[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.]

Midterm II

Philosophy 500 -- Introduction to Logic

Write your name here: ______________________________

Part One. Short Answer. (5 points each x 5 questions = 25 points)

1. Explain the difference between an individual constant and an individual variable.

2. Which instantiation and generalization rules have flagging restrictions, and which do not?

3. Explain the difference between a universal sentence and an existential sentence.

4. Is the following a quantifier statement, or a truth-functional compound? (x)(Fx) v (x)(Gx )

5. Can you use existential instantiation on ~(Ex)Fx in order to derive ~Fa? If so, why? If not, why not?

Part Two. Translations. (5 points)

Translate the following argument into logical symbolism.

6. Anyone who gets an A is intelligent and loves Cheezy Poofs. Some people who get an A have big MTV hair. Therefore, some people with big MTV hair love Cheezy Poofs.

Part Three. Proofs. (10 points each x 7 proofs = 70 points)

Construct proofs for the following arguments. You may use any of the methods we have studied.

7.

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

8.

1. (x) (Rx -> Sx)
2. ~Sb / .: (Ex) ~Rx

9.
1. (x) [ Sx -> (Ax v Bx) ]
2. (x) (Ax -> Px)
3. ~(x)(Sx -> Px) / .: ~(x) (Sx -> ~Bx)

10. Do the proof that was your answer to question 6.

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

12. / .: [(x)(Fx) & (x)Gx] -> (x)(Fx & Gx)

13.

1. Fa -> (x)(Hx & Gx)
2. (x)Jx
3. (x)Fx
4.( Jb & Hb) -> (x)Kx /.: Fa & Ka