LESSON 3 :PRACTICE WITH VALID/ INVALID;

MORE ON INDUCTIVE ARGUMENTS

Logic

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 impeccablecharacter,” I’m mainly using which form of appeal?(a) logos (b) ethos (c) pathos2. 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.

C

R

S

S

R

C

Diagrams: A test for validity

All murderers are violent offenders.All violent offenders are felons.So all felons are murderers.

All girls have hearts. TTT invalid, unsoundAll humans have hearts.Therefore, all girls are humans.

All reptiles are warm-blooded. FTF, valid, unsoundNo snakes are warm-blooded.Therefore, no snakes are reptiles.

All killers are a threat to society. TTF, invalid,unsndSome gun-owners are killers.Thus, all gun-owners are a threat to society.

warmINVALID

VALID

INVALID

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.

INVALID

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, unsoundAll humans have hearts.Therefore, all girls are humans.

All killers are a threat to society. TTF, invalid,unsndSome gun-owners are killers.Thus, all gun-owners are a threat to society.

All reptiles are warm-blooded. FTF, valid, unsoundNo snakes are warm-blooded.Therefore, no snakes are reptiles.

INVALID

VALID

INVALID

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.