[Note: The HTML format has forced me to make the following symbol substitutions. For conjunction, an ampersand (&) rather than the dot; for conditional, a dash and angle bracket (->) rather than the horseshoe; for biconditional, an angle bracket, dash, and angle bracket (<->) rather than the triple-bar; and for existential quantifier, a captial 'E' rather than a reversed capital 'E'. The real exam will use the normal symbols.]

Final Exam

Philosophy 500 -- Introduction to Logic

Write your name here: ______________________________

The exam consists of 15 questions. Point values vary. Show all work. Use the back of the sheets if you need more room.

Part One. Short Answer. (15 points total. 3 questions at 5 points each.)

1. If an argument has all true premises and a true conclusion, must it be valid? Explain.

2. Is 'A v A' a substitution instance of 'p v q'? Explain.

3. Explain the difference between a quantifier statement and a truth-functional compound of quantifier statements.

Part Two. Translations. (10 points total. 2 translations at 5 points each.)

Translate the following arguments into logical symbolism.

4. Translate the following into the formalism of propositional logic.

If the mind and the brain are identical, then the brain is a physical entity if and only if the mind is a physical entity. If the mind is a physical entity, then thoughts are material entities. Thoughts are not material entities, but the brain is a physical entity. Therefore, the mind and the brain are not identical.

5. Translate the following into the symbolism of quantifier logic.

Not everyone who is beautiful and rich is both famous and appreciated.

Part Three. Truth Tables. (10 points total, for 1 truth table.)

6. Construct a truth table of the following statement to determine if the statement is a contradiction, a contingency, or a tautology.

[S v (T & U)] <-> [(~S v ~T) & (~S -> ~U)]

Part Four. Proofs. (40 points total. 4 proofs at 10 points each.)

7.

1. C -> (D -> ~C)
2. C <-> D / .: ~C & ~D

8.

1. (Ex)~Hx -> (x)(Fx -> Gx)
2. ~(x)(Hx v Gx) / .: ~(x)Fx

9.

1. (Ex)Ax -> (Ex)(Bx & Cx)
2. (Ex)Cx -> (x)(Dx & Ex) / .: (x)(Ax -> Ex)

10. / .: ~(Ex)(Fx & Gx) -> [(x)Fx -> ~(Ex)Gx]

Part Five. Informal Fallacies. (25 points total. 5 questions at 5 points each.)

11. Mom! Why can't Snake and I get married just because we're 17? You and dad were only 17 when you guys got married!

12. Wife to husband: I think I deserve a vacation somewhere nice. After all, it would cost less than having me go shopping with your credit cards for five straight days.

13. Those who don't fight communism are helping it, and hence are communists themselves.

14. More people own a Chevy than any other car. Shouldn't you?

15. We should rehabilitate violent criminals rather than send them to prison. Even Darth Vader, who was about as nasty as they get, was redeemed by a little kindness, and even saved Luke.