PHIL 102 B. Rabern
INFORMAL FALLACIES: THE APPEAL TO IGNORANCE
There are many informal fallacies present in the media today; they can
be seen in statements made by politicians, the opinions expressed by a
columnist in an op-ed article. One fallacy that is
PHIL 103: Logic and Reasoning QRII
Homework #3
Due Monday, September 24
1. Translate the following argument into our formal language and then use truth tables to
determine whether the argument is valid or invalid.
Either Talan took an afternoon nap or he
PHIL 103: Logic and Reasoning QRII
Homework #7
Due Monday, October 22
1. Translate the sentence below into our formal language. Represent as much of the internal
structure of the sentence as possible.
If nothing in Professor Livengoods office weighs more
PHIL 103: Logic and Reasoning QRII
Homework #13
Due Monday, December 3
1. Show the following (~12 lines): cfw_ (a b), (b a) (a = b)
2. Show the following (~18 lines): cfw_ (a b) (a b) = a)
3. Use the simplified axiom of the empty set, (y)(y ) to show th
PHIL 103: Logic and Reasoning QRII
Homework #14
Due Wednesday, December 12
The problems in this homework set are worth two points each, meaning that there is effectively
one two-point extra credit problem.
1. Recall the childs book from the previous homew
Zeroth-Order Logic
Syntax and Translation
The Planning Fallacy
Humans tend to be overly optimistic about
our own abilities. We think we will work
harder and faster, spend less money, have
more control over outcomes, and generally
out-perform other people.
Zeroth-Order Logic
Truth Functions
Homework
The first homework assignment for the
course will be posted on the course website
by the end of the day. It is due on Monday,
September 10.
Internet Biases
Why almost no one ever wins an argument
online:
The Dun
Logic and Reasoning QRII
Introduction
A Note About Textbooks
This is the textbook that I
assigned when I taught
this course last year.
A Note About Textbooks
It is a pretty good basic
introduction to logic.
A Note About Textbooks
It is a pretty good basic
Zeroth-Order Natural
Deduction
Part 2
Confirmation Bias
Once a human intellect has
adopted an opinion (either as
something it likes or as
something generally accepted),
it draws everything else in to
confirm and support it.
Francis Bacon (15611626)
Confir
First-Order Logic
Formation Rules,
Translations
Homework
Turn in Homework #4.
The fifth homework assignment will be
posted on the course website by the end of
the day. It is due on Monday, October 8.
Syllabus Revision
We are slowing down a little to give
PHIL 103: Logic and Reasoning QRII
Homework #8
Due Monday, October 29
1. Show the following: cfw_ (x)(Fx Gx) (x)(Fx) (x)(Gx).
2. Show the following: cfw_ (x)(Gx Hx), (x)(Fx Gx) (x)(Fx Hx)
3. Show the following: cfw_ (x)(~Fx) (~(x)(Fx).
4. Show the foll
PHIL 103: Logic and Reasoning QRII
Homework #11
Due Friday, November 16
In problems 1-3, you should evaluate the set operations and give a single set in list notation. For
example, if the problem were (cfw_1, 2, 3 cfw_2, 4, 7), you would answer cfw_1, 2,
PHIL 103: Logic and Reasoning QRII
Homework #9
Due Monday, November 5
1. Show the following: cfw_ (x)(y)(x = y).
2. Show the following: cfw_ (x)(Fx Gx) (x)(Fx) (x)(Gx).
3. Show the following: cfw_ (~(x)(Fx) (x)(~Fx).
4. Show the following: cfw_ (x)(~Fx
PHIL 103: Logic and Reasoning QRII
Homework #10
Due Monday, November 12
1. Show the following: cfw_ (a (b (c d) (a c) (a d).
2. Show the following: cfw_ (a (b (c d) (a (b c).
3. Show the following: cfw_ (x)(y)(x y) (x (y y).
4. Show the following: cfw_
PHIL 103: Logic and Reasoning QRII
Homework #12
Due Wednesday, November 28
1. Show that the rule for identity introduction follows from the axiom of extensionality, i.e. using
only the axiom of extensionality and rules of inference other than identity int
PHIL 103: Logic and Reasoning QRII
Practice Problems #2
Translate the sentences below into first-order formal language. Then describe a small world that
is a model for the sentence and a small world that is not a model for the sentence.
1. Abby bought cer
PHIL 103: Logic and Reasoning QRII
Homework #6
Due Wednesday, October 17
Translate each of the following four sentences into our formal language. Represent as much of
the internal structure of the sentences as possible.
1. Sally only dates men who are sho
PHIL 103: Logic and Reasoning QRII
Homework #2
Due Monday, September 17
1. First, translate the following sentence into our formal language: Becky is a vegetarian, and
Percival eats meat only if Carl does. Second, assume that Becky really is a vegetarian,
PHIL 103: Logic and Reasoning QRII
Homework #5
Due Monday, October 8
An important and interesting fact about the material conditional is that (P Q) is equivalent to
(~Q) (~P). These two sentence types are related by contraposition. The second sentence is
A Philosophical Introduction to Formal Logic
Chapter 0: What is Logic?
Logic is the normative study of reasoning. In other words, logic is the study of what makes
reasoning good or bad. Since it is a normative study of reasoning, logic is different from
p
University of Illinois MATH 413 Test 1 Fall 2013
Answer as many problems as you can. Each question is worth 6 points
(total points is 30). Show your work. An answer with no explanation
will receive no credit. Write your name on the top right corner of eac
A Philosophical Introduction to Formal Logic
Chapter 4: Natural Deduction for First-Order Logic
In Chapter 3, we used small worlds to give a formal account of validity in first-order logic. An
argument in first-order logic is valid if and only if in every
A Philosophical Introduction to Formal Logic
Chapter 3: First-Order Logic
In Chapter 1, we began building our formal language, we introduced truth functions and truth
tables, and we described a special notion of evidential support in which the conclusion
A Philosophical Introduction to Formal Logic
Chapter 5: 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
Practice #2 Solutions
1. Let K = Katy goes to the mall, let G = Katys friends go to the mall, and let W = Katy
wishes she could go to the mall. The translation looks like:
(~K G)
(K ~G)
(~K W)
W
K
1
1
1
1
0
0
0
0
G
1
1
0
0
1
1
0
0
W
1
0
1
0
1
0
1
0
(~K G)
Practice #1 Solutions
1. Let N = Talan took an afternoon nap, and let G = Talan is grumpy now. The translation
looks like:
(N G)
G
~N
N
1
1
0
0
G
1
0
1
0
(N G)
1
1
1
0
~N
0
0
1
1
G
1
0
1
0
The argument is invalidowing to the first row.
2. Let P = Candace
PHIL 103: Logic and Reasoning QRII
Practice #5 Solutions
1. Sally only dates men who are shorter than she is.
Let D = dates -, let M = is a man, let S = is shorter than -, and let s = Sally.
Then one possible translation is this:
(x)(Dsx (Mx Sxs)
Possibly
PHIL 103: Logic and Reasoning QRII
Practice #6 Solutions
1. Translate the sentence below into our formal language. Represent as much of the internal
structure of the sentence as possible.
If nothing in Professor Livengoods office weighs more than 100 poun
PHIL 103: Logic and Reasoning QRII
Practice #7 Solutions
1. Show the following: cfw_ (x)(Fx Gx) (x)Fx (x)Gx)
1
2
1
2
1,2
1,2
1
(x)(Fx Gx)
(x)Fx
(Fa Ga)
Fa
Ga
(x)Gx
(x)Fx (x)Gx)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
A
A (for CP)
1 E
2 E
3,5 E
5 I
2,6 CP
Since no co
A Philosophical Introduction to Formal Logic
Chapter 1: Zeroth-Order Logic
In this chapter, we will begin building up our formal language. Our formal language will make
use of the following collection of symbols. We will use capital letters, like P, Q, an