Philosophy 111:
Practice With Validity

 
 


 

NOTE: The answers to the exercises are given below.

A. UNDERSTANDING DEDUCTIVE ARGUMENTS

Using the definitions of 'deductive', 'inductive', 'valid', 'invalid', 'sound', 'unsound', 'strong', and 'weak' given in class, indicate whether the following are true or false.

1. A deductive argument can have all false premises.

2. A deductive argument can have false premises and a true conclusion.

3. A valid deductive argument can have all false premises.

4. An invalid deductive argument can have all false premises and a true conclusion.

5. A valid deductive argument cannot have all false premises and a true conclusion.

6. No inductive arguments are valid.

7. No deductive arguments are strong.

8. A valid deductive argument can have all false premises and a false conclusion.

9. Whether an argument is valid has nothing to do with whether any of it's premises are actually true.

10. No sound deductive argument has a false premise.

B. EVALUATING DEDUCTIVE ARGUMENTS

Relying on your natural sense of what follows from various statements and your commonsense knowledge of the world, determine for each of the following arguments (1) whether the premises are true, (2) whether the argument is valid or invalid and (3) whether the argument is sound or unsound.

1. P1 There are banana stands in Bolivia and Afghanistan.
C There is an Afghanistan banana stand.

2. P1 Alaska is bigger than New York state.
P2 New York state is bigger than Rhode Island.
C Alaska is bigger than Rhode Island.

3. P1 If people find something offensive, then it's immoral.
P2 People find homosexuality offensive.
C Homosexuality is immoral.

4. P1 Some Albanians hail from Albania.
C Wealthy Albanians hail from Albania

5. P1 Barry Larkin plays for the Reds.
P2 Mark McGuire plays for the Cardinals.
C The Reds and the Cardinals are baseball teams.

6. P1 Either Descartes was French or Socrates was Greek.
P2 Socrates was not Greek.
C Descartes was French.





ANSWERS TO LOGIC EXERCISES:

A. UNDERSTANDING DEDUCTIVE ARGUMENTS

All are true except number 5.

B. EVALUATING DEDUCTIVE ARGUMENTS

1. P1 & C are true. Valid. Sound.

2. P1, P2 & C are true. Valid. Sound.

3. P1 is false (e.g. scrubbing toilets may be offensive, but it's not immoral). P2 is true, C is false (though controversial). Valid (because IF the premises WERE true, the conclusion would have to be true - this is an example of the valid argument form affirming the antecedent). Unsound, because P1 is false.

4. P1 & C are true. Invalid (The fact that some Albanians hail from Albania does not make it true that wealthy ones do. Even if some Albanians hailed from Albania, it could have been the case that all the wealthy ones hailed from some other country). Unsound, because the argument is invalid.

5. P1, P2 & C are true. Invalid (The premises say nothing about whether the Reds or the Cardinals are baseball teams, so it could have been the case that both premises were true yet the Reds and the Indians were soccer teams). Unsound, because the argument is invalid.

6. P1 & C are true, P2 is false. Valid (because IF the premises WERE true, the conclusion would have to be true). Unsound (because P2 is false).


 

 

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