Philosophical Subjects in Logic Courses

Question

Many of the notions, methods and theorems of the mathematical logic and its different sub-fields like set theory, model theory, etc. are closely related to some philosophical background. I believe understanding these philosophical aspects of mathematical arguments could be very useful for logic students to understand the subjects better.

When I am teaching logic, I usually talk about the philosophical backgrounds of each concept/theorem briefly. But there is a problem here. Introducing philosophical subjects causes questions and discussions amongst students which is fine in principal but sometimes these discussions become hot and too long and change the direction of the arguments from mathematical part to philosophical part of the subject.

Question. How can I explain philosophical aspects of the logical theorems without distracting attention of the students from the main teaching subject? In the other words how can I manage the discussion frame and time of the philosophical parts of my logic courses? Precisely I am searching for some discussion managing techniques which are useful for managing a philosophical discussion in a mathematical logic course.

Answer 1

Why not have the students talk about philosophical questions in small groups? That way you could allow them to grapple with the philosophical issues, but add more structure to your time together so that things don't spiral out of control.

Here's what I'm imagining:

1. You ask kids: "What do we mean by a tautology?"
2. You ask them to talk with the people they're sitting near and discuss this. You might even have a google doc open where their group can place their answer. You give them 5 minutes (10 minutes? whatever) to do this.
3. You bring everyone together, and give some time to go over the answers that various groups gave.
4. Then you say, "OK, cool. This was a problem that really bugged Wittgenstein. Here was his answer." And then you show them truth tables or whatever and you keep on running class as you would normally.

(I'm obviously pretty rusty on my history of logic and philosophy.)