Re: Categories in developmental psychology!

[Zinovy Diskin <zdiskin@gmail.com>]

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.
>

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