This volume provides a much needed, historically accurate narrative of the development of theories of space up to the beginning of the eighteenth century. It studies conceptions of space that were implicitly or explicitly entailed by ancient, medieval and early modern representations of the cosmos. The authors reassess Alexandre Koyré’s groundbreaking work From the Closed World to the Infinite Universe and they trace the permanence of arguments to be found throughout the Middle Ages and beyond. By adopting a long timescale, (...) this book sheds new light on the continuity between various cosmological representations and their impact on the ontology and epistemology of space. Readers may explore the work of a variety of authors including Aristotle, Epicurus, Henry of Ghent, John Duns Scotus, John Wyclif, Peter Auriol, Nicholas Bonet, Francisco Suárez, Francesco Patrizi, Giordano Bruno, Libert Froidmont, Marin Mersenne, Pierre Gassendi, Gottfried Wilhelm Leibniz and Samuel Clarke. We see how reflections on space, imagination and the cosmos were the product of a plurality of philosophical traditions that found themselves confronted with, and enriched by, various scientific and theological challenges which induced multiple conceptual adaptations and innovations. This volume is a useful resource for historians of philosophy, those with an interest in the history of science, and particularly those seeking to understand the historical background of the philosophy of space. (shrink)

Thought experiments play an important epistemic, rhetorical and didactic function in Galileo’s dialogues. In some cases, Salviati, Sagredo and Simplicio agree about what would happen in an imaginary scenario and try to understand whether the predicted outcome is compatible with their respective theoretical assumptions. There are, however, also situations in which the predictions of the three interlocutors turn out to be theory-laden. Salviati, Sagredo and Simplicio not only disagree about what would happen, but they reject each other’s solutions as question-begging (...) and somtimes even dismiss each other’s thought experiments as misleading or nonsensical. (shrink)

This article analyzes Galileo's mathematization of motion, focusing in particular on his use of geometrical diagrams. It argues that Galileo regarded his diagrams of acceleration not just as a complement to his mathematical demonstrations, but as a powerful heuristic tool. Galileo probably abandoned the wrong assumption of the proportionality between the degree of velocity and the space traversed in accelerated motion when he realized that it was impossible, on the basis of that hypothesis, to build a diagram of the law (...) of fall. The article also shows how Galileo's discussion of the paradoxes of infinity in the First Day of the Two New Sciences is meant to provide a visual solution to problems linked to the theory of acceleration presented in Day Three of the work. Finally, it explores the reasons why Cavalieri and Gassendi, although endorsing Galileo's law of free fall, replaced Galileo's diagrams of acceleration with alternative ones. (shrink)

Pierre Gassendi was a major figure in seventeenth-century philosophy whose philosophical and scientific works contributed to shaping Western intellectual identity. Among "new philosophers", he was considered Descartes’ main rival, and he belonged to the first rank of those attempting to carve out an alternative to Aristotelian philosophy. Given the importance of Gassendi for the history of science and philosophy, it is surprising to see that he has been largely ignored in the Anglophone world. This collection of essays constitutes the first (...) book on Gassendi that comprehensively covers his biography, bibliography, and all aspects of his philosophy. The book is divided into four parts. It begins with a brief sketch of the intellectual world of seventeenth-century France, Gassendi’s early attacks on Aristotle, and a bibliographical essay on early-modern publications of Gassendi’s writings. Part II explores Gassendi’s contributions to logic, natural philosophy, and astronomy and cosmology. Part III addresses Gassendi as a humanist and participant in seventeenth-century philosophical and scientific debates, including his advocacy of Epicurean philosophy and his relation to the sceptical tradition. The fourth and final part involves a brief discussion of the reception of Gassendi’s thought, including the paraphrases of his works published in France and England. This book is an essential resource for scholars and upper-level students of early modern philosophy, intellectual history, and the history of science who want to get acquainted with Pierre Gassendi as a major philosopher and intellectual figure of the early modern period. (shrink)

This article analyzes the evolution of Mersenne's views concerning the validity of Galileo's theory of acceleration. After publishing, in 1634, a treatise designed to present empirical evidence in favor of Galileo's odd-number law, Mersenne developed over the years the feeling that only the elaboration of a physical proof could provide sufficient confirmation of its validity. In the present article, I try to show that at the center of Mersenne's worries stood Galileo's assumption that a falling body had to pass in (...) its acceleration through infinite degrees of speed. His extensive discussions with, or his reading of, Descartes, Gassendi, Baliani, Fabri, Cazre, Deschamps, Le Tenneur, Huygens, and Torricelli led Mersenne to believe that the hypothesis of a passage through infinite degrees of speed was incompatible with any mechanistic explanation of free fall. (shrink)

In this introduction, we explain our choice to approach the topic of space from a cosmological perspective, that is, by studying the conceptions of space that were implicitly or explicitly entailed by ancient, medieval and early modern representations of the cosmos, and the role that imagination played in those conceptions. We compare our approach with those of Alexandre Koyré and Edward Grant, and we present the two important issues this book intends to shed light on, namely the continuity and discontinuity (...) between ancient, medieval, and early modern conceptions of space and the cosmos; and the role that metaphysical, cosmological, and theological considerations played in the elaboration of new theories of space in the course of history. This chapter also presents the main, recurring themes of this book: the relation between place and space; the notion of imaginary spaces; the role played by thought experiments in discussions concerning the nature of space and the structure of the cosmos; the impact of the condemnation of 1277 on subsequent theories of space; and the relation between God’s immensity and the infinity of space. (shrink)

: In the concluding pages of his Epistolae duae de motu impresso a motore translato (1642), Pierre Gassendi provides a brief summary of the explanation of the tides found in Galileo's Dialogue over the Two Chief World Systems (1632). A comparison between the two texts reveals, however, that Gassendi surreptitiously modifies Galileo's theory in some crucial points in the vain hope of rendering it more compatible with the observed phenomena. But why did Gassendi not acknowledge his departures from the Galilean (...) model? The present article argues that cautiousness was just one of the reasons that stopped the French priest from turning Galileo's theory into his own theory. He was probably also aware of the fact that Kepler's model of planetary motion, which he endorsed in the Epistolae, could not be reconciled with Galileo's explanation of the tides. In the postumously published Syntagma philosophicum (1658), Gassendi tried to mend this major inconsistency by arguing that Galileo's theory of the tides not only remained valid, but became even more coherent, if one attributed to the Earth an elliptic orbit. But given that in the Syntagma Gassendi officially adhered to the Tychonic system, his effort to reconcile Kepler and Galileo, while already unconvincing by itself, appears completely futile. (shrink)

While it is well known that Plutarch’s De facie in orbe lunae was a major source of inspiration for Galileo’s Sidereus nuncius, its influence on his Dialogo sopra i due massimi sistemi del mondo, and especially on his views on gravity, has not been sufficiently explored. This essay offers the first systematic comparison of Plutarch’s and Galileo’s accounts of gravity by focusing on four themes: the thought experiment of a stone falling in a tunnel passing through the center of the (...) Earth; the account of gravity as a tendency to unite with the whole; the view that the Moon is a separate center of attraction; and the impossibility of attraction by an incorporeal point. The essay analyzes the role that these themes play in De facie and in the Dialogo, trying to understand how Galileo appropriated, reworked, and expanded on Plutarch’s views. (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)

In 1996, Manuel Luna Alcoba published a transcription of LH XXXVII, IV, 57 r°-58v°, a manuscript written by Leibniz after 1693 and containing historical and systematic reflections on the problem of the continuum. The present article aims to show that the manuscript, to which Luna Alcoba attributed the title Geschichte des Kontinuumproblems, consists mainly of excerpts from, paraphrases of, and comments on the Labyrinthus sive de compositione continui (1631), a book by the Louvain philosopher and theologian Libert Froidmont to which (...) Leibniz often referred in his writings. By comparing LH XXXVII, IV, 57 r°-58v° with the Labyrinthus, I try to understand which parts of Fromondus’ book attracted Leibniz’ attention and why the latter, as late as 1693, still found it worth brooding over an Aristotelian treatise on the composition of the continuum. (shrink)

This article documents the general tendency of seventeenth-century natural philosophers, irrespective of whether they were atomists or anti-atomists, to regard space, time and matter as magnitudes having the same internal composition. It examines the way in which authors such as Fromondus, Basson, Sennert, Arriaga, Galileo, Magnen, Descartes, Gassendi, Charleton as well as the young Newton motivated their belief in the isomorphism of space, time and matter, and how this belief reflected on their views concerning the relation between geometry and physics. (...) Special attention is paid to the fact that most of the authors mentioned above regarded rarefaction and condensation, on the one hand, and acceleration and deceleration, on the other hand, as analogous phenomena, which consequently had to be explained in similar terms. (shrink)