EXFAC03-FIL Exfac, filosofivariant HØST 2007 Torsdag 13. desember kl ( 4 timer)

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1 EXFAC03-FIL Exfac, filosofivariant HØST 2007 Torsdag 1 desember kl ( 4 timer) Oppgavesettet består av åtte sider og er delt inn i to hoveddeler (1 og 2). I del 1 skal én av oppgavene besvares. I del 2 skal alle fire deler ( Part I, II, III og IV) besvares. Ingen hjelpemidler tillatt. Da all undervisning og hjemmearbeid i del 2 har vært på engelsk vil også eksamensoppgavene i denne delen være på engelsk. DEL 1 Besvar én av følgende oppgaver: 1. Hva er galt ved fysikalisme (physicalism) ifølge Thomas Nagel i What is it like to be a bat?? Har Nagel rett? Gi ett begrunnet svar. 2. Hva mener Nagel med verdienes fragmentering (the fragmentation of value)? Hvordan henger dette sammen med hans syn på distinksjonen mellom det personlige og upersonlige (subjektive og objektive)? Nynorsk: Svar på ein av desse oppgåvene: Kva er gale med fysikalisme (physicalism) i følgje Thomas Nagel i What is it like to be a bat?? Har Nagel rett? Grunngjev svaret. 2. Kva meiner Nagel med fragmentering av verdiar (the fragmentation of value)? Korleis heng dette saman med synet hans på skilnaden mellom det personlige og upersonlige (subjektive og objektive)?

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3 Del 2 Del 2 er delt i fire deler, alle fire skal besvares. PART I Translate each of the following statements into the language of sentential logic. Assign letters to each atomic statement; write down what atomic statement each letter stands for. Letters should stand for positively stated sentences, not negatively stated ones; for example, the negative sentence I am not hungry should be symbolized as ~ H using H to stand for I am hungry. Identify logical connectives. For example: Although it is raining I will jog It is raining.: A I will jogg.: B A & B Connectives: not ( ikke ): ~ and ( og ): & or / either or ( eller / enten eller ): v if then ( hvis.. da ): If and only if (hvis og bare hvis : 1. It is not raining, but it is still too wet to play. 2. Jay will win, or Kay will win. Jay will win, or Kay will win, but not both. 4. If Jones isn t a crook, then neither is Smith. 5. I will not graduate if I don t pass both logic and history. 6. I will graduate this semester only if I pass intro logic. 7. Taking all the exams is necessary, but not sufficient, for acing intro logic. 8. If you concentrate well only if you are alert, then provided that you are wise you will not fly an airplane unless you are sober.

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5 PART II 1. Symbolize the following sentences in PL using the given symbolization key. UD: Lxy: x loves y Txy: x is attracted to y Mx: is a man Rx: x is mortal Wx: x is a women Ax: x is almighty Bx: is beautiful a: Agatha b: Bertram a. All men are mortal. b. Some women are beautiful. c. No man is almighty. d. If men love Agatha then they are attracted to her. e. If any men is mortal then all women are (mortal) f. Bertram and beautiful women and men are mortal. 2. Determine the truth value of the following sentences on this interpretation UD: numbers Bxy: x is between y and z Dxy: x greater y Fx: is a positive number Gx x is a negative number a: -2 b: -5 c: 7 d: 5 e: 9 a. Bbac v ~Bcab b. (Fa Fe) Dde c. Baaa Bccc d. (Fa Dda) & ~(Dde v Ddc)

6 PART III All derivations in this section are in SD (NOT SD+). The complete set of rules for derivations is on the last page choose 1. Choose a) or b) a) Derive U 1. H U A 2. S & H A b) Derive (L v P) & D 1. ~N A 2. (~N L) & (D ~N) A 2. Choose a) or b) a) Derive ~U 1. (U&M) S A 2. M & ~S A b) Derive G (H K) 1. (G & H) K A 2. Choose a) or b) a) Derive ~N 1. H ~N A 2. (H v G) & ~M A ~N (G v B) A 4. b) Derive H & (S v N) 1. R v V A 2. R (H & S) A V (H & N) A 4.

7 PART IV All derivations are in PD (NOT in PD+). The complete set of allowed rules is on the last page. 1. Choose a), b) or c) a) Derive ( x)(fx & Gx) 1. ( x) Fx & ( x) Gx A 2. c) Derive ( x)( y) Fyx 1. ( x)( y) Fxy A 2. b) Derive ( x)(gx & Hx) 1. ( x) (Fx Gx) 2. ( x) (Gx Hx) Fa A Choose a) or b) a) Derive ( x) Fx ( x) Gx 1. ( x)(fx Gx) A 2. b) Derive ( x)(fx Hx) 1. ( x)(fx Gx) 2. ( x)(gx Fx) A

8 Choose a) or b) a) Derive ( x)(gx & Hx) b) Derive ( x)gx 1. ( x)(fx Gx) A 2. ( x)(fx & Gx) A 1. ( x)fx v ( x)gx A 2. ( x)~fx A 4. Derive ( x)( y) Rxy 1. ( x)( y) Rxy A 2. ( x)( y) [Rxy Ryx] A ( x)[( y)ryx ( y)ryx] A 4.

9 Derivation Rules for SD Conjunction Introduction &I Conjunction Elimination &E P P & P & P P & Disjunction Introduction vi Disjunction Elimination ve P P v P v P v P A R R R A Conditional Proof E Conditional Elimination I P A P P P Negation Introduction ~I Negation Elimination ~E ~P P A ~P A ~ ~ P Biconditional Introduction I Biconditional Elimination E P A P P P A P P

10 Derivation Rules for PD Universal Introduction I P(a/x) ( x) P Provided i) a does not occur in an undischarged premise ii) a does not occur in ( x) P Universal Elimination E ( x) P P(a/x) Existential introduction P(a/x) ( x) P Existential elimination ( x) P P(a/x) A Provided i) a does not occur in an undischarged premise ii) a does not occur in ( x) P iii) a does not occur in