: Although Galileo's struggle to mathematize the study of nature is well known and oft discussed, less discussed is the form this struggle takes in relation to Galileo's first new science, the science of the second day of the Discorsi. This essay argues that Galileo's first science ought to be understood as the science of matter—not, as it is usually understood, the science of the strength of materials. This understanding sheds light on the convoluted structure of the Discorsi's first day. (...) It suggests that the day's meandering discussions of the continuum, infinity, the vacuum, and condensation and rarefaction establish that a formal treatment of the "eternal and necessary" properties of matter is possible; i.e., that matter as such can be considered mathematically. This would have been a necessary, and indeed revolutionary, preliminary to the mathematical science of the second day because matter itself was thought in the Aristotelian tradition to be responsible for the departure of natural bodies from the unchanging and thus mathematizable character of abstract objects. In addition, the first day establishes that when considered physically, these properties account for matter's force of cohesion and resistance to fracture. This essay closes by showing that this dual style of reasoning accords with the conceptual structure of mixed mathematics. (shrink)

El reconocimiento de Dios a partir del conocimiento de las verdades matemáticas explica la presencia, en la totalidad de la obra filosófica de Marin Mersenne (1588-1648), de un discurso científico sobre la divinidad o de su representación a través de las ciencias matemáticas. Fácilmente, es posible encontrar, en los escritos del Mínimo, innumerables imágenes, comparaciones, analogías y expresiones que ilustran la concepción de un Dios matemático; experto no sólo en las ciencias puras, sino también en las matemáticas mixtas o subalternas. (...) Por esta razón, Mersenne se refiere a Dios como el Gran director del concierto cósmico o al Gran arquitecto del mundo, del unísono como la unión de las tres personas divinas, del Sol como fuente de la creación, del centro de la circunferencia… Este artículo tienecomo objetivo principal, en primer lugar, determinar si existe una asociación entre este discurso matemático sobre Dios y la teología natural. En segundo lugar, se pretende discutir si la hipótesis de la univocidad de las matemáticas justifica una identificación entre la teología, las matemáticas y la metafísica. Para ello, cuestionamos unos de los pocos e importantes aportes en la materia, a saber las hipótesis de Jean-Luc Marion y Vincent Carraud, publicadas en 1994. Ambos eruditos sostienen la identificación de las matemáticas con la metafísica y su consecuente univocidad. (shrink)

My dissertation lays out some of the chief philosophical precursors to Jonathan Israel's Radical Enlightenment. It investigates the principal question of Will Durant's The Age of Voltaire: "How did it come about that a major part of the educated classes in Europe and America has lost faith in the theology that for fifteen centuries gave supernatural sanctions and supports to the precarious and uncongenial moral code upon which Western civilization has been based?" The aim of this project is both broad (...) and specific: the first is to provide a general history of the philosophical precursors to the Radical Enlightenment up until the early modern period, and the second is to highlight one of these precursors in detail, which I do in the large Spinoza part. With the assistance of a great deal of scholarship in philosophy of religion, history of philosophy, theological analysis, biblical criticism, and historiography, my dissertation contends that the major philosophical precursors against orthodox faith in revelation and for the Radical Enlightenment have been derived primarily from several forces. I present some of the general arguments of some of the pre-Socratics and Greek philosophers, especially Socrates and Plato, emphasizing their rationalist and non-theological thinking. Then I point out how some of this Greek philosophical literature led to new philosophical and theological elements in some of the teachings of the Church Fathers, some of the medievals, and some of the scholastics, up to the early modern period. The core of my argument, however, begins to pick up steam at the Renaissance. With the Renaissance, the Scientific Revolution, and the early Enlightenment New Philosophy, everything changes. Renaissance textual criticism of ancient texts leads to the beginnings of some genuine biblical criticism. The explosion of naturalist-leaning explanations of nature via Copernicus, Galileo, Descartes and many others in the Scientific Revolution leads many to wonder if God is needed. The rejection of Aristotelian and Scholastic metaphysics by the New Philosophers, most notably, Descartes, undermine what for many provided the philosophical underpinnings for the Church and theology. And then "the most unkindest cut of all," the revolutionary historical and textual criticism of the Bible which utterly undermines and refutes Judaism and Christianity. (shrink)

This paper reconstructs the development of Mersenne's reflections concerning optics. I argue that Mersenne's optical writings provide crucial insights into Mersenne's Aristotelianism. I reconstruct Mersenne's attempt of explaining the new ideas on light, which were advanced by Kepler, Descartes and Hobbes within Aristotle's natural philosophy. Mersenne explained Kepler's work on light within the Scholastic tradition. In the 1640s, Mersenne was stimulated by the debate concerning Descartes' theory of light, which he accepted only in 1648. Indeed, Mersenne first explained Descartes' law (...) of refraction by means of Hobbes physics. However, Mersenne always wanted to remain faithful to Aristotle. (shrink)

In the ten years following the publication of Galileo Galilei's Discorsi e dimostrazioni matematiche intorno a due nuove scienze , the new science of motion was intensely debated in Italy, France and northern Europe. Although Galileo's theories were interpreted and reworked in a variety of ways, it is possible to identify some crucial issues on which the attention of natural philosophers converged, namely the possibility of complementing Galileo's theory of natural acceleration with a physical explanation of gravity; the legitimacy of (...) Galileo's methods of proof and of his theory of the composition of continuous magnitudes; and the adequacy of the experimental evidence in favor of his theory.Through his published works and his correspondence, Marin Mersenne contributed in a significant way to each of these discussions. In the following, I shall provide a sketch of Mersenne's multiple engagement with the new science of motion, while trying to account for his growing skepticism concerning Galileo's law of free fall. Whereas in the 1630s, Mersenne still firmly believed in the validity of this law and tried to devise experimental and mathematical proofs in its favor, in the 1640s he developed serious doubts regarding the possibility of constructing an exact science of motion. As we shall see, Mersenne's evolving attitude sheds an interesting light on his views concerning the relation between physics and mathematics.---------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ----------------------------------------------------. (shrink)

An understanding of the precise nature of the scientific method of Sir William Petty has proved elusive to historians of economic thought, in no small part because of a lack of Petty's own characterization of his scientific approach. This research clarifies the nature of Petty's method, as to whether it was primarily inductive or deductive, and to what extent it relied on empirical foundations. The paper employs a two-pronged analysis. First, it examines the main sources of Petty's method: the works (...) of Sir Francis Bacon and Thomas Hobbes, and the synergistic influences of the Hartlib Circle, the Royal Society, the Dublin Philosophical Society, and the Mersenne group. Second, four of Petty's most noted contributions to political economy are deconstructed in order to identify his scientific method. This research concludes that Petty relied almost exclusively on deduction in his scientific approach and that his analysis does not reveal any inductive reasoning. When data was available, Petty constructed his economic theories on empirical foundations. (shrink)

1. In the Physics and Metaphysics, Aristotle lays out four kinds of causes and provides examples of each. Bronze and silver are offered as examples of the material causes of artefacts, the father a...