A Credit Market à la David Hume

In Book III of his Treatise of Human Nature, David Hume considers the following simple interaction: "I suppose a person to have lent me a sum of money, on condition that it be restor'd in a few days, and also suppose, that after the expiration of the term agreed on, he demands the sum" and Hume asks: "What reason or motive have I to restore the money?" [1740, p. 479] The answer, he concludes, must be "that the sense of justice and injustice [which is the motive for repaying the loan] is not deriv'd from nature, but arises artificially, tho' necessarily, from education and human conventions." [p. 483] It is my purpose in this essay to offer formal (and modern) underpinnings for Hume's argument. I shall do so in the context of Hume's own example, cited above, where the interaction being considered is one between lender and borrower.lending, borrowing, credit market

A recursive construction of t-wise uniform permutations

We present a recursive construction of a (2t + 1)-wise uniform set of permutations on 2n objects using a (2t + 1) - (2n, n, \cdot) combinatorial design, a t-wise uniform set of permutations on n objects and a (2t+1)-wise uniform set of permutations on n objects. Using the complete design in this procedure gives a t-wise uniform set of permutations on n objects whose size is at most t^2n, the first non-trivial construction of an infinite family of t-wise uniform sets for t \geq 4. If a non-trivial design with suitable parameters is found, it will imply a corresponding improvement in the construction

Multiform Arguments in the Historiography of Individualism in Pre-Modern Europe

This dissertation argues that we can have a better, more effective illustrated historiography; that we can construct and communicate historical arguments that combine words and images, considering clear nomenclature, conventions and standards; and that we can develop an analytical and critical discourse about verbal-visual or multiform arguments and knowledge. We can do so because this dissertation offers a new analytical approach to historiography that combines words and images. This approach conceptualizes illustrated historiography and arguments as multiform, to emphasize their hybrid nature, and enhance the awareness of the various forms this hybridity takes. My investigation of this hybridity provides terminology to describe nuances of textual multiformity; analytical methods to explore the structure and function of multiform arguments (MFAs); and, finally, directions for future empirical research that will help scholars construct MFAs more effectively, and deepen our understanding of multiform grammar. This dissertation analyzes five MFAs from five different publications that explore pre-modern individualism in Europe (ca. 1050-1600). Their debate is on where and when individualism developed; what its catalysts, and cultural and social features were; and how to define individual. These illustrated publications range from 1958 to 2015. While the first publication was illustrated after the historians death, the other four were illustrated by the historians themselves. Therefore, the analysis of those five MFAs shows how historians and illustrators create historical notions, using primary sources of both verbal and visual sorts, and how they communicate those notions by juxtaposing words and images in printed books. Analyzing MFAs from a discourse that historicizes the self, and that addresses the methodological and epistemological problematic of the historians self doing so, promotes self-awareness, and analogy between selves and MFAs. Drawing on studies from historiography, linguistics, art history, literary criticism, psychology and computer science, this dissertation concludes that the rhetorical devices that serve historians in depicting the past through MFAs are the same devices that have enabled institutions and individuals to construct identities for individuals. Thus, awareness of multiformity in the past and its representation increases the effectiveness of using MFAs, as it illuminates the ideologies and playfulness that prevail between words and images