FIRST PUBLIC EXAMINATION. Preliminary Examination in Philosophy, Politics and Economics INTRODUCTION TO PHILOSOPHY TRINITY TERM 2013

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1 CPPE 4266 FIRST PUBLIC EXAMINATION Preliminary Examination in Philosophy, Politics and Economics INTRODUCTION TO PHILOSOPHY TRINITY TERM 2013 Tuesday 18 June 2013, 9.30am pm This paper contains three sections: Logic; General Philosophy; and Moral Philosophy. You must answer FOUR questions, including at least one question from each section. You may answer your fourth question from any section. In the Logic section, questions 1 and 2 are of an elementary and straightforward nature; the remaining questions are more demanding. You may answer only one of questions 1 and 2 (but are not obliged to attempt either). The numbers in the margin in the Logic section indicate the marks which the Moderators expect to assign to each part of the question. Please use a separate booklet for your answers in each section. Write your CANDIDATE NUMBER on each booklet. DO NOT write your name. Do NOT turn over until told that you may do so

2 SECTION A: LOGIC (Please use a separate booklet for each section) 1. (a) What does it mean for an English sentence to be a propositional contradiction? [2] (b) Which of the following sentences are propositional contradictions? Substantiate your answers by formalizing the sentences in the language L 1 of propositional logic. Comment on any difficulties and points of interest. (i) It s possible that God exists and it s not possible that God exists. [3] (ii) This question isn t easy because it s easy and completely trivial. [3] (c) Formalize the following as a valid argument in L 1, rewording its premisses as necessary. Demonstrate the validity of your formalization using truth-tables or Natural Deduction. Specify your dictionary carefully. Note any difficulties and points of interest. [10] The argument is valid. For unless you slip up on the formalization, or make a mistake in the truth-table, there is no way to assign every premiss a T and the conclusion a F in the reverse truth-table. I know you won t slip up on the formalization and will take due care. Clearly, moreover, you ll only make a mistake in the truth-table if you don t take due care. And, if there is no way to assign T to every premiss and F to the conclusion, that means the argument is valid. (d) Using the dictionary below, translate the sentences (i) (iii) of the language L 2 of predicate logic into idiomatic English. P 1 :... is an ordered pair P1 1 :... is a set Q 2 :... has... as an element R 1 :... is a binary relation a : the empty set (i) Qaa [2] (ii) x(qxa Rx) [2] (iii) x(p 1 x (Rx y(qxy Py))) [3]

3 2. (a) Which of the following expressions abbreviate sentences of the language L 1 of propositional logic in accordance with the Bracketing Conventions? In each case, reintroduce the brackets dropped in accordance with the Bracketing Conventions to obtain an unabbreviated L 1 -sentence, or explain briefly why this is not possible. (i) P Q R [2] (ii) P P P P [2] (iii) (P Q) P R 23 [2] (b) Express the following claim without using metavariables: [3] If φ is a sentence of L 1, then the expression φ is a sentence of L 1. (c) Explain what it means for a relation to be (i) symmetric, (ii) asymmetric and (iii) antisymmetric. [3] (d) Determine for each of the following relations whether they are functions and, if they are, what their range is. Explain your answers briefly. (i) { England, England, Scotland, England, Wales, Scotland } [3] (ii) the relation containing all ordered pairs d,e such that d is the monarch of e [3] (iii) the relation containing all ordered pairs d,e such that e is the monarch of d [3] (e) Discuss whether the following argument is logically valid. [4] Paris is a European capital. Therefore Paris is an element of the set of European capitals TURN OVER

4 3. (a) Classify the following strings as L 2 -formulae, L 2 -sentences or neither. Briefly justify your answers. [3] (b) (i) ( x 3 (P 4 xx 3 xx R 2 36 x 3x) P) (ii) x x xp 3 xxx (iii) xp 3 x (i) What is an L 2 -structure? What is an assignment over an L 2 -structure? [3] (ii) State the satisfaction clause for the universal quantifier which specifies how the truth of the L 2 -formula vφ under assignments relates to the truth of φ under assignments. [2] (iii) Deduce an analogous condition which specifies how the falsity of the L 2 -formula vφ under assignments relates to the falsity of φ under assignments. [2] (c) Classify each of the following L 2 -sentences as logically true, a contradiction, or neither. Justify your answers either by using Natural Deduction or by specifying L 2 -structures as appropriate. (i) Rab (ii) x y(rxy (Ryx Rxy)) [3] (iii) ( x y(rxy Ryx) x y z(rxy (Ryz Rxz))) xrxx [2] (iv) x yrxy x Rxx x y z(rxy (Ryz Rxz)) [3] (v) x yrxy xrxx [5] [2]

5 4. (a) Which of the following sentences can be adequately formalized using Russell s theory of descriptions, that is, the formalization of definite descriptions used in the Logic Manual? In each case provide a formalization in the language L = of predicate logic with identity, or briefly explain why no adequate formalization is possible. Comment on any difficulties and points of interest. (b) (i) The willow is a deciduous tree. [3] (ii) The highest peak in Wales is a mountain. [3] (iii) The winner is the fastest. [3] (i) Show that the following argument is not valid in predicate logic with identity. Formalize it in L = and specify a counterexample. [7] Hannah has at least one pet cat. She also has exactly one pet dog. Therefore, Hannah has no fewer than two pets in total. [You need only state the counterexample; there is no need to prove that the structure you specify is a counterexample.] (ii) Specify a further premiss that the speaker might naturally be taken to rely upon in order to make the argument valid in predicate logic with identity. Demonstrate the validity of the resulting argument using Natural Deduction. [6] (iii) Is the argument in part (b)(ii) valid in predicate logic (without identity)? Briefly explain why or why not. [3] TURN OVER

6 5. (a) State the rule for introducing, that is, Intro, in words. [2] (b) Establish the following claims by means of proofs in Natural Deduction. (i) (P Q) (Q P) P Q [3] (ii) x(px yryx) zrza xpx [5] (iii) x y(pxy Qxy) x ypxy [7] (c) Consider the rule with the following graphical representation: φ ψ ψ φ If this rule were added to the system of Natural Deduction, would more sentences become provable (with all assumptions discharged)? Explain your answer. [4] (d) Consider the rule with the following graphical representation: φ ψ φ ψ If this rule were added to the system of Natural Deduction, would the Soundness Theorem still hold? Explain your answer. [4]

7 SECTION B: GENERAL PHILOSOPHY (Please use a separate booklet for each section) 6. EITHER (a) Do you know that you are now sitting a philosophy exam? Are you certain? (b) If it was 20 degrees Celsius in a room and there was a thermometer in the room that believed that it was 20 degrees Celsius in the room, would that thermometer know that it was 20 degrees Celsius in the room? 7. EITHER (a) What appeal does Hume make to custom in his discussion of induction, and does he appeal to it in an appropriate way? (b) Should we be disturbed by the claim that our beliefs about the future cannot be established deductively? 8. EITHER (a) I know that everything which I clearly and distinctly understand is capable of being created by God so as to correspond exactly with my understanding of it. (DESCARTES) How does Descartes rely on this claim to try to establish that he is really distinct from his body, and can exist without it, and does he succeed? (b) Does Frank Jackson s thought experiment concerning Mary show us anything about the relationship between the mental and the physical? TURN OVER

8 9. EITHER (a) But is not a man drunk and sober the same person? Why else is he punished for the act he commits when drunk, though he be never afterwards conscious of it? (LOCKE) Discuss. (b) Could you survive having half of your brain transplanted into one body and half into another? 10. EITHER (a) Could there be freedom in a world where everything was necessary? (b) Is a person free only if she can do otherwise? 11. EITHER (a) Was Descartes right to think that his understanding that existence belongs to the nature of God was no less clear and distinct than his understanding that having three sides belongs to the nature of triangles? (b) Is the existence of horrendous evil inconsistent with the existence of God? SECTION C: MAL PHILOSOPHY (Please use a separate booklet for each section) 12. Can the fulfillment of his sadistic impulses make a sadist genuinely happy? 13. Can a utilitarian account for the badness of death? 14. Is it possible to prove a moral theory? 15. Does rule-utilitarianism provide a good alternative to act-utilitarianism?

9 16. Can a utilitarian be genuinely committed to promoting justice? 17. If you see a person drowning, what matters is that you save her life; it does not matter what your intentions for doing so are. Do you agree? 18. If the only way to save a human being is by killing a cat, a utilitarian is committed to the view that one must kill the cat. Do you agree? [END OF PAPER] LAST PAGE