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 impeccablecharacter,” 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. Mr. Simms’s powerpoints are online now!
Argumenttypes: 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. 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. INVALID INVALID warm VALID 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 INVALID VALID
Evaluating inferential claims Strong inductive argument: one in which the conclusion probably follows if premises are true (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. This barrel has 100 apples in it.Three apples selected from it at random were ripe.Therefore, probably all 100 apples are ripe.
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
Classify arguments as either strong or weak; note whether premises and conclusion are true or false; then classify them as cogent or uncogent • Coke is a very popular soft drink. Therefore, probably someone, somewhere, is drinking a Coke right now. • People have been listening to rock music for over 100 years, so they will probably be listening to it a year from now. • [bad example] Most charter school teachers are millionaires, and Mrs. Casey teaches charter school, so she’s probably a millionaire. • FDR said we have nothing to fear but fear itself. Therefore, women have no reason to fear serial rapists.
 The contamination of underground aquifers represents a pollution problem of catastrophic proportions.  Half the nation’s drinking water, which comes from these aquifers, is being poisoned by chemical wastes dumped into the soil for generations.
 The selling of human organs, such as hearts, kidneys, and corneas, should be outlawed.  Allowing human organs to be sold will inevitably lead to a situation in which only the rich will be able to afford transplants. This is so because  whenever something scarce is bought and sold as a commodity, the price always goes up.  The law of supply and demand requires it.
The selling of human organs, such as hearts, kidneys, and corneas, should be outlawed. If this practice is allowed to get a foothold, people in desperate financial straits will start selling their own organs to pay their bills. Alternately, those with a criminal bent will take to killing healthy young people and selling their organs on the black market. In the final analysis, the buying and selling of human organs comes just too close to the buying and selling of life itself.
Getting poor people off the welfare rolls requires that we modify their behavior patterns. The vast majority of people on welfare are high school dropouts, single parents, or people who abuse alcohol and drugs. These behavior patterns frustrate any desire poor people may have to get a job and improve their condition in life.
All dogs are mammals. Lassie is a dog. Therefore, Lassie is a mammal.