unit 2 Exercise (3.1-3.6)
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Exercise 3.1
What is a deductive argument?
Answer: A deductive argument is intended to give logically conclusive support to its conclusion. It asserts that if the premises are true, the conclusion must also be true.
What is an inductive argument?
Answer: An inductive argument is intended to give probable support to its conclusion. It suggests that if the premises are true, the conclusion is likely to
be true.
Are inductive arguments truth-preserving? Why or why not?
Answer: No, inductive arguments are not truth-preserving. Even if the premises are true, the conclusion might still be false because inductive reasoning involves making generalizations based on specific cases.
The terms valid and invalid apply to what types of arguments?
Answer: Valid and invalid apply to deductive arguments.
What kind of guarantee does a deductive argument provide when it is valid?
Answer: A deductive argument, when valid, guarantees that if the premises are true, the conclusion must also be true.
Can an inductive argument guarantee the truth of the conclusion if the premises are
true? Why or why not?
Answer: No, an inductive argument cannot guarantee the truth of the conclusion even if the premises are true. Inductive reasoning involves probability, not certainty.
What is the difference between an inductively strong argument and an inductively weak one?
Answer: An inductively strong argument is one where the conclusion is likely based on the premises. An inductively weak argument has a conclusion that is less likely based on the premises.
What is the term for valid arguments that have true premises?
Answer: Sound arguments have true premises and are valid.
What is the term for strong arguments that have true premises?
Answer: Cogent arguments have true premises and are strong.
Can a valid argument have false premises and a false conclusion? False premises and a true conclusion?
Answer: Yes, a valid argument can have false premises and a false conclusion
or false premises and a true conclusion.
What logical conclusion can you draw about an argument that is valid but has a false conclusion?
Answer: Validity only ensures that if the premises are true, the conclusion must be true. It doesn't speak to the truth of the conclusion itself.
Is it possible for a valid argument to have true premises and a false conclusion?
Answer: Yes, it is possible for a valid argument to have true premises and a false conclusion.
In what way are conclusions of deductive arguments absolute?
Answer: Conclusions of deductive arguments are absolute. If the argument is valid and the premises are true, the conclusion is certain.
Exercise 3.2
For each of the following arguments, follow the four-step procedure to determine whether it is deductive or inductive, valid or invalid, and strong or weak. Indicate the results of applying each step. EXAMPLE 1:
Colonel Mustard did not commit the murder. Someone who had committed the murder would have dirt on his shoes and blood on his hands. Colonel Mustard has neither. Step 1: Conclusion: Colonel Mustard did not commit the murder. Premises: Someone
who had committed the murder would have dirt on his shoes and blood on his hands. Colonel Mustard has neither. Step 2: Deductively valid. Step 3: Does not apply. Step 4: Does not apply. EXAMPLE 2: Most people who smoke pot are irresponsible and forgetful. Looks like you smoke pot all the time. Ergo, you’re irresponsible and forgetful. Can you remember that? Step 1: Conclusion: Ergo, you’re irresponsible and forgetful. Premises: Most people who smoke pot are irresponsible and forgetful. Looks like you smoke pot all the time. Step 2: Not deductively valid. Step 3: Inductively strong. Step 4: Does not apply
Exercise 3.3
For each of the following arguments, indicate whether it is valid or invalid, strong or weak
Alice says that nothing is sacred. So intolerance toward other religions is okay.
Validity/Invalidity: Invalid (non-sequitur)
Strength/Weakness: Weak
Social welfare is, by definition, a handout to people who have not worked for it. But giving people money that they have not earned through labor is not helping anyone. It follows then that social welfare does not help anyone.
Validity/Invalidity: Invalid (non-sequitur)
Strength/Weakness: Weak
If CNN reports that war has started in Iraq, then war has started in Iraq. CNN has reported exactly that. War must have started.
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Validity/Invalidity: Valid (deductive)
Strength/Weakness: Strong
If r = 12, then s = 8; r = 12; therefore, s = 8.
Validity/Invalidity: Valid (deductive)
Strength/Weakness: N/A (deductive arguments don't have strength/weakness)
Any sitcom that tries to imitate The Big Bang Theory is probably a piece of trash. All
of this season’s sitcoms try to ape Big Bang. They’ve gotta be trash.
Validity/Invalidity: Invalid (non-sequitur)
Strength/Weakness: Weak
“Poetry is finer and more philosophical than history; for poetry expresses the universal and history only the particular.” [Aristotle, Poetics]
Validity/Invalidity: Invalid (subjective and not logically connected)
Strength/Weakness: Weak
Either you’re lying or you’re not telling the whole story. You’re obviously not lying, so you’re just relating part of the story.
Validity/Invalidity: Valid (deductive)
Strength/Weakness: Strong
Exercise 3.4
For each of the following arguments, identify the implicit premises that will make the argument valid. EXAMPLE:
The engine is sputtering. It must be out of gas. Implicit premise: Whenever the engine sputters, it’s out of gas
Any senator who is caught misusing campaign funds should resign his seat. Senator
Greed should resign.
Implicit Premise: Senator Greed was caught misusing campaign funds.
Not everyone in this country has health insurance. Therefore, health care is a disaster.
Implicit Premise: A lack of universal health insurance constitutes a healthcare
disaster.
In the first week at the box office, the movie grossed over $30 million. So it’s sure to
win at least one Oscar.
Implicit Premise: Movies that gross over $30 million in the first week are sure to win at least one Oscar.
The FBI doesn’t have a very serious focus on stopping terrorism. Another major terrorist attack will happen in this country.
Implicit Premise: A serious focus by the FBI is necessary to prevent major terrorist attacks.
The author of the book on interventionist wars is either biased or incompetent as a journalist. So she’s biased.
Implicit Premise: If someone is not incompetent as a journalist, they are not biased.
Exercise 3.5
For each of the following arguments, determine whether it is valid or invalid and indicate the argument pattern.
If the Pilgrims built that wall, there would be archaeological evidence of that. But there is no such evidence. So the Pilgrims did not build that wall.
Validity: Valid
Argument Pattern: Modus Tollens
If the butler didn’t kill the master, then the maid did. The butler didn’t kill him. So the maid killed him.
Validity: Invalid
Argument Pattern: Affirming the consequent
Either John drove home or he stayed late. He didn’t drive home. Therefore, he stayed late.
Validity: Valid
Argument Pattern: Disjunctive Syllogism
If the South Africans have nuclear weapons, the South African jungle will be radioactive. The South African jungle is radioactive. Therefore, the South Africans have nuclear weapons.
Validity: Invalid
Argument Pattern: Affirming the consequent
If the New York Times comes out in favor of the liberal democrats, they will win the election. But the newspaper will not come out in favor of the liberal democrats, so they will not win.
Validity: Valid
Argument Pattern: Modus Tollens
Explanation of Argument Patterns:
Modus Tollens: If P, then Q. Not Q, therefore not P.
Affirming the Consequent: If P, then Q. Q, therefore P (invalid).
Disjunctive Syllogism: Either P or Q. Not P, therefore Q.
Exercise 3.6
For each of the following premises, fill out the rest of the argument to make it valid in two different ways—modus ponens and modus tollens.
If God is in his heaven, then all is right with the world.
Modus Ponens: God is in his heaven.
Modus Tollens: All is not right with the world; therefore, God is not in his heaven.
If Lino is telling the truth, he will admit to all charges.
Modus Ponens: Lino admits to all charges.
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Modus Tollens: Lino is not admitting to all charges; therefore, he is not telling the truth.
If some wars are just, then pacifism is false.
Modus Ponens: Some wars are just.
Modus Tollens: Pacifism is not false; therefore, no wars are just.
If the new vaccine prevents the spread of the virus, the researchers who developed the vaccine should get the Nobel Prize.
Modus Ponens: The vaccine prevents the spread of the virus.
Modus Tollens: The researchers did not get the Nobel Prize; therefore, the vaccine does not prevent the spread of the virus.
If religious conflict in Nigeria continues, thousands more will die.
Modus Ponens: Religious conflict in Nigeria continues.
Modus Tollens: Thousands more will not die; therefore, religious conflict in Nigeria does not continue.
If p, then q.
Modus Ponens: p is true.
Modus Tollens: q is false; therefore, p is false.