8 ms·
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 un
by glimshe 2mo 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 2mo agoYou 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.
- deleted 2mo ago[deleted]
- voxadam 2mo 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.
- analog31 2mo agoGEB 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.
- black_knight 2mo agoI showed up to first day at university and an older student talked to me for like two minutes before declaring that I needed to read GEB. I dutifully went ahead and bought it, and I still work in logic today.
- m-hodges 2mo agoI 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.
- voxadam 2mo agoIt's been years since I cracked open a copy, maybe I should give it another shot.
- floxy 2mo agoIf you want to get to the meat of the issue, without the extraneous stuff, you might also tackle: Godel's Theorem Simplified. https://www.amazon.com/Godels-Theorem-Simplified-Harry-Gensler/dp/081913869X https://www.amazon.com/Godels-Theorem-Simplified-Harry-Gensl...
- lanstin 2mo agoThe extraneous stuff is honestly fabulous, IMO of course. Just being able to listen to a four part fugue sensibly is a rare but accessible pleasure. And amusing dialogs as an instantiated dialectic for showing the truth synthesized from apparent opposites, is a great pedagogical learning.
- m-hodges 2mo agoExtremely agree. The extraneous stuff is what makes the book magical.
- anthonygd 2mo agoI read it on my honeymoon 25 years ago. That book sticks with you.
- debo_ 2mo agoAre you still married?
- deleted 2mo ago[deleted]
- scubbo 2mo agoI'm surprised to hear that that was your perspective! I felt that it dealt with otherwise-opaque topics in a very approachable way.
- annzabelle 2mo agoMy brother's favorite book in 6th grade was Godel, Escher, Bach. Why, yes, he works as a compiler engineer.
- suslik 2mo ago> Gödel, Escher, Bach by Douglas Hofstadter. I gave that book to my mathematician grandma, and she found it so boring she couldn’t finish it - “All this stuff was known for decades”. True anecdote.
- eru 2mo agoWell, it's a pop-sci tome, not a research article. However, it is pretty dated these days.
- taybin 2mo agoHow is it dated?
- jcranmer 2mo agoA large chunk of the book is philosophizing about AI and the nature of the mind and intelligence. And when it's betting on the AI that existed pre-AI winter... yeah, that part is quite dated.
- taybin 2mo agoYou should see his book "Fluid Concepts and Creative Analogies, which is entirely about his experiments with AI in The Fluid Analogies Research Group with his grad students. Although I wonder if those techniques could be paired with LLMs somehow.
- eru 2mo agoEh, that's just a pop-science tome. Nothing impenetrable about it.
- onraglanroad 2mo agoI'd have thought so too, but when I went looking for a copy in Waterstones and failed to find it under popsci section, or in maths, I tried the enquiry desk. After a few attempts where I eventually tried "goddle s-chair batch" we found it. It was under Western Philosophy.
- sorokod 2mo agoTo each their own, I read GEB several times and enjoyed the intellectual challenge and the humour. Hofstadter wrote a followup book: I am a strange loop. https://en.wikipedia.org/wiki/I_Am_a_Strange_Loop https://en.wikipedia.org/wiki/I_Am_a_Strange_Loop
- taybin 2mo agoHe wrote a number of follow-up books. I love GEB, but the follow ups were often disappointing in surprising ways. He has another book about the beauty and challenges of translating poetry, but it’s actually about the sudden death of his wife and it's been too sad for me to finish.
- steppi 2mo agoThis is commonly believed, but Gödel didn't identify a logical error at the heart of the whole enterprise, he proved astonishing theorems revealing limitations of any sufficiently powerful formal system. One can kind of think of the Principia as a science experiment to find the extent to which known mathematics could be proven from foundational axioms that could be thought of as "laws of logic". To make their system work, Russell and Whitehead themselves had to add extralogical axioms, such as their Axiom of Reducibility [0] and the Axiom of Infinity, giving empirical evidence (but not a proof) that "laws of logic" alone were not enough. They were also aware of limitations in their own system, such as the inability to define the cardinal $\aleph_\omega$ [1]. Like the article says, what they did was ahead-of-its-time, and a monumental influence on all subsequent work on formal systems, including Gödel's work, regardless of whether Russell and Whitehead achieved their initial aims. [0] https://en.wikipedia.org/wiki/Axiom_of_reducibility https://en.wikipedia.org/wiki/Axiom_of_reducibility [1] https://www.gutenberg.org/files/78255/78255-h/78255-h.htm#Page_190 https://www.gutenberg.org/files/78255/78255-h/78255-h.htm#Pa...
- gumby 2mo agoThe flaw was the belief that it was possible (though they were not sure that they two could pull it off). Gödel showed that it was not an impossibly difficult task but an actually impossible task.
- steppi 2mo agoA failed hypothesis is not the same thing as a logical error. Would they have been more free of flaws if they believed it was impossible and thus didn't try? We'd all be the poorer for it
- jibal 2mo agoIt cannot be overstated how flawed your own statements here are. You shouldn't be talking about logical error regarding a work of logic when you don't even know enough logic to know what a logical error is. And there was no "flaw" in attempting to resolve foundational paradoxes in set theory, primarily to address Frege's error and deal with Russell's paradox, or in attempting to prove that all mathematics can be derived from pure logic. Seeking to demonstrate a hypothesis that is later shown to be erroneous is not "flawed", else the entire knowledge-seeking enterprise is "flawed". And switching from "logical error" to the very vague notion of a "flaw" is goalpost moving that looks a lot like bad faith. I won't comment further.
- robobro 2mo agoThat's not how to spell Ludwig Wittgenstein!
- steppi 2mo agoWittgenstein didn't find logical flaws in the Principia and deeply admired it. He found flaws in Russell's follow up work on Epistemology, "The Theory of Knowledge."
- jibal 2mo agoUtter nonsense ... there is no known logical error in PM. Gödel proved that Russell and Whitehead's goal was unachievable but that's a totally different matter. OTOH, Russell found a logical error at the heart of Frege's work, and PM fixed it by introducing the theory of types.
- kjellsbells 2mo agoI 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?
- inigyou 2mo agoapocryphally a typesetter saw "make x as small as possible" at the end of a math problem to be typeset, and did exactly that
- taneq 2mo ago“Find x” <— here it is!
- gjm11 2mo agoThe version of this story I heard is in Littlewood's "A Mathematician's Miscellany"[1] and it's a sigma rather than an x. But he tells it as something that happened specifically to him -- he wrote a memo that ended with "thus sigma should be made as small as possible", and that bit was absent but there was in its place a very very tiny sigma. Unless he's outright lying, I think this one actually happened! [1] The more recent edition is titled "Littlewood's Miscellany"; I am fairly sure this story is in both the older and the newer version.
- WillAdams 2mo agoThere'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.
- keltor 2mo agoIt 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 2mo agoNo 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.
- mathisfun123 2mo agoI'm with you - I hate when people exaggerate their bonafides beyond all belief
- derrida 2mo agoLLMs 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”.
- my-next-account 2mo agoDerrida, go back to your grave, you messed up the quote!
- deleted 2mo ago[deleted]
- derrida 2mo agoHa! Thanks. True! I'll leave it (p.s. this whole comment section is wild - the green & getting downvoted accounts? They said the most credible things of anyone )
- sergevar 2mo agoInterestingly, there was a Show HN last year formalizing PM in Lean (https://news.ycombinator.com/item?id=43797256 https://news.ycombinator.com/item?id=43797256), and the Principia Rewrite project (https://www.principiarewrite.com https://www.principiarewrite.com) verified all 189 propositional logic theorems (sections 1-5) in Coq against the original proof sketches