the quotes were already in fair use on the page of reviews of Lakoff and Nunez referenced at the bottom - I presumed (perhaps wrongly?) that this means that they were cleared for quotation. Only the Santa Fe one seemed to be long, but it's quite specific, and justifies the claims int he rest of the article, so I'm not sure the scope of this is very clear without it... but I'll go with consensus, obviously.
It's significant to the article that "counting up to four" and moving along a line are empirically observed cognitive phenomena. Does it really make sense without that?
The Sigma Xi review is of the first edition which had technical errors.
My careful read of the other reviews, which include some pretty prominent journals and institutes, didn't make note of those errors, and the reviews have been up for some time, so presumably they'd object if they thought the overall theory was wrong.
Nonetheless, it speaks to the care of the authors that the technical errors be mentioned by some neutral party, so the Sigma Xi review belongs there - maybe with a note to the effect that these errors don't seem to have caused the other later reviewers to give up on the theory.
OK- scratch that - I see there's now a link to their "warning" about this.
Removed this from the article:
- It may well be that turning mathematics into an empirical science will involve a great deal of animal testing, to determine what's shared - and what is merely a widely shared human bias, arising out of our over-complex brains.
Many things may be, but this is unlikely to be one of them. Who says this? Other than you?
The objection is legit, thanks, but when you changed it you said this was deleted for being "surreal" - I admit it's speculative, but what's "surreal" about empirical testing of a cognitive science thesis, to see what we say share with apes and what is uniquely or bizarrely human?
Most of anthropology and primatology recently seems to be testing what things apes can do, what they can't, where we share a foundation ontology with them, where we don't. For instance how do they see 'family', or 'friend', or etc..
I also can't be the first person to call the human brain "over-complex"... I thought it was kind of a crack on the whole community arguing this stuff, as well... many wouuld just say "mathematics works" and leave it at that...
But the article is controversial enough without this suggestion of a path to validating... I'll actually see if I can get a quote out of Lakoff or find the material on chimps being tested to determine who real "number" is to them - saw this being done in a lab in Japan - on the Discovery channel - as usual the credits scroll by too fast adn the researchers name is too Japanese. ;-) But I'll dig it up.
"Clearly, when a man shoots a bear it is not only the man whose experience of the bullet is defined by "F=MA"."
This was actually the exact sentence (in private converation) that convinced me that mathematics could not be wholly a human invention...
The bit about nuclear weapons seems to be totally unrelated to the topic in the first and second sentences of that paragraph. The article as a whole is a little confused and poorly organised - perhaps a re-write is in order? As to animal testing... You mean experiments conducted using animals which is an different kettle of fish. -- The Ostrich