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.
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.