Last Day!
Casey Hart
Lecture 40, 5/8/2015
Plan
Moving Quantifiers
Questions about the Final, or Really Anything Else
Announcements
Make sure to e-mail me if youd like to meet sometime. Im trying to keep
my schedule as free as possible next week. And, Im a
Warm-up Exercises
Show:
(x)Fx (x)Fx
(x)(Fx v ~Fx)
Is the relation being an enemy of reflexive? Symmetric? Transitive?
Plan
Review
More Relational Properties
Proofs
More Relational
Properties and Proof
Strategies
Casey Hart
Lecture 31, 4/15/2015
Announcem
Warm Up Exercise
Congratulate yourself and classmates for making it through the
midterm, and almost making it to Spring Break! Take a minute to
celebrate the Badger win over UNC last night as well.
Plan
Logical, Truth Functional, and Quantificational Rela
Warm Up Exercise
Are the following arguments quantificationally valid? Try making a
counter-example interpretation (one in which the premises are true and
the conclusion is false). If you can, then youve shown its q-invalid. If
you cant, think about why y
Warm Up Exercise
If possible, create English arguments that have the following features. If
its impossible to make an argument with said features, then say so and
explain why.
1. Invalid; has the conclusion: Its Spring Break next week.
2. Valid; Sound; ha
Warm Up Exercise
Demonstrate that each of the following statements are true:
1.
(x)(Gx~Fx) doesnt quantificationally entail that ~(x)Fx.
2.
(x)(Px Lxa) doesnt quantificationally entail that (x)Lax.
Plan
Nested Quantifiers
Formal Interpretations
Tricks for
Warm Up Exercise
Create a PL sentences that have each of the following properties:
1.
P is quantificationally true and has a universal quantifier as its main
connective. What could it be?
2.
Q and P are both quantificationally equivalent and quantificatio
Warm Up Exercise
Consider the following PL wffs:
(x)Fx&(y)~Gy
(x)(~Px&~Qx) ~S
ScRc
Come up with translation keys to translate these PL wffs into English. There
are MANY acceptable answers. You just need to come up with a UD and
names for the various predi
Warm Up Exercise
Show: (F&G)(H&J), (J&H) (KvL), (LvK)M (G&F) M
Translate to PL:
All vegetables are delicious.
All foods are delicious.
The carrot is delicious.
The carrot is an orange type of food.
WFFs in PL and AEIO
Casey Hart
Lecture 19, 3/6/2015
Plan
Warmup Exercises
Show/Answer:
1. (x)~Fx ~(x)Fx
In quasi-English: If everything doesnt have F, then theres nothing
with F.
2. (x)(Fx&Hx) (x)Fx&(y)Hy
3. Does (x)Fx&(y)Hy (x)(Fx&Hx) ?
Plan
Quantifier Negation
PD Strategies
Practice Proofs
Quantifier Negation
Plan
Quantifier Negation
PD Strategies
Types of Relations
Proof Strategies and
Types of Relations
Casey Hart
Lecture 31, 4/13/2015
Announcements
Exam keys are posted.
PSET #5 is posted, and the due date is pushed back to next Monday,
4/20.
The last quiz w
Warm-up
Give PLI translations for the following:
Exactly two people shot Kennedy.
At least three people will get perfect scores on the 211 final.
If Kanye loves himself, then at most one person loves Kanye.
More Identity Stuf
Casey Hart
Lecture 35, 4/22/2
Warm-up
Translate the following argument into PLI:
Either Kelly or Charlie was in the house. The person in the house had
long hair. Kelly doesnt have long hair. So, Charlie was in the house.
Is this argument logically valid? If so, show it by doing a PDI
Final Review
Casey Hart
Lecture 39, 5/6/2015
Plan
Final Review
Inductive Logics
Announcements
I have to cut my office hour today after class a little short. But, Ill still
be here for a half hour. As always, Im happy to schedule
appointments with people.
Exercises
Translate the following argument into PLI:
There were exactly two men in the room, and the short one tied the
other one up.
The first person to finish their final exam will get an A. (this is not a
promise or anything, by the wayits just a sente
Plan
Motivating Identity
PLI
PLD
Identity
Casey Hart
Lecture 34, 4/20/2015
Announcements
PSET #5 is due today.
Quiz: the quiz will be next Wednesday and will look similar to the quiz
earlier this semester when you filled in blanks in a completed proof. In
Some Practice Proofs from your
Book
Fa (x)(x=a Fx)
b = a, c = a b = c
Some Practice Proofs from your
Book
Well be doing these shortly. If you want a head start on thinking
about them, take a look!
Fa (x)(x=a Fx)
b = a, c = a b = c
Counting with
Identity
C
Warm Up Exercise
Are the following English arguments logically valid? Why or why not?
1. Some official made a horrible call during the Badger game. Any official
who makes a horrible call should face consequences. So, someone
should face consequences.
2. S
Warm-up Exercises
(x)(HxGx)v(GxHx)
Show this by providing a PD proof.
What does this translate into in English, if we pick some UD and
predicates for G and H? Does it sound right to you? What does this
tell us about our formal system that were developing
Warm Up Exercise
Let UD: 1, 2, 3, 4, 5
The following statements are true. If you can, finish building
interpretations to demonstrate that each of the following statements are
true, given the above UD:
1.
Ga&~Fa is not quantificationally false.
2.
(x)~Gx~(
Warm Up Exercise
Let UD: names of states in the US (for instance: Alaska, Idaho, and so
on)
a: Alaska
m: Michigan
w: Wisconsin
i: Idaho
Lxy: x is a longer name than y
Mx: x begins with the letter M
Ax: x has more than one a in it
Are the following sentenc
Warm Up Exercise
Come up with an interpretation on which the following PL sentences are true:
(z)Mz
~Mb
(x)(Mx Gx)
Your interpretation will need to fill in:
UD:
Mx:
Gx:
b:
Plan
Quantificational Properties and What to Show
Demonstrating Single Sentence Pro
Warm Up Exercise
Translate the following sentences from English into SL.
1.
The plant will die unless its watered.
2.
Neither Jim nor Bill was at the party.
3.
Its not the case that Im wearing a coat and Im wearing a
scarf.
Using Truth Tables
Casey Hart
L
Warm Up Exercise
Get ready for the quiz! It will begin right at the start of class,
and youll have five minutes to complete the five truth tables
(one for each connective in SL).
Truth Table Terms
Casey Hart
Lecture 9, 2/9/2015
Plan
Using Truth Tables in
Warm Up Exercise
Translate the following sentences from English into SL.
1.
The plant will die unless its watered.
2.
Neither Jim nor Bill was at the party.
3.
Its not the case that Im wearing a coat and Im wearing a
scarf.
Using Truth Tables
Casey Hart
L
Warm Up Exercise
Are the following arguments logically valid?
1.
If the plant is not watered, it will die.
1. Every grad student is smart.
2.
The plant didnt die.
2. Emi is a grad student.
3.
So, the plant was watered.
3. So, Emi is smart.
1. The killer i
Warm Up Exercise
Try translating the following sentences from SL to English using
the following translation key.
H: The next card drawn is a heart.
K: The next card drawn is a king.
D: The next card drawn is a diamond.
R: The next card drawn is red.
1.
R-
Warm Up Exercise
Which of the following sentences have truth values? Of the ones that
do, which are: true in some possible world, true full-stop, and logically
true?
1.
Bananas are yellow.
2.
Are you married?
3.
2+2 = 4.
4.
The Packers are in the Super Bo
Warm Up Exercise
Ill usually start off class with a warmup exercise featuring material
weve already covered. We havent covered any material yet, so this
weeks a little different.
Suppose someone says the following:
The Pope said that parents should not ha
Warm Up Exercise
True or False: For each of the following, identify whether it is true or
false. Explain. cfw_Note: explanations will require you to use the
definitions for terms we learned last class.
1.
Philosophy is fun and easy and Philosophy is not f