PHIL 103: Logic and Reasoning QRII
Homework #9
Due Monday, November 17
1. Describe three ways in which a set is different from an ordinary group or collection of things.
2. Describe a set having five elements using list notation and also using predicate n
Probability Theory
Conditional Probability and
Independence
Review: Probability
Probability is a measure.
Review: Probability
We will think of the probability function as a
mapping from events, which are subsets of the
universe, into real numbers.
Suppose
Probability Theory
Variables and Distributions, Part 2
The Big Picture
Statistical inference is a logic of induction.
The aim of statistics is to make reliable
inferences about the character of a
population on the basis of a sample
drawn from that populat
Probability Theory
Humes Problem of Induction
And
Bayes Solution
Conditional Probability
Let and be arbitrary sentences in our formal
language. Then we define the conditional
probability of given , denoted Pr( | ) as:
Pr( | ) = Pr( ) / Pr()
Under the assu
Probability Theory
Confirmation
And
Evidential Favoring
Review: Total Probability
Suppose that in a certain field, there are two
varieties, A and B, of a grassy plant. Each plant
grows to be tall or short. Plants of type A grow
to be tall with probability
Set Theory
Introduction
Review
What have we done so far?
Preview
In upcoming lectures, we will be thinking about
inferences that are not necessarily truth
preserving. Such inferences are called ampliative
or (sometimes) inductive.
Interlude
But before get
Please get your flu shot soon.
Set Theory
Intersection, Union,
Set Difference, and Power Set
Review
Last time we talked about how to represent sets
with diagrams and curly-brace notation.
Trustworthy
Politicians
Set Operations
Today, we are going to talk
Set Theory
Diagrams, Notation, and Paradox
Review
Last time we introduced the idea of sets by
analogy with boxes.
Sets and Diagrams
A set is a collection or grouping of objects,
which are called the elements or members of
the set.
We sometimes restrict at
First-Order Natural Deduction
Part 1: Universal Introduction and
Elimination
Happy Birthday to Talan
Three years old!
Business
Homework #7 has been posted. It is due on
Monday, October 20.
The Midterm Exam is also on October 20.
Business
The midterm exam
Professor Livengood is on his way to Utah
for a conference on Inductive Logic and
Confirmation in Science.
Homework
There is no homework this week! Enjoy the
break.
First-Order Natural Deduction
Part 3: Existential Elimination
New Rules
Existential Elimin
First-Order Natural Deduction
Part 2: Existential Introduction and
Elimination
Business
Midterm Exam on Monday, October 20.
Business
A practice midterm exam is online.
Review session this Sunday at 4:00 PM.
In Gregory Hall 402.
Review
Universal Eliminatio
First-Order Natural Deduction
Part 4: Identity Introduction and
Elimination
An Advertisement
Next semester, I am teaching PHIL 471:
Contemporary Philosophy of Science.
We will be studying how people think and
reason about similarity, analogies and
relatio
A Philosophical Introduction to Formal Logic
Chapter 6: Probability
The actual science of logic is conversant at present only with things either certain,
impossible, or entirely doubtful, none of which (fortunately) we have to reason on.
Therefore the tru
A Philosophical Introduction to Formal Logic
Chapter 5: Set Theory
In previous chapters we have developed a formal language adequate for translating many
ordinary English sentences, and we have developed techniques, including a formal proof theory,
that l
PHIL 103: Logic and Reasoning QRII
Homework #10
Due Monday, December 1
Problems 1-7 refer to the same childs book. Facts introduced in earlier problems should be
assumed to be true for later problems as well.
1. In a certain childs book there are 20 pages
Sunk Costs and Escalation
The sunk cost fallacy occurs when we take into
consideration costs we have already paid when
making decisions about what we should do in
the future.
Ive been with this boyfriend (girlfriend) for a long time,
I shouldnt break up w