This article is the sequel to an article published in the previous issue of Science in Context that dealt with homeomeric lines (Acerbi 2010). The present article deals with foundational issues in Greek mathematics. It considers two key characters in the study of mathematical homeomery, namely, Apollonius and Geminus, and analyzes in detail their approaches to foundational themes as they are attested in ancient sources. The main historiographical result of this paper is to show that there was a well-established mathematical field of discourse in “foundations of mathematics,” a fact that is by no means obvious. The paper argues that the authors involved in this field of discourse set up a variety of philosophical, scholarly, and mathematical tools that they used in developing their investigations.

Created in 1884, the U.S. Bureau of Labor Statistics (BLS) has been the major federal source for data in the United States on labor-related topics such as prices, unemployment, compensation, productivity, and family expenditures. This essay traces the development and transformation of formal and informal consulting relationships between the BLS and external groups (including academic social scientists, unions, businesses, and other government entities) over the twentieth century. Though such a history cannot, of course, provide a comprehensive analysis of how political values have shaped the construction of labor statistics during this period, I argue that it can nevertheless provide important insights into the political context for the construction of knowledge about American workers and their living and working conditions.

For more than thirty years after World War II, the unconventional economist Kenneth E. Boulding (1910–1993) was a fervent advocate of the integration of the social sciences. Building on common general principles from various fields, notably economics, political science, and sociology, Boulding claimed that an integrated social science in which mental images were recognized as the main determinant of human behavior would allow for a better understanding of society. Boulding's approach culminated in the social triangle, a view of society as comprised of three main social organizers – exchange, threat, and love – combined in varying proportions. According to this view, the problems of American society were caused by an unbalanced combination of these three organizers. The goal of integrated social scientific knowledge was therefore to help policy makers achieve the “right” proportions of exchange, threat, and love that would lead to social stabilization. Though he was hopeful that cross-disciplinary exchanges would overcome the shortcomings of too narrow specialization, Boulding found that rather than being the locus of a peaceful and mutually beneficial exchange, disciplinary boundaries were often the occasion of conflict and miscommunication.