(And if I actually ever arrived at a coherent theory, I’d have no way of testing it. But I guess that’s another story.)
The lack of feedback leads directly to all of you. I decided to pretty much write papers and put them here for your comments, questions and ability to find the holes in my logic. There are a number of areas to looks at – the evolution and development of the brain and of cognition in general, the historical development of mathematics, studies of brain “use” while doing mathematics (or arithmetic), studies of mathematical learning disabilities, and possibly the effect of changes in society.
I’ll post the first of these “papers” in the next few days. Just to get it out of the way, I’ll talk about my ideas of whether or not mathematics is a language and whether or not mathematical cognition can be understood that way. (Aren’t you just way too excited?)
In the meantime, here are the definitions for arithmetic and mathematics from The Oxford English Dictionary, Second Edition (1989).
1. Originally: (a collective term for) geometry, arithmetic, and certain physical sciences involving geometrical reasoning, such as astronomy and optics; spec. the disciplines of the quadrivium collectively. In later use: the science of space, number, quantity, and arrangement, whose methods involve logical reasoning and usually the use of symbolic notation, and which includes geometry, arithmetic, algebra, and analysis; mathematical operations or calculations. Colloq. abbreviated maths, (N. Amer.) math.