CPPE 4266 FIRST PUBLIC EXAMINATION Preliminary Examination in Philosophy, Politics and Economics INTRODUCTION TO PHILOSOPHY LONG VACATION 2013 Thursday 05 September 2013, 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. 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. 4266 1
SECTION A: LOGIC (Please use a separate booklet for each section) 1. (a) What does it mean for an English connective to be truth-functional? [2] (b) Which of the following English connectives are truth-functional? In each case give a partial truth table and justify your answer, using examples as appropriate. (i) A or it is not the case that B. [3] (ii) A or it has never been the case that B. [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. [12] God is omnibenevolent. It follows that causation is non-transitive. For supposing causation to be transitive, given that God caused the existence and flourishing of humankind, it must also be the case that God caused global climate change if humankind s existence and flourishing did. Every honest scientist knows that exactly this human activity did cause our present climate predicament. But although every good Christian knows that God created humankind and caused it to flourish, a God behind global climate change is far from omnibenevolent. (d) Using the following dictionary, formalize the English sentences (i) and (ii) below in the language L 2 of predicate logic. P 1 :... is an ordered pair Q 1 :... is a set R 2 :... has... as an element a : the empty set (i) The empty set is a set but not an ordered pair. [2] (ii) Some set has no elements. [3] 4266 2
2. (a) Describe all the ways in which quotation marks may be added to the following expressions to obtain true English sentences. Explain your answers, commenting on any difficulties or points of interest. (i) π is a Greek letter, but π is not. [3] (ii) is a string of opening quotation marks. [2] (b) Determine for each of the following relations whether it is symmetric on the set of sentences of the language L 1 of propositional logic and whether it is reflexive on this set. Substantiate your answers. (i) the relation containing exactly the pairs φ,ψ of sentences of L 1 such that φ ψ is a tautology [4] (ii) the relation containing exactly the pairs φ,ψ of sentences of L 1 such that φ ψ is a tautology [4] (iii) the relation containing exactly the pairs φ,ψ of sentences of L 1 such that φ ψ is a contradiction [4] (c) What s the difference between Lady Margaret Hall,New College and {Lady Margaret Hall,New College}? [3] (d) Consider the relation containing exactly the following ordered pairs: Merton, Balliol, Univ, Merton, the oldest Oxford college, Univ Somebody proposes the following diagram for this relation: Balliol Merton Univ the oldest Oxford college (i) Under what conditions is this the correct diagram for this relation? Explain your answer. [2] (ii) It s commonly thought that either Balliol, Merton or Univ is the oldest Oxford college. Draw the diagram for each of these possibilities. [3] 4266 3 TURN OVER
3. (a) Establish the following claims by means of proofs in the system of Natural Deduction. (i) x(px yrxy) zrzz [3] (ii) P Q R R P Q [4] (iii) x yrxy y z(ray Ryz) [6] (b) The following is an abbreviation of an L 2 -sentence. x y z(qxyz Py Pz Qxxz Qxyx) (i) Give the full unabbreviated sentence. [2] (ii) Specify an L 2 -structure with as few elements in its domain as possible in which the sentence is true. Sketch an argument why the sentence is true in the structure you have specified. [6] (iii) Explain why there cannot be such a structure with fewer elements in its domain. [4] 4. (a) Formalize the following as a valid argument in L 2, using the dictionary below. Demonstrate the validity of your formalization using Natural Deduction. Comment on any difficulties and points of interest. [12] Q: Matter is atomless P 2 :... is a proper part of... R 2 :... is smaller than... a: the smallest object Matter is not atomless. Assuming, on the contrary, that it is, then every object has a proper part. A proper part of anything is smaller than it is. If something is smaller than the smallest object, then something is smaller than everything. But this is impossible: nothing is smaller than itself. (b) Formalize the argument in part (a) once more, this time as an invalid argument in L =, using the same dictionary but without the constant a. Demonstrate the invalidity of your formalization by specifying a counterexample. [8] (c) What is it that makes the L 2 formalization valid when the L = formalization is not valid? [5] 4266 4
5. (a) (i) What is an atomic L 2 -formula? [3] (ii) What is an L 2 -formula? [3] (b) Recall that a set of L 2 -sentences is semantically consistent if there is an L 2 -structure in which all members of the set are true. Specify structures to show that each of the following sets is semantically consistent. [You need only specify the structure; there is no need to prove that the sentences in the set are true in the structure.] (i) { Pc,((Pa Pb) Pc),Pa} [2] (ii) { x y(rxy Qyx), x Rxx} [3] (iii) { x(rxx Qxx), x y(rxy Qxy), xrxx, xqxx} [3] (c) Which of the following sets is semantically consistent? Justify your answers. (i) The set of all L 2 -sentences [2] (ii) {φ : φ is an atomic L 2 -sentence} [3] (iii) { φ : φ is an atomic L 2 -sentence} [3] (d) Say that a set of English sentences is compossible if it is possible for all of the sentences to be true together. Give an example to show that the compossibility of a set of English sentences is not a necessary condition for the consistency of the set of their L 2 -formalizations. [3] 4266 5 TURN OVER
SECTION B: GENERAL PHILOSOPHY (Please use a separate booklet for each answer) 6. EITHER (a) How often have I dreamt that I was in these familiar circumstances, that I was dressed, and occupied this place by the fire, when I was lying undressed in bed? (DESCARTES) How, if at all, does Descartes consideration bear on your belief you are not asleep here and now? (b) Does knowledge require epistemic responsibility? 7. EITHER (a) All reasonings concerning matter of fact seem to be founded on the relation of Cause and Effect. By means of that relation alone we can go beyond the evidence of our memory and senses. (HUME) Assuming this claim is correct, does it have any relevance to the issue of whether our beliefs about the future are justified? (b) Is it reasonable to believe that the daffodils in the Oxford University Parks will flower next spring? 8. EITHER (a) [M]erely because I know with certitude that I exist, and because, in the meantime, I do not observe that anything necessarily belongs to my nature or essence beyond my being a thinking thing, I rightly conclude that my essence consists only in my being a thinking thing. (DESCARTES) Discuss. (b) Red things look different to people who have monochrome vision and people with normal vision. Assuming this is true, does it entail that the mind is not a physical thing? 4266 6
9. EITHER (a) [T]o find wherein personal identity consists, we must consider what person stands for; which, I think, is a thinking intelligent being, that has reason and reflection, and can consider itself as itself, the same thinking thing, in different times and places; which it does only by that consciousness which is inseparable from thinking. (LOCKE) Does this conception of a person provide Locke with the basis for a plausible account of personal identity? (b) Could Jane be the same person in five years time without being the same animal? 10. EITHER (a) [L]iberty, when opposed to necessity, not to constraint, is the same thing with chance; which is universally allowed to have no existence. (HUME) Is Hume correct? (b) Did Sarah act freely when she wrote her prize-winning philosophy essay only if she could have decided not to write it? 11. EITHER (a) But now if because I can draw from my thought the idea of an object, it follows that all I clearly and distinctly apprehend to pertain to this object, does in truth belong to it, may I not from this derive an argument for the existence of God? (DESCARTES) Can Descartes derive a convincing argument for the existence of God in this way? (b) Does the existence, or otherwise, of human freedom have any relevance to the problem of evil? 4266 7 TURN OVER
SECTION C: MAL PHILOSOPHY (Please use a separate booklet for each answer) 12. In what sense, if any, is reading poetry better than playing push-pin? 13. On what grounds, if any, can a utilitarian convincingly argue that killing another human being is morally wrong? 14. Is utilitarianism an egalitarian moral theory? 15. According to consequentialism, if I have to choose between saving the life of my father, who is a handyman, and saving the life of a world-class brain surgeon at the height of her career, I should save the surgeon. Do you agree? If the statement is true, does it constitute a decisive objection to consequentialism? 16. Must one be virtuous in order to be happy? 17. What would a utilitarian justification for punishment look like? 18. Can something be good for me even though I am not aware of its existence or occurrence? 4266 8 LAST PAGE