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Principia Mathematica is modern and insightful

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Re: Principia Mathematica is modern and insightful

#161

Post by rramadass »

eru wrote: post #160
rramadass wrote: post #127

Earlier quoted context omitted.

We have to agree to disagree then. You definitely need a good background in Physics to understand them. For a general reader, even though they might not get the whole thing they can still get an appreciation for the whole from the commentary/details added by the editor. The book contains the English translations of the 5 papers with Einstein's original introduction and a short discussion on each, a informative introd…

Oh, the book is probably good and entertaining! It's just not necessary, if you paid attention in high school.

> if you paid attention in high school.

A very hard Nope!

No high school teaches you Electrodynamics at the level needed to understand his Relativity/Photoelectric-effect papers, the idea of Stochastic Randomness behind Kinetic theory/Brownian motion etc. You need both background physics theory and the mathematical tools.

For your edification see;

John Stachel: Einstein papers - https://www.symmetrymagazine.org/article/february-2005/john-...

Annus Mirabilis Papers - https://en.wikipedia.org/wiki/Annus_mirabilis_papers

Re: Principia Mathematica is modern and insightful

#162

Post by jibal »

gumby wrote: post #154
steppi wrote: post #23

Earlier quoted context omitted.

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…

The flaw was the belief that it was possible (though they were not sure that they two could pull it off). Gödel showed that it was not an impossibly difficult task but an actually impossible task.

It cannot be overstated how flawed your own statements here are. You shouldn't be talking about logical error regarding a work of logic when you don't even know enough logic to know what a logical error is.

And there was no "flaw" in attempting to resolve foundational paradoxes in set theory, primarily to address Frege's error and deal with Russell's paradox, or in attempting to prove that all mathematics can be derived from pure logic. Seeking to demonstrate a hypothesis that is later shown to be erroneous is not "flawed", else the entire knowledge-seeking enterprise is "flawed".

And switching from "logical error" to the very vague notion of a "flaw" is goalpost moving that looks a lot like bad faith.

I won't comment further.

Re: Principia Mathematica is modern and insightful

#163

Post by [deleted] »

bulbar wrote: post #152
makerdiety wrote: post #82

Earlier quoted context omitted.

Yikes, guys/girls. I got downvoted to -4 points for a misunderstanding or something. Because the author of the website would probably agree with my simple point that although the Principia Mathematica tried to do the impossible, there is still utility for its value as a programming self-teaching resource for serious students of computer science. Wow. Yeah. You guys ironically didn't just throw out the baby with the b…

That would have made more sense as a reply to your own posting, because it doesn't bring the discussion forward or address my points (if any).

[deleted]

Re: Principia Mathematica is modern and insightful

#164

Post by [deleted] »

gjm11 wrote: post #116
makerdiety wrote: post #82

Earlier quoted context omitted.

Yikes, guys/girls. I got downvoted to -4 points for a misunderstanding or something. Because the author of the website would probably agree with my simple point that although the Principia Mathematica tried to do the impossible, there is still utility for its value as a programming self-teaching resource for serious students of computer science. Wow. Yeah. You guys ironically didn't just throw out the baby with the b…

> I got downvoted to -4 points > You burned me at the stake like a witch for heresy. I think you should try to get a better sense of proportion. Also: > my simple point that although the Principia Mathematica tried to do the impossible, there is still utility for its value as a programming self-teaching resource I don't know what your original intention actually was, but your comment read to me very much as (1) imply…

[deleted]

Re: Principia Mathematica is modern and insightful

#165

Post by [deleted] »

asimpletune wrote: post #121
makerdiety wrote: post #82

Earlier quoted context omitted.

Yikes, guys/girls. I got downvoted to -4 points for a misunderstanding or something. Because the author of the website would probably agree with my simple point that although the Principia Mathematica tried to do the impossible, there is still utility for its value as a programming self-teaching resource for serious students of computer science. Wow. Yeah. You guys ironically didn't just throw out the baby with the b…

Sometimes it's worth revisiting the site guidelines on comments https://news.ycombinator.com/newsguidelines.html#comments I'm guessing people downvoted you for snark.

[deleted]

Re: Principia Mathematica is modern and insightful

#166

Post by tsoukase »

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.

The foundations of math can equally by ZFC as well as in my basement. From any initial concept you can bootstrap mathematics.

Re: Principia Mathematica is modern and insightful

#167

Post by lioeters »

pngwen wrote: post #97

You might be interested in Kurt Goedel’s extended book review wherein he proves that Principia cannot do what it sets out to do, nor can any such system. I do teach PM when I teach theory of computation, but largely to tell the story of how we discovered the limits to computation.

> Goedel’s extended book review wherein he proves that Principia cannot do what it sets out to do

Perhaps it's this one:

On Formally Undecidable Propositions of Principia Mathematica and Related Systems

https://en.wikipedia.org/wiki/On_Formally_Undecidable_Propos... - PDF: https://monoskop.org/images/9/93/Kurt_G%C3%B6del_On_Formally...

Re: Principia Mathematica is modern and insightful

#168

Post by eru »

rramadass wrote: post #161
eru wrote: post #160

Earlier quoted context omitted.

Oh, the book is probably good and entertaining! It's just not necessary, if you paid attention in high school.

> if you paid attention in high school. A very hard Nope! No high school teaches you Electrodynamics at the level needed to understand his Relativity/Photoelectric-effect papers, the idea of Stochastic Randomness behind Kinetic theory/Brownian motion etc. You need both background physics theory and the mathematical tools. For your edification see; John Stachel: Einstein papers - https://www.symmetrymagazine.org/artic…

You can read the original photoelectric effect paper at https://myweb.rz.uni-augsburg.de/~eckern/adp/history/einstei...

It's a bit more involved than the one about Brownian motion, but it's still fairly accessible for the motivated layman.

I'm not sure why you are so convinced that this is so hard. Nor what you are trying to convince me that I should find it hard: I've literally had a look at the German originals. No amount of secondary or tertiary writing is going to overrule that.

Schools differ in what they teach, of course. And many of them aren't very good. But Wikipedia is always available and these days you can ask your favourite LLM for explanations, too.

Of course, as I said already, the books you are suggesting are probably great and fun to read. They just aren't necessary.

Re: Principia Mathematica is modern and insightful

#169

Post by rramadass »

eru wrote: post #168
rramadass wrote: post #161

Earlier quoted context omitted.

> if you paid attention in high school. A very hard Nope! No high school teaches you Electrodynamics at the level needed to understand his Relativity/Photoelectric-effect papers, the idea of Stochastic Randomness behind Kinetic theory/Brownian motion etc. You need both background physics theory and the mathematical tools. For your edification see; John Stachel: Einstein papers - https://www.symmetrymagazine.org/artic…

You can read the original photoelectric effect paper at https://myweb.rz.uni-augsburg.de/~eckern/adp/history/einstei... It's a bit more involved than the one about Brownian motion, but it's still fairly accessible for the motivated layman. I'm not sure why you are so convinced that this is so hard. Nor what you are trying to convince me that I should find it hard: I've literally had a look at the German originals. No…

I am now beginning to suspect that you are validating the skepticism that i expressed in my original comment. You have been pretty cavalier about your claims (a high school student, really?) which cannot be accepted at face value.

As already mentioned, I already have the english translations of all the five papers, have spent some time with them, and they most certainly are not "accessible for the motivated layman" without the necessary physics/mathematics background. No amount of motivation/enthusiasm can make up for lack of necessary knowledge.

Since you kept mentioning the brownian motion paper as being "easy to read", the second section on "osmotic pressure from the standpoint of the moleculer-kinetic theory of heat" starts with the equations for entropy and free energy of the system which i would like to see a "motivated layman"/"high school student" understand, much less derive. They need knowledge of thermodynamics and statistical mechanics (assuming they are already comfortable with multivariable calculus/PDEs) to even get started.

Similar criticisms apply to the rest of your claims regarding other papers.

That is why you need guidance from teachers who do have knowledge of all the required sub-domains and can help the student navigate the paper. Of course one can also use all other available tools like LLMs etc. but their veracity again needs to be checked by a human in conceptually complex subjects like these.

Re: Principia Mathematica is modern and insightful

#170

Post by voidhorse »

igravious wrote: post #65
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 sket…

Hey man, I completely agree. I love the begriffschrift and recognize the very important role it played in the history of logic.

The reason I say it's in the rubbish heap is because basically only experts and people with strange hobbies know about it. The set of people familiar with the Principia is vastly greater than those who know what the Begriffschrift is. That's what I meant, not that it wasn't important, but that it's importance is now under recognized and under appreciated.

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