I raced through this book, but i didn't much enjoy any part of it. Rather than just reiterate what everybody else has said, i'll pointlessly include mI raced through this book, but i didn't much enjoy any part of it. Rather than just reiterate what everybody else has said, i'll pointlessly include my attempt from mid-2014 to create a list of nonfiction books that might represent modern American culture. (What would you add/delete to improve it?)
I thank DM Daniel for the work but i don't applaud it. For people like me who require 3 and 4 readings of a work for it to stick in my memory even a lI thank DM Daniel for the work but i don't applaud it. For people like me who require 3 and 4 readings of a work for it to stick in my memory even a little bit, this book provides a lazyman's way out of rerereading Ayer's Language, Truth and Logic. Daniel's efforts were merely to delete sentences and paragraphs from the original ... so that students could have something slightly shorter?...more
An utter disappointment but not devoid of value. I doubt i'll bother to continue reading, so here are my initial thoughts.
I'm far too dim to understanAn utter disappointment but not devoid of value. I doubt i'll bother to continue reading, so here are my initial thoughts.
I'm far too dim to understand Lakoff + Núñez's ideas. Or maybe they're not saying anything other than people have to use language to express and explain mathematical ideas and language is entirely metaphorical. Or maybe they're saying that mathematics is entirely metaphorical and language is fundamental. There's a philosophical chicken-and-egg problem with this entire book. Or maybe i don't know what i'm talking about. Or maybe i don't know what L+N are talking about. I'm a 25 watt bulb in an array of Klieg lights.
I've always wanted to share my love for this crazy Chick Publication and now might be my best/only chance. While reading L+N's first few "mappings" of a "metaphor" from a "source domain" onto a "target domain," i couldn't stop thinking of the 4th-from-last page of Are Roman Catholics Christians? (note: Chick Pubs are only good if you wanna laugh at a fundamentally disabled mind]
Obviously L+N's book is yet another that i'm unqualified to critique so i searched the interwebs for reviews and found one by a professional mathematician that i wish i'd written.
Assuming you hold no strong prejudices regarding "cognitive science" or "the embodied mind" or "Platonism" or "Aristotelianism," maybe the following quotes from James Madden's article (Notices of the AMS. 2001;48:1182–88) will convince you to be on my side of this futile debate.
Presumably, when an individual is engaged in mathematical work, that person is guided by metaphors that are somehow represented in his or her own brain.... Unfortunately, Lakoff and Núñez do not provide any illustrations of what they suppose goes on in "real time," so this is about as much as I can say.
This brings me to my first main criticism concerning the metaphor hypothesis: What is the quality of the evidence for it?... I would like to have seen direct support for the metaphor hypothesis from the observation of mathematical behaviors. (1184-5)
"After a while, the notion of metaphor seems to become a catchall." (1185) Did Madden grow as tired of the vagueness and ubiquity of the term metaphor as i did?
Madden damns with faint praise and cuts deep into the heart of L+N's premise:
The idea that metaphors play a role in mathematical thinking is quite attractive, but what is needed is a notion specific and precise enough so that people working independently and without consulting one another can discover the same metaphors and agree on the functions they perform. I do not think we have this yet. (1185)
And a summary of sorts:
If I think about the portrayal of mathematics in the book as a whole, I find myself disappointed by the pale picture the authors have drawn. In the book, people formulate ideas and reason mathematically, realize things, extend ideas, infer, understand, symbolize, calculate, and, most frequently of all, conceptualize. These plain vanilla words scarcely exhaust the kinds of things that go on when people do mathematics. (1187)
Madden does give L+N credit for "shar[ing] with us their intuitions about the way the mathematical mind operates," but he's not convinced that anything they said has been scientifically tested even though it's presented to us as if it had been proven....more