Wednesday, February 27, 2008

Quote from Barwise

In reading the intro to Barwise's Admissible Sets and Structures, I came across the following paragraph that I liked.
"A logical presentation of a reasonably advanced part of mathematics (which this book attempts to be) bears little relation to the historical development of that subject. This is particularly true of the theory of admissible sets with its complicated and rather sensitive history. On the other hand, a student is handicapped if he has no idea of the forces that figured in the development of his subject. Since the history of admissible sets is impossible to present here, we compromise by discussing how some of the older material fits into the current theory."
I confess that I know nothing of the details of the history of admissible set theory. I have enough handicaps in that general area. I like Barwise's sentiment, that knowing about how the area developed helps one get a grip on the topic. Actually, I'll trot out the opening to Structure of Scientific Revolutions, an opening which I forgot about till we read it in intro to philosophy of science.
"History, if viewed as a repository for more than anecdote or chronology, could produce a decisive transformation in the image of science by which we are now possessed. That image has previously been drawn, even by scientists themselves, mainly from the study of finished scientific achievements as these are recorded in the classics and, more recently, in the textbooks from which each new scientific generation learns to practice its trade. Inevitably, however, the aim of such books is persuasive and pedagogic; a concept of science drawn from them is no more likely to fit the enterprise that produced them than an image of a national culture drawn from a tourist brochure or a language text."
Rhetorically, that is an impressive opening to the book. It is easier to get fully behind Barwise's more modest sentiment though. Of course, I find these when I'm doing practically no historical work.

1 comment:

Justin said...

One thing I've often noted is how contemporary presentations tend to make ideas look so easy. It sometimes looks like the old guys were just plain slow, with the advantage of hindsight.

Mark's book has an example comparing the utterances "Jane has a strong understanding of the calculus after completing this course," with "Euler didn't really understand the fundamental notions of the calculus."

This is almost entirely tangential to your post, I suppose.