Quine’s early proof from the foundations of logic
A Journal Article in the Calculus of Classes
“A Theorem in the Calculus of Classes” is a technical article by Willard Van Orman Quine, written in English and published in the Journal of the London Mathematical Society. It is a journal paper rather than a standalone book. Its subject lies in the calculus of classes, a formal branch of symbolic logic that treats classes—collections treated as objects of exact reasoning—through symbols and rules of derivation. Reference records classify the work under foundations, philosophy, and logic, placing it among Quine’s early contributions to the logical and mathematical foundations of the field.
The Published Proof of a Theorem from Principia Mathematica
The article is centered on the theorem announced in its title. An account of Quine’s intellectual relationship to Bertrand Russell records that Quine’s doctoral thesis was devoted to establishing a new theorem from Principia Mathematica and that the proof was published in this article. The paper thus stands as the printed technical result of that early project and as an early item in Quine’s bibliography, tying the work directly to the Principia Mathematica tradition. Its audience is the specialist reader concerned with formal foundations and logical derivation.
The DOI recorded for the article is 10.1112/JLMS/S1-8.2.89; the full work is available at https://doi.org/10.1112/jlms/s1-8.2.89. It is indexed under zbMATH Open 0007.09802, MaRDI QID Q4753172, and OpenAlex W2015942362. The zbMATH record notes that it is cited in 1 document, while the MaRDI portal lists one related item.
Publication and Citation Records
Catalog metadata gives “First published: 1932,” whereas the MaRDI portal gives a publication date of 1933. The zbMATH record gives J. Lond. Math. Soc. 8, 89–95 (1933), and the UCI Libraries bibliography compiled by Eddie Yeghiayan lists the item with the date and pagination April 1933, 8(30):89–95. The Cairn.info chapter “Quine & Russell” (pages 89–158) also cites “The Logic of Sequences, A Generalisation of Principia Mathematica” (1932) and a positive appreciation by Russell in a letter dated 6.6.35 in Autobiographie, pp. 254–255.
