What was the basis for the adoption of mathematics as the primary mode of discourse for describing natural events by a large segment of the philosophical community in the seventeenth century? In answering this question, this book demonstrates that a significant group of philosophers shared the belief that there is no necessary correspondence between external reality and objects of human understanding, which they held to include the objects of mathematical and linguistic discourse. The result is a scholarly reliable, but accessible, account of the role of mathematics in the works of (amongst others) Galileo, Kepler, Descartes, Newton, Leibniz, and Berkeley. This impressive volume will benefit scholars interested in the history of philosophy, mathematical philosophy and the history of mathematics.

An analysis of Newton's mathematical work, from early discoveries to mature reflections, and a discussion of Newton's views on the role and nature of mathematics. Historians of mathematics have devoted considerable attention to Isaac Newton's work on algebra, series, fluxions, quadratures, and geometry. In Isaac Newton on Mathematical Certainty and Method, Niccolò Guicciardini examines a critical aspect of Newton's work that has not been tightly connected to Newton's actual practice: his philosophy of mathematics. Newton aimed to inject certainty into natural philosophy by deploying mathematical reasoning (titling his main work The Mathematical Principles of Natural Philosophy most probably to highlight a stark contrast to Descartes's Principles of Philosophy). To that end he paid concerted attention to method, particularly in relation to the issue of certainty, participating in contemporary debates on the subject and elaborating his own answers. Guicciardini shows how Newton carefully positioned himself against two giants in the “common” and “new” analysis, Descartes and Leibniz. Although his work was in many ways disconnected from the traditions of Greek geometry, Newton portrayed himself as antiquity's legitimate heir, thereby distancing himself from the moderns. Guicciardini reconstructs Newton's own method by extracting it from his concrete practice and not solely by examining his broader statements about such matters. He examines the full range of Newton's works, from his early treatises on series and fluxions to the late writings, which were produced in direct opposition to Leibniz. The complex interactions between Newton's understanding of method and his mathematical work then reveal themselves through Guicciardini's careful analysis of selected examples. Isaac Newton on Mathematical Certainty and Method uncovers what mathematics was for Newton, and what being a mathematician meant to him.

Infinite Variety offers a brilliantly learned analysis of a seventeenth-century aesthetic framed not by the rise of secularism, but by its opposite, and embraced by English writers including Thomas Hobbes, Richard Blackmore, John Locke, Jonathan Swift, and Daniel Defoe.

In this monograph, Steffen Ducheyne provides a historically detailed and systematically rich explication of Newton’s methodology. Throughout the pages of this book, it will be shown that Newton developed a complex natural-philosophical methodology which encompasses procedures to minimize inductive risk during the process of theory formation and which, thereby, surpasses a standard hypothetico-deductive methodological setting. Accordingly, it will be highlighted that the so-called ‘Newtonian Revolution’ was not restricted to the empirical and theoretical dimensions of science, but applied equally to the methodological dimension of science. Furthermore, it will be documented that Newton’s methodology was far from static and that it developed alongside with his scientific work. Attention will be paid not only to the successes of Newton’s innovative methodology, but equally to its tensions and limitations. Based on a thorough study of Newton’s extant manuscripts, this monograph will address and contextualize, inter alia, Newton’s causal realism, his views on action at a distance and space and time, the status of efficient causation in the /Principia/, the different phases of his methodology, his treatment of force and the constituents of the physico-mathematical models in the context of Book I of the /Principia/, the analytic part of the argument for universal gravitation, the meaning and significance of his regulae philosophandi, the methodological differences between his mechanical and optical work, and, finally, the interplay between Newton’s theology and his natural philosophy.

The Historical Dictionary of Hobbes's Philosophy offers a comprehensive guide to the many facets of Hobbes's work. Through its chronology, introductory essay, bibliography, and hundreds of cross-referenced dictionary entries on concepts, people, works, and technical terms, Hobbes's impact on philosophy and related fields is made accessible to the reader in this must-have reference. Intended as a reference to learn about particular aspects of Hobbes, it also serves as a quick guide to check information and find the relevant secondary literature on Hobbes. It is an excellent access point for students, researchers, and anyone wanting to know more about Thomas Hobbes.

This book interrogates the ontology of mathematical entities in Spinoza as a basis for addressing a wide range of interpretive issues in Spinoza’s epistemology—from his antiskepticism and philosophy of science to the nature and scope of reason and intuitive knowledge and the intellectual love of God. Going against recent trends in Spinoza scholarship, and drawing on various sources, including Spinoza’s engagements with optical theory and physics, Matthew Homan argues for a realist interpretation of geometrical figures in Spinoza; illustrates their role in a Spinozan hypothetico-deductive scientific method; and develops Spinoza’s mathematical examples to better illuminate the three kinds of knowledge. The result is a portrait of Spinoza’s epistemology as sanguine and distinctive yet at home in the new Cartesian and Galilean scientific-philosophical paradigm.