PHIL50S - Section 1
Peter Hawke
July 2, 2015
1. Example 1 (Argument Construction)
Q: Construct an argument with true premises, a true conclusion and
of the modus tollens form.
A: P1. For any number n, if n is even, then n + 1 is odd. P2. 3+1 is
not an odd

PHIL50S Lectures 4 and 5: Set Theory II:
Orders of Infinity
Peter Hawke
July 13, 2015
1. Overview Our goals:
Introduce a precise notion of the size of a set: cardinality
Use this notion to prove some (extremely surprising) results: most
famously, that t

PHIL50S - Lectures 12, 13, 14: Metalogic
Peter Hawke
August 10, 2015
1. Overview
Our goals:
Familiarize ourselves with the distinction between studying metalogic as opposed to logic per se.
Introduce two important notions of consequence: semantic vs.
sy

PHIL50S Lectures 9, 10, 11
Peter Hawke
August 2, 2015
1. Overview
Our goals:
Introduce and familiarize ourselves with a certain mathematical
theory: probability theory (sometimes called the probability calculus)
Locate two diverse and useful interpretat

PHIL50S Lecture 1 - General Introduction
Peter Hawke
June 24, 2015
1. Overview Our course, two perspectives:
An introduction to certain important formal methods frequently
discussed and applied in modern philosophy
An introduction to logic, in a broad s

PHIL50S Section 4
Peter Hawke
July 20, 2015
1. Answering Summary Questions Sometimes in the homework we
will ask you to summarize a portion of the material. Normally, what
we are interested in is for you to summarize a line of argument.
What constitutes a

PHIL50S - Lecture 3: Set Theory I: Russells
Paradox
Peter Hawke
July 5, 2015
1. Overview
Our goals:
(a) Motivate and introduce the basic ideas and notation of set theory
(b) Introduce a simple axiom system for set theory, known as Naive
Set Theory (NST)
(

PHIL50S - Lecture 2: Basic Logical Notions
Peter Hawke
June 25, 2015
1. Logic and Language
Logicians study consequence, a relation between pieces of information
(at least when we think about things as abstractly as possible).
Typically, we convey informat

PHIL50S Section 5
Peter Hawke
July 27, 2015
1. Simple Chance Set-ups
Q: Consider the following chance set-up: from a normal pack of 52
playing cards, one card is chosen completely randomly. There are,
then, 52 possible outcomes of this procedure, each, in

PHIL50S Lectures 6,7,8: Kinds of Truth
Peter Hawke
July 21, 2015
1. Overview Our goals:
Introduce and understand three key distinctions: analytic/synthetic;
a priori/a posteriori; necessary/contingent
Study the interaction of these distinctions
The app

PHIL50S Section 3
Peter Hawke
July 13, 2015
1. Complementation
Q: Let background set U be given, and define complementation relative
to that set. Let A be a subset of U . Prove that A Ac = U .
A: As per usual, we aim to show two conditionals: if x A Ac th

PHIL50S - Section 2
Peter Hawke
July 6, 2015
1. Identity Statements
Q: Prove that cfw_a, b = cfw_b, a for any a, b.
A: By extensionality, two sets are equal if and only if they contain
the same members, and cfw_a, b and cfw_b, a contain the same members.

PHIL50S Section 6
Peter Hawke
August 3, 2015
1. Our goal in section this week is to get some sense of what it is to
construct a formal proof using a precise system of proof rules and
precise language, and observe some examples of such formal proofs
using