PLEASE NOTE this is a sample reading list for the 2015-16 academic year
– precise seminar content may change from year to year.
 Resources:
Our primary text will be
Logic and Structure, 5th edition by Dirk van Dalen, Springer Verlag, 2008
in which we will cover most of chapters 1-3, plus parts of chapters 4, 5, and 6. Much
of this material is covered at a more elementary level in chapters 15-19 of
Language, Proof and Logic, Jon Barwise and John Etchemendy, CSLI Publications, 2002.
Students lacking a background in elementary discrete maths (e.g. basic set theory,
mathematical induction) are encouraged to obtain
How to Prove It: A Structured Approach, Daniel J. Velleman, Cambridge University
Press, 2006.
Students considering taking further logic modules will also benefit from
looking at The Open Logic Book (which is part of the Open Logic Project)
 Seminar
All students are expected to attend and participate in seminar. This is
particularly important for Philosophy students as attendance information is
collected on Tabula and feeds in to the monitoring point system. Seminar is your
opportunity to clarify any issues which may be unclear from lecture or the
readings and to get help with exercises.
 Assessment:
The module will be assessed on the basis of a two hour exam. There will also be
weekly unassessed problem sets. Although these will not count towards your
final mark, doing a selection of the posted exercises during term will not only
help with your understanding of the material as we go along but will also
facilitate exam revision. Solutions will be posted on the module website and
discussed in seminar.
 Approximate schedule
Week
Date
Topics
Readings
1
5 October
7 October
12 October
14 October
19 October
21 October
26 October
28 October
2 November
Introduction and set theory review
PL syntax, proofs by induction on syntax
PL semantics (part 1)
PL semantics (part 2), natural deduction for PL (part 1)
Natural deduction for PL (part 2)
PL Soundness
PL Completeness (part 1)
Completeness (part 2)
FOL syntax
LS
LS
LS
LS
LS
LS
LS
LS
LS
2
3
4
5
1, LPL 8.3, LPL 15
2.1, LPL 16, HP 6
2.2, 2.3
2.2, 2.3, 2.4
2.4, 1.6
2.5
2.5, HP 7.1
2.5, HP 7.1
3.1, 3.2, 3.3
6
7
8
9
10
4 November
9 November
11 November
16 November
18 November
23 November
25 November
30 November
2 December
7 December
9 December
FOL semantics (part 1)
LS 3.2, 3.4, 3.5
Reading week (no lecture)
Reading week (no lecture or seminar)
FOL semantics (part 2)
3.2, 3.4, 3.5
Identity, examples of theories and models
LS 3.6, 3.7
Natural deduction for FOL
LS 3.8, 3.9, 3.10
FOL completeness (part 1)
LS 4.1, LPL 19
FOL completeness (part 2)
LS 4.1, LPL 19
The Compactness Theorem and applications
LS 4.2
Properties of models, the Löwenheim-Skolem Theorem LS 4.2, 4.3
LS 5, 6
Beyond: Peano Arithmetic and incompleteness,
intuitionistic, modal, and second-order logic
LPL = Logic, proof and language
LS = Logic and structure
HP = How to prove it