matt_d · 272 points · 151 comments · gisteren · Open original
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TRtristrambgisteren
"Principia Mathematica is an odd book, worth looking into from a historical point of view as well as a mathematical one. It was written around 1910, and mathematical logic was still then in its infancy, fresh from the transformation worked on it by Peano and Frege. The notation is somewhat obscure, because mathematical notation has evolved substantially since then. And many of the simple techniques that we now take for granted are absent. Like a poorly-written computer program, a lot of Principia Mathematica's bulk is repeated code, separate sections that say essentially the same things, because the authors haven't yet learned the techniques that would allow the sections to be combined into one."
- Mark Dominus (https://blog.plover.com/math/PM.html)
WIWillAdamsgisteren
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/
PNpngwen22 uur geleden
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.
GLglimshegisteren
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.
RAradford-neal21 uur geleden
The notation for avoiding parentheses is interesting, and I've thought that it might be useful in programming languages.
To illustrate, suppose you have a non-associative operator $. Rather than write a$(b$c), you can write a$.b$c - the . makes the $ before it be lower precedence on the right side. More dots make things be even lower precedence.
So, for example,
a$b .$: x$y .$. p$q
means
(a$b) $ ((x$y) $ (p$q))
At least, that's my recollection. It's been over fifty years since I read (significant parts of) it...
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"Principia Mathematica is an odd book, worth looking into from a historical point of view as well as a mathematical one. It was written around 1910, and mathematical logic was still then in its infancy, fresh from the transformation worked on it by Peano and Frege. The notation is somewhat obscure, because mathematical notation has evolved substantially since then. And many of the simple techniques that we now take for granted are absent. Like a poorly-written computer program, a lot of Principia Mathematica's bulk is repeated code, separate sections that say essentially the same things, because the authors haven't yet learned the techniques that would allow the sections to be combined into one." - Mark Dominus (https://blog.plover.com/math/PM.html)
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/
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.
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.
The notation for avoiding parentheses is interesting, and I've thought that it might be useful in programming languages. To illustrate, suppose you have a non-associative operator $. Rather than write a$(b$c), you can write a$.b$c - the . makes the $ before it be lower precedence on the right side. More dots make things be even lower precedence. So, for example, a$b .$: x$y .$. p$q means (a$b) $ ((x$y) $ (p$q)) At least, that's my recollection. It's been over fifty years since I read (significant parts of) it...