The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmatic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting with (...) the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes' Geometrie, the relation between geometrical and epistemological theories of the infinite, and the Leibnizian calculus and the opposition to infinitesimalist procedures. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics. (shrink)

This book offers a major reassessment of Leibniz's metaphysics. Christia Mercer has exposed the underlying doctrines of Leibniz's philosophy. By analysing Leibniz's early works she demonstrates that the metaphysics of pre-established harmony developed many years earlier than previously believed and for reasons which have not been understood. As a result of this analysis she has unearthed a philosophical school that Leibniz scholars have not recognized. A much deeper understanding of some of Leibniz's key doctrines emerges. Moreover, since the Leibniz that (...) is revealed here does not fit neatly into the standard accounts of the history of philosophy and science, Christia Mercer's study will prompt scholars to reconsider their basic assumptions about early modern philosophy and science. (shrink)

While visiting a friend's family in Cornwall during the traditional May Day celebrations, eighteen-year-old Laura becomes involved in an old family mystery concerning the disappearance of ancient heirlooms.

To the medieval thinker, man was the center of creation and all of nature existed purely for his benefit. The shift from the philosophy of the Middle Ages to the modern view of humanity's less central place in the universe ranks as the greatest revolution in the history of Western thought, and this classic in the philosophy of science describes and analyzes how the profound change occurred. A fascinating analysis of the works of Copernicus, Kepler, Galileo, Descartes, Hobbes, Gilbert, Boyle, (...) and Newton, it not only establishes the reasons for the triumph of the modern perspective but also accounts for certain limitations that characterize contemporary scientific thought. (shrink)

Review of T. S. Kuhn's The Essential Tension.

The title of this book, Adventures of Ideas, bears two meanings, both applicable to the subject-matter.

History of the human race from the point of view of mankind's changing ideas--sociological, cosmological, philosophica.

This paper investigates Newton’s ontology of space in order to determine its commitment, if any, to both Cambridge neo-Platonism, which posits an incorporeal basis for space, and substantivalism, which regards space as a form of substance or entity. A non-substantivalist interpretation of Newton’s theory has been famously championed by Howard Stein and Robert DiSalle, among others, while both Stein and the early work of J. E. McGuire have downplayed the influence of Cambridge neo-Platonism on various aspects of Newton’s own spatial (...) hypotheses. Both of these assertions will be shown to be problematic on various grounds, with special emphasis placed on Stein’s influential case for a non-substantivalist reading. Our analysis will strive, nonetheless, to reveal the unique or forward-looking aspects of Newton’s approach, most notably, his critical assessment of substance ontologies, that help to distinguish his theory of space from his neo-Platonic contemporaries and predecessors. (shrink)

This paper is a critical response to Hylarie Kochiras’ “Gravity and Newton’s substance counting problem,” Studies in History and Philosophy of Science 40 267–280. First, the paper argues that Kochiras conflates substances and beings; it proceeds to show that Newton is a substance monist. The paper argues that on methodological grounds Newton has adequate resources to respond to the metaphysical problems diagnosed by Kochiras. Second, the paper argues against the claim that Newton is committed to two speculative doctrines attributed to (...) him by Kochiras and earlier Andrew Janiak: i) the passivity of matter and ii) the principle of local causation. Third, the paper argues that while Kochiras’ arguments about Newton’s metaphysical commitments are mistaken, it qualifies the characterization of Newton as an extreme empiricist as defended by Howard Stein and Rob DiSalle. In particular, the paper shows that Newton’s empiricism was an intellectual and developmental achievement that built on non trivial speculative commitments about the nature of matter and space.Keywords: Newton; Substance; Action at a distance; Space; Matter; Empiricism. (shrink)

(No abstract is available for this citation).

This study considers Newton's views on space and time with respect to some important ontologies of substance in his period. Specifically, it deals in a philosophico-historical manner with his conception of substance, attribute, existence, to actuality and necessity. I show how Newton links these “features” of things to his conception of God's existence with respect of infinite space and time. Moreover, I argue that his ontology of space and time cannot be understood without fully appreciating how it relates to the (...) nature of Divine existence. In order to establish this, the ontology embodied in Newton's theory of predication is analysed, and shown to be different from the presuppositions of the ontological argument. From the historical point of view Gassendi's influence is stressed, via the mediation of Walter Charleton. Furthermore, Newton's thought on these matters is contrasted with Descartes's and Spinoza's. In point of fact, in his earliest notebook Newton recorded observations on Descartes's version of the ontological argument. Soon, however, he was to oppose the Cartesian conception of the actuality of Divine existence by means of arguments similar to those of Gassendi. Lastly, I suggest that the nature and extent of Henry More's influence on Newton's conception of how God relates to absolute space and time bears further examination. (shrink)

: This article is concerned with Newton's appropriation of Descartes' ontology of true and immutable natures in developing his theory of infinitely extended space. It contends that unless the part played by the Platonic distinction between "being a nature" and "having a nature" in Newton's thinking is properly appreciated the foundation of his doctrine of space in relation to God will not be fully understood. It also contends that Newton's Platonism is consistent with his empiricism once the mediating role is (...) made clear that the geometry of moving loci play in grounding his intuitions concerning infinite natures. (shrink)

This paper draws attention to the crucial importance of a new kind of precisely defined law of nature in the Scientific Revolution. All explanations in the mechanical philosophy depend upon the interactions of moving material particles; the laws of nature stipulate precisely how these interact; therefore, such explanations rely on the laws of nature. While this is obvious, the radically innovatory nature of these laws is not fully acknowledged in the historical literature. Indeed, a number of scholars have tried to (...) locate the origins of such laws in the medieval period. In the first part of this paper these claims are critically examined, and found at best to reveal important aspects of the background to the later idea, which could be drawn upon for legitimating purposes by the mechanical philosophers. The second part of the paper argues that the modern concept of laws of nature originates in René Descartes's work. It is shown that Descartes took his concept of laws of nature from the mathematical tradition, but recognized that he could not export it to the domain of physico-mathematics, to play a causal role, unless he could show that these laws were underwritten by God. It is argued that this is why, at an early stage of his philosophical development, Descartes had to turn to metaphysics. (shrink)

This paper is in three sections. The first establishes that Newton, in spite of a well-known passage in a letter to Richard Bentley of 1692, did believe in action at a distance. Many readers may see this merely as an act of supererogation, since it is so patently obvious that he did. However, there has been a long history among Newton scholars of allowing the letter to Bentley to over-ride all of Newton’s other pronouncements in favour of action at a (...) distance, with devastating effects on our understanding of related aspects of his physics and his theology. Furthermore, this misconceived scholarly endeavour shows no sign of abating. The second section then offers a historical reconstruction, based on Newton’s writings, of how, when and why he began to accept actions at a distance and make them one of the cornerstones of his physics. Finally, using this chronological account of Newton’s use of actions at a distance, the paper re-assesses the claims of B. J. T. Dobbs that Newton’s important manuscript, De gravitatione et aequipondio fluidorum, was written, not in the late 1660s or early 1670s as was previously supposed, but during the composition of the Principia, in 1684 or 1685.Keywords: Isaac Newton; Action-at-a-distance; Gravity; Force; Aether; Attraction. (shrink)

Beginning with Berkeley and Leibniz, philosophers have been puzzled by the close yet ambivalent association in Newton's ontology between God and absolute space and time. The 1962 publication of Newton's highly philosophical manuscript De Gravitatione has enriched our understanding of his subtle, sometimes cryptic, remarks on the divine underpinnings of space and time in better-known published works. But it has certainly not produced a scholarly consensus about Newton's exact position. In fact, three distinct lines of interpretation have emerged: Independence: space (...) and time are not essentially related to God. Causation: space and time are caused by God. Assimilation: space and time are attributes of God. This paper defends the third interpretation against the first two by drawing out the under-appreciated influence of Descartes' metaphysics on Newton's ‘physico-theology’. (shrink)

Isaac Newton is a legendary figure whose mythical dimension threatens to overshadow the actual man.

Laws form counterfactually stable sets -- Natural necessity -- Three payoffs of my account -- A world of subjunctives.

David Hume's philosophy, especially the positive project of his science of man, is often thought to be modeled on Newton's successes in natural philosophy. Hume's self-described experimental method (see the subtitle to Treatise) and the resemblance of his rules of reasoning (Treatise, 1.3.15)1 with Newton's are said to be evidence for this position (Noxon 1973; De Pierris 2002). Hume encourages this view of his project by employing Newtonian metaphors: he talks of an attraction in the mental world on a par (...) with that in the natural world (1.1.4.6). Hume infers the existence of habits as a kind of mental force (EHU 5.2.2) analogous to gravity; the discovery of the the principles of association, which in thehe calls his most important achievement see the section on Association in the entry on Hume in this Encyclopedia, are, then, analogous to the laws of motion. Hume certainly appears to want his readers to feel that he is modeling his project on the successes of natural philosophy, exemplified by Newton. In the Introduction to the Treatise and even more explicitly in the opening pages of EHU (1.15), Hume suggests that his science of man can parallel recent achievements in natural philosophy (with rather obvious nods to Newton's successes in planetary astronomy). And at the start of EPM, he echoes Newton's rejection of hypotheses (1.10). There is, thus, no doubt that Hume wants his readers to believe that Newton forms a kind of model. (shrink)