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William Thompson Boos

William Thompson Boos (1943–2014) was a mathematician and philosopher, with specialties in mathematical logic, set theory, epistemology, and the application of mathematical ideas to the history of philosophy and physics. His Metamathematics and the Philosophical Tradition appeared in 2018. Combining observations spanning several decades, it developed his conviction that the attempts of philosophers from Aristotle and the skeptics onwards to posit first principles as a basis for truth claims are undercut by the insights of twentieth century metalogic into the necessary limitations of certainty. Its arguments are of special relevance to historians and philosophers of science and mathematics, with special emphasis on scholars of classical skepticism, the Enlightenment, Kant, ethics, and mathematical logic.

Boos published in "specialized philosophy journals like Erkenntnis and Synthese" (Verburgt 380). In his review of Metamathematics and the Philosophical Tradition, Lukas M. Verburgt points out what is notable — what "stands out" — about Boos's thought: his

oeuvre stands out for its idiosyncratic and singular application of twentieth-century mathematical logic — very roughly, the study of formal systems (e.g., predicate logic, arithmetic) and proofs about these systems (e.g., Hilbert's consistency proof, Gödel's incompleteness theorems) — to canonical problems in philosophy. (Verburgt 380)

Birth, Early Life, and Education

Born March 16th, 1943 in Janesville, Wisconsin, William Boos (“Bill”) was the son of Ethel Connell Boos and Col. Francis H. Boos. As the child of a military officer he lived in several places during boyhood, among them Taiwan, Tehran, Colorado, Kentucky, Fort Sheridan, and Glenview, Illinois. After graduating from New Trier High School in 1960, William studied German at the University of Heidelberg and obtained degrees in mathematics from the University of Wisconsin (B. A., 1964), the University of Massachusetts (M. A., 1965), and the University of Wisconsin (Ph. D., 1971), where he specialized in set theory and wrote Nonstandard Large Cardinals. His advisor at the University of Wisconsin was Kenneth Kunen, whose adviser was Dana Stewart Scott and who has, according to Math Genealogy, "31 students and 76 descendants" ("Kenneth Kunen"). He received a second Ph.D. in 1981, in Philosophy (philosophical logic), from University of Chicago, under the direction of Manley Thompson.

Teaching Career

Boos taught mathematics for some years before earning his 2nd Ph.D. in Philosophical Logic. Over the course of his life he taught philosophy at the universities of North Carolina, New Mexico, Copenhagen, and British Columbia, and mathematics at the State University of New York at Buffalo and the University of Iowa. He also enjoyed a brief period of work at the Wittgenstein Archive in Bergen, Norway.

Mathematical and Philosophical Writings

Boos's publications applied mathematical models to classical philosophical problems in epistemology, and before his death he engaged in writing a series of articles on the relevance of set theoretical methods to uncertainty problems in physics. A gifted and rigorous stylist, he helped edit his wife Florence Boos’s writings on nineteenth-century literature and co-authored with her several articles on topics related to nineteenth-century British socialism and feminism.

Book and Views

Originally titled The Boundaries of Experience, Metamathematics and the Philosophical Tradition explores in historical depth the relationship between philosophical debates regarding knowability, proof, and meta-mathematical notions of consistency and completeness. Using the insights of twentieth-century logicians from Gödel through Hilbert and their successors, William Boos revisits the writings of Aristotle and the ancient skeptics, Anselm and medieval logicians, and the claims of enlightenment and seventeenth and eighteenth century philosophers Leibniz, Berkeley, Hume, Pascal, Descartes, and Kant. The final chapters critique and extend more recent insights of Frege, Wittgenstein, Skolem, and late 20th-century quantum physicists, and offer new applications of the completeness theorem.

Metamathematics and the Philosophical Tradition is syncretic in range and addresses fundamental and recurring problems of epistemology. Boos’s elegant writing style, often framed as a series of condensed postulates, renders accessible a wealth of allusions from varied traditions and in several languages.

In a review of the book in Isis, Lukas M. Verburgt says,

Metamathematics and the Philosophical Tradition represents about half of the nearly one thousand pages that resulted from his attempt, begun around 2011, to gather, revise, and extend his writings in this direction into book form under the title "The Boundaries of Experience." [get more of this review]

Personal Life

William Boos loved classical music and the study of European languages, among them German, French, Latin, Greek, Danish, Norwegian, and Icelandic, and he took pleasure in semesters spent abroad with his wife Florence in Iceland, Denmark, France, and Cambridge, England.

Boos married Florence Saunders in 1965, and their son Eugene Boos was born in 1972. Officially listed as a conscientious objector during the Vietnam War, he was a pacifist and over the years worked for several political campaigns on behalf of anti-war, progressive, and socialist candidates [let's name them?].

Boos also loved mountain scenery, and in later years took satisfaction in jogging and hiking near the home he had designed on the Sunshine Coast, British Columbia, facing mountains and ocean. In private life, he was a man of orderly and frugal habits, generous in supporting charitable causes, and greatly attached to his family and close friends. He died unexpectedly of cardiac arrest on April 1st, 2014.

Selected Publications

• Metamathematics and the Philosophical Tradition. Walter de Gruyter, 2018. Edited by Florence S. Boos.
• “Reflective Inquiry and ‘The Fate of Reason,’” Synthese, October 2014.
• “Stochastic Representations of Feynman Integration,” Journal of Mathematical Physics, December 2007.
• “A Metalogical Critique of Wittgensteinian ‘Phenomenology,’” in Quantifiers, Questions and Quantum Physics, eds. Dan Kolak and J. Symons, November 2007.
• “Theory-relative Skepticism,” Dialectica, May 2007.
• “Virtual Modality,” Synthese, September 2003.
• “Parfaits miroirs de l’universe”: A ‘virtual’ interpretation of Leibnizian metaphysics.” Synthese, August 2008.
• “The Transzendenz of Mathematical ‘Experience,’” Synthese, January 1998.
• “Mathematical quantum theory I: Random ultrafilters as hidden variables.” Synthese, April 1996.
• “‘The True’ in Gottlob Frege’s ‘Űber die Grundlagen der Geometrie,’” Archiv for History of the Exact Sciences, January 1985.
• “A Self-referential ‘Cogito,’” Philosophical Studies, September 1983.
• “Consistency and Konsistenz,” Erkenntnis, April 1987.
• “Thoralf Skolem, Hermann Weyl and ‘Das Gefühl der Welt als Begrenztes Ganzes.’” In From Dedekind to Gödel, ed. Jaakko Hintikka. January 1995.
• “The World, the Flesh, and the Argument from Design,” Synthese, October 1994.
• “The Limits of Inquiry.” Erkenntnis, September 1983.
• “Infinitary Compactness without Strong Inaccessibility,” Journal of Symbolic Logic, March 1976.
• “Boolean Extensions which Efface the Mahlo Property,” Journal of Symbolic Logic, January 1971.
• Lectures on Large Cardinal Axioms. January 1970.
• “Cynics and Cyrenaics,” in Philosophy of Education, ed. J. J. Chambliss, 1996.
• “Sparsely Connected Neural Networks with Strikingly Large Storage Capacities,” Neural Networks, July 1997. With David Vogel.
• “Minimally Connective, Auto-associative Neural Networks,” Connection Science, January 1994. With David Vogel.
• “Orwell’s Morris and ‘Old Major’’s Dream,” English Studies, August 1990. With Florence Boos.
• “News from Nowhere and Victorian Socialist Feminism,” Nineteenth-Century Contexts, January 1990. With Florence Boos.
• “Curvature Scalars as Quantum-Theoretic ‘Potentials,’” June 2010. Paper.
• “Asymptotic Path-Theoretic Representations of Quantum Field Equations,” Paper, June 2013.
• “Abstract Gauge Structures,” January 29th, 2013.

References

• "Kenneth Kunen." Mathematics Genealogy Project. https://www.mathgenealogy.org/id.php?id=9055.
• Verburgt, Lukas M. Review of William Boos, Metamathematics and the Philosophical Tradition. Isis, a Publication of the History of Science Society, Volume 111, Number 2 June 2020. DOI: https://doi.org/10.1086/709141.