
both parts might be true, one disjunct is not eliminated
when we affirm the other.
Disjunctives: Either/Or Alternatives III
• For example:
• Either I am paranoid or someone is out to get me.
My therapist says I am paranoid.
Therefore No one is out to get me.
• The fallacy is that I could be paranoid and someone may
be out to get me.
• Another example,
“Either it is Monday or we are in Critical Thinking class.”
Actually, both might be true. Affirming one does not rule
out the other. In diagram form the mistake looks like this:
– Either P or Q
P
 not Q
Disjunctives: Either/Or Alternatives
III
• This leads us to the two rules about disjunctives: In a valid
disjunctive argument we deny one of the disjuncts to affirm
the other. An invalid disjunctive argument is one in which
we affirm one of the disjuncts and deny the other.
Disjunctives: Either/Or Alternatives
IV
• One qualification should be mentioned. In some types of
disjuncts we do eliminate one part by affirming the other:
• Either I am in Critical Thinking class today or I am absent.
I am in Critical Thinking class today.
 I am not absent.
• This is not a rule, though. Do not count on it to always
hold.
• It is important to note that the word “or” has two possible
senses. In its exclusive sense, the word “or” eliminates or
excludes one of the possibilities. For example, if a waiter
tells you, “You can have soup or salad,” he usually means
that you can have either soup or salad but not both. In its
non-exclusive sense, the word “or” does not exclude either
possibility. For example, your advisor may inform you,
“To fulfill your science requirements, you can take biology
or chemistry.” What your advisor usually means is that
you can take biology, chemistry, or both.
• In which sense are we supposed to understand the word “or” for
the purpose of logic? In logic, the convention is to take the
word “or” in its nonexclusive sense. A disjunction such as “The
steak is good or the salad is fresh,” is true if either the steak is
good, or the salad is fresh, or both.
• Therefore, saying the steak is good does not proven anything
about the freshness of the salad. Since the steak is good makes
the statement true, it will still be true whether the salad is fresh
or not.
• However, if we say the steak is not good, then we can conclude
that the salad is fresh. Because one of the disjuncts (but not
necessarily only one) must be true.
• A disjunction is false if and only if both of its disjuncts are false.
The steps for judging disjunctive arguments are
similar to those for hypotheticals, namely:
1. Arrange the statements into disjunctive form.
2. Judge the argument’s validity in terms of the
rules.
3. Determine whether the premises and conclusion
are true, and the argument sound.
• Please turn to page 173 of your textbook.