Thinking about Mathematics by Stewart Shapiro

Thinking about Mathematics by Stewart Shapiro

  • Paperback: 328 pages
  • Publisher: Oxford University Press, USA (October 5, 2000)
  • ISBN-10: 0192893068
  • ISBN-13: 978-0192893062

comment by hsymbolicus

General comment: good dense read even if at times it looses its pace/appeal and becomes IMO somewhat misrepresenting


  • very dense and comprehensive, in less than 300 pages professor Shapiro gives us a true and detailed account of differing and conflicting theories and methodological isms in the history of Mathematics
  • I generally like the “say-and-exemplify” style of reading for these kinds of subject matters, because there is way more to concepts than simple sentences can express
  • I found myself going LOL sometimes while I read the book, e.g., when author Shapiro said something like that Goedel was not that “prolific” compared to our standards (he meant that he just authored a few papers), but great Lord!!!, some papers by any standards!!! Goedel has been one of these semi-Gods that has brought humankind closer to God . . . how much sh!t can one say when you are that close to God?!? Did he expect for him to turn not only logic, but also physics and along with it the universe upside down?!?

CONS (I guess this was what you were interested in ;-)):

  • He used explanatory comments from the source/main authors of math fundo-philosophical ism’s, some times he uses his own in ways that I found lacking (and here I am using a neutral adj.)
  • Shapiro is a teacher and the book reads like he is lecturing you. Sometimes his style of presenting subjects and section them in paragraphs get to you as micro lessons. I enjoyed a lot more the writing style of Philosophies of Mathematics by Alexander George and Daniel J. Velleman) these authors manage to present the topics true to their matters/without getting “opinionated”, so you don’t hear their voices “louder” than the matter they are trying to explain to you
  • Shapiro’s own philosophical outlook seems to permeate his presentation of the book itself quite a bit (he clearly and “safely” states he does not claim to be unbiased), so your own ideas/doubts may not agree with the ones authored by him and Resnik. Sometimes it just depends on “where you are coming from”; I myself as a Mathematician/Physicist interested in Philosophy and Semiotics do not share some of their views
  • I would have liked if he had shed some more light on the similar concepts that relate to other Sciences, for example, de Saussure introduced the signifier-signified dichotomy in linguistics. I clearly saw a relationship with the type-token dichotomy, with the difference that in linguistics it is clear what is meant, whereas in math philo things get more involved and messy
  • Towards the end of the book he engages the reader with some neuro/cognitive Sciences talk that was so shallow that made me wonder why he included it (probably as an outline to the next edition of the book?) It was hard to tell if he was describing a personal “thought experiment” of contextually explaining some scientifically proven facts. Even though most of what he said made plain sense, given that neuro/cognitive Sciences are a hot and promising research topic and the unprecedented importance it could have in math fundos, there were some issues I think he (or one of his research students) could have spent some more time getting straight/substantiating/polishing (at least with some references)
    On page 282 citing Resnik he writes about some: “‘genetic’ process by which our ancestors (and presumably ourselves) may have been committed to at least small abstract (ante rem) structures” … I think by “genetic” he meant “biologically endowed”, but he is forgetting about the -social- part of these (not that) “ante rem” capabilities we are endowed too. Native American Indians found inextricably odd the count/numbering obsession of the “white man”. Humans lost and grown in the hoods among animals never learn to count, whereas animals/dogs can and do count. I think when parents talk to their new born babies there are lots of “social gens” that they exposed them to.
  • Now, the thing that really annoyed the hell out of me was the obsession author Shapiro has with Bill Clinton, who was cited nominally or indirectly (the “impeached” president this and that …) more than ten times throughout the book in, to me, not only questionable, but also totally off-topic ways that were insulting on a number of counts. Why the f#ck do we need to include politicians in our books?!? Also, I guess he could have included some Republican nonsense as well, while he was at it. Had Rush Limbaugh written a book about math philo and use these examples, fine!, but please!!!, do we need that kind of cr@p in our books?!?

Mr. Shapiro the chess examples were fine, the basketball ones were “acceptable” (just consider some people may not be familiar with what you are basing your explanations on).

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Originally posted Sat, Oct 11 2008 3:35 pm, on sci.math: Book Review: Stewart Shapiro’s “Thinking about Mathematics”


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