In lieu of an abstract, here is a brief excerpt of the content:Isaac Barrow on the Mathematization of Nature: Theological Voluntarism and the Rise of Geometrical OpticsAntoni MaletIntroductionIsaac Newton’s Mathematical Principles of Natural Philosophy embodies a strong program of mathematization that departs both from the mechanical philosophy of Cartesian inspiration and from Boyle’s experimental philosophy. The roots of Newton’s mathematization of nature, this paper aims to demonstrate, are to be found in Isaac Barrow’s (1630–77) philosophy of the mathematical sciences.Barrow’s attitude (...) towards natural philosophy evolved from his earnest interest in medicine of around 1650, when a young Cambridge graduate, to natural philosophy (apparently under Henry More’s influence); from his thesis on the insufficiency of the Cartesian hypothesis to geometrical optics and the strong program of mathematization of natural philosophy of the middle 1660s; from Lucasian professor of Mathematics to Chaplain of his Majesty and eminent Restoration divine. Contemporary accounts of Barrow’s life suggest that he grew ever more skeptical about the worth of natural philosophy and mathematics. 1 In his last years he became a prolific [End Page 265] author of sermons and theological works. Published shortly after his death by John Tillotson (1630–94), later archbishop of Canterbury, they occupy over two thousand folio pages. Overloaded with involved philosophical arguments, Barrow’s sermons were apparently not very popular, but they were highly regarded by scholars and the Anglican hierarchy. 2 It is on certain of his sermons, as well as on the philosophical discussions contained in the Mathematical Lectures that our account of Barrow’s philosophy of the mathematical sciences will rest. 3 Barrow’s understanding of the mathematical sciences will allow us to discuss together three issues often analyzed independently: the theological background to English natural philosophy, the changing notion of mixed mathematical sciences during the seventeenth century, and finally the philosophical foundations of modern geometrical optics.It has long been recognized that significant relationships exist between theological voluntarism or intellectualism and views on natural philosophy. In particular Robert Boyle’s theological voluntarism is seen as grounding his experimentalist approach to natural philosophy. It is not quite so clear, however, how well theological voluntarism may relate to a strong program of mathematization such as the one embodied in Newton’s Principia Mathematica. In fact it has been suggested that the relationship is a negative one. This is derived from the necessary character of mathematical laws, which would put unwanted restrictions on God’s absolute dominion over nature, and also from the notion that theological intellectualism is conducive to a deductive, a priori science—the paradigm of which is of course geometry. However, Barrow’s theological voluntarism lead him to heighten the role of mathematics within natural philosophy.During the seventeenth century the so-called mixed or subalternate mathematical sciences changed profoundly. In the Enlightenment mixed mathematics—meaning above all rational mechanics—became one of the most prestigious and influential disciplines. The mixed mathematics of the Enlightenment, however, was markedly different from the Aristotelian [End Page 266] mixed mathematical sciences. The differences are noticeable both in the subject matter and in the substitution of mathematical infinitesimal analysis for geometrical synthesis, but also in the way of grounding mathematical theory on empirical evidence. Barrow’s Mathematical Lectures (delivered at Cambridge from 1664 to 1666) offer a fresh insight into the metamorphosis of these sciences just when Newton’s “mathematical principles” were in the making. Not the least interesting feature of Barrow’s discussion is that God’s omnipotence allows an evaluation of the truth of mathematical theories that do not apply to this world. Therefore, Barrow is led to introduce the distinction between the internal consistency, or mathematical truth, of a mathematical theory and its physical truth. This, in turn, leads him to the notion that theories need testing.Barrow on Matter and GodRecent literature has established significant correlations between theological voluntarism and empiricism, as well as between theological intellectualism and rationalism. As E. B. Davis writes, “the Christian doctrine of creation is a dialogue between God’s unconstrained will, which utterly transcends the bounds of human comprehension, and God’s orderly intellect, which serves as the model for the human mind.” Intellectualist theology considers God’s omniscience His... (shrink)

The Jesuit C.F. Milliet Dechales, author of one of the most famous early modern mathematical encyclopedias, Cursus seu mundus mathematicus, wrote a hundred-folio-page long treatise devoted to the “progress of mathematics,” which was published in the second, enlarged edition of his encyclopedia. His historical treatise covers the gamut of mixed mathematics—including astronomy, mechanics, optics, music, geography and navigation, ars tignaria, and architecture. The early modern historical narratives about the mathematical sciences, from Regiomontanus’s Oratio onwards, have been aptly characterized by their (...) literary form and goals rather than their historical content. Rhetoric, humanistic topoi, and philosophical filiation turned the histories of mathematics into powerful tools for different purposes. My account of Dechales’ tract on the “progress of mathematics” analyzes the ways in which it dovetails with Jesuit approaches to mathematics, provides legitimation to the mathematical sciences as well as to their authors, and contributes to define the role and boundaries of the discipline, in particular vis-à-vis natural philosophy. (shrink)

This paper deals with Hobbes's theory of optical images, developed in his optical magnum opus, ‘A Minute or First Draught of the Optiques’, and published in abridged version in De homine. The paper suggests that Hobbes's theory of vision and images serves him to ground his philosophy of man on his philosophy of body. Furthermore, since this part of Hobbes's work on optics is the most thoroughly geometrical, it reveals a good deal about the role of mathematics in Hobbes's philosophy. (...) The paper points to some difficulties in the thesis of Shapin and Schaffer, who presented geometry as a ‘paradigm’ for Hobbes's natural philosophy. It will be argued here that Hobbes's application of geometry to optics was dictated by his metaphysical and epistemological principles, not by a blind belief in the power of geometry. Geometry supported causal explanation, and assisted reason in making sense of appearances by helping the philosopher understand the relationships between the world outside us and the images it produces in us. Finally the paper broadly suggests how Hobbes's theory of images may have triggered, by negative example, the flourishing of geometrical optics in Restoration England. (shrink)

There is an uncanny unanimity about the founding role of Kepler's Dioptrice in the theory of optical instruments and for classical geometric optics generally. It has been argued, however, that for more than fifty years optical theory in general, and Dioptrice in particular, was irrelevant for the purposes of telescope making. This article explores the nature of Kepler's achievement in his Dioptrice . It aims to understand the Keplerian 'theory' of the telescope in its own terms, and particularly its links (...) to Kepler's theory of vision. It deals first with Kepler's way to circumvent his ignorance of the law of refraction, before turning to Kepler's explanations of why lenses magnify and invert vision. Next, it analyses Kepler's account of the properties of telescopes and his suggestions to improve their designs. The uses of experiments in Dioptrice , as well as the explicit and implicit references to della Porta's work that it contains, are also elucidated. Finally, it clarifies the status of Kepler's Dioptrice vis-à-vis , classical geometrical optics and presents evidence about its influence in treatises about the practice of telescope making during roughly the first two-thirds of the seventeenth century. (shrink)

This paper takes Franco's Spain to be a powerful case study for analyzing the ways in which power shapes science and technology and is shaped by them in return. Spain was the last country in Western Europe to establish closer links with any of the international cooperative institutions emerging after WWII. As such, developments internal to Spanish society were quite autonomous and relatively free from foreign influences. The paper focuses first on the brand new, powerful institution that the Francoist regime (...) created to promote scientific research under tight political control, the Consejo Superior de Investigaciones Científicas. Next it turns to applied science and technology, top priorities for the regime's state-supported programs of industrialization. They were implemented through the politically and financially powerful Instituto Nacional de Industria. Using diplomatic sources, the paper next argues that, until the late 1950s, Spain maintained substantial political and economic isolation essentially because the regime bet on autarkic policies and a model of largely isolated development. In this model, it was crucial for the regime to develop its own technological and scientific resources. Finally, the paper examines how the regime fostered a new Spanish identity in which science had a new role. (shrink)

Summary José María Albareda (1902–1966) was an applied chemist and a prominent member of the Roman Catholic organization, Opus Dei, who played a crucial role in organizing the Consejo Superior de Investigaciones Científicas (CSIC), the new scientific institution created by the Franco regime in 1939. The paper analyses first the formative years in Albareda's scientific biography and the political and social context in which he became an Opus Dei fellow. Then it discusses the CSIC's innovative features compared with the Junta (...) para Ampliación de Estudios (JAE), the institution in charge of scientific research and science policy in Spain from 1907 up to the Civil War (1936–1939). Next it goes into Albareda's ideas about science and science policy. Finally, it shows how they shaped the organization of the CSIC, of which Albareda was the General Secretary from 1939 to his untimely death in 1966. (shrink)

This article focuses on some theoretical developments prompted by the use and construction of telescopes in the first half of the seventeenth century. It argues that today's notion of "scientific instrument" cannot be used to categorize these optical devices or explain their impact on natural philosophy. The article analyzes in historical terms the construction of conceptual references for the telescope as an instrument of a new kind, which possessed capabilities and working principles unlike those of traditional "mathematical instruments." It shows (...) that through the 1650s, in both rhetorical and explanatory terms, first-rank telescope makers, theoreticians, and astronomers found it useful to equate the telescope with the eye, suggesting that the data the telescope produced was as reliable as that obtained in naked-eye vision. Kepler's and Descartes' theory of the telescope will be shown to dovetail uncannily with this understanding of the telescope. (shrink)

This paper is an essay-review of J. Yoder's "Unrolling Time: Christian Huygens and the Mathematization of Nature" (Cambridge, 1989). Highlighting the scholarly thoroughness and mathematical competence of Yoder's reconstruction of Huygens's heuristic path to his ground-breaking results on centrifugal force, cycloidal motion and evolutes, the essay also deals with Yoder's attempts to characterize Huygens's way of using mathematics in physical problems. In opposition to Yoder's thesis, this paper argues that evidence internal to Huygens's work as well as the contemporary reaction (...) to it suggest the existence of substantial methodological differences between Huygens's mathematization of nature and Newton's. (shrink)