This book deals with a topic that has been largely neglected by philosophers of science to date: the ability to refer and analyze in tandem. On the basis of a set of philosophical case studies involving both problems in number theory and issues concerning time and cosmology from the era of Galileo, Newton and Leibniz up through the present day, the author argues that scientific knowledge is a combination of accurate reference and analytical interpretation. In order to think well, we (...) must be able to refer successfully, so that we can show publicly and clearly what we are talking about. And we must be able to analyze well, that is, to discover productive and explanatory conditions of intelligibility for the things we are thinking about. The book’s central claim is that the kinds of representations that make successful reference possible and those that make successful analysis possible are not the same, so that significant scientific and mathematical work typically proceeds by means of a heterogeneous discourse that juxtaposes and often superimposes a variety of kinds of representation, including formal and natural languages as well as more iconic modes. It demonstrates the virtues and necessity of heterogeneity in historically central reasoning, thus filling an important gap in the literature and fostering a new, timely discussion on the epistemology of science and mathematics. (shrink)

This chapter treats the reception and assessment of the two English translations of Simone de Beauvoir's Le deuxième sexe, the first by Howard M. Parshley in 1953 and the second by Constance Borde and Sheila Malovany‐Chevallier in 2009. We examine both the criticisms and the appreciations, concluding that the second is superior in many ways to the first. On that basis, we propose a digital edition of the original book and its earlier drafts en face the 2009 English translation, which (...) would also allow as hypertext the addition of curated scholarly notes and textual exegesis, alongside crowd‐sourced discussion. This would both make the book more accessible worldwide, and add the scholarly dimension for which many Beauvoir scholars have long been waiting. (shrink)

The question of how and why mathematics can be applied to physical reality should be approached through the history of science, as a series of case studies which may reveal both generalizable patterns and salient differences in the grounds and nature of that application from era to era. The present examination of Descartes' Principles of Philosophy Part II, reveals a deep ambiguity in the relation of Euclidean geometry to res extensa, and a tension between geometrical form and 'common motion of (...) parts' as principles of individuation for matter in Cartesian physics. (shrink)

Cartesian method both organizes and impoverishes the domains to which Descartes applies it. It adjusts geometry so that it can be better integrated with algebra, and yet deflects a full-scale investigation of curves. It provides a comprehensive conceptual framework for physics, and yet interferes with the exploitation of its dynamical and temporal aspects. Most significantly, it bars a fuller unification of mathematics and physics, despite Descartes' claims to quantify nature. The work of his contemporaries Galileo and Torricelli, and of his (...) successor Newton, illustrates conceptual possibilities Descartes left aside, due to his attachment to method. (shrink)

In this essay, I consider the use of mathematical statistics in the study of biological systems in the field, using as case studies the work of Ruth Geyer Shaw and her colleagues at the University of Minnesota. To address practical issues, like how to enhance prairie restoration, and how to prepare for (and perhaps prevent) the effect of rapid climate change, she and her colleagues combine mathematical modeling and intensive data collection in the field. Using ANOVA and the more versatile (...) approach of Aster Models, they show the effects of inbreeding (which follows from the fragmentation of prairie) to lower the fitness of plant populations. They study the genetic variance of plants in stable populations, which is important when that population must deal with changing conditions. And they study the consequences of rapid climate change: even good genetic variance and initial fitness may not save a given population from extinction. This leads to a new alliance of science with local, state, federal and global politics. (shrink)

The existence of mathematical objects may be explained in terms of their occurrence in problems. Especially interesting problems arise at the overlap of domains, and the items that intervene in them are hybrids sharing the characteristics of both domains in an ambiguous way. Euclid's geometry, and Leibniz' work at the intersection of geometry, algebra and mechanics in the late seventeenth century, provide instructive examples of such problems and items. The complex and yet still formal unity of these items calls into (...) question certain tenets of Resnik's structuralism, and of the reductive projects of the logicists. (shrink)

This collection of new essays treats the historical, philosophical, and literary dimensions of Simone de Beauvoir's thought, and celebrates the 50th anniversary of her most influential book, The Second Sex. A team of distinguished philosophers and literary critics locate her work in the intellectual and political upheavals that marked Paris in the 1930s and 1940s; analyse her philosophical links to 17th-century rationalism, and to Kant, Hegel, Merleau-Ponty, Sartre, Simone Weil, and Heidegger; and study the connections between her philosophical and literary (...) writings. Above all, the collection tackles the relationship between theory and concrete situation with fresh insight and renewed urgency. (shrink)

The narrative about the nineteenth century favored by many philosophers of mathematics strongly influenced by either logic or algebra, is that geometric intuition led real and complex analysis astray until Cauchy and Kronecker in one sense and Dedekind in another guided mathematicians out of the labyrinth through the arithmetization of analysis. Yet the use of geometry in most cases in nineteenth century mathematics was not misleading and was often key to important developments. Thus the geometrization of complex numbers was essential (...) to their acceptance and to the development of complex analysis; geometry provided the canonical examples that led to the formulation of group theory; and geometry, transformed by Riemann, lay at the heart of topology, which in turn transformed much of modern mathematics. Using complex numbers as my case study, I argue that the best way to teach students mathematics is through a repertoire of modes of representation, which is also the best way to make mathematical discoveries. (shrink)