WKU News

On June 7-9, Philosophy major Ethan Huffaker presented a co-authored paper, “Close Reconstruction of Proofs in the Quantificational Logic of Principia Mathematica” at the Bertrand Russell Society’s 51^st annual meeting in Amherst, NY.

Huffaker previously won a Faculty-Undergraduate Student Engagement (FUSE) grant to work with Dr. Landon Elkind, Assistant Professor of Philosophy. The conference paper is the result of their joint research activity. In the paper, they supply complete proofs to theorems in the landmark Principia Mathematica by Alfred North Whitehead and Bertrand Russell.

“The text of Principia contains more symbolism than English,” says Dr. Elkind. “The actual text contains demonstrations, which are more like recipes for cooking up a proof that the reader has to follow.”

To this day, 114 years since Principia appeared, most of the recipes have not been fully reconstructed from the text. However, this paper contains 126 complete proofs constructed by following the recipes provided by Principia’s authors. The complete proof reconstructions ran 137 pages as compared with the 33 pages of proof recipes provided in the text. This indicates how much detail was uncovered through Huffaker and Dr. Elkind’s work about the proof strategies developed in Principia.

“Through our complete proof reconstructions, we discovered some things about authorial proof practices, corrected typos, and identified previously unclear references and citations in the text,” says Dr. Elkind. “We plan to publish these so that nobody else needs to reinvent the wheel, as it were, and they can instead follow our complete proofs if the demonstration is ever unclear to the reader.”

Having presented the paper at a specialist conference, Huffaker and Dr. Elkind plan to submit the paper for peer review and eventual publication at the end of the summer.

To learn more about the Philosophy program, please visit https://www.wku.edu/political-science/philosophymajor.php.