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Ordinary life oscillates between dichotomies: from work to leisure, from reality to fantasy, from private to public. These are distinct worlds that bring order to the chaos of experience; their boundaries contain what philosopher James Carse calls finite games. As we move from game to game, we find ourselves in perpetual motion. SUPER ORDINARY explores Carse‚s other type of game: the infinite game. It is an architectural investigation of its potential to transcend the serious and experience the truly playful, an attempt to manifest a place without boundaries in a world defined by them. Lamport Stadium is the setting for this journey. In this theatre of finite games, our experiences are limited to its rules and boundaries. However, where we truly play, we liberate personal narratives from finite games. Architecture, rather than categorizing experience, is instead redefined through experience. Ergo, rather than the site of finite games, SUPER ORDINARY imagines Lamport Stadium as an infinite game. The dichotomies of finite play˜field and bleacher, player and observer, inside and out, and so on˜are dissolved, and the stadium becomes a place of possibility and adventure; here, we can at once submit to the ecstasy of the place while forging our own narratives. It is a building that is never quite finished, but always open to our imaginations.

Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Mathematics Education." Includes bibliographical references (p. 469-473).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1941. / Typescript. Includes abstract and vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaf [61]).

Thesis (PH. D.) - University of Michigan. / Reprinted from Duke mathematical journal, vol. 4, no. 3, September, 1938.

Issued also as inaugural dissertation, Bonn. / "Überblick über die neuere Literatur zur Frage des Unendlichen": p. 8-18.

Text in Afrikaans / A study of the philosophical and historical foundations of infinity highlights the problematic development of infinity. Aristotle distinguished between potential and actual infinity, but rejected the latter. Indeed, the interpretation of actual infinity leads to contradictions as seen in the paradoxes of Zeno. It is difficult for a human being to understand actual infinity. Our logical schemes are adapted to finite objects and events. Research shows that students focus primarily on infinity as a dynamic or neverending process. Individuals may have contradictory intuitive thoughts at different times without being aware of cognitive conflict. The intuitive thoughts of students about both the actual (at once) infinite and potential (successive) infinity are very complex. The problematic nature of actual infinity and the contradictory intuitive cognition should be the starting point in the teaching of the concept infinity. / Educational Studies / M.Ed. (Mathematic Education)

I provide an interpretation of Hume’s argument in Treatise 1.2 Of the Ideas of Space and Time that finite extensions are only finitely divisible (hereafter Hume’s Finite Divisibility Argument). My most general claim is that Hume intends his Finite Divisibility Argument to be a demonstration in the Early Modern sense as involving the comparison and linking of ideas based upon their intrinsic contents. It is a demonstration of relations among ideas, meant to reveal the meaningfulness or absurdity of a given supposition, and to distinguish possible states of affairs from impossible ones. It is not an argument ending in an inference to an actual matter of fact. Taking the demonstrative nature of his Finite Divisibility Argument fully into account radically alters the way we understand it. Supported by Hume’s own account of demonstration, and reinforced by relevant Early Modern texts, I follow to its logical consequences, the simple premise that the Finite Divisibility Argument is intended to be a demonstration. Clear, abstract ideas in Early Modern demonstrations represent possible objects. By contrast, suppositions that are demonstrated to be contradictory have no clear ideas annexed to them and therefore cannot represent possible objects—their ‘objects,’ instead, are “impossible and contradictory.” Employing his Conceivability Principle, Hume argues that there is a clear idea of a finite extension containing a finite number of parts and therefore, finitely divisible extensions are possible. In contrast, the supposition of an infinitely divisible finite extension is “absurd” and “contradictory” and stands for no clear idea. Consequently, Hume deems this supposition “impossible and contradictory,” that is, without meaning and therefore, descriptive of no possible object. This interpretation allays concerns found in the recent literature and helps us better understand what drives Hume’s otherwise perplexing argument in the often neglected or belittled T 1.2.