Date: Sun, 7 Jul 1996 01:47:52 -0500
From: rahul-AT-peaches.ph.utexas.edu (Rahul Mahajan)
Subject: Re: A priori synthetic knowledge


>Chris,
>
>Today, your posts asking how do we develop a critique of Kant had me
>thinking again "a priori synthetic knowledge", a subject I had thought about
>long years ago.
>
>As I retraced the steps I had taken while thinking out the question of
>knowledge and cognition processes, - I remembered that I was most influenced
>by the work of Jean Piaget (and a few others I've forgotten the names of)
>which dealt with how children learn concepts, especially mathematical
>concepts. You probably know a lot more than I do. According to Piaget, they
>learn in reverse order of historical development - they start with
>perceiving topology and go on to later develop Euclidean and projective
>geometry, more or less at the same time.
>
>Which happens to be in the scope of your professional training as I've
>recently learned. Why don't you bring in your specialty to the question?
>
>Zeynep

I believe we can be more precise than this. What children learn to perceive
first is not just general topology, but specifically differential topology
-- they know early on that sharp corners tend to cause booboos. Sadly, the
abovementioned reversal generally continues in life, to the point that
adults often have trouble doing arithmetic.

Rahul




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