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Consider the Particular Case
The analysis of particular problems for the application and illumination of
principles has long been a central activity in the physical sciences. The
attempt to take guidance for the human sciences from the physical sciences has
often been unconvincing and subject to criticism. Instead of borrowing notions
from the physical sciences, I reflect here on the process of problem solving
in a particular case and from that process abstract objectives, methods, and
values which can help us identify and solve our own problems and judge the
value of those solutions. My aim is not to develop a single, universal method
from this example. It is an analysis of how we can proceed to conclusions of
interest that we can have confidence in. I begin with a focus on the
importance of analyzing particular cases. I make use of a particularly
illuminating description by Feynman of a complex physical effect as a concrete
example of a specific form of analysis. I use that worked example to
illuminate the meaning of research I have done. I believe that this comparison
is useful in understanding epistemological analyses based on computational
modeling.
Publication notes:
- Written in 1990-92.
- An abstract with this title was accepted for discussion at the International Conference of the Psychology of Mathematics Education, Tsukuba, Japan, 1993., Vol. III, p. 243.
- A short paper with this title, abstracted from the complete form of the paper, was published in the Journal of Mathematical Behavior, Vol. 13,, No, 2, 1994.
- The complete paper titled On the Merits of the Particular Case, appears as Chapter 1 of Case Study and Computing, Lawler and Carley, Ablex, 1996.
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