Principia Mathematica is modern and insightful • Hacker News Board

Re: Principia Mathematica is modern and insightful

#21

Post by nimih » Thu, Aug 13, 2026, 2:31 AM UTC

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…

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/

Re: Principia Mathematica is modern and insightful

#22

Post by floxy » Thu, Aug 13, 2026, 2:39 AM UTC

voxadam wrote: post #13

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.

It's been years since I cracked open a copy, maybe I should give it another shot.

If 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-Gensl...

Re: Principia Mathematica is modern and insightful

#23

Post by steppi » Thu, Aug 13, 2026, 2:43 AM UTC

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.

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...

Re: Principia Mathematica is modern and insightful

#24

Post by [deleted] » Thu, Aug 13, 2026, 2:43 AM UTC

nimih wrote: post #21

derrida wrote: post #12

Earlier quoted context omitted.

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…

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 t…

[deleted]

Re: Principia Mathematica is modern and insightful

#25

Post by [deleted] » Thu, Aug 13, 2026, 2:46 AM UTC

nimih wrote: post #21

derrida wrote: post #12

Earlier quoted context omitted.

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…

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 t…

[deleted]

Re: Principia Mathematica is modern and insightful

#26

Post by TimorousBestie » Thu, Aug 13, 2026, 2:55 AM UTC

nimih wrote: post #21

derrida wrote: post #12

Earlier quoted context omitted.

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…

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 t…

> As a point of reference, MIT's capstone mathematical logic course[1] has a syllabus that requires at least as much mathematical maturity,

The textbooks they use in that course are written in modern notation and are accessible to a knowledgeable reader; neither can be said of the Principia Mathematica. The archaic syntax is a serious issue.

Re: Principia Mathematica is modern and insightful

#27

Post by mathisfun123 » Thu, Aug 13, 2026, 3:00 AM UTC

keltor wrote: post #9

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.

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

Re: Principia Mathematica is modern and insightful

#28

Post by TimorousBestie » Thu, Aug 13, 2026, 3:02 AM UTC

Instead of spending time beating one’s head against Russell and Whitehead, I would advise reading Homotopy Type Theory (aka the HoTT Book). Dependent types are cool and mind-expanding, but higher inductive types are downright mind-altering.

The Little Schemer/Typer could be used as a preparatory text to gear one up for HoTT.

It also has the advantage of being a bit more applicable to functional programming languages, maybe even more so than Mac Lane’s Categories for the Working Mathematician (which I sometimes see suggested to mathematically-inclined Haskell novices).

Re: Principia Mathematica is modern and insightful

#29

Post by buildsjets » Thu, Aug 13, 2026, 3:03 AM UTC

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’m working on it every day during lunch break. Good old hardcopy.

Re: Principia Mathematica is modern and insightful

#30

Post by annzabelle » Thu, Aug 13, 2026, 3:14 AM UTC

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.

My brother's favorite book in 6th grade was Godel, Escher, Bach.

Why, yes, he works as a compiler engineer.