CASE STUDY

I Argument Structure Exercises

Exercise: Put the following simple arguments into standard form.

  1. Tuition rates have not increased, but room and board has. College is therefore more expensive, since students have to cover both of these costs.
  2. I followed the recipe on the box, but the dessert tasted awful. Some of the ingredients must have been spoiled.
  3. Capital punishment is not a deterrent to crime. In those states which have abolished the death penalty, the rate of incidence for serious crimes is lower than in those which have retained it.

Exercise: Put the following complex arguments into standard form.

  1. The Tigers are likely to lose this final game since it is a road game and they’ve done poorly on the road all season. If they lose this one, the coach will almost certainly be fired. The coach’s job is therefore in jeopardy.
  2. We know that Miss Scarlett and Professor Plum were in the study at the time of the murder since they were seen there. And Reverend Green had the candlestick in the ballroom, and so we know that Green was not involved in the murder. Hence Colonel Mustard did it in the kitchen with the lead pipe. Recall, after all, that the gun had not been fired.
  3. He signed on to teach Phil 3, and therefore he should lecture all quarter. So if he cancels the last 4 weeks of class, he has not done his job.
  4. You’ll pass Phil 3 if you work hard. There has never been a hard-working student who failed, so there probably never will be one.

Exercise: Put the following arguments (all of which have implicit premises and/or an implicit conclusion) into standard form.

  1. Jacob eats meat, which just goes to show that you don’t have to be vegetarian to be a good person.
  2. If you were a good father, you wouldn’t have allowed me to watch so much television.
  3. The only people who had access to the midterm were the TAs and the professor. None of the TAs had posted the midterm online, but it had indeed been posted online.

II. Argument Evaluation Exercises

Exercise: Consider the following deductive argument. Are the premises true? Is it valid? Are the premises relevant to the conclusion? In each case briefly explain why.

Everyone who smokes gets lung cancer.

Everyone who gets lung cancer suffers a painful death. ∴ Everyone who smokes suffers a painful death.

Exercise: For each of the following deductive arguments: Is it valid? Why or why not? 1.

Some Americans like hamburgers.

Joe likes hamburgers.

  • ∴ Joe is American.2.
    Some Americans like hamburgers. Joe is American.
  • ∴ Joe likes hamburgers. 3.No Americans like hamburgers.Joe is not American.
  • ∴ Joe likes hamburgers.4.
    No Americans like hamburgers. Joe likes hamburgers.
  • ∴ Joe is not American. 5.Socrates is a man.All men are carrots.
  • ∴ Socrates is a carrot.6.
    Abe Lincoln was either born in Illinois or he was once president. Abe Lincoln was never president.
  • ∴ Abe Lincoln was born in Illinois. 7.If I pull the trigger, Abe Lincoln will die.I do not pull the trigger.
  • ∴ Abe Lincoln will not die.8.
    Abe Lincoln was either from France or from Luxembourg. Abe Lincoln was not from Luxembourg.
  • ∴ Abe Lincoln was from France. 9.If the world were to end today, then I would not need to get up tomorrow morning.I will need to get up tomorrow morning.
  • ∴ The world will not end today.

Exercise: Evaluate the following inductive arguments with respect to Criterion 2. Is it a strong inductive argument? Why or why not?

1.
Most Americans like hamburgers. Joe is American.

  • ∴ Joe likes hamburgers. 2.Most Americans like hamburgers.Joe likes hamburgers.
  • ∴ Joe is American.3.
    Philosophy majors are rarely enrolled in Phil 3.
    Anthropology majors are often enrolled in Phil 3.
    Bob is a student in Phil 3.
    There are only two kinds of students in Phil 3, philosophy majors and anthropology majors.
  • ∴ Bob is an anthropology major.Exercise: Consider the statement A): Santa Barbara is in California.
  1. Give an argument for A that satisfies Criterion 1. Give an argument for A that fails tosatisfy Criterion 1. (Recall that an argument for A is one that has A as its conclusion.)
  2. Give an argument for A that satisfies Criterion 2 (i.e. either it is valid or it is inductivelystrong). Give an argument for A that fails to satisfy Criterion 2 (i.e. it is not valid nor is itinductively strong).
  3. Give an argument for A that satisfies Criterion 3. Give an argument for A that fails tosatisfy Criterion 3.
  4. Can you give an argument for A that satisfies all three criteria? If yes, then give one, ifno, then say why.

Exercise: Consider the statement B): Santa Barbara is not in California.

  1. Give an argument for B that satisfies Criterion 1. Give an argument for B that fails tosatisfy Criterion 1. (Recall that an argument for B is one that has B as its conclusion.)
  2. Give an argument for B that satisfies Criterion 2 (i.e. either it is valid or it is inductivelystrong). Give an argument for B that fails to satisfy Criterion 2 (i.e. it is not valid nor is itinductively strong).
  3. Give an argument for B that satisfies Criterion 3. Give an argument for B that fails tosatisfy Criterion 3.
  4. Can you give an argument for B that satisfies all three criteria? If yes, then give one, ifno, then say why.

Exercise: Can there be:

  1. A valid argument with one false premise and one true premise?
  2. A valid argument that only has false premises?
  3. A valid argument with only false premises and a false conclusion?
  1. A valid argument with a false conclusion?
  2. A valid argument with only true premises and a false conclusion?
  3. A sound argument with one false premise and one true premise?
  4. A sound argument that only has false premises?
  5. A sound argument with only false premises and a false conclusion?
  6. A sound argument with a false conclusion?
  7. A sound argument with only true premises and a false conclusion?

In each case: if so, give an example; if not, explain why not.

III. Argument Formalization Exercises

Exercise: Consider these sentence letters. P: Plato is a philosopher. Q: Plato lives in Athens. R: Aristotle is a philosopher. Express the form of each of the following English sentences in the language of propositional logic.

  1. If Plato is a philosopher, then he lives in Athens.
  2. Plato and Aristotle are both philosophers.
  3. If Plato is a philosopher and Aristotle is a philosopher, then Plato does not live in Athens.
  4. Either Plato is a philosopher or he lives in Athens.
  5. Aristotle is a philosopher if and only if Plato is a philosopher and lives in Athens.
  6. It is not the case that if Aristotle is a philosopher, Plato is a philosopher too.
  7. If Aristotle is not a philosopher, then Plato is a philosopher.

Exercise: Consider these sentence letters. M: Those creatures are men in suits. C: Those creatures are chimpanzees. G: Those creatures are gorillas. Express the form of each of the following English sentences in the language of propositional logic.

  1. Those creatures are not men in suits.
  2. Those creatures are men in suits, or they are not.
  3. Those creatures are either gorillas or chimpanzees.
  4. Those creatures are neither gorillas nor chimpanzees.
  5. If those creatures are chimpanzees, then they are neither gorillas nor men in suits.

Exercise: Consider these sentence letters. P: Pam is going. Q: Quincy is going. R: Richard is going. S: Sara is going. Translate each of the following arguments into the language of propositional logic. (In other words, put them into standard form and then translate their premises and conclusion into the language of propositional logic.)

  1. Pam is going. If Pam is going, then Quincy is going. Quincy is going if and only if Richard is not going. If Sara is going, then Richard is going. Therefore, Sara is not going.
  2. Either Quincy is going or Pam is going. Pam is going only if Sara is going. Sara is not going. Therefore, Quincy is going.