Principia Mathematica's Second Edition in Its Century, 1925-2025

Principia Mathematica's Second Edition in Its Century, 1925-2025

Principia Mathematica was and remains a fixture of ongoing discussions in logic, philosophy of language, philosophy of mathematics, metaphysics, and early analytic philosophy. The second edition of Principia, however, received a lukewarm reception and its significance, both for understanding Principia’s first edition and for later developments in early analytic philosophy, have not been fully explored. This workshop convenes scholars to further explore developments between the editions of Principia and the impact of the second edition itself on 20th century philosophy.

Call for Papers

We invite contributed papers on Principia Mathematica and its second edition, broadly construed, for a peer-reviewed collection that also brings together the papers stemming from this workshop. Topics of interest include but are not limited to the following:

1. What was Whitehead’s influence on the Principia’s second edition? According to Whitehead himself, the second edition of Principia was “solely undertaken by Mr. Bertrand Russell.” Nonetheless, Whitehead notes that he did discuss and concur in the changes to any first edition materials. What proposals did Whitehead influence, and how did he influence them? 
2. To what extent did the second edition of Principia support a move among logicians and mathematicians towards the now-preferred (set-theoretic) foundation for mathematics? The logic of Principia was decidedly intensional such that two relations might not be identical even if they have the same extension (that is, they apply to the same things). But Quine (1941, 147-148) for example argued at length that the intensional logic of Principia was best replaced by the extensional logic. In the 1930s and 1940s, notable logicians like Kurt Gödel (1944) and Alfred Tarski (1944) similarly moved in this direction (and argued explicitly for doing so). Arguably, though, the second edition of Principia apparently departs remarkably from its earlier intensional stance. Not only that, but the second edition departs (if it does) from the earlier intensional logic and embraces an extensional logic due to different influences, especially that of Ludwig Wittgenstein. Taken as a newly extensional work, Principia’s second edition rather supported the gathering momentum towards extensional logics. This belies the lukewarm reception of Principia’s second edition among reviewers, who largely repeated their impressions of the first edition with minimal discussion of the second edition’s innovations.
3. What parts of Principia’s first edition, like the multiple relation theory of judgment, are rejected in its second one? Perhaps the most difficult and longstanding textual question concerning Principia’s first edition concerns the highly technical matter of its formal grammar or syntax. Similarly, a difficult and longstanding controversy persists concerning Russell’s multiple relation theory of judgment. These two issues are related, though there has been little interaction across these two literatures.
4. What results from Principia’s text can be saved if other parts are rejected? Perhaps the most significant inquiry undertaken in Principia’s second edition is to what extent the first edition’s two axioms of reducibility (❋12·1 and ❋12·11) can be abandoned without critically damaging the rest of the work. Kurt Gödel (1944) identified an error in a key demonstration within this appendix, and subsequently scholars intermittenly discussed whether a repair was possible and how it might be done.18 But how might other results be recovered without the axioms of reducibility? For example, Wittgenstein (1922, 5.53-5.5303) in his Tractatus Logico-Philosophicus criticized Principia’s account of identity. This definition hinges on the axioms of reducibility in Principia’s first edition. So also does the recovery of important results about classes, like the principle of extensionality (theorem ❋20·11). Which results besides induction are jeopardized by
   abandoning reducibility in Principia’s second edition? How are these to be recovered?
5. Applications of interactive theorem provers to Principia's theorems and proofs are especially welcome.
6. Contributions utilizing the PM-MATS digital resource are especially welcome. Read more about this resource here: https://principia.lib.uiowa.edu/about.html

Absent alternative arragnements, papers are due no later than December 14, 2026. Expressing interest in submitting a contribution is strongly encouraged by October 15, 2026. Papers should be at least 5,000 words and no more than 15,000. Papers should be anonymized for blind review and submitted with a cover page indicating the author's name, affiliation, email, paper title, and abstract to Landon Elkind, [email protected], with the subject line PM2 Paper Submission.  

TeX format is encouraged for contributions, but Word formats are also acceptable. Typesetting of equations using the principia package (for TeX users: https://ctan.org/pkg/principia) or the PMifier (for Word users: https://principia.lib.uiowa.edu/pmifier/index.html) is strongly encouraged. 

Support

The Principia Mathematica’s Second Edition in Its Century, 1925-2025 workshop has been made possible in part by a major grant from the National Endowment for the Humanities (Collaborative Research, RZ-206663-26). 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 McMaster University. We are grateful for their support.