CPPE 4266 FIRST PUBLIC EXAMINATION Preliminary Examination in Philosophy, Politics and Economics INTRODUCTION TO PHILOSOPHY LONG VACATION 2014 Thursday 4 September 2014, 9.30am - 12.30pm 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. IMPTANT You must use a separate booklet for your answers to 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. 4266 1
SECTION A: LOGIC (Please use a separate booklet for each section) 1. (a) Define what it is for a relation R on a set S to be (i) reflexive; (ii) symmetric; (iii) transitive; (iv) an equivalence relation. [4] (b) A relation R on a set S is serial if for every a in S there is a (not necessarily distinct) b in S such that a, b is in R. (i) Let S be the set of human beings currently alive. Give an example of a relation R on S that is serial. Briefly justify your answer. (ii) Let S once more be the set of human beings currently alive. Give an example of a relation R on S that is not serial. Briefly justify your answer. (iii) Suppose that a relation R on a set S is reflexive. Must R be serial on S? Justify your answer. (iv) Suppose that a relation R on a set S is symmetric, transitive and serial. Must R also be reflexive on S? Justify your answer. (v) Suppose that a relation R on a finite set S is transitive and serial. Must there be an element a in S such that a, a is in R? Justify your answer. [4] (c) (i) Suppose that the set S has one element and that R is a relation on S. Must R be an equivalence relation? Justify your answer. (ii) Suppose that the set S has one element and that R 1 and R 2 are distinct relations on S. Must at least one of R 1 or R 2 be an equivalence relation on S? Justify your answer. (ii) Suppose that the set S has two elements. How many distinct equivalence relations are there on S? 4266 2
2. (a) Define what it is for an L 1 -sentence to be an L 1 -tautology. (b) Using truth-tables or otherwise, determine whether the following are L 1 - tautologies: (i) (P P) (Q Q) (ii) (P P) (Q R) (iii) ((P Q) R) (P (Q R)) [8] (c) (i) Suppose that 1 and 2 are L 1 -tautologies that do not share a sentence letter. Must 1 2 be an L 1 -tautology? Justify your answer. (ii) Suppose that 1 and 2 are L 1 -sentences that do not share a sentence letter. If 1 2 is an L 1 -tautology, what can you say about each of 1 and 2? Justify your answer. [5] (d) Asked about the relation of logical consequence in L 1, a student says: means that if then, which may be formalised as. Explain in detail where the student s argument goes wrong. [7] 3. (a) State the natural deduction rules for propositional logic (the language L 1 ). You should justify any conditions imposed on the application of a rule. [10] (b) State the natural deduction rules for predicate logic without identity (the language L 2 ) supplementary to the ones stated in (a). You should justify any conditions imposed on the application of a rule. [12] (c) State the natural deduction rules for predicate logic with identity (the language L = ) supplementary to the ones stated in (a) and (b). You should justify any conditions imposed on the application of a rule. 4266 3 TURN OVER
4. (a) Which of the following English connectives are truth-functional? Justify your answers. (i) A unless B. (ii) If John remembers that A then it was the case that A. (iii) A because B. (iv) If it were the case that A then it would be the case that B. [12] (b) Formalise the following sentences in predicate logic with identity (the language L = ), including a dictionary. (i) (ii) (iii) (iv) Abraham likes a subject only if it s easy. Two queens of England have been called Elizabeth. The three musketeers surrounded the statue. To lose one parent is a misfortune; to lose two is carelessness. [13] 5. For each claim below, either provide a natural deduction proof showing that the entailment holds, or else provide a counterexample to show that it does not. (i) {Q, P Q } P (ii) { (P Q) } Q (iii) {P 1 (P 2 ( P 3 P 4 )), P 4 (P 1 P 2 )} ( P 1 P 2 P 3 P 4 ) (iv) { x(px Qx)} x(qx Px) (v) { x y(rxy Ryx), x y z(z = x z = y)} xrxx (vi) { x y(rxy Ryx), x y z((rxy Ryz) Rxz)} xrxx [25] 4266 4
SECTION B: GENERAL PHILOSOPHY (Please use a separate booklet for each section) 6. EITHER (a) Is there a satisfactory way to save the account of knowledge as justified true belief from Gettier s challenge? (b) Do you know whether or not you are a brain in a vat? 7. EITHER (a) What are Hume s concerns about induction? Does he answer them? (b) Do you know whether the laws of nature will still be the same at the end of this exam as they were when you started it? 8. EITHER (a) Does Descartes offer a compelling argument for substance dualism in the 2 nd Meditation? (b) What does Jackson s thought experiment about Mary establish? 9. EITHER (a) Is there any more to freedom than acting without coercion? (b) I want you to perform a certain action A. If you decide to do A, then I will do nothing. But if you do not decide to do A, then I will press a button which makes you do A. You decide to do A, so I do nothing. What does this case tell us about what it is to be free? 4266 5 TURN OVER
10. EITHER (a) Does Locke provide good reasons for thinking the diachronic identity conditions for human beings differ from those of persons? (b) What, if anything, can we learn about personal identity from reflecting on the possibilities of fission and fusion? 11. EITHER (a) Does God s existence follow from God s essence? (b) Does awareness of the suffering inflicted on humans by large scale natural disasters make it irrational to believe in God? SECTION C: MAL PHILOSOPHY (Please use a separate booklet for each section) 12. Since utilitarianism is a philosophy of reform, the fact that its prescriptions so often go against common sense is a mark in its favour, not a mark against it. Is this correct? 13. Should utilitarians look to actual consequences, intended consequences or foreseeable consequences? 14. Are intensity and duration of pleasure any more commensurable with each other than quality and quantity? 15. If Mill is correct that the origin of the notion of justice is connected with the ordinances of law (Utilitarianism, ch.5) what sense can be made of the notion of natural justice? 16. Mill fails to prove utilitarianism because no ethical theory can ever be proven. Discuss. 17. Utilitarianism only compromises the integrity of non-utilitarians. Discuss. [END OF PAPER] 4266 6 LAST PAGE