Talk:Where Mathematics Comes From

I've renamed the article to the name of the Lakoff/Nunez book. The article "Cognitive science of mathematics" should be broader, covering all the findings of cognitive science related to math (and not just those identified in the book), and perhaps being less attached to these two authors' "embodied realism". --Ryguasu 06:11 Dec 27, 2002 (UTC)

all good moves

Now that structure of these articles is agreed on, and old talk gone, can we please discuss the book and the implications of the book and what can be said about it? If you look in the article history there was a great deal of material directly related to the book, including commentary on reviews etc.. This appears to have been deleted, contrary to wikipedia conventions, by people who evidently had not read the book nor understood its claims - perhaps bad writing was the issue - and perhaps some of that old text should be reviewed and re-incorporated by third parties? The book also has undergone some revisions and the authors have responded to criticisms. Does that response go here, or in w:cognitive science of mathematics ?

I think it would be highly appropriate to discuss criticisms about the book and responses thereto in this particular article. We can always move it somewhere else if that later turns out to be more appropriate. --Ryguasu

Am I missing something, or does the book not provide a way to conceptualize multiplication of a*b or a/b, when a and b are both non-integer, for any of the "4 Gs"? (The book provides ways to conceptualize many other simple operations, including these ones for integers.) If not, could somebody suggest a way to visualize such multiplications, or at least suggest why the standard procedure is reasonable? --Ryguasu 01:51 Feb 25, 2003 (UTC)

"This idea analysis is distinct from mathematics itself and cannot be performed by mathematicians not sufficiently trained in the cognitive sciences."

This is clearly a fantastic argument that beats all others: "my analysis is based on special techniques that you cannot understand, former experts in {insert subject here}".

Although there is certainly some room for the criticism that Lakoff, in particular, is too quick to presume himself one of the leading authorities on anything he's thought about, your paraphrase here is not particularly accurate. The argument is not that mathemeticians cannot understand the ideas in Where Mathematics Comes From; it's that a normal mathematical education doesn't teach anything like this. In particular, a normal mathematical education devotes approximately no time to considerations of A) what about the mind/brain allows it to do mathematics, or B) the philosophy of mathematics. These are precisely the topics that the book is about. Of course, the article could probably be clearer about all this. --Ryguasu 16:11 Mar 21, 2003 (UTC)