Principia mathematica
Principia Mathematica has been described as one of the greatest intellectual achievements of human history. It attempts to rigorously reduce mathematics to logic. Among other things, it defines the concept of number. It is obviously a very dense and abstract work which has been made all the more difficult to read in light of more recent developments in the symbolic representation of logical concepts. It would be helpful in any new edition of the book to provide a summary of the reactions to and developments of the ideas in the work, a list of corrections, a bibliography, and a table of equivalent current logical symbols.
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- I think this highly depends on what is being rated. Non-durable consumer goods, sure, there is very little assurance that what you're getting now is even what you would have gotten ten years ago. Processes and inputs both change. A previously reputable brand might have been purchased by private equity and enshittified on purpose.
On the other hand, if you're reading reviews of Moby Dick, I don't think the perceived quality or relevance of the writing is going to change much on the scale of decades. Maybe it starts to get archaic at some point, but people still get a lot out of reading Homer. If it's something like Principia Mathematica, that might honestly be timeless as long as human-like creatures exist who can read and understand math and physics.
- > how would the Homo sapiens and the cosmos progress and advance if more people understood Principia Mathmatica?
It's important to separate historical importance from importance to understanding by most people.
The presence of Whitehead & Russell's Principia Mathematica (PM) in history is a very important historical event. In at least one list, it's one of the most important books in the 20th century. PM shattered any argument that mathematics couldn't have rigorous foundations. PM instead showed that it was possible to start from relatively simple axioms and really prove all the way up to a higher level.
PM is NOT, however, important to read or understand itself in detail, as it's been superseded by later works. Syntactically, PM uses a dotted notation instead of parentheses that most people find hard to read & generally undesirable. From a deeper point-of-view, PM uses a set of axioms built on a hierarchy of types. This hierarchy of types was an early effort to avoid various paradoxes. Almost no one uses a hierarchy of types like this today; it's far more common to use Zermelo-Fraenkel set theory with the axiom of choice (ZFC). Even if you wanted to use a hierarchy of types, which is rare, you're probably more likely to use Quine's "New Foundations" which provides a much simpler foundation for mathematics.
It's not important to understand PM in detail, but knowing that it's possible has inspired many more recent efforts, and that is more important.
I argue in my video "Metamath Proof Explorer: A Modern Principia Mathematica" that the Metamath Proof Explorer (MPE) is a successor to PM. MPE uses modern notation (e.g., parentheses) and ZFC set theory combined with classical logic, so it uses modern conventions, but it also tries to prove "everything" from a very few axioms. Thankfully, we can now use computers to verify every last step (with multiple independent implementations), so we can have much more confidence in the proofs. Here's my video, I think you might like it: https://www.youtube.com/watch?v=8WH4Rd4UKGE
That video focuses on MPE, but of course there are several efforts inspired by PM. Understanding the impact that PM had on mathematics is, to me, the important thing.
- I have a similar impression as you but I also found this quote illuminating:
"I never read the Pricipia Mathematica; almost no one has. You know it's not really traditional in Physics to go back and read the original papers of the great people before us. I'll confess I've never read Einstein's original papers on Relativity even though I've written a textbook on Relativity. In Physics the idea is it's the ideas matter, not their original presentation."
"Newton's original presentation of this stuff in the Principia - number one, it was in Latin (laughs). It took a while for it to be translated into English and number two, he was apparently afraid of using all of the new mathematical techniques he invented. So he tried very hard to only use existing mathematical techniques so people would believe him, so people would accept it right away.
"Subrahmanyan Chandrasekhar, who is a great 20th century astrophysicist, actually wrote a version of the Principia Mathematica for the common reader. If you ever want to know what Newton was actually up to in the in his great masterwork the Principia I would advise not buying either the original Latin or English but buying Chandrasekhar's explanation of what was going on."
- Sean Carroll The Biggest Ideas in The Universe pt 2 @15:55 (youtube)
- Here is a classic which is lacking: The Principia Mathematica (often abbreviated PM) is a three-volume work on the foundations of mathematics written by Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. https://en.wikipedia.org/wiki/Principia_Mathematica
- I had a look. I recognise Allan Hazlett's name, but that's as much as I can say. Epistemology, PoM and stuff are all fairly interesting but depend a lot on the quality of teaching, in my experience.
If you don't want to just read Kenny's ANHWP, and I were to provide a reading list:
* Plato: Meno, Gorgias, Parmenides, Charmides, Apology. If you enjoy it, then try reading The Republic.
* Aurelius' Meditations. Democritus and Epicurus are worth reading about too, to summarise the Greeks. And Zeno's paradoxes.
* meaningness.com as an entry-point to Buddhist philosophy in general.
* Logicomix as an introduction to Russell & his project in Principia Mathematica.
* Mill's Utilitarianism, Hannah Arendt 'The Human Condition', and Henry George 'Progress & Poverty' for politics, history and economy, throw in a bit of Rawls. Schiller's 'The Robbers' is also very much worth reading.
* SEP articles for the classic writers: Augustine, Aquinas, Hume, Kant; then Kripke, Tyler Burge, and Searle present some interesting problems.
Other mentions off the top of my head: Dreyfus, Chalmers, Parfitt, Singer.
There are some great YouTube channels out there that teach to the intelligent adult. Gregory B Sadler, Mark Thorsby, Daniel Bonevac, Carneades.org are the ones I remember being useful. Some good series' are out there: Human, All Too Human; Alan Watts' TV series; The Reith Lectures...
I've missed a ton, of course, this is just stuff I remember enjoying or gaining something from. I hope this list isn't too overwhelming. I'd start with the Greeks, then flick around some YouTube channels, then meaningness, then off into whatever takes your fancy. I don't really fancy digging through MOOCs so sorry I can't recommend any in particular.
My personal favourite philosophers/philosophical writers: Nietzsche, Wittgenstein, Darwin, Hegel, Camus, CS Pierce, Feyerabend, Epicurus.
- If one is into this kind of thing, one should really read these books: [1]
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