arguments

Valid arguments and invalid

Do the exercises below. Be sure to scroll down for the full set.

  1. Which of the following arguments are valid? Which are invalid?
  2.   Donna will get an A in philosophy if an only if she writes a good paper. Donna got an A in philosophy. Therefore, she wrote a good paper. B.  If Donna writes a good paper, she will get an A in philosophy. Donna got an A in philosophy. Therefore, she wrote a good paper. C. If whales are mammals, then they are not fish. Whales are fish. Whales are not mammals. D. If the rapture has occurred, then either some of the cars on the highway will be unoccupied or all drivers are damned. Some drivers are not damned. None of the cars on the highway are unoccupied. Therefore, the rapture has not occurred. E  Some snarks are bandersnatches. All bandersnatches are igglypoofs. So, some snarks are igglypoofs.
  3. Answer the following questions. Give short explanations that reason from the definitions of the relevant logical concepts
  4. Does an argument provide a good reason for believing its conclusion if it is valid? Explain.
  5. Can a valid argument have a false conclusion? Explain.
  6. Can a sound argument have a false conclusion? Explain.
  7. What is it for a statement to be valid? (trick question)
  8. Which of the following arguments are inductively strong? Which are weak?
  9. It has rained every day in the Darién Gap for the past twenty-five years. Thus it will probably rain in the Darién Gap tomorrow.
  10. People try on shoes before buying them. People drive cars before signing up for a three-year lease. People take a close look at travel information before committing to an expensive vacation. Thus people should have sex with each other before committing to marriage.
  11. Two teenagers were found writing graffiti on the school walls yesterday. Thus all teenagers are delinquents.
  12. A reliable study showed that 90 percent of Bellevue College’s students want better food in the school cafeteria. Latisha is a student at Bellevue College. It follows that Latisha probably wants better food at the cafeteria.
  13. Upon landing at the SeaTac Airport, plane passengers saw broken buildings, large cracks in the runway, fire engines running about, and paramedics assisting injured people. The passengers concluded that an earthquake just occurred.
  14. Answer the following questions. Give short explanations based on the definitions of the relevant concepts.
  15. Explain how deductive validity and inductive strength differ.
  16. Can the conclusion of an inductively cogent argument be false? Explain.
  17. Must an inductively strong argument have true premises? Explain.

THIS BELOW PART IS THE READING FOR THE ASSIGNMENT (NOT PART OF THE QUESTIONS)

Validity Recap:

It will help to keep these categories separate:

Statements or claims can be true or false, but not valid, sound, strong or cogent.

Arguments are sets of statements. Arguments can’t be true or false. The can be valid, sound strong or cogent.

Properties of Statements (or claims) Properties of Arguments
True or false Valid

Sound

Strong

Cogent

When we way an argument is valid (or strong) we are not claiming that its premises are true. We are only claiming that IF they are true, then the conclusion is true (or likely to be true in the case of strength).

Arguments Deductive Inductive
Premises support conclusion Valid

If the premises are then the conclusion must be true

Strong

If the premises are true then the conclusion is likely to be true

Support + true premises Sound

Valid an all premises are true

Cogent

Strong and all premises are true

Valid argument can have false premises and they can have false conclusions. When we say an argument is valid we are only saying that the conclusion must be true IF all the premises are true. Each of the arguments in the chart below is valid:

True Premises Some false premises
True conclusion 1.      If cats are felines then they nurse their young.

2.      Cats are felines

3.      So cats nurse their young.

1.       If dogs are felines then they nurse their young

2.      Dogs are felines

3.      So dogs nurse their young

False conclusion No such thing. For an argument to be valid is for it to be impossible for it premises to be true and its conclusion false. 1.      If fish are felines then they nurse their young

2.      fish are felines

3.      So fish nurse their young