Week 3 readings:

We'd like to push things towards considering the role of models in building knowledge. From the encyclopedia entry, it is clear that there is an enormous range of different kinds of models. Are these distinctions subtle and important, or an irrelevance for what we typically do? As ever, read, digest, and cogitate. Email cogitations to us please by Tuesday evening.

Levins, strategy of model building in Population biology (pdf)
Stanford encyclopedia on models, Frigg et al., 2006 (as for last week) (pdf)
Polya - how to solve it, 1944 (selections) (pdf)

If you have the time read all of the Polya excerpts, it is a lovely book. The problem-solving dialogue between a teacher and a student is a gem If not enought time, focus on:
1. the problem solving check list (p. xvii)
2. part II. How to solve it - a diaglogue (p. 33)
3. the entries on practial problems (p.149), progress and achievement, (p157), signs of progress, (p178)

David's notes from last class:

Other thoughts

Is the following true? Understanding means explaining things which are complicated or numerous in terms of things which are simpler or fewer. Any given piece of work can be divided up into the background knowledge which is assumed and the problem which is tackled. Big progress in understanding can be judged by the difference between the compexity of the phenomena and the  simplicity of the building blocks of that explanation. But it must also be measured by the level of confidence in those building blocks.

From last time: Induction is creative. Deduction is logical. Both are necessary for moving forward.

Questions that should be asked at every seminar.
- how confident are you of your 'background knowledge'?
- how have you critically evaluated your argument?
- how wrong might your argument be?
- what would form a critical test that would cause you to reject your argument?