Quine’s Harvard dissertation on a more general logical foundation than Russell and Whitehead’s
A Dissertation in Symbolic Logic
The Logic of Sequences is the doctoral dissertation of W. V. Quine, written in English at Harvard University and running to some 290 pages. Its subject matter, as catalogued, is twofold: symbolic and mathematical logic on the one hand, and the philosophy of mathematics on the other. It belongs to the earliest phase of Quine’s career, the period in which his work was concentrated on formal logic and set theory, well before the postwar writings on ontology, epistemology, and language that made him one of the most influential analytic philosophers of the twentieth century. At Harvard his thesis supervisor was Alfred North Whitehead, who had himself, with Bertrand Russell, been the co-author of the very work Quine’s dissertation sets out to generalize.
Generalizing Principia Mathematica
The book’s subtitle states its project directly: it offers a generalization of Principia Mathematica. Whitehead and Russell’s Principia was the great attempt to derive mathematics from logic, and it supplied the logical apparatus against which a generation of logicians measured their own systems. Quine’s dissertation takes that apparatus as its starting point and seeks a more general formulation of it — not a refutation of the Principia programme but an extension of its reach. The title’s key term, “sequences,” names the device through which that greater generality is pursued; the work is a technical study in the foundations of logic rather than an essay in exposition, and its argument is carried by formal construction.
Logic and Its Foundations as a Single Subject
The double classification of the work — symbolic logic and the philosophy of mathematics — reflects the character of the foundational enterprise it joins. Questions about which formulas can be derived and questions about what logic itself is, and what it can legitimately be asked to ground, were for Quine not separate inquiries but aspects of one technical discipline; his later insistence that logic be sharply delimited, and his construction of alternative set theories, grew out of exactly this kind of close engagement with formal systems. Read in that light, The Logic of Sequences documents a young logician working through the inheritance of Principia Mathematica from the inside, reworking its machinery rather than surveying it. It stands as the technical point of departure for a body of work that would go on to reshape how analytic philosophers thought about logic, mathematics, and meaning.
The book was published in New York by Garland Pub. in 1990 and issued in the series Harvard Dissertations in Philosophy. Catalog records give the ISBNs 0824032101 and 9780824032104 and the OCLC number 20797392; the University of Chicago record supplies the call number QA9.Q54 1990, while HathiTrust records a copy as “Limited (search only)” with the University of Michigan as the original source. WorldCat lists an additional online version, and catalog records give the physical size as 24 cm. The source material records two different first-publication dates: the catalog metadata gives 1990, and Wikidata gives 1932.
