Course Syllabus

Welcome to PHIL.222 Intermediate Logic. This course builds on PHIL 101, introducing proof methods, particularly natural deduction. In the first part of the course, you will learn to construct natural deductions in propositional and predicate logic, and formal arithmetic. You will be working with purely formal languages, manipulated according to precise rules. The methods are less mechanical than those of PHIL 101, requiring problem-solving skills and a facility with abstract reasoning at a higher level. The next part of the course introduces sequents, which are rules for describing and manipulating systems, including natural deductions, but also strings of characters, formulas, and sentences in natural language. We introduce inductive definitions for these systems, and the notions of derivable and admissible rules. The final section of the course adds the minimal symbols and tools for arithmetic, including identity (=), addition (+) and multiplication (×), proofs by induction, and the role of logic in arithmetic. As well as completing a foundation in logic, the course aims to provide an understanding of the process of constructing complex arguments that is applicable in philosophy and other disciplines.

PHIL 222 is a Core Course for Logic and Computation (BA major and minor, BSc major). It is a 15 pt Stage II course with a workload of up to 10 hours / week. PHIL 101 is the prerequisite course.

Staff

Lecturer: Andrew Withy
Class Rep: TBA

Timetable

• Lecture: Tues 3-5, 206-315.
• Tutorial 1: Mon 2-3, 114-G15. (starts week 2)
• Tutorial 2: Tues 11-12, 253-101. (starts week 2)
• Office Hour: Fri 1-2, 206-449.

Assessment

Weekly Assignments (best 10 of 11): 20%
Two Tests: 30%
Final Exam: 50%

Written or Recorded Material

There is no recommended text. The material will be taught through interactive lectures and exercise-based tutorials. We will provide extensive notes forming a draft textbook for the first four weeks, and shorter notes for the remaining weeks. You will be expected to attend all the lectures and take your own notes. There will be no lecture recordings. Attending all the tutorials is highly recommended.

Course Schedule (approximate)

1. Fitch-style Natural Deduction
2. Assumptions in Natural Deduction
3. Quantifiers in Natural Deduction
4. Classical Natural Deduction
5. Genzten Sequents
6. Advanced Gentzen Sequents
7. String Parsing & Informal Induction
8. Derivable and Admissible Rules
9. Identity & Equational Reasoning
10. Robinson Arithmetic & Functions
11. Peano Arithmetic & Formal Induction
12. Informal Induction