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Principia Mathematica is modern and insightful

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Re: Principia Mathematica is modern and insightful

#61

Post by blipvert »

karmakurtisaani wrote: post #56
WillAdams wrote: post #17

Earlier quoted context omitted.

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 spaci…

> the current version is 3.141592653 Another instance of a "clever" joke that becomes annoying very fast.

I suppose that to make it slightly less tedious we could just refer to the version using the number of significant digits: 10

Re: Principia Mathematica is modern and insightful

#62

Post by igravious »

hasley wrote: post #55
WillAdams wrote: post #14

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/

Of you prefer an even more entertaining approach and a very gentle introduction into the topic, I recommend the comic "Logicomix" which tells Russel's journey (though not historically correct all the time for story telling reasons). https://en.wikipedia.org/wiki/Logicomix

Logicomix is novel, and done well, but flawed … it's deficiencies lie in what it leaves out which may come across as an unfair charge but in this case the charge is warranted. There is a more historically correct and less orthodox work waiting in the wings for whosoever should attempt it.

Re: Principia Mathematica is modern and insightful

#63

Post by igravious »

emil-lp wrote: post #59
nitsuaeekcm wrote: post #52

For those who aren't familiar with the great but tragic story of Principia and Russell's quest for the foundation of math (spoiler: there is none), there's a really great graphic novel called Logicomix https://en.wikipedia.org/wiki/Logicomix I haven't read it in probably ten years, but it's one of those books and stories I spend an inordinate amount of time thinking about, for whatever reason.

The foundation of math is (mostly) ZFC.

It is not. The foundation of math is contested -- but afaik it is widely held that HoTT is the, erm, hottest contender to the throne https://en.wikipedia.org/wiki/Homotopy_type_theory

Re: Principia Mathematica is modern and insightful

#64

Post by jstanley »

eru wrote: post #39
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 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.

What hasn't aged well? I don't think any of it is dated to any particular time period.

Re: Principia Mathematica is modern and insightful

#65

Post by igravious »

voidhorse wrote: post #15

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.

The Begriffschrift has in no way been consigned to the rubbish heap of history. What gave you that impression? It is seminal. That it had one unresolved paradox in its set-theoretic foundations does not scupper the philosophical insights, nor the creative notation, nor the more-or-less novel approach of conjoining mathematical functions and logic to give us predicate logic (apologies for this brutally simplified sketch)

i like to think of Frege and the Begriffschrift like this

Boole: logic + algebra = algebraic logic

Frege: logic + functions = predicate logic

ergo, if Boole is rightly deified then so should Frege regardless of minor infelicities (which prompted type theory anyhow) -- again, apologies if this is totally misleading

Re: Principia Mathematica is modern and insightful

#66

Post by black_knight »

analog31 wrote: post #7
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.

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.

Re: Principia Mathematica is modern and insightful

#67

Post by my-next-account »

rramadass wrote: post #37
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…

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 Elect…

I've certainly read and studied material explaining f), but I haven't read the original paper (besides, isn't that in German?). The proofs aren't that hard, as I remember them, maybe they're harder in original form? To be clear: I specialized in logic, formal verification and programming language theory at uni. This was a while ago, and I'm on new parent amounts of sleep, so pls b nice.

Re: Principia Mathematica is modern and insightful

#68

Post by my-next-account »

derrida wrote: post #19
mathisfun123 wrote: post #18

Earlier quoted context omitted.

I'm with you - I hate when people exaggerate their bonafides beyond all belief

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”.

Derrida, go back to your grave, you messed up the quote!

Re: Principia Mathematica is modern and insightful

#69

Post by bebimbop »

rramadass wrote: post #37
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…

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 Elect…

[dead]

Re: Principia Mathematica is modern and insightful

#70

Post by black_knight »

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.

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!

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