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The Greatest Contribution to Logic since Aristotle - the Working Copy of Norbert Wiener's Doctoral Supervisor. First edition of all three volumes of the monumental work that crowned the logicist programme in the foundations of mathematics - "the greatest single contribution to logic that has appeared" in two thousand years (DNB). The present set is of singular historical interest. 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 exactly to the framework of that dissertation. The annotations appear, in other words, to be the working notes of the scholar who set Wiener the agenda - one of the earliest serious confrontations between the Peirce-Schröder algebraic tradition and the Frege-Russell logicism, whose reverberations run through Tarski's 1941 axiomatisation of the calculus of relations and into the architecture of modern mathematical logic. Volume II bears on its title page the inscription "Mihailovi? 7. IV. 1925", marking the set's transmission into Central European hands at precisely the moment when Schmidt was preparing his move from mathematics at Tufts to the chair of philosophy at Carleton - the pivot in which he would have been dispersing his working logic library. Principia Mathematica represents the fullest realisation of the logicist thesis - the claim that mathematics is, at bottom, a branch of logic, its whole body deducible from a small number of primitive ideas and a small number of primitive principles of logical inference. The programme had its first major articulation in Frege's Begriffsschrift (1879) and Grundgesetze der Arithmetik (1893-1903), but it was Russell's 1901 discovery of the paradox that bears his name - that the class of all classes that are not members of themselves generates a contradiction - that forced a reconstruction of the logical foundations on a new basis. The theory of types devised by Russell and elaborated with Whitehead in the three massive volumes of the Principia was that reconstruction. It is, as Grattan-Guinness has written, one of the most impressive intellectual monuments of the twentieth century - and also, as its authors ruefully acknowledged, one of the least read. G. H. Hardy famously remarked in his Times Literary Supplement review that "perhaps twenty or thirty people in England may be expected to read this book"; Erwin Schrödinger went further, doubting that even Whitehead and Russell themselves had read all of it. Russell himself wrote in 1959 that he used to know of only six people who had read the later parts. Complete sets of the first edition are genuinely scarce. The Cambridge University Press printed 750 copies of Volume I; disappointing sales caused the publishers to reduce the print runs of Volumes II and III to 500 copies each, so that no more than 500 complete sets could ever have existed. Ex-library copies dominate the market; sets retaining their original publisher's cloth, unrebacked and unsophisticated, are uncommon. The price the set commanded on its first appearance was felt even by leading mathematicians: the authors themselves had to contribute £50 each toward the cost of printing, a contribution refunded by the Press some forty years later, without interest. The intellectual character of the Principia rests on four linked achievements. First, the construction of a rigorous symbolic language - an extension and systematisation of Peano's notation, informed by Frege's Begriffsschrift - capable of expressing mathematical propositions without the ambiguities of natural language. The familiar signs of modern logic, many of them still in use today, make their decisiv.
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