Logic
LESSON 3:
PRACTICE WITH VALID/INVALID;
MORE ON INDUCTIVE ARGUMENTS
BR: Answer all the following on your own paper. Open note. No discussing.
1. If I say, “We can believe her, because she’s a woman of impeccable
character,” I’m mainly using which form of appeal?
(a) logos
(b) ethos
(c) pathos
2. Supply the premise needed to reach the conclusion given.
P1: All whales are mammals. P2: _____ C: So all whales have lungs.
3. Which statement is the conclusion? (Hint: there are 3 statements in
total)
College people need to leave early. So Alicia needs to leave early, since she is
a college person.
4. Is the argument below a deductive or inductive argument?
Our tennis team is about to play the #1 team in the state, so we’re probably
going to get schooled.
5. Determine whether the argument below is valid or invalid; then whether
it is sound or unsound. Explain how you reached both decisions.
All snakes are mammals, and all mammals are warm-blooded, so all snakes
are warm-blooded.
Argument types: Deductive
 Deductive argument:
an argument in which
the arguer claims that
the premise(s) cannot be
true and the conclusion
false; the conclusion
follows necessarily from
the premise(s)
Examples:
 Mathematics (except statistics!)
 Argument from definition
 Categorical syllogism

All poodles are canines.
Smitty is a poodle.
Thus, Smitty is a canine.
 Hypothetical syllogism
 If Smitty is mad, he’ll bite.
Smitty is mad.
Thus, Smitty will bite.
 Disjunctive syllogism

Either Smitty’s asleep or he’s awake.
Smitty’s not asleep.
Therefore, Smitty’s awake.
Evaluating inferential claims
 Valid deductive
argument: one in which
it is impossible for the
premise(s) to be true and
the conclusion false
 Invalid deductive
argument: one in which
it is possible for the
premise(s) to be true and
the conclusion false (a
“bad” argument)
 All dogs are mammals.
Lassie is a dog.
Therefore, Lassie is a
mammal.
 All SUVs have 4 wheels.
Mrs. Casey’s car has 4
wheels.
Therefore, Mrs. Casey’s
car is an SUV.
Diagrams: A test for validity
 All snakes are reptiles.
All reptiles are cold-blooded animals.
Therefore, all snakes are cold-blooded animals.
R
C
R
S
S
C
Diagrams: A test for validity
 All murderers are violent offenders.
All violent offenders are felons.
So all felons are murderers.
INVALID
 All girls have hearts. TTT invalid, unsound
All humans have hearts.
Therefore, all girls are humans. INVALID
 All reptiles are warm
warm-blooded. FTF, valid, unsound
No snakes are warm-blooded.
Therefore, no snakes are reptiles. VALID
 All killers are a threat to society. TTF, invalid,unsnd
Some gun-owners are killers.
Thus, all gun-owners are a threat to society. INVALID
Substitution: Another test of validity
 All SUVs have 4 wheels.
Mrs. Casey’s car has 4 wheels.
Therefore, Mrs. Casey’s car is an SUV.
 All S are F.
“All” C are F.
Therefore, “all” C are S.
 All safeties are football players.
The center is a football player.
Therefore, the center is a safety.
Substitution: Works for hypotheticals, too
 If Mr. Simms says there will be a pop quiz, then we
need to understand this.
Mr. Simms did not say there will be a pop quiz.
Therefore, we do not need to understand this.
 If A then B.
Not A.
Therefore, not B.
 If Abe Lincoln died in a dirt bike accident, then he is
dead.
Abe Lincoln did not die in a dirt bike accident.
Therefore, Abe Lincoln is not dead.
Substitution: Another test for validity
Try to prove these invalid by substitution, creating true premises with a false
conclusion (HINT: dogs, cats, mammals, fish, animals will almost always work in
some arrangement—if the argument is really invalid)
 All girls have hearts. TTT invalid, unsound
All humans have hearts.
Therefore, all girls are humans. INVALID
 All killers are a threat to society. TTF, invalid,unsnd
Some gun-owners are killers.
Thus, all gun-owners are a threat to society. INVALID
 All reptiles are warm-blooded. FTF, valid, unsound
No snakes are warm-blooded.
Therefore, no snakes are reptiles. VALID
Evaluating inferential claims
 Strong inductive
argument: one in which
the conclusion probably
follows from true
premises (50% or better
likelihood)
 Weak inductive
argument: one in which
the conclusion does not
probably follow from the
premises
 We had no school for the
last 1,000 Sundays. We
will probably have no
school next Sunday.
 When a lighted match is slowly
dunked into water, the flame
goes out. Gasoline is a liquid,
like water. So when a lighted
match is slowly dunked into
gasoline, the flame will go out.
Judging by degrees
 Unlike deductive arguments, which are either valid
or invalid, inductive arguments can have degrees of
strength and weakness.
 This barrel has 100 apples in it.
Three apples selected from it at random were ripe.
Therefore, probably all 100 apples are ripe.
 This barrel contains 100 apples in it.
Eighty apples selected from it at random were ripe.
Therefore, probably all 100 apples are ripe. [forks]
Qualifying strong arguments
 An inductive argument won’t work if it ignores
important evidence! For example . . .
 When a lighted match is slowly dunked into water,
the flame goes out. Gasoline is a liquid, like water.
So when a lighted match is slowly dunked into
gasoline, the flame will go out. Ignored evidence:
Gasoline, though a liquid, does not have the same
properties as water!
The counterexample method is no good on
inductive arguments, but . . .
The last word on inductive arguments
 Cogent inductive
argument: argument that
is (1) strong, (2) has all
true premises, and (3)
doesn’t overlook
important evidence that
would lead to another
conclusion
 Uncogent inductive
argument: inductive
argument that is either
(1) strong, but has at
least one false premise,
OR (2) was weak to begin
with, OR (3) overlooks
important evidence that
would lead to another
conclusion
In groups, classify arguments as either strong or weak; note whether
premises and conclusion are true or false; then classify them as cogent or
uncogent
1. Coke is a very popular soft drink. Therefore, probably someone,
somewhere, is drinking a Coke right now.
2. People have been listening to rock music for over 100 years, so they will
probably be listening to it a year from now.
3. Most charter school teachers are millionaires, and Mrs. Casey teaches
charter school, so she’s probably a millionaire.
4. FDR said we have nothing to fear but fear itself. Therefore, women have
no reason to fear serial rapists.