Show HN: Bertrand Russell's Principia Mathematica in Lean
Published on: 2025-06-05 04:49:30
Formalizing Bertrand Russell’s Principia Mathematica Using Lean4
This project aims to formalize the first volume of Prof. Bertrand Russell’s Principia Mathematica using the Lean theorem prover. The goal is to ensure that the formalization aligns clearly with the corresponding theorems in the book to avoid confusion (See Metaprogramming =Syll=)
Notation
Principia Mathematica’s notation (Peano-Russell notation) is exceptionally known for its sophistication that it has a separate entry on the Stanford Encyclopedia of Philosophy (SEP). Also, Prof. Landon Elkind’s Squaring the Circles: a Genealogy of Principia’s Dot Notation explains the notation skillfully.
I do not think there is a need to read them, I would like to believe that after reading a few examples of how some formulas were formalized and contrasting them against Prof. Russell’s notation should make it clear.
Throughout the formalization, I tried to rigorously follow Prof. Russell’s proof, with no or little added statements
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