Dissertation/Thesis Abstract

Non-Euclidean Geometry and Russian Literature: A Study of Fictional Truth and Ontology in Fyodor Dostoevsky's Brothers Karamazov, Vladimir Nabokov's The Gift, and Daniil Kharms's Incidents
by Brookes, Alexander, Ph.D., Yale University, 2013, 211; 3578319
Abstract (Summary)

This dissertation is an investigation of a theoretical problem—the determination of truth and being in a work of literary fiction—in the context of a momentous event in the history of mathematics—the discovery of a consistent non-Euclidean geometry. Beginning with the first interpretations of the philosophical significance of non-Euclidean geometry to enter the Russian cultural sphere in the 1870s, I analyze how the works by three Russian authors—Fyodor Dostoevsky, Vladimir Nabokov, and Daniil Kharms—integrate the principles of mathematical truth into their construction of a fictional ontology and methods of fictional truth evaluation. Each author, I argue, combines their own aesthetic program with the changes in the philosophy of mathematics underwent in their respective eras and historical contexts. The diversity of these contexts provides the variables, against which this theoretical problem is analyzed.

The first chapter deals with Dostoevsky's interpretation of non-Euclidean geometry and its philosophical significance expressed in Ivan Karamazov's rebellion against God in Brothers Karamazov. I argue that Dostoevsky deploys the Euclidean/non-Euclidean binary to juxtapose two methods of fictional truth evaluation—a traditional model, obsolete in light of the principles of non-Euclidean geometry, and another model, which Dostoevsky embraces in Brothers Karamazov, based on the paradoxical and yet true axioms of the new geometry. I phrase the distinction in the terms of possibility and necessity: the new model of fictional truth evaluation is for propositions which are true in all possible worlds except the actual. In Chapter Two, I draw upon previous analysis of Nabokov's The Gift and the mention of Lobachevsky's geometry in the internal biography of Chernyshevsky, to argue that the narrative structure of The Gift returns to the Euclidean/non-Euclidean binary as introduced by Dostoevsky, but re-interprets the otherworldly according to Nabokov's own aesthetic praxis and the interpretation of non-Euclidean geometry by late-nineteen and early twentieth century geometers and physicists. Nabokov applies concepts of non-Euclidean geometry and space to the actual world. This analysis provides a framework for interpreting the space and time of The Gift according to structures suggested within the novel itself. The third chapter investigates Kharms's interpretation of the significance and meaning of geometry in light of the impact that non-Euclidean geometry had on mathematical propositions as a means of describing possible states of affairs. I place Kharms's fictional objects, such as the red-headed man of "Blue Notebook no. 10," and implications to truth evaluation in "Sonnet" and "Symphony no. 2," in the context of anti-Kantian theories of truth and logic, which arose in the period around the turn of twentieth century.

Indexing (document details)
Advisor: Alexandrov, Vladimir E.
School: Yale University
School Location: United States -- Connecticut
Source: DAI-A 75/05(E), Dissertation Abstracts International
Subjects: Slavic literature
Keywords: Logic, Non-Euclidean geometry, Philosophy of language, Russian literature
Publication Number: 3578319
ISBN: 978-1-303-71592-1
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