Philosophy Teaching Sequence 4: Zeno's Paradox

Teaching Sequence: Second week of classes
By this time, we have decided as a group which topics within the frame of this course are of general interest, constructed a detailed day-by-day syllabus that incorporates the students' interests, and discussed at length what is philosophy.

Aim: Philosophical theories are tested by looking for counterexamples, that is, situations where the theory should hold but doesn't. In this unit I introduce Zeno's paradox of bisection, which is used to demonstrate how thought experiments generate counterexamples. Concerning writing skills I will focus on the nature of a critical philosophy essay, formulating a thesis statement, and constructing an introductory paragraph. This unit will take 3 classes to complete (we meet only two times a week for longer class periods).

Day 1: In-class Collaborative Work
The first day of this unit employs in-class collaborative work that focuses on Zeno's argument for the claim that motion (or change) is impossible. Zeno's paradox of the stadium provides an apparent counterexample to any theory that claims that motion occurs. As a result, it helps explain why change is impossible. Have the students identify the issues orally, and list them on the board.
Homework: (1) Write a page stating your personal beliefs about Zeno's paradox; (2) read pages 17-18 and 21-31 from Doing Philosophy (An introduction to philosophy through thought experiments) by T. Schick and L. Vaughn; (3) bring to class a one-page summary/response with any comments or questions about the reading assignment.

Day 2: Discussion Questions
Collect the personal responses. Read out loud some of the personal responses and lead naturally into a class discussion on the assigned reading.

1. What is a thought experiment?
2. What are the steps involved in conducting a thought experiment?
3. On what grounds can thought experiments be criticized?
4. On what grounds can philosophical theories be criticized?
5. What are the criteria of adequacy that good theories should meet?

Homework: (1) Read "Philosophical Essays: Critical Examination of a View" (Chapter 6/pages 56-61) of The Practice of Philosophy: A Handbook for Beginners (A writing handbook) by J. F. Rosenberg; (2) on the basis of Zeno's argument for the claim that motion (or change) is impossible, write a statement of the thesis that you will support in your first five-page essay. The thesis can be to the effect that some premise in Zeno's argument is false, or to the effect that his argument is defective, or a claim to the effect that his argument usually considered defective can avoid the alleged defect.

Day 3/Writing Lecture

Collect thesis statements. Read out loud some of the thesis statements and lead naturally into a lecture about some writing guidelines. Refer to "Grading Scale for Papers" and "Term Papers--Some Guidelines." Put up on the board a sample Introductory Paragraph.
Homework: (1) Read handout from A Preface to Philosophy by M. B. Woodhouse: "Writing Philosophy", (2) bring to class a one-page summary/response with any comments or questions about the reading assignment.

In-Class Collaborative Work

Zeno's Argument for the Claim that Motion (or Change) is Impossible

Begin by selecting a recorder/presenter who will be responsible for taking notes and reporting back to the entire class when we reassemble. Then the recorder/presenter should read the following aloud to the rest of the group,

Introduction: Zeno's Paradox of Bisection

Just as philosophical theories can explain how something is possible, they can also explain why something is impossible. To explain why something is impossible is to show that it involves a logical contradiction. The ancient Greek philosopher, Zeno of Elea, was a master of this type of thought experiment. Zeno, like his mentor, Parmenides, wrestled with the question "How is it possible for something to remain the same through change?" The problem is that if something changes, it's different, and if it's different, it is no longer the same. Zeno thought that maintaining identity through change was logically impossible. To prove his point, he presented a number of thought experiments designed to show that the concept of motion (or change) involved a contradiction. Here we will consider the paradox of bisection where Zeno does not deny that people seem to move from place to place. What he denied was that the way the world seems is an accurate reflection of the way it really is. Like his teacher, Parmenides, he claimed that whatever involves a logical contradiction can't exist. And because motion (or change) involves a logical contradiction, it can't exist.

Group Task: Is Motion (or Change) Impossible?

Suppose you are in a stadium at a given distance from the exit door. Then you can never get out of the stadium because before you reach the door you must reach the point halfway there. But before you can reach the halfway point, you must reach a point halfway to that. And since it takes some finite interval of time to move from one point to another, and there are an infinite number of halfway points, it would take you an infinite time to pass through them all and get out. But, not only can we never get out of the stadium, we can never take the first step toward the door. Before we reached the halfway point, we would first have to reach a point halfway to that. And before we reached that point, we would have to reach a point halfway to that, and so on. So just as it would take an infinite amount of time to get out of the stadium, it would take an infinite amount of time to take the first step. And since finite beings like ourselves do not have an infinite amount of time on our hands, motion is impossible. Reformulate Zeno's argument in your own words by listing his key premises and conclusion. Assess the argument. Do the premises in fact support the conclusion? Are the premises true? Does he rely on assumptions that are not openly stated? If so, state them now. Are you convinced by the argument?

Take turns telling the rest of your group your preliminary thoughts. Try not to get too anxious about what you have to present. Note that people will be at different stages of thinking, but nobody is likely to have it all worked out. After each person presents, every other member of the group must respond with at least one question. The recorder/presenter should try to answer each question in turn. Questioners might request definition or clarification of particular terms, solicit more evidence, ask whether the presenter has considered x or y, and so on. The idea here is simply to open up new avenues of thought. After you have all presented, decide as a group which of your observations seem most promising. The recorder/presenter will start off the discussion when we reassemble by reporting your deliberations to the class. The entire class will then discuss the group topics.