Up-to-date version of Principia Mathematica?

2011-11-24T04:32:32Z

Background: I found this interesting translation of Godel's On formally undecidable propositions of Principia Mathematica and related systems I that, along with translating it into English, uses more modern and understandable symbols, includes some hyper text links throughout the paper, and, if I'm not mistaken, makes the language a little more readable. This seems like a good and noble undertaking: taking an important paper and revamping it to make it more accessible, or at least less intimidating for modern readers.

So while looking through it, I couldn't help but think of another work that could benefit from such a treatment, Russell and Whitehead's Principia Mathematica. Every review I have read about it is something like "It lead to a lot of important developments in logic, but is mostly a historical curiosity. And besides, it is incredibly difficult to read, so putting forth the necessary effort is probably not worth it."

Here is the question: does such a thing exist, and would such a paper be worthwhile? Is there anything in the Principia that would be of interest to modern mathematicians. (Finding some points of interest and reproducing them seems like a better idea than trying to reproduce all three volumes.) Godel's theorem and his proof are still interesting, in spite of the fact that there are many other (better?) ways of getting to the Incompleteness theorems.

Another example of this sort of revision is The Annotated Turing.

I'd appreciate any knowledge of such a source, or any insight into why one wouldn't be too valuable, or really any thoughts on looking at Principia Mathematica at all.

Answer by Carl Mummert for Up-to-date version of Principia Mathematica?

2011-11-29T03:34:52Z

In his Stanford Encyclopedia of Philosophy article "The Notation of Principia Mathematica", Bernard Linsky makes the following claim:

This translation is offered as an aid to learning the original notation, which itself is a subject of scholarly dispute, and embodies substantive logical doctrines so that it cannot simply be replaced by contemporary symbolism. Learning the notation, then, is a first step to learning the distinctive logical doctrines of Principia Mathematica.

The point is that Principia was not intended simply to be a development of mathematics in type theory: it was intended to make a philosophical argument that mathematics could be carried out using only "logic". Thus translating PM so that the underlying mathematical principles are more clearly described would miss the point that there are not supposed to be any underlying mathematical principles, only "logical" ones. This differs sharply from Gödel's paper, which was intended to be mathematical (the result can be viewed as just a particular type of combinatorics or number theory) rather than philosophical.

Up-to-date version of Principia Mathematica? - MathOverflow

Up-to-date version of Principia Mathematica?

Answer by Carl Mummert for Up-to-date version of Principia Mathematica?