Conceptual Mathematics informs cognitive science.
Subject: categories: Re: Natural Functorial Categorical Intuition, Sender: posina; Recipient: email@example.com; Date 28.09.2011
My understanding, having studied in some detail the behavioral, psychological, and cognitive scientific studies, is that a serious study of mathematics (beginning with Conceptual Mathematics textbook of Lawvere & Schanuel) 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.
On Tue, 27 Sep 2011 17:20:41 -0400, “Ellis D. Cooper” wrote:
My motto has been “Rigor cleans the window through which intuition shines.” It seems to me that a great deal more is known about mathematical rigor than about mathematical intuition. Economics Nobelist Daniel Kahneman recently published at http://www.edge.org a survey of several men-decades of research on flaws of human statistical intuition. A paper, “The Intuitive Experience” in “The View from Within” (Journal of Consciousness Studies, V.6 1999) discusses in considerable detail schema and methods of invocation of intuition in psychotherapy, art, and biology research. My overall question is whether there really are different kinds of intuition depending on the research discipline. In particular, is there some kind of kinetic intuition specific to category theory that crucially involves visualization of time-varying diagrams? Do conjectured adjoint functors arise from distinct algebraic, or geometric, or logical intuitions? Do categorists deploy special methods to access their intuition, or do intuitions just happen to those with a knack for category theory? Does categorical intuition just develop with experience, or is there a specialized training to enhance it? Is categorical intuition any different from mathematical intuition in general? Ellis D. Cooper