Welcome to the Principia Mathematica Maps and Table Site (PM-MATS). The goal of this project is to make clear structural connections between different parts of Principia and to make analyzable data about the theorems, definitions, and primitive postulates in its text. We do this by providing three digital tools:

1. A map of Principia that allows you to see the whole book.
2. 9,944 mini-maps (one for every starred number in Principia) that show you everything used to prove it and everything that it is used to prove (❋13.1 for example).
3. A table of Principia that allows users to search for specific starred numbers, sections, chapters, and more, and also allows exportation of search results to JSON or CSV files.

This project is supported by a Scholarly Editions and Translations grant from the National Endowment for the Humanities running from 2023 to 2025. This project is also part of the broader initiative, the Principia Rewrite project.

You can read about the people working on this project here.

Principia Mathematica and PM-MATS

Principia Mathematica by the two Cambridge mathematicians Alfred North Whitehead and Bertrand Russell appeared as three volumes with Cambridge University Press in 1910 to 1913 (the fourth volume, planned for publication in 1914, was never published). It was among the symbolically densest works ever published and attempted to demonstrate Logicism, the view that all mathematical truths are logical truths. Principia ranks among the most influential books ever produced.

Principia served as both an instructional and a research text for logicians in the years before World War II and profoundly influenced, and for thirty years even shaped, the interrelated fields of philosophy, mathematical logic, and computer science. Principia showed its influence on in the logical works of Kurt Gödel, Alan Turing, Alonzo Church, David Hilbert, Willard van Orman Quine, and Rudolf Carnap (among others). Principia also demarcated a new philosophical research program in what is now often called, more or less imperfectly, analytic philosophy, leading a global generation of philosophers looking to apply its symbolic techniques to lasting effect.

Despite Principia's enormous significance, the text appeared without an editorial apparatus (like a bibliography, an index of symbols or significant terms, and a table of citations of theorems in proofs). The text has also never been digitized: we only have OCR scans of the text that do not facilitate even baseline searches of the text, much less data about the dependencies between parts of Principia that would facilitate a structural or “bird's-eye” view of the text. This digital humanities project is changing all that. First, we have created a JSON file that encodes the text's theorem citation network and posted that file on GitHub. Second, we created PM-MATS, a surveyable map and a filterable table to improve the study of Principia for researchers and members of the public.

Further information

To get further information about Principia or the PM-MATS project, contact us [here]. You can also submit an issue on [the PM-MATS GitHub repository].

Support

The Principia Mathematica Maps and Table Site (PM-MATS) project has been made possible in part by a major grant from the National Endowment for the Humanities. Any views, findings, conclusions, or recommendations expressed in this publication do not necessarily reflect those of the National Endowment for the Humanities.

The PM-MATS project is also supported Western Kentucky University and the University of Iowa. We are grateful for their support.