The Contemporary Encyclopedic Novel

This dissertation will define the contemporary American encyclopedic novel and the significant role that irony plays in shaping meaning. The dissertation constructs a model of the encyclopedic novel based upon the history of the encyclopedia – from Denis Diderot\u27s Enlightenment influenced Encyclopédie – and Northrop Frye\u27s conception of the encyclopedic form. It claims (1) that the contemporary encyclopedic novel continues in the cycle of modal progression toward mythic integration that Frye proposes in Anatomy of Criticism; and (2) that the encyclopedic novel utilizes different forms of irony to challenge authoritative discourse and elevate marginal discourse. The first chapter defines the encyclopedic novel by examining the history of the encyclopedia and existing criticism on the encyclopedic text in literature. It draws on theorists such as Denis Diderot and Richard Yeo to define an “encyclopedic project” that adopts a dialogic rhetorical style and seeks to democratize access to information. This chapter also defines the encyclopedic novel as a generic form that combines other forms into a unified whole and utilizes irony as a tool for integration. The second and third chapters form a thematic pairing that shows the self-reflexive progression of the encyclopedic novel from individualistic to humanistic focus. The second chapter argues that Thomas Pynchon\u27s Gravity\u27s Rainbow is an “anarchistic encyclopedic novel” that promotes associational thinking – in the form of paranoia, open forms, and horizontal transmission of knowledge. Gravity\u27s Rainbow adopts a disintegrative irony to empower the oppressed individual against industry-state collusion in the post-WWII era. The third chapter argues that David Foster Wallace\u27s Infinite Jest seeks to reinvent irony as an integrative force and redirect Pynchon\u27s individualistic anarchism toward an inclusive humanism. The fourth chapter demonstrates a break from both of the preceding chapter and argues that Leon Forrest\u27s Divine Days adopts a syndetic model of composition that further works to incorporate forms and integrate irony. Using Northrop Frye\u27s “interpenetration,” I argue that Divine Days integrates competing traditions and discourses by demonstrating their mutual-necessity. In the concluding chapter, I examine “meta-encyclopedic” by Jorge Luis Borges and Roberto Bolaño as an extension of the dissertation

Hilbert's Metamathematical Problems and Their Solutions

This dissertation examines several of the problems that Hilbert discovered in the foundations of mathematics, from a metalogical perspective. The problems manifest themselves in four different aspects of Hilbert’s views: (i) Hilbert’s axiomatic approach to the foundations of mathematics; (ii) His response to criticisms of set theory; (iii) His response to intuitionist criticisms of classical mathematics; (iv) Hilbert’s contribution to the specification of the role of logical inference in mathematical reasoning. This dissertation argues that Hilbert’s axiomatic approach was guided primarily by model theoretical concerns. Accordingly, the ultimate aim of his consistency program was to prove the model-theoretical consistency of mathematical theories. It turns out that for the purpose of carrying out such consistency proofs, a suitable modification of the ordinary first-order logic is needed. To effect this modification, independence-friendly logic is needed as the appropriate conceptual framework. It is then shown how the model theoretical consistency of arithmetic can be proved by using IF logic as its basic logic. Hilbert’s other problems, manifesting themselves as aspects (ii), (iii), and (iv)—most notably the problem of the status of the axiom of choice, the problem of the role of the law of excluded middle, and the problem of giving an elementary account of quantification—can likewise be approached by using the resources of IF logic. It is shown that by means of IF logic one can carry out Hilbertian solutions to all these problems. The two major results concerning aspects (ii), (iii) and (iv) are the following: (a) The axiom of choice is a logical principle; (b) The law of excluded middle divides metamathematical methods into elementary and non-elementary ones. It is argued that these results show that IF logic helps to vindicate Hilbert’s nominalist philosophy of mathematics. On the basis of an elementary approach to logic, which enriches the expressive resources of ordinary first-order logic, this dissertation shows how the different problems that Hilbert discovered in the foundations of mathematics can be solved

Mathematical Explanation and Ontology: An Analysis of Applied Mathematics and Mathematical Proofs

The present work aims at providing an account of mathematical explanation in two different areas: scientific explanation and within mathematics. The research is addressed from two different perspectives: the one arising from an ontological concern about mathematical entities, and the other originating from a methodological choice: to study our chosen problems (mathematical explanation in science and in mathematics itself) in mathematical practice, that is to say, looking at the way mathematicians understand and perform their work in these diverse areas, including a case study for the context of intra-mathematical explanation. The central target is the analysis of the role that mathematical explanation plays in science and its relevance to the success or failure of scientific theories. The ontological question of whether the explanatory role of abstract objects, mathematical objects in particular, is enough to postulate their existence will be one of the issues to be addressed. Moreover, the possibility of a unified theory of explanation which can accommodate both external and internal mathematical explanation will also be considered. In order to go deeper into these issues, the research includes: (1) an analysis how the question of what is involved in internal mathematical explanation has been addressed in the literature, an analysis of the role of mathematical proof and the reasons why it makes sense to search for more explanatory proofs of already known results, and (2) an analysis of the relation between the use of mathematics in scientific explanation and the ontological commitment that arises from these explanatory tools in science. Part of the present work consists of an analysis of the explanatory role of mathematics through the study of cases reflecting this role. Case studies is one of the main sources of data in order to clarify the role mathematical entities play, among other methodological resources

Merging the Natural with the Artificial: The Nature of a Machine and the Collapse of Cybernetics

This thesis is concerned with the rise and fall of cybernetics, understood as an inquiry regarding the nature of a machine. The collapse of this scientific movement, usually explained by external factors such as lack of funding, will be addressed from a philosophical standpoint. Delving deeper into the theoretical core of cybernetics, one could find that the contributions of William Ross Ashby and John von Neumann shed light onto the particular ways in which cybernetics understood the nature and behavior of a machine. Ross Ashby offered an account of the nature of a machine and then extended the scope of “the mechanical”. This extension would encompass areas that will later be shown to be problematic for mechanization, such as learning and adaptation. The way in which a machine-ontology was applied would trigger effects seemingly contrary to cybernetics’ own distinctive features. Von Neumann, on the other hand, tinkered with a mechanical model of the brain, realizing grave limitations that prompted him to look for an alternative for cybernetics to work on. The proposal that came out of this resulted in a serious blow against the theoretical core of cybernetics. Why did cybernetics collapse? The contributions coming from both thinkers, in their own ways, spelled out the main tenets of the cybernetic proposal. But these very contributions led to cybernetics’ own demise. The whole story can be framed under the rubric of a serious inquiry into the metaphysical underpinnings of a machine. The rise and fall of cybernetics could thus help us better understand what a machine is from a philosophical standpoint. Although a historical component is present, my emphasis relies on a philosophical consideration of the cybernetic phenomenon. This metaphysical dissection will attempt to clarify how a machine-based ontology remained at the core of cybernetics. An emerging link will hopefully lead towards establishing a tri-partite correlation between cybernetics’ own evolution, its theoretical core, and its collapse. It will hopefully show how cybernetic inquiries into the nature of a machine might have proved fatal to the very enterprise at large, due to unsolvable theoretical tensions

The art and architecture of mathematics education: a study in metaphors

This chapter presents the summary of a talk given at the Eighth European Summer University, held in Oslo in 2018. It attempts to show how art, literature, and history, can paint images of mathematics that are not only useful but relevant to learners as they can support their personal development as well as their appreciation of mathematics as a discipline. To achieve this goal, several metaphors about and of mathematics are explored