Syllabus: Tom Donaldson’s ‘Introduction to Logic’, Fall 2011
Basic Information
Instructor:
Tom Donaldson (email: tmedonaldson@gmail.com)
Number:
01:730:201
Class Location: SC 207 (College Avenue)
Class Times:
Usually Mondays and Wednesdays, 7:40pm to 9pm (there are exceptions – see below).
Office Hours:
5pm-7pm on the same day as class, or as arranged. Office hours will be held in room
113, 3 Seminary Place.
Textbook:
Volker Halbach, The Logic Manual
Other materials will be put on the Sakai site for the course.
Course Description
The course will be a rigorous introduction to logic. The course is offered by the philosophy department,
but this is somewhat misleading – most of the material is mathematics. Here’s what we will cover:

We will learn about informal proofs, and practice constructing such proofs by doing puzzles.

We will look at some famous mathematical proofs – such as the proof that there is no largest
prime number, and the proof that 2 is irrational.

We will study some basic set theory.

We will investigate the syntax and semantics of propositional logic…

…and predicate logic.

We will learn how to ‘translate’ sentences from English into formal languages.

We will study a formal proof system – more specifically, a ‘natural deduction’ system.

We will discuss, but not prove, the soundness and completeness theorems for this formal proof
system.

We will look at the logic of identity, and Russell’s theory of descriptions.

Time permitting, we may finish by looking at some basic modal logic.
Course Goals

Philosophers regularly appeal to logic in their work. Without some understanding of basic logic,
it is impossible to understand much recent work in philosophy. Having completed this course,
students will be able to understand much of the logic used in contemporary philosophy.

Students who study subjects in which proofs are used – mathematics, philosophy, computer
science, physics, economics – will be better able to construct and understand proofs, and better
able to identify errors in putative proofs.

Students will gain a better understanding of how natural languages work. They will learn to
identify structural ambiguities in sentences of natural languages.

Having completed the course, students will be less prone to certain sorts of error in reasoning.
They will for example be less likely to confuse ‘All Fs are Gs’ with ‘All Gs are Fs’, and less likely to
commit the quantifier shift fallacy.

Logic is a fascinating a rewarding subject in its own right. I hope that at least once in the course,
each student will look at a clever proof, and smile.
List of Classes
Week 1:
Sep 7, 8
Week 2:
Sep 12, 14
Week 3:
Sep 19, 21
Week 4:
Sep 26, 28
Week 5:
Oct 3, 5
Week 6:
Oct 10, 12
Week 7:
Oct 17, 19
Week 8:
Oct 24, 26
Week 9:
Oct 31, Nov 2
Week 10:
Nov 7, 9
Week 11:
Nov 14, 16
Week 12:
Nov 21
Week 13:
Nov 28, 30
Week 14:
Dec 5, 7
Week 15:
Dec 12
(NB: This week there is a Thursday class instead of a Monday class)
(NB: No class on Wednesday – it’s Thanksgiving.)
List of Topics
Topic Number
0
1
2
3
4
5
6
7
8
9
Topic
Informal Proof
Sets, Relations and Arguments
Syntax and Semantics of Propositional Logic
Formalization in Propositional Logic
The Syntax of Predicate Logic
The Semantics of Predicate Logic
Natural Deduction
Formalization in Predicate Logic
Identity and Definite Descriptions
Basic Modal Logic
Reading
None
TLM ch. 1
TLM ch. 2
TLM ch. 3
TLM ch. 4
TLM ch. 5
TLM ch. 6
TLM ch. 7
TLM ch. 8
I’ll write something for this topic,
which I’ll distribute in good time.
Assessment
There will be an in-class exam after topics 2, 4, 6 and 9, each of which will take up one class. These will
be closed book exams, and collaboration will not be permitted. Each student’s final grade will be
determined entirely by their scores on these exams (and their attendance record). Each student will be
given a ‘raw score’ for each exam, as a fraction. These scores will then be converted to a ‘cooked score’
on the following four-point scale:
A
Outstanding
B+
B
4.0
3.5
Good
C+
3.0
2.5
C
Satisfactory
2.0
D
Poor
1.0
F
Failing
0.0
The function used to convert raw scores to cooked scores will vary from exam to exam. I may award
scores in excess of 4.0. To calculate each student’s final grade, I will begin by calculating the mean of
their cooked scores for the assessments. If necessary, I will then remove points for unexcused absences
(see below). Finally, I will round the score to the nearest half point – rounding up if the score is a
multiple of 0.25 – and give the student the appropriate letter grade. I will be completely strict about this
rounding process: if a student’s score is 3.24 I will round it down to 3.0 and give the student a B. This is
non-negotiable. I will not reply to emails that say ‘…but I was only 0.01 away from a B+…’.
Attendance
Students are expected to attend all classes; if you expect to miss one or two classes, please use the
University absence reporting website https://sims.rutgers.edu/ssra/ to indicate the date and reason for
your absence. An email is automatically sent to me. My attendance policy is as follows. Each student
will be allowed up to three unexcused absences, without penalty. For every unexcused absence after the
third, the student will lose a tenth of a point from their final score (see ‘Assessment’, above). Each
student should come to office hours at least once in the semester. There is a penalty of a tenth of a
point for failing to do this. If a student misses one of the exams, he or should contact me to arrange a
make-up exam.
Problem Sheets
I will produce a problem sheet for each topic. These are obligatory, but not graded. I encourage students
to work on these in groups. Once the students have had sufficient time to work on a problem sheet, I
will put an answer sheet up on Sakai. I will be happy to help students with their work on these sheets; I
will also be happy to help students understand the answer sheets. The questions on the exam will be
similar to those on the problem sheets – so students who skip the problem sheets will very likely get low
grades.
Disability Accommodation
Students with disabilities who consequently require special accommodations should contact me.
Students who have questions about the university's accommodation policies should refer to the Rutgers
Office of Disability Services, at http://disabilityservices.rutgers.edu/
Classroom Conduct
Laptops will not be permitted in class. Students may not use mobile phones, except with prior
permission from me. An atmosphere of jovial conviviality is expected and required.