Preliminary Examination in Mathematics and Philosophy

A

• 1. The subject of the examination shall be (a) Mathematics, and (b) Philosophy. The syllabus and number of papers shall be prescribed by regulation from time to time by the Mathematical, Physical and Life Sciences Board and the Board of the Faculty of Philosophy.

• 2. A candidate shall offer both subjects for examination.

B

• 1. Candidates shall take five written papers. The titles of the papers shall be:

  • A. Mathematics I (as specified by the Preliminary Examination in Mathematics)

  • B. Mathematics II (as specified by the Preliminary Examination in Mathematics)

  • C. Mathematics III(P)

  • D. Philosophical Topics in Logic and Probability

  • This paper shall consist of three sections:
  • • A. Introduction to Logic
    •  
    • Subjects to be studied include: syntax and semantics of propositional and predicate logic, identity and definite descriptions, proofs in Natural Deduction, and the critical application of formal logic to the analysis of English sentences and arguments.  These topics 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.
    •  
    • B. Philosophical topics in Logic
    •  
    • Subjects to be studied include: Putnam's model-theoretic argument; Skolem's paradox.
    •  
    • C. Philosophical topics in Probability

  •  

    • Subjects to be studied include: technical basics (including field/algebra of events; Kolmogorov axioms; finite vs. sigma-additivity; definition of conditional probability; elementary useful theorems; definition of a Bernoulli trial/i.i.d. sequence; Bernoulli’s Theorem; and Bayes’ Theorem); matters of application (including applications of probabilities; conditionalisation; correlations and screening off; probability of a conditional vs conditional probability; Bayesian jargon; and frequentist jargon); and interpretations of probabilities (including classical probability; logical probability; personal probability; frequentism; and propensities).

  • Candidates shall be required to attempt questions from at least two sections. Proper study of the Faculty reading list for each section will serve as complete preparation for that section.

  • E. Introduction to Philosophy

    The paper shall consist of two parts:

    • 1. General Philosophy Subjects to be studied are: knowledge; skepticism; perception; induction; the relation between mind and body; personal identity; free will; the problem of evil.

    • 2. Frege 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.

  • Candidates will be required to attempt four questions, and answer at least one question from Part 1 and at least one question from Part 2.

• 2. Candidates shall be deemed to have passed the examination if they have satisfied the Moderators in all five papers A-E either at a single examination or at two examinations in accordance with the proviso of cl 3.

• 3. A candidate who fails to satisfy the Moderators in one or two of papers A-E may offer the papers failed on one subsequent occasion. A candidate who fails to satisfy the Moderators in three or more of papers A-E may offer all five papers on one subsequent occasion, except that a candidate who fails to satisfy the Moderators in all of papers A-C, but who has satisfied the Moderators in papers D and E, may offer papers A-C only on one subsequent occasion.

• 4. The Moderators may award a distinction to candidates of special merit who have passed all five written papers at a single examination.

• 5. The syllabus for each paper in Mathematics shall be published by the Mathematical Institute on the departmental website by the beginning of the Michaelmas Full Term in the academic year of the examination, after consultation with the Mathematics Teaching Committee.

• 6. The use of hand held pocket calculators is generally not permitted but certain kinds may be permitted for some papers. Specifications of which papers and which types of calculator are permitted for those papers will be announced by the Moderators in the Hilary Term preceding the examination.