Hello, some comments are below. On Tue, Feb 12, 2013 at 9:12 AM, Jamie Vicary <jamie.vicary@cs.ox.ac.uk>wrote:
Dear all,
I recently came across an intriguing volume entitled "Morphisms and Categories: Comparing and Transforming". The lead author is Piaget, one of the foremost names in developmental psychology, who died in 1980. The volume is a collection of papers, many of which seem to enthusiastically apply ideas of category theory to developmental psychology.
I tried reading the book some time ago: it was interesting but not an easy read. What is left in my head are vague memories and a rough schema of Piaget's view on intellectual development in children: 2-7 year olds: pre-operational thinking, when a child concentrates on objects rather than operations with them (recall Euclid's definitions of point and line); 7-11(?) years: operational thinking (related to Bourbaki structures: I do not care what points and lines are, but here are operations I can perform with them); 11-... years: comparative and transformational thinking (structures could be thought of and operated as integral entities, e.g., be compared and transformed, hence, category theory). The papers in the book describe several series of experiments --- some very clever --- that reveal these qualities. As with any other experiments in psychology, whether these experiments really prove what they claim is a non-trivial question.
Reading the introduction, it's clear that Piaget took very seriously the idea that category theory could provide a formal foundation for psychology.
I'd not say it's about a formal foundation for psychology. Rather, it's about patterns of categorical thinking as a natural part of human intellectual development.
Does this perspective survive in the modern psychology literature?
It's probably not widely known, but some people are well aware of it -- Marian Petre from the Open University, for example. Perhaps she can provide references.
Does anybody know how Piaget came to be acquainted with these categorical ideas in the first place?
If I remember correctly, the preface to the book describes Piaget's mathematical evolution, and that his coming to category theory was a natural step in his epistemological studies. Not in the technical sense of CT being a formal foundation for psychology, but in the qualitative sense of the three-stage schema above.
Is there anything here that could be of interest to modern category theorists?
That categorical thinking is quite natural for a human being (but is suppressed by math education in school). Best regards, Zinovy
Best wishes, Jamie.
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]