LPS/PHILOS 105A/205A-H01VIEWORK 2
DUE FRIDAY OCTOBER 14 BY 5PM.
Name: flLf/gy V0220
Student ID number: 3 / q 445 3,-
Note 1. It is permissible and you are encouraged to work in groups of 23, but everyone
must write up their own solutions. Please indic
Lecture 12-13
Cantor, one of the founders of set theory
1
Goals Today
Introduce the concept of ordinals by:
defining ordinals (= transitive set well-ordered by membership)
stating and proving structure theorem on ordinals
define union and successor operat
LPS/PHILOS 105A/205A HOMEWORK 4
DUE FRIDAY DECEMBER 2 BY 5PM.
Name:
Student ID number: 5 (A");
Note 1. It is permissible and you are encouraged to work in groups of 23, but everyone
must write up their own solutions. Please indicate here the names of th
LPS/PHILOS 105A/205A HOMEWORK 3
DUE FRIDAY NOVEMBER 18 BY 5PM.
Name:
SLIM
Student ID number:
Note 1. It is permissible and you are encouraged to work in groups of 23, but everyone
must write up their own solutions. Please indicate here the names of the
Lecture 8
Ernst Zermelo, first to describe cumulative hierarchy
1
Goals Today
Describe Transfinite Induction and Recursion
The Cumulative Hierarchy of Sets
Describe the Stage Axioms
2
Recall: Ordinal Structure
Theorem
For all , , $
1. Set-Transitivity: $.
Lecture 16
von Neumann, who had a role introducing
foundation and replacement
1
Outline
Last Three Axioms of Set Theory:
Foundation
Replacement
Choice
2
Outline, where we are at
Last Three Axioms of Set Theory:
Foundation
Replacement
Choice
3
Recall: The
Lecture 10
Cantor, one of the founders of set theory
1
Plan
Define isomorphic linear orders, define well-orders,
look at some examples
Define ordinals, look at simple examples.
2
Plan, where we are at
Define isomorphic linear orders, define well-orders, l
LPS/PHILOS 105A/205A HOMEWORK 2
DUE FRIDAY OCTOBER 14 BY 5PM.
Name:
Student ID number: g; Lulcb 05
Note 1. It is permissible and you are encouraged to work in groups of 2-3, but everyone
must write up their own solutions. Please indicate here the names
LPS/PHILOS 105A/205A HOMEWORK 3
DUE FRIDAY NOVEMBER 18 BY 5PM.
lName:
Jag/67 M0210
Student ID numberi 3/ (/ng
Note 1. It is permissible and you are encouraged to work in groups of 2-3, but evegyone
must write up their own solutions. Please indicat
Lecture 08
Georg Cantor, Founder of Set Theory
1
Goals
Define the notion of cardinality, look at examples
Develop methods for calculating cardinalities
Prove Cantors Theorem on Cardinality of Powerset
2
Definition of Cardinality
Recall that f:XY is a bije
Lecture 4
Richard Dedekind, Axiomatized Arithmetic
1
Goals Today
Review ZFC axioms thus far: extensionality, comprehension, pairing,
powerset.
Introduce two more ZFC axioms: union and infinity.
Show how we can use this to recover our earlier knowledge of
Lecture 6
Georg Cantor, Founder of Set Theory
1
Goals Today
Define cardinal addition, multiplication, and exponentiation
2
Cardinal Addition, Multiplication,
and Exponentiation
So the way that were going to proceed is by defining, for arbitrary
sets A and
LPS/PHILOS 105A/205A HOMEWORK 1
DUE FRIDAY SEPTEMBER 30 BY 5PM
Name:
Student ID number: S; lkflw
Note 1. It is permissible and you are encouraged to work in groups of 23, but everyone
must write up their own solutions. Please indicate here the names of
LPS/PHILOS 105A/205A HOMEWORK 2
DUE FRIDAY OCTOBER 14 BY 5PM.
Name:
Student ID number:
Note 1. It is permissible and you are encouraged to work in groups of 2-3, but everyone
must write up their own solutions. Please indicate here the names of the other 1
Lecture 07
Marshall Stone, of Stones Theorem
1
Plan
Define isomorphic linear orders, define well-orders,
look at some examples
Define Boolean algebras, look at examples, define
isomorphism of Boolean algebras, state Stones
theorem.
2
Isomorphisms of Linea
Lecture 3
Bertrand Russell, of the Russell Paradox
1
Goals Today
Review what we know about sets so far: extensionality, abstraction,
lists, and set operations.
Describe the Russell paradox and the related result that there is no set
of all sets.
Introduce
Lecture 05
Kazimierz Kuratowski, defined ordered pair function we use
1
Recall: Functions & their Properties
Recall from Lecture 2:
a function f:XY is an operation
which, when given an input
xX, returns an output yY.
Here, X is called domain and Y
called
Lecture 6
Picture of Equivalence Classes
1
Other Binary Relations:
Equivalence Relations
An important kind of binary
relation is an equivalence relation.
A binary relation E on XX is a
is an equivalence relation on X if
it satisfies three properties, for
LPS/PHILOS 105A/205A
MIDTERM STUDY GUIDE
The midterm exam is an in-class exam that we will do in-class on Thursday October 27.
The exam is closed-book, and so please come with just pencils we will provide blue books.
The exam consists of two parts.
In par
1
Third_Meeting_First_Topic_Humans_Phil1_16
Aristotle Human Rationality; the Rational Soul.
A hierarchy of living beings:
Wehavenutritionalsoulorsoulelements,ananimalsoulorsoulelements,andsoul
elementsofthemindorintellect(nous).Theyareorganizedandintegrat
PHIL 1 Intro Phil - Spring 16
Instructor: SCHWAB, M. (marschwab@aol.com)
Midterm Prompt
Write on one of the following questions. Your paper is to be ca. 1500 words long (5-7
pages). It is due on Th, May 5. You will submit an electronic copy on turnitin.co
Week 9
Crawfords objection
To specialization, per se?
The basis of wealth
Yeoman farmer ideal? Despite poverty?
Marx vs. capitalism
Division of labor creates time for more meaningful,
specialized work
e.g., writing a book without having to
print it onesel
Week 8
Zen in the Art of Archery, Eugen Herrigel
The how-to of archery as a window into Buddhist selftranscendence
How to draw the bow and release the string without
a powerful jerk that causes the shot to wobble
https:/www.youtube.com/watch?v=fZNdx_g_mr8
Week 10
Larger questions:
What place does work and leisure have in a meaningful life?
Is one more important than the other? Views:
Just enough leisure to be as productive (and as rich) as
possible in (remunerated) work. The workaholic
Just enough work to
Week 8
Zen in the Art of Archery, Eugen Herrigel
The how-to of archery as a window into Buddhist selftranscendence
How to draw the bow and release the string without a
powerful jerk that causes the shot to wobble
https:/www.youtube.com/watch?v=fZNdx_g_mr8
Week 6: freedom
Sartres existentialism
Join the Free French?
Kantian morality instructs us to never treat another as a means,
but always as an end. Very well; therefore, if I stay with my
mother, I will treat her as an end, not as a means. But by the
same
Week 5
Immanuel Kant, Groundwork for the Metaphysics of Morals (1785)
J.P. Sartre, Existentialism as a Humanism (1945)
Review
Moral virtue, a matter of know-how, is constitutive of happiness
Aristotle: happiness depends on skill and fortune (e.g., in
ones
Week 9
Crawfords objection
To specialization, per se?
The basis of wealth
Yeoman farmer ideal? Despite poverty?
Marx vs. capitalism
Division of labor creates time for more meaningful,
specialized work
e.g., writing a book without having to print it
onesel
Week 4: quality of life, happiness, wellbeing, welfare
What is it for a persons life to go better rather than worse?
What are the elements of a good life?
Is there one general kind of element, or many?
Different questions:
What is the best life for a pers
Aristotle: ethical virtue is similar to athletic virtue
Both are an exercise of skill
An action or activity; your behavior, and not something
merely happening to you.
Done skillfully, whether well or badly, according to
standards of performance
Perhaps wi