Principia Mathematica is modern and insightful

(okmij.org)

52 points | by matt_d 3 hours ago

3 comments

  • WillAdams 52 minutes ago
    For an accessible introduction before beginning this, consider his _Introduction to Mathematical Philosophy_:

    https://en.wikipedia.org/wiki/Introduction_to_Mathematical_P...

    and for ease of reading see the various PDF versions at:

    https://people.umass.edu/klement/imp/

  • glimshe 2 hours ago
    If you can read this book cover-to-cover, you're an absolute hero. Sometimes I wonder if they inserted a big logical error in the middle just to troll people under the assumption nobody would bother to read it.
    • gumby 1 hour ago
      You mean you don’t have a framed, signed, bug-bounty cheque from Alfred North Whitehead on your wall??

      More seriously, there is indeed a huge logical error at the heart of the whole enterprise but it was not discovered until much later by Kurt Gödel.

      • voxadam 1 hour ago
        >there is indeed a huge logical error at the heart of the whole enterprise but it was not discovered until much later by Kurt Gödel.

        Which leads us to our next borderline impenetrable book, Gödel, Escher, Bach by Douglas Hofstadter.

        • m-hodges 1 hour ago
          I read GEB cover to cover and haven’t stopped thinking about it for years. Not a brag, a nudge that it’s not impenetrable and more people should read it.
          • anthonygd 24 minutes ago
            I read it on my honeymoon 25 years ago. That book sticks with you.
          • voxadam 55 minutes ago
            It's been years since I cracked open a copy, maybe I should give it another shot.
        • analog31 1 hour ago
          GEB was one of the books that inspired me to study math in college. It made math come to life in way that my high school courses didn't.
        • scubbo 49 minutes ago
          I'm surprised to hear that that was your perspective! I felt that it dealt with otherwise-opaque topics in a very approachable way.
    • kjellsbells 1 hour ago
      I used to wonder how likely it was that the printers made some typesetting errors. Who among us could, say, type a thousand pages of APL symbols without introducing a bug?
      • WillAdams 46 minutes ago
        There's a reason mathematics was known as "penalty copy" and was notoriously difficult to typeset and even more difficult to turn a profit on.

        For a deep dive into both ends of that, see the history of publication of Knuth's TAoCP where the text was originally published traditionally by setting metal type on a composition machine (to the extent possible), then compositors would add the additional characters and spacing material necessary to compose the equations and so forth so as to lay out a galley (which would then be proofed/corrected) --- a successive edition was then typeset using an early imagesetter, which looked so ghastly that DEK considered giving up, but when informed that the imagesetter was controlled by a computer declared, "I am a computer scientist, I can fix that." and expected to knock out a typesetting system over his next sabbatical....

        Roughly a decade later, TeX 1.0 was released.... the current version is 3.141592653 (with new versions adding another decimal place as the version tends towards \pi) --- while we're still waiting on the full publication of Vol. 4, it is widely considered that TeX was worth the delay.

      • inigyou 1 hour ago
        apocryphally a typesetter saw "make x as small as possible" at the end of a math problem to be typeset, and did exactly that
    • keltor 1 hour ago
      It was required reading for my Logics class in undergrad. Pretty sure it was also on the optionals (aka required) for my Set Theory class as well.

      It's also pretty typically a part of History Of Mathematics and Philosophy of Mathematics courses.

      • derrida 55 minutes ago
        No it's not.

        No it wasn't.

        And you did not read it.

        EDIT: source: took logic as undergrad + wrote on the tractatus which required a lot of pre-reqs to understand. 0 chance a course at undergrad level ever assigns principia mathematica. I don't care if you went to yale or oxford or ecole normale ... 0 chance. Most charitable interepretation: some pages of it + was on a bibliography. not required reading.

        if feel embarrassed, that is the consequence for lieing. There is such a thing as intellectual honesty.

        • nimih 3 minutes ago
          Honestly, other than the length and tedious presentation, I don't really think the material in the Principia Mathematica is outside the reach of an advanced undergraduate. As a point of reference, MIT's capstone mathematical logic course[1] has a syllabus that requires at least as much mathematical maturity, and it wouldn't really surprise me that much to see it as an ancillary or excerpted text.

          That said, even if the OP was assigned the text at some point as an undergraduate, I remain a bit doubtful it was actually read.

          [1] https://cfreer.org/18.515/

        • mathisfun123 32 minutes ago
          I'm with you - I hate when people exaggerate their bonafides beyond all belief
          • derrida 27 minutes ago
            LLMs giving some people way too much confidence to conceptually shoot from the hip hehe

            - “effort to refute bullshit is order of magnitude more than to refute it”.

  • voidhorse 51 minutes ago
    I have a copy and like it much. However, i was always partial to Frege's Begriffschrift. His notation was really creative. It's a shame Russel's deflation of that project has sentenced it to the rubbish heap of history.