Syllabus for PHIL231: Introduction
to Deductive Logic
Course
Hours: Monday, Wednesday, Friday 11.15-12.05
Prof: Brian Weatherson
brian at weatherson dot net
(preferred method of contact)
TA: to be determined
Office
hours for each to be determined
I have two aims for the course. By
the end of the course you should be able to:
Ò
Carry out proofs in a powerful formal system; and
Ò
Be familiar with many of the logical concepts you will
need for completing any non‑logic subject in a philosophy graduate
course.
These two aims are in some tension.
If I just cared about the first, I would spend all our time working with (more
or less) uninterpreted formal systems, and seeing who
could master the most complicated proofs. (For a little sample of what I would
try and have you do, try exercise 13.51 in LPL without using any of the Con
rules.) If I just cared about the second, I would focus on things like the
informal reasoning discussed in chapter 5 of LPL, and then leave the book for a
more extended discussion of concepts like necessity and provability. Since I
care about both these things, I will try and balance these aims as much as
possible.
The
primary textbook for the course, as you probably know by now, is:
Jon Barwise and John Etchemendy,
Language, Proof and Logic. CSLI Press, 2002.
This book will be (and has been)
referred to as LPL in these notes, and in most notes I distribute. The first
eleven or so weeks of the course will be heavily based around this book, though
I may distribute some supplemental notes on various topics when they become
salient.
In
the notes, as well as listing the reading for each class, I note the exercises
from the book I expect you to do (and turn in!) before each Monday class. These
should be considered more important
than the reading. Logic is not like other parts of philosophy; you cannot
passively learn it. (More precisely, you will get even less out of a logic
course if you try to passively learn it than you would get out of courses in
metaphysics, or ethics, or other areas – not that passive learning is
particularly encouraged in those areas either.)
As
you will have noticed already, the textbook is a text/software package. One
implication of this is that many of the exercises can be (and should be) submitted
electronically. One problem is that people who bought second hand textbooks may
not be able to submit work electronically. Since the bookshop was advised not
to sell second-hand books, hopefully this won’t be a serious problem. If it is
a serious problem, let me know and we’ll try and work out a new arrangement.
At
the end of the course we will do a small section on extending what we’ve
learned to deal with counterfactual and modal claims. These concepts are very
important throughout philosophy and may be the most useful things you’ll learn
in this course. For this section we will use David Velleman’s
web-based textbook Blogic,
available at
http://www-personal.umich.edu/~velleman/Logic/
We’ll be looking mainly at chapter
4, but since Velleman uses slightly different
notation to LPL, we’ll have to spend a little time getting up to speed on his
notation.
Grading
System
Regular
submitted work: 60%
Midterm
test: 10%
Final
test: 30%
For each week’s classes I list
reading and exercises. The reading should be done before the relevant week, or
at the latest during the week we are discussing the material in class. The work
is due by 8 a.m. the following Monday (if to be done electronically)
or the following Monday’s class (if to be done on paper). You can (and where
possible should) do the work while doing the reading, but in some cases it will
be difficult, and you will want to wait until hearing my pearls of wisdom
before doing the work. But there will often be too much work to be done on the weekend, and you will need to do
some of the exercises after Monday’s and Wednesday’s classes in order to keep
the workload manageable. In the work
section of the syllabus I list a series of numbers; these are exercises from
LPL.
NB: Many of the terms in the syllabus will probably be rather
unfamiliar to you if you haven’t taken a logic course before. Some will be
unfamiliar even if you have. This is a common problem in technical courses -
see any advanced mathematics syllabus for similar examples. But that doesn’t
mean that it isn’t a problem. If you want any of the terms explained in more
detail, let me know.
Unit One: Propositional Logic
Aims and nature of course
The textbook and the software
Syntax of atomic sentences in FOL
Work (due
August 30): 1.1-1.6
Syntax of functional notation, arithmetic and set theory
Alternative notations
Tarski’s World program
Validity and soundness
Fitch-style proofs, and the program
Fitch
Proofs using identity
Demonstrating non‑consequence
Work (due
September 6): 1.9-11, 2.1, 2.15-2.21
Three Boolean connectives (and, or, not)
Role of parenthesis in removing ambiguity
Important equivalences between Boolean sentences
Use of truth tables in determining: truth conditions,
tautologies, equivalence, validity, invalidity
Work (due
September 13): 3.1-3.3, 3.5-3.18, 3.20-3.22, 4.1-4.9, 4.12-4.19, 4.24
Truth tables on the cheap
Some important informal patterns of
reasoning: argument by cases, indirect proof
Arguments with inconsistent
premises
Formal proofs using Boolean
connectives
Rules for conjunction
Rules for disjunction
Rules for negation
The nature of subproofs
Work (due September 20): 5.1, 5.3, 5.6, 5.8,
5.9, 5.20, 5.26, 6.1-6.9, 6.12, 6.18-6.20
Elimination rules for the material
conditional
Introduction rules for the material
conditional
Important equivalences of
statements containing conditionals
Important types of proof
Work (due
September 27): 7.1-7.8, 7.10-7.19, 7.25-7.28, 8.1-8.3, 8.8, 8.16
Soundness and completeness
Review
Class Test – in class on October 1 – 45 minute test on all the material in Unit One.
Work (due
October 4): 8.18-8.25, 8.41-8.43
Unit Two: Predicate Logic
Introducing the two central quantifiers: $ and"
Syntax for the quantifiers
Semantics for the quantifiers
Translating complex English sentences into quantified
sentences
Quantifiers and Gricean implicature
Multiple quantifiers in a single sentence
Work (due
October 13): 9.16, 9.19, 11.13-11.15, 11.45
(Note the
short week due to Fall Break)
Propositional Logic and Predicate Logic
First‑Order validity
Some important equivalences in first‑order
logic
Informal introduction to the quantifier rules
Work (due October 18): 10.1, 10.8, 10.9, 10.22-10.29
Rules of proof for the universal quantifier
Rules of proof for the existential quantifier
Proof strategies for quantified
logic
Work (due
October 25): 13.23-13.31, 13.49-13.52
(Note the
short week due to my being away at a conference)
Basic set theory: singletons, empty
set, subset, intersection, union
Properties of relations
Semantics for quantified logic
Models for first‑order logic
Work (due November 1): 15.4-6, 15.11-13, 15.22, 15.29-35
(Note the
short week due to my being away at a conference)
Soundness proof for rules of FOL
Work (due
November 8): 18.7-9, 18.14-17
Numerical quantification
Russell’s theory of definite
descriptions
Conservativity, Monotonicity and Persistence
Review of Predicate Logic
Work (due
November 15): 14.1-5, 14.8-9, 14.13, 14.26, 14.28, 14.51, 14.56
Unit Three: Modal Logic and Counterfactuals
Survey of Velleman’s notation
The differences between counterfactual and regular
conditionals
Possible worlds diagrams
Subjunctive Conditionals
Work (to be
assigned)
Complex Counterfactuals
(Note that
there’s no class on Wednesday December 1 due to my being away at a conference)
Logical Relations
Representing other modal operators using possible worlds