Proof, Justification, & Argumenation

Final Assignment

For our final class, we'll be discussing the film 12 Angry Men.

Final Assignment

For this project, you will work in groups of three (please email me and let me know who you're working with). Each of you will will create a thread and begin by writing a 350-500 word argument about any topic. You should incorporate ideas about argumentation that we've discussed throughout the quarter, but need not describe those explicitly. Your argument should include at least two good citations in either APA or MLA format. You will then write a 250-350 word critique of each of your group member's arguments (as comments to their original threads). This critique should incorporate some of the ideas about argumentation that we described over the course of the term. Once you've received a critique from each group member, you will revise your original argument, incorporating their suggestions (again, as a comment on your original thread).

Here are the dealines:

  • Original post: Sunday, June 4th
  • First critique: Wednesday, June 7th
  • Second critique: Sunday, June 10th
  • Revised Argument: Wednesday, June 14th
***For graduating seniors, I'll leave it to your group to impose deadlines that get everything done before graduation.

Week 8

This week we're going to continue working with Toulmin's argumentation model in addition to considering some other models. In class on Thursday, we will be constructing arguments in small groups based short prompts that I will assign at the beginning of class. Here are a few readings for the week:

Midterm Assignment

Over the past 6 weeks, we’ve discussed proof, justification, and argumen- tation in mathematics, the sciences, and the social sciences. The goal for this writing assignment is to develop and refine your own perspective on proof, justification, and argumentation based on the course readings, our discussions, your exploration of scientific and social-scientific phenomena, and, of course, the views you’ve brought with you to this course. What I’m looking for is a well thought out comparison of the modes of proof and justification that we’ve covered, backed by the literature we’ve read and any other sources you find useful. I want to know what you think about the ideas we’ve discussed, and I want your ideas to be expressed clearly and to be substantiated.

Detailed instructions for the midterm assignment can be found here.

Week 4

Continuing the discussion from Week 3

This week we're going to hear from the rest of the group on natural phenomena about which our scientific understanding has changed. If you didn't get a chance to look at any of the reading/watching material from last week, please do so for Thursday. Additionally, do a little research on the peer review process and its role in your field(s) of interest. Here are a few articles to start with check out (nothing too dense or lengthy).

Week 3

Initial Thoughts

For the next couple weeks, we'll be looking at proof, justification/verification, and argumentation in the sciences. There are to perspectives I think we can take here...

To do

Do some light research on the evolution of our understanding about some natural phenomenon and be prepared to give us a brief introduction and lead a discussion. This can be large or small in scale, from any branch of science, and from any point(s) in history. A quick example I gave in class was the model of the solar system. Ptolemy's geocentric model envisioned the planets as moving on small spheres, which in turn moved on larger circles. On the road to our current understanding of the solar system, Copernicus and then Keplar provided significant updates to the Ptolomaic Model. This is up for grabs.

Having thought a bit more about this, you don't necessarily have to pick a topic about which our understanding changed over time - you can also pick a current controversial topic in the sciences. E.g. Climate change, nutrition, etc.

Work individually or with a partner. So that we're not repeating ourselves, fill in this table with your name(s) and a brief description of what you'll be discussing.

Use the following readings/videos to help guide your discussion.

To read/watch

To provide some frameworks within which we can situate our discussion this week, read/watch the following:

Week 2

Initial Thoughts and Recap

In our first session, we outlined our big-picture goals for this course. We are going to spend these first couple weeks looking at mathematical proof...

Readings

In this week's readings and discussion we will continue to explore the nature and practice of mathematical proof.

  • Imre Lakatos wrote an essay/play, titled Proofs and Refutation, in which a teacher and several students discuss Euler's Formula. Read part one of that essay here.

Questions to Ponder

  • What proof schemes can you pick out in Lakatos' characters?
  • What are some of the key features of the process of continual revision that are playing out in Proofs and Refutations?
  • Are you less convinced by proof by contradiction than by direct proof?
  • Can you think of, or construct, an example of an argument by contradiction?

Week 1

Initial thoughts

My goal in this course is for us to become better at constructing and evaluating arguments in whatever form(s) they take in our respective fields. We will examine...

Readings

This week's readings and discussion focus on mathematical proof and logic. Don't panic, you're reading about math and logic, not doing any math! Yet...

You don't have to read these in any particular order.

  • This paper by Harel and Sowder defines proof schemes, which we'll use to situate our discussion on proof. You're welcome to read the whole thing if you're interested in learning more about mathematical proof, but definitely read the section on Proof Schemes that goes from page 5 to the top of page 10.
  • This is a pretty interesting read from Aeon magazine on logic. Before you get started, think about what logic is and what its function is or ought to be.
  • If you want to dig real deep, this book has a great article titled Mathematical Domains: Social Constructs? You'll have to sign into you Drexel account to get to it.

Resources

Here's a running list of the readings we have used throughout the term...