[Until 1 October 2012: Special Regulations for Honour Moderations in Mathematics and Philosophy

[1] A

1. [2] 1. The subjects of Honour Moderations in Mathematics and Philosophy shall be (a) Mathematics, (b) Philosophy.
2. [3] 2. All candidates must offer both (a) and (b).
3. [4] 3. The Moderators shall indicate on the pass list each candidate who has not passed this examination, but has passed in one subject, and shall indicate in which subject the candidate has passed.
4. [5] 4. The examination shall be under the joint supervision of the Divisional Board of Mathematical, Physical and Life Sciences and the Board of the Faculty of Philosophy, which shall appoint a standing joint committee to make regulations concerning it, subject always to the preceding clauses of this subsection.
5. [6] 5. (i) The Honour Moderators for Mathematics shall be such of the Moderators for Honour Moderations in Mathematics as may be required, not being less than two; those for Philosophy shall be nominated by a committee of which the three elected members shall be appointed by the Board of the Faculty of Philosophy.
6. [7] (ii) It shall be the duty of the chairman of the Honour Moderators in Mathematics to designate such of their number as shall be required for Mathematics in Honour Moderations in Mathematics and Philosophy, and when this has been done and the Honour Moderators for Philosophy have been nominated, the number of the Honour Moderators in Mathematics and Philosophy shall be deemed to be complete.

[8] B

[9] The highest honours can be obtained by excellence either in Mathematics or in Philosophy provided that adequate knowledge is shown in the other subject of the examination.

1. [10] 1. Four papers shall be set in the examination. Each candidate shall take all four papers.
2. [11] 2. The papers will each be devoted to the appropriate sections of the schedule.
3. [12] 3. The use of calculators is generally not permitted but certain kinds may be allowed for certain papers. Specifications of which papers and which types of calculators are permitted for those exceptional papers will be announced by the examiners in the Hilary Term preceding the examination.

[13] Schedule

[14] Section 1. Pure Mathematics I - as specified for Honour Moderations in Mathematics

[15] Section 2. Pure Mathematics II - as specified for Honour Moderations in Mathematics

[16] Section 3. Elements of Deductive Logic.

[17] Subjects to be studied include: propositional and predicate languages; truth tables; Natural Deduction; relations; the critical application of formal logic to the analysis of English sentences and inferences (problems of symbolization; scope, truth-functionality, quantification, identity, descriptions); elementary metatheorems about propositional calculus (including the following topics: expressive adequacy, duality, substitution, interpolation, compactness, consistency, soundness and completeness). Some questions of a mathematical nature will be set.

[18] These subjects shall be studied in conjunction with Volker Halbach’s Introduction to Logic manual, published by Oxford University Press. The logical symbols to be used are those found in this publication. Philosophical questions about logic may be studied by reading Mark Sainsbury, Logical Forms, 1st or 2nd edition (Blackwell), Chapters 1-2.

[19] Section 4. Introduction to Philosophy.

[20] The paper shall consist of two parts:

1. [21] A. General Philosophy [22] Subjects to be studied include: knowledge, scepticism, perception, induction, primary and secondary qualities, the relation of mind and body, personal identity, and free will. Candidates will have the opportunity to show first-hand knowledge of some canonical writings on these topics.
2. [23] B. Frege [24] This section shall be studied in connection with Frege Foundations of Arithmetic, trans. J. L. Austin, Blackwell, 1980. This section, while not being confined to the detailed views of the author of the set text, will be satisfactorily answerable by a candidate who has made a critical study of the text. There will not be a compulsory question containing passages for comment. [25] Candidates will be required to attempt four questions, and answer at least one question from Part A and at least one question from Part B.]