Comment by gumby
18 hours 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.
This 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 [1] https://www.gutenberg.org/files/78255/78255-h/78255-h.htm#Pa...
Utter 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.
That's not how to spell Ludwig Wittgenstein!
Wittgenstein 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."
>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.
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.
I’m working on it every day during lunch break. Good old hardcopy.
GEB is not a difficult read. It is delightful!
It is a popular science book which catches the vibe of mathematical logic in an excellent way. It is not a textbook, nor a piece of research. It's all vibes, but high-quality vibes. If you are in the right headspace it can be really inspiring!
I read it cover to cove back in the day and enjoyed it. But I'm not sure more people should read it today.
If they do and enjoy it, good for them! But many parts haven't aged all that well.
However, I can still very warmly recommend 'The Pleasures of Counting' to this very day.
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I had my copy signed by Prof Hofstadter; a treasure to this day. Led to a maths degree, years of organ playing classes, a career in software, and a Zen practice going on 20 years. And I'm pescatarian. I even wrote a few haiku when my babies were little. Hmm, time for another listen to a Tocatta and Fugue.
I read it on my honeymoon 25 years ago. That book sticks with you.
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It's been years since I cracked open a copy, maybe I should give it another shot.
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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.
I 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.
I'm surprised to hear that that was your perspective! I felt that it dealt with otherwise-opaque topics in a very approachable way.
To 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
He 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.
> 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.
Well, it's a pop-sci tome, not a research article.
However, it is pretty dated these days.
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My brother's favorite book in 6th grade was Godel, Escher, Bach.
Why, yes, he works as a compiler engineer.
Eh, that's just a pop-science tome. Nothing impenetrable about it.
I'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.