Syllabus: Philosophy 192I
Infinity
Spring 2005


Catalog Description

Examines the concept of infinity as understood from ancient times to the present.  Emphasis on philosophical, cultural, and mathematical significance.   Topics covered include:  physical infinities, temporal infinities, spatial infinities, infinitesimal, the absolute infinite, transfinite numbers, paradoxes of infinity, the continuum, the one and the many, the comprehensibility of the infinite, implications for science and  the philosophies of mind, religion, and metaphysics. 

Course Description

David Hilbert, a 20th century logician, wrote “The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification….”  Infinity is a truly mind altering concept, but the moment one grasps the idea that infinity is more than just a concept, that the world, and collections of things in it may actually be infinite can be utterly frightening.  Pascal, the 17th century French philosopher and theologian expressed it well: “When I consider the small span of my life absorbed in the eternity of all time, or the small part of space which I can touch or see engulfed by the infinite immensity of spaces that I know not and that know not me I am frightened and astonished to see myself here instead of there… now instead of then.”  Ancient philosophers like Plato and Aristotle rejected actual infinities as incoherent, but later philosophers like Plotinus and St. Augustine disagreed, arguing that God must exist as an infinite being.  Subsequent philosophical exploration of the concept of infinity illuminated some of history’s most difficult philosophical problems, and laid the groundwork for some of our most important achievements in mathematics and science.  

Course Goals

Our goal in this course will be to develop as sophisticated an understanding of the infinite as can be achieved through non technical means.  The course presupposes no experience in advanced mathematics or symbolic logic, but we will study basic logical and mathematical concepts and proofs.  We will learn how thinking about the infinite has developed from ancient times, how our current understanding of the infinite informs our understanding of the universe, and what it implies about  the power and the limitations of the human mind

Course Requirements

In this course you will be given an opportunity to submit 7 essays.   You are required to submit at least five, the best four of which will count toward your final grade. These essays will be roughly 3-4 single-spaced pages long.  Of the essays you submit, you will select one to expand and improve upon (roughly twice the original length).  You will submit the expanded version on the date scheduled for the final exam.  All assignments are worth 20 pts, which is 1/5 of your total grade.

In each essay you will analyze an assigned article.  The article will typically be one that we have not covered in class, but one which will be relevant to the material we have studied.  Instructions for writing analyses are available on the website.  You must follow the prescribed format.


Grading Criteria for Individual Assignments

Your written work will be evaluated primarily for the quality of the thought it represents and how well it applies the concepts learned in class. Of course, it is absolutely essential that these essays represent a college level comprehension of English . Exams and papers must be typed.  By this point in your education you know the requirements of philosophical writing.  If you need clarification consult:  Instructions for Writing Essays.

Attendance

Attendance is compulsory. You are allowed a maximum of three absences. For each absence over three your final point total will be reduced by 5 points. Please note that I do not distinguish between excused and unexcused absences. You are late if you come to class after I take roll. If you are late you must tell me on that day or it will be counted as an absence. Three times late is equal to one absence. Students who accumulate in excess of three absences may earn absence credits by attending academic events sponsored by the philosophy department and/or philosophy club.  

Grading

Best 4 of 5 essays

4 x 20 pts. = 80 pts.

Final essay

20 pts.

Total Possible

100 pts.

In calculating your final grade fractional point totals are to the nearest whole point, with point totals ending in .5 being rounded up.  Grades are assigned on a standard scale with minuses (-) added to scores less than 100 ending in 0 and 1 and plusses (+) added to scores less than 98 ending in 8 or 9.  Hence, after rounding: :  A= 92-100,  A- =  90-91,  B+ = 88-89,  B= 82-88,  B- = 80-81, etc..

Important:: You and only you are responsible for monitoring your performance in this course. Be sure to pay close attention to the drop deadline. Do not hesitate to talk to me if you are experiencing problems at any time during this course.

Nammour Student Essay Contest

To encourage participation in the Nammour Student Essay Contest, I will allow you to substitute your entry  for one of the essays you write for this class.   If your essay is one of the winners of the competition, it will receive an A grade, and  you will be excused from writing the final paper.  If it does not win, I will grade the paper.  You many not revise this essay for submission as your final paper.

Collaboration Policy

You are free to work together on essays outside of class. Be advised, however, that if multiple essays exhibit striking similarities (e.g., identical sentence structure, even in places) they will all be summarily failed. Use each other as a source of ideas, but do your writing by yourself.

Late Assignment Policy

Late assignments are downgraded by 10% for every day they are late. An assignment is a day late if I receive it anytime up to 24 hours after the beginning of the class period when it is due.  No assignment will be accepted over a week late. 

Internet Submissions

You may submit your work by e-mail in order to stop the late clock.  However, you must follow this up with hardcopy at the next class meeting.  Failure to do this nullifies the original e-mail submission.

Texts

The Infinite, by A.W. Moore
Online Articles and Handouts

Students with Disabilities

Students with disabilities who have special learning or testing needs must notify the instructor with the appropriate documentation by the end of the second week of the semester.

Course Schedule


Date
 Topic
 Readings
 Assignments
Week 1-2
 Paradoxes of the Infinite
 Chapter 1
Week 2-3
 Early Greek Thought
 Chapter 2
 Essay 1
Week 3-4
 Aristotle, Medieval and Renaissance Thought
 Chapter 3,4
Week 5
 The Calculus
 Chapter 5
 Essay 2
Week 6
 Rationalism, Empiricism, Kant
 Chapter 6
Week 7
 Post Kantian Metaphysics of the Infinite
 Chapter 7
 Essay 3
Week 8
 Cantor and the Mathematics of the Infinite
 Chapter 8
Week 9
 Reactions to Cantor
 Chapter 9
 Essay 4
Week 10
 Transfinite Mathematics
 Chapter 10
Week 11
 The Lowenheim-Skolem Theorem
 Chapter 11
 Essay 5
Week 12
 Godel's Theorem
 Chapter 12
Week 13
 Saying, Showing, and Effability
 Chapter 13
 Essay 6
Week 14
 Infinity Assessed
 Chapter 14
Week 15
 Human Finitude
 Chapter 15
 Essay 7
Finals Week

Final Exam Date

 

Caveat

With the exception of the final exam, dates, times and the schedule of readings are subject to minor revisions at the discretion of the instructor.