The mathematics of common sense

I will be joining a few colleagues for a symposium at CogSci2014 and I’ve been gathering some notes for my talk.  The talk will focus on the impact of embodiment theories on a philosophy of mathematics.  As I looked again at some of the things I’ve chosen to highlight in my blogs, I came upon […]

What the experience of mathematical beauty could imply

Back in September, 1992 Semir Zeki wrote an article for what was then a special issue of Scientific American called Mind and Brain. In it he described what was known about how the brain produces visual images.  I have referred back to the article many times because it highlights the philosophical implications of our current […]

A continuum of senses

I was intrigued by a paper that came to my attention in the December 2013 issue of Philosophical Studies by Anna Farennikova in which she argues that we ‘see’ absence.  In other words, seeing that something is not there is as much a product of our visual system as seeing an object.  The example with […]

What does our experience have to do with mathematics?

This is something of a follow-up to my last post.  I checked out a series of links related to Max Tegmark in the last few days, having heard about the release of his first book Our Mathematical Universe.  But I was also motivated by having observed that the latest conference organized by the Foundational Questions […]

Pigeons, rats, monkeys and real numbers

I’d like today to stay on the topic of mathematics from the cognitive science perspective, and in particular, to make available another set of interesting studies summarized by C. R. Gallistel, Rochel Gelman and Sara Cordes. The studies are described in their contribution to the book Evolution and Culture (edited by Stephen C. Levinson and […]

Life’s music, movement, language and mathematics

Things happen in nature.  Cells socialize and build structure, organisms grow, and move, and interact, and then more things grow – like music, language, and mathematics. Generally, talk about evolution is very pragmatic.  Cell organization, the shaping of roots, leaves, nourishment mechanisms, reproductive drives, are all usually understood as fairly specific purposeful processes.  Perhaps by […]

Infinities, metaphors and being human

Our thoughtful, imaginative worlds are married to our physical experiences but the subtleties of their union are almost impossible to fully appreciate.  Mathematics, I often argue, has the potential to provide a better view of the situation, perhaps because of the inexhaustible depth of its abstraction, together with the precision it brings to a concept, […]

Embodied and dis-embodied meaning

I found a short paper today by Mark Andrews, Stefan Frank and Gabriella Vigliocco focused on reconciling two trends in the study of meaning in cognitive science.  These two trends are represented by embodied cognition theories (which treat meaning as a simulation of perceptual and motor states) and by computational or distributional accounts of meaning […]

Pollock, fractal expressionism and a mathematical thought

In a blog back in January, I referenced a talk given by David Deutsch in which he made the argument that, while empiricism has been the basis of science, empiricism alone is inadequate because scientific theories explain the seen in terms of the unseen.

What we see, in all these cases, bears no resemblance to […]

The Irrationality of Mathematics?

When I write, I often choose my words very carefully in order to remove any opportunity the reader might have to make a quick judgment about the content of what I am saying.  I’m hoping they will keep thinking about what I am saying.  The unexpected pairing of words often accomplishes this, and in this […]