Well, you could try looking at Michael Arbib's work: he has, in the past, written a book on category theory, and he's done a huge amount of work on cognitive science. Graham On 17/10/11 12:46, Jocelyn Ireson-Paine wrote:
On Wed, 28 Sep 2011, posina wrote:
Dear All,
My understanding, having studied in some detail the behavioural, psychological, and cognitive scientific studies, is that a serious study of mathematics (beginning with Lawvere & Schanuel's Conceptual Mathematics) can inform cognitive sciences more so than the other way around, with all due respect to Dan Kahneman and those 'where mathematics comes from' guys.
Do tell us more. Mathematics has informed cognitive science on, for example, the structure of natural-language grammars, how neurons compute, and how the brain uses the geometric constraints on 3D shapes when understanding images. But you mention Lawvere & Schanuel's "Conceptual Mathematics". What can category theory contribute? I suggested some possibilities in http://www.j-paine.org/why_be_interested_in_categories.html , "What Might Categories do for AI and Cognitive Science?". There must be lots more.
Thank you, posina
Jocelyn
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