Antoni Malet

José María Albareda (1902–1966) and the formation of the Spanish Consejo Superior de Investigaciones Científicas

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 Albaredas scientific biography and the political and social context in which he became an Opus Dei fellow. Then it discusses the CSICs 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 Albaredas 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.

Between Mathematics and Experimental Philosophy: Hydrostatics in Scotland About 1700

Many years ago J.B. Conant contrasted Pascal’s and Boyle’s approach to hydrostatics and pneumatics in terms of “two traditions,” one mathematical, the other experimental. Peter Dear has brilliantly recast Conant’s suggestion by linking Pascal’s (so-called) mathematical approach and Boyle’s experimental approach to their contrasting theological views. In a more general way, there is a broad consensus that the experimental approach was the distinguishing feature of the teaching of natural philosophy in Britain from the late seventeenth century on. In the early Enlightenment in Britain, Larry Stewart and others have shown, the utilitarian, manipulative, visual, experimentalist side of natural philosophy was favored and stressed to the point that the mathematical content almost disappeared. It was an approach in which hands-on experience and observation not only helped to overcome difficulties in concept-clarification and in mathematical arguments, but appeared as real alternatives to them. Although there is much truth in those accounts, we present here evidence that a British mathematical approach to hydrostatics and pneumatics was successfully developed by John Wallis, James Gregorie (or Gregory), Newton, and others. In a sense that we will specify here, their approach is more deeply and more genuinely mathematical than Pascal’s. Finally we also present evidence that such a mathematical understanding of hydrostatics and pneumatics occupied a prominent place in the teaching of natural philosophy in Scottish universities from the late seventeenth century on.

The power of images: mathematics and metaphysics in Hobbes's optics

Abstract This paper deals with Hobbess theory of optical images, developed in his optical magnum opus, ‘A Minute or First Draught of the Optiques’ (1646), and published in abridged version in De homine (1658). The paper suggests that Hobbess theory of vision and images serves him to ground his philosophy of man on his philosophy of body. Furthermore, since this part of Hobbess work on optics is the most thoroughly geometrical, it reveals a good deal about the role of mathematics in Hobbess philosophy. The paper points to some difficulties in the thesis of Shapin and Schaffer, who presented geometry as a ‘paradigm’ for Hobbess natural philosophy. It will be argued here that Hobbess 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 Hobbess theory of images may have triggered, by negative example, the flourishing of geometrical optics in Restoration England.

Mersenne and Mixed Mathematics

One of the most fascinating intellectual agures of the seventeenth century, Marin Mersenne (1588–1648) is well known for his relationships with many outstanding contemporary scholars as well as for his friendship with Descartes. Moreover, his own contributions to natural philosophy have an interest of their own. Mersenne worked on the main scientiac questions debated in his time, such as the law of free fall, the principles of Galileo’s mechanics, the law of refraction, the propagation of light, the vacuum problem, the hydrostatic paradox, and the Copernican hypothesis. In his Traite de l’Harmonie Universelle (1627), Mersenne listed and described the mathematical disciplines:

Newton on Indivisibles

Though Wallis’s Arithmetica infinitorum was one of Newton’s major sources of inspiration during the first years of his mathematical education, indivisibles were not a central feature of his mathematical production.

Wallis on Indivisibles

The present chapter is devoted, first, to discuss in detail the structure and results of Walliss major and most influential mathematical work, the Arithmetica Infinitorum ([51]). Next we will revise Walliss views on indivisibles as articulated in his answer to Hobbess criticism in the early 1670s. Finally, we will turn to his discussion of the proper way to understand the angle of contingence in the first half of the 1680s. As we shall see, there are marked differences in the status that indivisibles seem to enjoy in Walliss thought along his mathematical career. These differences correlate with the changing context of 17th-century mathematics from the 1650s through the 1680s, but also respond to the different uses Wallis gave to indivisibles in different kinds of texts—purely mathematical, openly polemical, or devoted to philosophical discussion of foundational matters.