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Principia Mathematica is modern and insightful

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Re: Principia Mathematica is modern and insightful

#31

Post by suslik »

voxadam wrote: post #5
gumby wrote: post #3

Earlier quoted context omitted.

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.

>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.

> 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.

Re: Principia Mathematica is modern and insightful

#32

Post by sergevar »

glimshe wrote: post #2

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.

Interestingly, there was a Show HN last year formalizing PM in Lean (https://news.ycombinator.com/item?id=43797256), and the Principia Rewrite project (https://www.principiarewrite.com) verified all 189 propositional logic theorems (sections 1-5) in Coq against the original proof sketches

Re: Principia Mathematica is modern and insightful

#33

Post by taneq »

inigyou wrote: post #10
kjellsbells wrote: post #6

Earlier quoted context omitted.

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?

apocryphally a typesetter saw "make x as small as possible" at the end of a math problem to be typeset, and did exactly that

“Find x” <— here it is!

Re: Principia Mathematica is modern and insightful

#34

Post by debo_ »

anthonygd wrote: post #20
m-hodges wrote: post #8

Earlier quoted context omitted.

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 read it on my honeymoon 25 years ago. That book sticks with you.

Are you still married?

Re: Principia Mathematica is modern and insightful

#35

Post by debo_ »

mathisfun123 wrote: post #27
keltor wrote: post #9

Earlier quoted context omitted.

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.

link the syllabi for the classes

What if they link the axioms for the classes and leave it as an exercise to the reader to derive the syllabi?

Re: Principia Mathematica is modern and insightful

#36

Post by robobro »

gumby wrote: post #3
glimshe wrote: post #2

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.

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.

That's not how to spell Ludwig Wittgenstein!

Re: Principia Mathematica is modern and insightful

#37

Post by rramadass »

derrida wrote: post #12
keltor wrote: post #9

Earlier quoted context omitted.

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.

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 embar…

Well said.

Thanks for calling out these sort of posers and charlatans on HN. We should not tolerate these people if we are to discuss/argue/motivate interesting/hard subjects productively.

I automatically discount anybody on HN (until i have looked at their profile/comment history/any personal bio websites etc.) who claim they have read/studied a) Euclid's Elements b) Newton's Principia c) Maxwell's Treatise on Electricity and Magnetism d) Einstein's 1905 Annus Mirabilis papers. e) Principia Mathematica by Russell/WhiteHead f) Godel's Theorem g) Bourbaki's mathematics books etc. etc. They might have browsed it out of curiosity but that is not the same as reading/studying it.

Actual conceptual mathematics/science is intrinsically hard even ignoring the archaic language/notations.

As a good example; the Nobel-prize winning physicist S.Chandrasekhar wrote Newton's Principia for the Common Reader where he explains a subset of the principia (only dealing with gravitation) using modern notation and language. He himself found it quite hard and thus the "common reader" in the title is somebody who has had a good course in calculus and has the motivation to put forth the effort in understanding it.

Re: Principia Mathematica is modern and insightful

#38

Post by eru »

voxadam wrote: post #5
gumby wrote: post #3

Earlier quoted context omitted.

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.

>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.

Eh, that's just a pop-science tome. Nothing impenetrable about it.

Re: Principia Mathematica is modern and insightful

#39

Post by eru »

m-hodges wrote: post #8
voxadam wrote: post #5

Earlier quoted context omitted.

>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 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.

Re: Principia Mathematica is modern and insightful

#40

Post by eru »

suslik wrote: post #31
voxadam wrote: post #5

Earlier quoted context omitted.

>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.

> 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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