Talk:Where Mathematics Comes From

message: The following is actually a good example of the ignorance with which the book has been received in some quarters:
Apparently Joseph Auslander did not read the book, because if he had he would have found a discussion of the conceptual metaphors involved in raising real numbers to an imaginary power at the very beginning of the section on Euler's equation.  The whole point of that discussion is that raising a real number to a complex power is the metaphor. 
I think this is a bad and misleading example of criticism of the book, and should be removed.
K.S.  —Preceding unsigned comment added by 99.231.49.9 (talk) 01:25, 27 April 2009 (UTC)
thread_title:  Terrible example 

message: I don't understand how people can put forth things such as this in the Criticisms section: "WMCF does not explain where arithmetic comes from (if that is even possible or makes sense). Rather, it merely concluded that humans possess innate arithmetical ability."  ??  I'd say it quite clearly follows, and should be obvious to any sensible person, that mathematics is but mathematical thought which directly maps to the physical world through the neural correlates of said thought--this is so trivial that I'm startled at the need to point it out!  There is no contradiction in having mathematics both reflecting a structuring in the physical world and the subjective mental aspect, since mind is just an aspect of brain and part of that world.  Thus saying "WMCF is entirely consistent with the Platonic philosophy which it rejects" is ludicrous since Platonism not only proposes mathematics is independent of mind, but that it is independent of the physical world, and that is a religious proposition and hardly has a place in a technical, rational discussion. ThVa (talk) 13:35, 21 July 2008 (UTC)
thread_title:  ?? 

message: I own a copy of WMCF, and this entry does not do justice to the book at all. For starters, WMCF is a wonderful meditation on the cognitive origins of real analysis, complex numbers, the exponential function, and so on. There are also nice chapters on Boolean algebra, first order logic, and set theory, although the deepest passion of Lakoff and Nunez rests with analysis. Certain aspects of WMCF trace back to Lakoff's 1987 Women Fire and Dangerous Things. Nobody seems to notice that.
I think that Lakoff and Nunez have made a major contribution to our civilization's ongoing conversation about the philosophy of mathematics. The entry does not do justice to that conversation. For my part, I have long been suspicious of Platonism and the associated notion that mathematics is "discovered" rather than "invented." I agree with Lakoff when he writes "there is no way we can ever find out." No way, that is, until we interact with another technogically advanced civilization, which is unlikely to ever happen, if you agree with Barrow & Tipler, and Ward and Brownlee, that homo sapiens is the only technology manipulating species in our Galaxy.
I tell my students that mathematics is a vast "toolbox for the mind" and that mathematics, like all tools, was crafted by humans to serve human purposes. Euclidian geometry and number theory excepted, nearly all of our mathematics came into being after the start of the scientific revolution that began with Copernicus and Galileo, not before.
(I would except also plane and spherical trigonometry, probability, Gaussian elimination by Chinese to solve simultaneous linear equations, election theory, the mathematical logic of Ramon Llull, and so many other things that I can hardly count. In short, the Renaissance wasn't the beginning of an awful lot of things. -- Gene B. Chase 14:44, 15 March 2012 (UTC)
replies: text: Though this may be true, just in the same way that you praise the book, changing the article reflects your personal opinion about mathematics, mathematicians and the book, which, just as the article, may do no justice to mathematicians or mathematics. I suppose the best option is that if you feel strongly about this, you find sources that both agree and disagree with the book, as this would be the purpose of an encyclopedia. At the same time, someone could interpret your thoughts on mathematicians to be very opinionated such as "unwitting" and "unreflective". Any group can make such a claim about any other group and I think we can agree that it rarely holds. So even if understand your dismay towards this article, its problem is precisely that it reflects opinions whereas it should reflect a general consensus.GabKBel (talk) 23:20, 14 May 2010 (UTC)
thread_title:  This entry is seriously deficient 

message: Can someone add the missing bracket to the quote in the first section?  Should it enclose "and human communities"? —Viriditas | Talk 01:41, 17 October 2006 (UTC)
thread_title:  Unclosed bracket 

message: Most of mathematics is analogious to easy navigation or to moving objects in a seen landscape. The pictorial form of thinking is humans' most efficient way of handling information. The capacity of humans who live in a nature environment is enermous: compare the number of technical kind of details in a nature landscape (lines, curves,  shapes, structures, etc) to the number of them in a city landscape. My memory for mathematical things used to be much better when I had wandered in nature. Has there been any research on this?Htervola 10:30, 8 December 2006 (UTC)
thread_title:  Mathematics and nature stimuli 

message: I think the following can be deleted:
:It can be argued that only the first of the above quotes really describes Platonism. The second is rather vague, the third is obviously true (logic is a subset of mathematics), while the fourth is not necessarily associated with Platonism. For example, the Platonists Kurt Godel and Roger Penrose deny that artificial intelligence is possible.
"It can be argued" is classic weasel wording - who argues this? Secondly, the section above does not appear to be direct critique of platonism anyway, but rather a critique of several common romantic ideas about mathematics. Thirdly, the third statement is not "obviously true" to me, nor to the authors of the book who apparently "dismiss it as an intellectual myth"! Reasoning can be non-logical (eg. linguistic or emotional reasoning).
Any objections to removing this small paragraph? ntennis 03:36, 4 May 2007 (UTC)
replies: text: Mathematics has grown into an extremely powerful toolbox for the mind, one whose potential applications extend well beyond those traditional bastions of mathematical application, science and technology. For example, logic and abstract algebra have much to offer to the social sciences and humanities. But communicating these riches to the wider community of nonmathematicians has proved difficult, and the problem is worsening. Even formal systems as basic as first order logic and axiomatic set theory are nowadays learned only by the more technical philosophy majors, and by a small fraction of mathematics students. Hence only a few specialists learn any mathematics beyond calculus, applied statistics, differential equations, and a bit of linear algebra. Just how many persons with a university education know what an equivalence class, partial order, or morphism are? What it means for a collection of axioms to have a model? If the cognitive approach to mathematics suggests improvements to the basic mathematical toolbox and better ways to communicate that toolbox to nonspecialists, it will move humanity closer to the fulfillment of Leibniz's great dream of a universal symbolistic.
Again, any objections? ntennis 03:59, 4 May 2007 (UTC)

text: OK, a week has passed so I removed the passsages. They are retained here on the talk page should anyone want to argue for their reinclusion. ntennis 01:20, 11 May 2007 (UTC)
thread_title:  The romance of mathematics 

message: I have removed the text below, which is variously irrelevant, OR, unencyclopedic in style, ungrammatical, or doesn't reflect a coherent understanding of the text. Please feel free to hash this out in sandbox or talk, and be sure that it fits the book before posting in the article. And cite sources.
:But this critique can also be challenged under the light of theory of multiple intellegences provided by Howard Gardner. So a person might posses good intellegence of certain types but not necessarily of other types. One such example is  Munshi Premchand - the famous story writer and novelist in Hindi literature - who was weak in mathematics. Further, by the same logic, the claim - " ... it would be required to show that intelligence and mathematical ability are separable, and this has not been done" can also be said to be untenable, since here the author seems to presume that intellegence is of one universal nature. 
:From this point of view, whatever one's views on Platonism (right, wrong, meaningless), the 'invention' of mathematical concepts such as number would be impossible since they are hard-wired into our brains from the moment we are born. Also, the word "invention" insinuates that things could somehow be different, so that we could have invented a number theory where 1+1=3, or prime decomposition is false. However, any such number theory immediately falls apart in the face of simple reasoning. In reality, 1+1=3 is obviously false, and Euclid and the ancient Indians stumbled upon prime decomposition rather than inventing it. [But - It can be said that these critics have not enough grounding in the ideas of Lakoff to raise the relevant, valid criticism. Lakoff, Nunez can be interpreted that the experiences of the bodies we have with the external world has resulted in the emergence of unique 'affordance' ( J.J. Gibson's term) characteristic of the type of bodies we have. This has laid down the basis of emergence of mathematics we have. So it is merely regarding the origin of basis of 'ours type' of mathematics which the work of Lakoff, Nunez is refering.]
:Another criticism is that WMCF does not explain where arithmetic comes from (if that is even possible or makes sense).[ Again, they have but simply the critic don't seem to have understood that]. Rather, it merely concluded that humans possess innate arithmetical ability. Some argue that WMCF is entirely consistent with the Platonic philosophy which it rejects. [ No way it seems tenable. Rather the central attack of Lakoff is to undermine Platonic view of mathematics]
"alyosha" (talk) 05:51, 6 April 2009 (UTC)
thread_title:  material removed from Critical response 

message: :The link to the WMCF site is to a prohibited site. Is there a better on that should be used?
Jbottoms76 (talk) 15:22, 1 September 2009 (UTC)
thread_title:  External Links 

message: I agree with Seberle's criticism that this article contains a considerable amount of original research and synthesis.  Much of it is less than entirely sympathetic to the book under discussion.  Tkuvho (talk) 15:04, 21 March 2010 (UTC)
replies: text: It should not be too difficult to clean this article up, but I am unfamiliar with the criticism of this book beyond the single working link offered in the criticism section. Here is what needs to be done by someone knowledgeable of the criticism of the book:
* There are two criticism sections that need to be combined. The first one appears to be entirely original research. (If it is, it can simply be deleted.)
* Any criticism which is original research should be removed. 
* Any criticism which is explaining what critics have said needs to be referenced. 
* The two quotes need to have their links fixed. If there are no longer valid links, simple footnoted references would suffice.
* There are a few good sentences which can be kept, such as the criticism of math error and the authors' response, which is properly linked. This sentence could be expanded to include some of the other responses included in that link, such as the authors' insistence that the embodiment aspect of their claims is being overlooked. It might also be good to reference the original Bonnie Gold review which the authors are responding to and mention the criticisms contained in that review.
* As Tkuvho pointed out, everything should be stated as a neutral report on what critics have said and the authors have responded. Some of the current sentences are POV in that they are directly criticizing the authors rather than stating what critics have said. This is both POV and original research. We don't want to know Wikipedia editors' thoughts on this book; we want to know what the public reaction of experts has been. --seberle (talk) 16:24, 22 March 2010 (UTC)
replies: text: I would like to raise the following additional issue.  Jbottoms76 reports above that the link to the book site is, regrettably, a prohibited one.  Who prohibited it and why?  The link should certainly be included here.  Is it correct to assume that the site was prohibited by an overzealous wikipedian who happens to disagree with the thesis contained in the book?  Tkuvho (talk) 17:00, 22 March 2010 (UTC)
replies: text: I am not sure what Jbottoms76 is referring to. The link actually no longer works. You can access an archived copy of the link from June 20, 2008, at http://web.archive.org/web/20071101135617/perso.unifr.ch/rafael.nunez/2ndprint.html. But I don't think it is proper to link to an archived copy. (Is that what he meant by "prohibited"?) I have not yet been able to locate the new site. Perhaps there is not one? In that case, this link should simply be removed. --seberle (talk) 20:06, 22 March 2010 (UTC)
thread_title:  original research 

message: I've removed an old neutrality tag from this page that appears to have no active discussion per the instructions at Template:POV:
::This template is not meant to be a permanent resident on any article. Remove this template whenever:
::#There is consensus on the talkpage or the NPOV Noticeboard that the issue has been resolved
::#It is not clear what the neutrality issue is, and no satisfactory explanation has been given
::#In the absence of any discussion, or if the discussion has become dormant.
Since there's no evidence of ongoing discussion, I'm removing the tag for now. If discussion is continuing and I've failed to see it, however, please feel free to restore the template and continue to address the issues. Thanks to everybody working on this one! -- Khazar2 (talk) 00:02, 30 June 2013 (UTC)
thread_title:  removing POV tag with no active discussion per [[Template:POV]] 

message: Hello fellow Wikipedians,
I have just added archive links to  on Where Mathematics Comes From. Please take a moment to review my edit. If necessary, add  after the link to keep me from modifying it. Alternatively, you can add  to keep me off the page altogether. I made the following changes:
*Added archive https://web.archive.org/20060718161407/http://www.unifr.ch:80/perso/nunezr/warning.html to http://www.unifr.ch/perso/nunezr/warning.html
When you have finished reviewing my changes, please set the checked parameter below to true to let others know.
Cheers. —cyberbot IITalk to my owner:Online 05:51, 28 August 2015 (UTC)
thread_title:  External links modified 

message: In the article it is written: "Lakoff and Núñez cite Saunders Mac Lane (the inventor, with Samuel Eilenberg, of category theory) in support of their position. Mathematics, Form and Function (1986), an overview of mathematics intended for philosophers, proposes that mathematical concepts are ultimately grounded in ordinary human activities, mostly interactions with the physical world."
I have searched the book by Lakoff and Nunez for this fact. However, Mac Lane is never mentioned (except of listing his book in a general bibliography, without any comment). 
Zbisem (talk) 14:31, 7 November 2018 (UTC)
thread_title:  Non-existent Mac Lane 

message: The last few paragraphs under the "Human cognition and mathematics" section were recently deleted. User:Metalmikebot explained the deletion as follows:
:I deleted the last several paragraphs, which were attached as criticisms without relevant citations; these would be better suited to a separate section under "criticisms", in which criticisms were **cited** rather than written into the entry like an op-ed. They appeared to use original research and did not accurately represent the book.)
I do not have sufficient expertise on this book and its criticism to judge the quality of the deleted paragraphs. However, in apparent contradiction to the stated reasons for the deletion, the deleted paragraphs did have several citations. Also, there does exist a separate "Critical response" section where the paragraphs could have been moved to, in contradiction to the implication that such a section needs creating.
I am restoring the deleted paragraphs until a better justification can be given for their removal. Perhaps there are genuine reasons for believing the references were not valid? Perhaps these paragraphs should be moved to the "Critical response" section? --seberle (talk) 15:28, 8 January 2022 (UTC)
thread_title:  Criticism deletion