PHIL 213: Deductive Logic

Larkin: Fall 2003

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First Test Review Problems

I. True/False Questions: 1.1 B

1. FALSE. A valid argument can have all true premises (making it sound as well as valid).

2. TRUE. This is just the definition of an argument.

3. FALSE. A valid argument can have false premises.

4. TRUE. Definition of logic.

5. FALSE. An individual statement is not the kind of thing that can be valid or invalid. Only arguments have a structure/form that can be called ‘valid’ or ‘invalid’. Statements are either true or false, but validity is not the same thing as truth.

6. FALSE. A valid argument can have false premises; and it can have a false conclusion. But if a valid argument has all true premises, then it must have a true conclusion.

7. FALSE. A sound argument is both valid and has all true premises. Since a sound argument is valid, it is such that if all the premises are true then the conclusion must be true. Since a sound argument also has all true premises, it follows that a sound argument must have a true conclusion.

8. TRUE. Definition of deductive logic.

9. TRUE. By definition of validity. A valid argument cannot have all true premises but a false conclusion.

10. FALSE. Arguments are not the kinds of things that can be true or false. Only individual statements have a truth value, and arguments are sets of statements.

11. FALSE. A valid argument can have all false premises and a true conclusion. Example:

P1: If Lassie is a frog, then she is a mammal.

P2: Lassie is a frog.

C: Lassie is a mammal.

12. TRUE. All invalid arguments are such that it is possible for them to have true premises and a false conclusion; and some invalid arguments actually do have all true premises and a false conclusion.

13. TRUE. Validity is a necessary condition for being sound.

14. FALSE. A valid argument can have a true conclusion and false premises (see #11); and if an argument does not have all true premises, then it is not sound.

15. TRUE. By definition, a valid argument cannot have a false conclusion and all true premises. So if a valid argument has a false conclusion it must have some false premise.

16. FALSE. Some unsound arguments are valid. They are unsound because they do not have all true premises.

17. FALSE. Premises are individual statements and individual statements are simply not the kinds of things that can be valid (in our sense of the term).

18. FALSE. All true premises is a necessary but not a sufficient condition for being a sound argument. It is also necessary that the argument be valid.

19. TRUE. If an argument does in fact have all true premises and a false conclusion, then it is obviously possible for an argument with that form to have true premises and a false conclusion; and by definition an argument with a form that can have all true premises but a false conclusion is invalid.

20. TRUE. If an argument has even one false premise, then not all the premises are true; but having all true premises is a necessary condition for being sound.

II. Argument Form Recognition/Counter-Examples: 1.3 B

1. See book.

2. W = Abortion in the case of ectopic pregnancy is wrong.

A = It is always wrong to kill an innocent human being.

P1: Not-W

P2: If A, then W.

C: Not-A

Form = Modus Tollens, VALID

3. W = Kidnapping is wrong.

D = Society disapproves of kidnapping.

P1: W, if D. P1: If D, then W.

P2: W. P2: W.

C: D. C: D

Form = Affirming the consequent, INVALID

4. See book.

5. L = Principle is interpreted literally.

F = Principle is interpreted figuratively

S = State should…

D = Principle necessarily demands death for murderers

P1: Either L or F.

P2: If L, then S.

P3: If F, then not-D.

C: So either S or not-D.

FORM = Constructive Dilemma, VALID

6. P = Affirmative action is preferential treatment of disadvantaged groups.

R = Preferential treatment for disadvantaged groups is reverse discrimination.

W = Affirmative action is wrong.

P1: P, and R.

P2: If P and R, then W.

C: W.

FORM = Modus Ponens, VALID

7. See book.

8. S = Mary is a psychiatrist.

H = Mary is a physician

P1: If S, then H.

P2: Not-H.

C: S.

Not one of our famous forms.

INVALID

Counter-example:

P1: If Lassie is a lizard, then she is a reptile.

P2: Lassie is not a reptile.

C: Lassie is a lizard.

III. Truth-Functional Translations: 7.1 E

1. D = Fido is a dog

A = Fido is an animal

F ® A

2. M = Josey is a mammal.

C = Josey is a cat.

C ® M

3. C = Physical laws can be changed.

N = Physical laws are necessary.

E = Physical laws are eternal.

(N v E) ® ~ C

4. M = Snakes are mammals.

N = Snakes nourish their young with milk.

(M ® N) · ~ N

5. E = Evil exists

G = God exists

~(E ® ~G)

6. G = Smith is guilty.

B = Smith’s blood is on the murder weapon.

(G ® B) ® (~B ® ~G)