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Interesting post but I think you're wrong in the following sentence: A bunch of logical signs were invented by Frege and later popularized / amended by Wittgen

Interesting post but I think you're wrong in the following sentence: A bunch of logical signs were invented by Frege and later popularized / amended by Wittgenstein. Jan Von Plato goes into this in The Great Formal Machinery Works. Frege's notation never become popular - his notation involved lines from one part of an expression to another (!) and is fairly incomprehensible. A more or less modern system of symbols of mathematical logic was created by Russel and Whitehead in Principia Mathematica extending the symbols of Peano (but using the ideas of Frege). Russel and Whitehead syntax, ("there exists" and "for all" symbol) was taken up by Hilbert and the Gottingen school which crafted a lot of the basic theories of mathematical logic. Von Plato doesn't refer to Wittgenstein influencing notation and I don't think he did - he was a popular but idiosyncratic philosopher, not a mathematician. Von Plato's history of mathematical logic in Great Formal Machinery... is fascinating. Edit: Wikipedia describes Frege's notation. You have draw lines connecting expressions, an approach that quickly gets unwieldy. I believe that only Frege used Frege's notation. Wittgenstein refers to Frege but that's it. https://en.wikipedia.org/wiki/Begriffsschrift https://en.wikipedia.org/wiki/Begriffsschrift

crabbone 3y ago
To the best of my knowledge, Wittgenstein lived with Russel for quite some time and was a very influential force in writing the Principa. I believe I saw a lot of prototypes of the modern logical symbols in his Traktatus. I also believe that Russel traveled to meet Frege in his quest for writing the book. He definitely saw his work even before it was published / had private conversations with him face-to-face. Not sure how much of the invented language made it into Principia, but the author was definitely familiar with Frege's work.
- joe_the_user 3y ago
  All I know is Von Plato and some random readings in foundations for my degree, but this[1] seems to indicate Russel met Wittgenstein after Principia was completed. I also believe that Russel traveled to meet Frege in his quest for writing the book. No doubt, as I said above, Principia was very influenced by Frege's ideas. But it absolutely did not use Frege's notation(which was a disaster as I describe above). Von Plato really emphasizes how much of an advance the notation of Principia was. And seriously, it's remarkable how new modern mathematical logic notation is, it didn't have true modern form 'till the 20s or 30s. [1] "It was October 1911, volume one of Principia Mathematica was newly out, and Bertrand Russell, fellow of Trinity College, Cambridge, was having his tea when a young man suddenly appeared. He introduced himself as "Loot'vig Vit'gun-shteyne". https://www.independent.co.uk/life-style/when-ludwig-wittgenstein-met-bertrand-russell-1596995.html https://www.independent.co.uk/life-style/when-ludwig-wittgen...
codeflo 3y ago
That Wikipedia section is uncharacteristically bad. It doesn’t even define or explain the notation, it’s just some examples and a long quote. I’m sure that there was more to it than that.
- Hendrikto 3y ago
  The German version has more details and better explanations.

crabbone 3y ago

To the best of my knowledge, Wittgenstein lived with Russel for quite some time and was a very influential force in writing the Principa. I believe I saw a lot of prototypes of the modern logical symbols in his Traktatus. I also believe that Russel traveled to meet Frege in his quest for writing the book. He definitely saw his work even before it was published / had private conversations with him face-to-face. Not sure how much of the invented language made it into Principia, but the author was definitely familiar with Frege's work.

joe_the_user 3y ago
All I know is Von Plato and some random readings in foundations for my degree, but this[1] seems to indicate Russel met Wittgenstein after Principia was completed. I also believe that Russel traveled to meet Frege in his quest for writing the book. No doubt, as I said above, Principia was very influenced by Frege's ideas. But it absolutely did not use Frege's notation(which was a disaster as I describe above). Von Plato really emphasizes how much of an advance the notation of Principia was. And seriously, it's remarkable how new modern mathematical logic notation is, it didn't have true modern form 'till the 20s or 30s. [1] "It was October 1911, volume one of Principia Mathematica was newly out, and Bertrand Russell, fellow of Trinity College, Cambridge, was having his tea when a young man suddenly appeared. He introduced himself as "Loot'vig Vit'gun-shteyne". https://www.independent.co.uk/life-style/when-ludwig-wittgenstein-met-bertrand-russell-1596995.html https://www.independent.co.uk/life-style/when-ludwig-wittgen...

codeflo 3y ago

That Wikipedia section is uncharacteristically bad. It doesn’t even define or explain the notation, it’s just some examples and a long quote. I’m sure that there was more to it than that.

Hendrikto 3y ago
The German version has more details and better explanations.