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Principia Mathematica is modern and insightful

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Re: Principia Mathematica is modern and insightful

#41

Post by eru »

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…

Einstein's 1905 Annus Mirabilis papers seem like they easiest of the bunch to just read through. I just pulled up 'Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen', the one about Brownian motion, and read the whole thing. It's only 12 pages and fairly accessible; more prose than equations.

(Of course, if you don't read German, you should get yourself a translation.)

See https://myweb.rz.uni-augsburg.de/~eckern/adp/history/einstei...

I don't think I'm smart enough to casually read and understand original works on General relativity, but the Annus Mirabilis work seems much simpler. The famous E=MC2 paper is only three pages.

See https://myweb.rz.uni-augsburg.de/~eckern/adp/history/einstei...

About Gödel: if you are interested in the theorems, and not necessarily their original presentation, you can get plenty of rigorous modern treatments. It's very common for mathematicians to work out simpler proofs and more appealing presentations of famous results over time.

See https://dn721807.ca.archive.org/0/items/uber-formal-unentsch... if you want to give one of Gödel's work a go. It's only 26 pages. Footnote 48a is especially interesting. Overall the prose is crisp, but the notation is rather archaic to modern eyes.

I agree with your general sentiment, and your heuristic in general.

Re: Principia Mathematica is modern and insightful

#42

Post by steppi »

robobro wrote: post #36
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.

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."

Re: Principia Mathematica is modern and insightful

#44

Post by bryanrasmussen »

debo_ wrote: post #34
anthonygd wrote: post #20

Earlier quoted context omitted.

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

Are you still married?

finally we shall be able to answer the age old question - does Gödel, Escher, Bach: an Eternal Golden Braid stick with you better than a spouse!

Re: Principia Mathematica is modern and insightful

#45

Post by zote »

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/

similarly the work itself is available here: https://people.umass.edu/klement/pom/

Re: Principia Mathematica is modern and insightful

#46

Post by jibal »

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.

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.

Re: Principia Mathematica is modern and insightful

#47

Post by sorokod »

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.

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

Re: Principia Mathematica is modern and insightful

#48

Post by bulbar »

TimorousBestie wrote: post #26
nimih wrote: post #21

Earlier quoted context omitted.

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.

I did give it a try many years ago, I think as undergrad, but gave up after a few pages, because for me it was nearly impossible to parse the syntax.

Re: Principia Mathematica is modern and insightful

#49

Post by bulbar »

makerdiety wrote: post #43

So... the ancient childish attempt to prove mathematics using mathematics (Gödel's Incompleteness slew the challenger) can be used to help me be a better TypeScript programmer? I learned something new today.

Why the belittling language? You actually can prove the completeness and consistency of portions of mathematics.

While axioms were known in ancient times, only Hilbert started the whole "prove Mathematics" thing.

How else would you prove mathematics and why would that be childish to use math? The limitations discovered were quite surprising back then.

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