Matthew L. Jones. The Good Life in the Scientific Revolution: Descartes, Pascal, Leibniz and the Cultivation of Virtue. Chicago: University of Chicago Press, 2006. 269 pp. $65.00 (cloth), ISBN 978-0-226-40954-2; $27.50 (paper), ISBN 978-0-226-40955-9.
Reviewed by Kelly J. Whitmer (Max Planck Institute for the History of Science, Berlin)
Published on H-German (February, 2007)
Better Living through Mathematics
When prompted to reflect upon the capacity of advanced mathematics to make our lives better, many of us may be able to point to how specific concepts are applied (usually by others somewhere far away) and, therefore, make life easier for us. Imagining a world in which mathematicians were sages and the honing of advanced mathematical techniques the key to a better life might be a bit more challenging. If we are to understand why and how certain knowledge-making practices become prevalent and impact our lives, as well as the lives of those whose histories we tell, then the ability to imagine the latter is essential. Matthew L. Jones's book promises to be quite helpful with this matter.
This volume is a study of historical epistemology and, as the author states in the introduction, aims to "contribute to the history of truth and falsity" (p. 7). Instead of seeking to show the reader how a truth that appears self-evident today acquired its status, Jones aims to interrogate what truth and falsity meant in the seventeenth century, including how one recognized the difference between what was true and what was not and how one made it known that one could distinguish between the two. In taking such an approach, Jones places himself firmly within the ranks of historians of science concerned with the myriad practices involved in the social construction of knowledge. Readers familiar with the work of Simon Schaffer and Steve Shapin, and Lorraine Daston and Mario Biagioli, to name just a few, will find themselves in familiar territory.[1] Gracefully, piece by piece, Jones presents the reader with the building blocks of the natural philosophies of Rene Descartes, Blaise Pascal and Gottfried Leibniz, identifying their reference points, models and influences, the forms of argumentation they employed to construct epistemological frameworks and the ways in which they circulated and attempted to popularize their contributions to knowing, or what some might call science. Linking these frameworks reveals distinct patterns that historians of all stripes will find quite instructive.
Jones's ability to discern a common thread running throughout the practices and discourse we now associate with these three philosophers holds the building blocks together. Each philosopher was convinced that rigorous intellectual exercise was necessary in order to know or begin to understand how to recognize truth. Each offered, in turn, new mathematical mechanisms for facilitating this process: Descartes's geometry, Pascal's arithmetical triangle, and Leibniz's quadrature of the circle were intended to exercise the mind. These innovative techniques, now mostly relegated to advanced high school algebra classes, were derived from deeply held concerns about the fate of humanity and the moral obligation to apply cognitive reasoning faculties to the solution of some pressing social problem or the perfection of humanity. Perhaps one might use the methods of these philosophers to find peace or a good life through the acquisition of highly sophisticated forms of knowledge about world.
Jones begins the book with a discussion of Descartes's geometry of 1637, which he describes as "famous, if too little known ... neither Euclidean or algebraic," with its "own standards, its own rigor, and its own limitations" (p. 17). To practice Descartes's geometrical method, one needed to make use of the new instruments he developed for drawing a wider range of curves. These instruments, when properly applied to the solution of geometric problems unresolved by the ancients, could actually help the student sharpen his thinking skills or, as Descartes explained in his preface, train his mind to "conceive its objects more sharply and more distinctly" (p. 24). Key is Descartes's interest in new techniques for training the imagination not only to understand individual pieces of knowledge and their relationships clearly and distinctly, but also to grasp, in a single glance, the underlying order behind these relationships. In effect, rigorous practice of geometrical techniques could help one train for more advanced forms of philosophical inquiry and self-cultivation.
Of course, Jones is not the first historian to emphasize Descartes's interest in providing new philosophical practices for the honnĂȘte homme; however, he stresses that most scholars have underemphasized just how central "doing" geometry was to Descartes's philosophy (p. 53). More than anything else, Descartes believed geometry best demonstrated his method and was an essential part of the series of steps civilized people had to take in their quest to discern certain truths about the world. Geometrical practice would lead to more advanced forms of philosophical inquiry and truth making; it was a form of "spiritual exercise." In the second chapter of his discussion of Descartes, Jones explores how Descartes's exercises emerged from his engagement with Jesuit spirituality, rhetorical strategies, and pedagogy. He argues that Descartes "offered a radical new version of the Ignatian procedure of bringing oneself into proper epistemic, emotional and spiritual states through imagining concrete, detailed situations and pondering their implications" (p. 71).
In the second section, Jones's central task becomes slightly encumbered by a pronounced emphasis on the differences between Pascal and Descartes. The young Pascal also believed in the power of mathematics to exercise the mind, but not necessarily to discern truth, as Descartes did. Instead, engaging in vigorous debate with other honorable gentlemen about mathematical problems, such as the properties of numbers or how to comprehend infinity, was a form of philosophical practice that allowed one to recognize the limits of human reason. While Descartes hoped to limit astonishment and wonder through rigorous mathematical exercises that would gradually lead to higher levels of understanding or the discernment of truth, Pascal tended to see the function of mathematics as a crucial tool for promoting astonishment about truths, such as an infinite series, that humans would never be able to fully grasp. Astonishment would come from doing mathematics and be quickly followed by dismay or even feelings of worthlessness, as individuals recognized that a fundamental disproportion exists between what we see or know and truth. Jones links this tendency in Pascal with the latter's Jansenist leanings and points out that for Pascal, mathematics exercised the mind and helped one better appreciate the incomprehensibility of truth and the divine. Mathematics was practiced for entirely different reasons than those Descartes advocated. But is this not also a form of spiritual exercise?
Specifying a spiritual exercise, Jones explains in his introduction, "means something like determining (1) a set of practices, (2) a conception of the self ... and (3) the people the exercises are for, that is, the social field of the application of the exercises" (p. 18). Jones discusses all three of these components in Pascal's work, although, for reasons that are not entirely clear, he seems to reserve the phrase "spiritual exercise" itself for a mystical or meditative component underlying Descartes's appreciation of geometrical method exclusively, one later abridged and reworked by Leibniz. Jones's initial and broad definition of "spiritual exercise" in the opening of the volume made me wonder why the phrase itself was not used consistently throughout the Pascal section as well, especially considering the book's more general preoccupation with continuities. The phrase comes to the fore again in the Leibniz chapters, but only in a very limited fashion (pp. 223-228). The complexity of Leibniz's relationship to Jesuit spirituality and science, apparent in his interest in the establishment of an evangelical mission that would simultaneously mimic and challenge Jesuit missions abroad, is not engaged.
While the final section on Leibniz may be the one to which scholars of German history will be most immediately drawn, the first two sections are worth engaging in order to appreciate the inheritance of ideas at work in Leibniz's studies. From Descartes, Leibniz acquired his interest in "grasping all the singulars in a glance," Jones notes, as well as his emphasis in "the utility of algebra as an exercise" (p. 224). But Leibniz also sought to develop new notational strategies to help make mathematical techniques more accessible, functional and applicable to every day life. Like Pascal, Leibniz recognized the limitations of human capacity for knowledge; Leibniz was, however, more optimistic about what humans might still be able to accomplish despite their limitations (p. 230). Leibniz insisted humans were in a position to discern certain ordering principles at work in the world and had the ability to create new modes of expression: a universal language, for example, that would allow more people to recognize the underlying harmony at the heart of the universe. Having this ability to discern, through practice and the rigorous application of the new mathematical techniques Leibniz advocated, automatically involved an obligation to help others learn how discern and apply the same principles. Perfecting oneself meant helping others recognize the utility of mathematical practices so that they might also perfect themselves and become more useful.
Cultivating virtue, perfecting the self and promoting change were the central concerns animating the natural philosophies of Descartes, Pascal, and Leibniz. Whether one chooses to label them as spiritual or not, it is hard to deny that innovative scientific practices emerged out this quest for perfection. Indeed, Jones concludes that "self-cultivation involving natural and mathematical work fueled no small part of the dynamism in natural knowledge making in the seventeenth-century" and wonders how natural philosophy and mathematics lost their power to cultivate the moral person (p. 269). The answer to the question lies well beyond the scope of this volume, but it speaks to the overall force of the argument and the challenge of imagining mathematics with the capacity to make the world more peaceful, humane and just.
Notes
[1]. For an introduction to the work of these prolific scholars, see Steven Shapin and Simon Schaffer, Leviathan and the Air-Pump: Hobbes, Boyle and the Experimental Life (Princeton: Princeton University Press, 1985); Lorraine Daston, Classical Probability in the Enlightenment (Princeton: Princeton University Press, 1988); and Mario Biagioli, Galileo, Courtier: The Practice of Science in the Culture of Absolutism (Chicago: Chicago University Press, 1993).
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Citation:
Kelly J. Whitmer. Review of Jones, Matthew L., The Good Life in the Scientific Revolution: Descartes, Pascal, Leibniz and the Cultivation of Virtue.
H-German, H-Net Reviews.
February, 2007.
URL: http://www.h-net.org/reviews/showrev.php?id=12897
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