Principia Mathematica

The Greatest Contribution to Symbolic Logic - the Working Copy of Norbert Wiener's Doctoral Supervisor. First edition of all three volumes, and an association set: Volume I carries the ownership signature of Karl Schmidt (1874-1961), the German-trained philosopher-mathematician who supervised Norbert Wiener's 1913 Harvard doctoral dissertation comparing the algebra of relatives in Schröder with that in Whitehead and Russell, and is extensively annotated throughout in an English-language hand whose Schröderian orientation, critical perspective, and proposition-level engagement with the text correspond closely to the framework of that dissertation. The work these margins interrogate crowned the logicist programme in the foundations of mathematics - in the words of the Oxford Dictionary of National Biography, "the greatest single contribution to symbolic logic". The annotations appear to be the working notes of the scholar who set Wiener the agenda. That agenda was one of the earliest serious confrontations between the Peirce-Schröder algebraic tradition and the Frege-Russell logicism, conducted on precisely the ground that Tarski's 1941 axiomatisation of the calculus of relations would later reclaim for the algebraic school. Volumes I and II each bear at the head of the title page the inscription "Mihailovi? 7. IV. 1925". The inscription marks the set's transmission into Central European hands at precisely the moment when Schmidt was preparing his departure from Tufts for the chair of philosophy at Carleton - the pivot in which he would have been dispersing his working logic library. The signature on the front free endpaper of Volume I identifies a reader trained in the Marburg School, which met the logicist programme critically. Karl Schmidt studied at Marburg in 1893-94, Berlin in 1894-97, and again at Marburg in 1897-98, taking his doctorate from the Philipps-Universität in 1898 with a dissertation on the development of Kantian ethics (Beiträge zur Entwicklung der Kant'schen Ethik) supervised by Paul Gerhard Natorp (1854-1924), co-founder of the Marburg School of Neo-Kantianism. Natorp's Die logischen Grundlagen der exakten Wissenschaften, published in 1910 in the same year as the first volume of the Principia, was a systematic engagement with the philosophy of logic, arithmetic, geometry, and physics that ran directly parallel to Russell and Whitehead's project and, at key points, in critical opposition to it. The Marburg neo-Kantians endorsed logicism as a mathematical achievement but questioned the epistemological foundations that Russell attached to it, and a student of Natorp's would have been trained to engage the Principia as an object of critical interrogation from the standpoint of an alternative tradition in the foundations of mathematics. Schmidt's career matches the intellectual profile that the annotations demand. After his Marburg doctorate he served as First Assistant in the Physical Laboratory at Marburg in 1900-1901, then as Lecturer on Mathematics at Harvard in 1901-1903, Professor of Physics at Bates College in 1903-1904, and Professor of Mathematics and Astronomy at the University of Florida in 1904-1908, before taking up a professorship at Tufts College, where he was publishing on the philosophy of logic by 1909. His 1913 paper 'Studies in the Structure of Systems' appeared in the Journal of Philosophy, Psychology and Scientific Methods - a title echoed almost verbatim in one of the book's most philosophically pointed marginal notes, which observes that these are "Primitive ideas of a Structure of Systems rather than of Logic". From 1928 until his retirement in 1946 Schmidt chaired the Department of Philosophy at Carleton College, returning at the end of his working life to the philosophy that, as he recalled in 1944, his Marburg professor had once warned him he was "wasting [his] time studying". His 1944 book From Science to God: Prolegomena to a Future Theology (Harper & Brothers) marks the final articu.…