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Euclid Vindicated from Every Blemish
This first complete English language edition of Euclides vindicatus presents a corrected and revised edition of the classical English translation of Saccheri's text by G.B. Halsted. It is complemented with a historical introduction on the geometrical environment of the time and a detailed commentary that helps to understand the aims and subtleties of the work. Euclides vindicatus, written by the Jesuit mathematician Gerolamo Saccheri, was published in Milan in 1733. In it, Saccheri attempted to reform elementary geometry in two important directions: a demonstration of the famous Parallel Postulate and the theory of proportions. Both topics were of pivotal importance in the mathematics of the...
Leibniz and the Structure of Sciences
The book offers a collection of essays on various aspects of Leibniz’s scientific thought, written by historians of science and world-leading experts on Leibniz. The essays deal with a vast array of topics on the exact sciences: Leibniz’s logic, mereology, the notion of infinity and cardinality, the foundations of geometry, the theory of curves and differential geometry, and finally dynamics and general epistemology. Several chapters attempt a reading of Leibniz’s scientific works through modern mathematical tools, and compare Leibniz’s results in these fields with 19th- and 20th-Century conceptions of them. All of them have special care in framing Leibniz’s work in historical context, and sometimes offer wider historical perspectives that go much beyond Leibniz’s researches. A special emphasis is given to effective mathematical practice rather than purely epistemological thought. The book is addressed to all scholars of the exact sciences who have an interest in historical research and Leibniz in particular, and may be useful to historians of mathematics, physics, and epistemology, mathematicians with historical interests, and philosophers of science at large.
Geometry and Monadology
This book reconstructs, from both historical and theoretical points of view, Leibniz’s geometrical studies, focusing in particular on the research Leibniz carried out in his final years. The work’s main purpose is to offer a better understanding of the philosophy of space and in general of the mature Leibnizean metaphysics. This is the first ever, comprehensive historical reconstruction of Leibniz’s geometry.
Leibniz on the Parallel Postulate and the Foundations of Geometry
This book offers a general introduction to the geometrical studies of Gottfried Wilhelm Leibniz (1646-1716) and his mathematical epistemology. In particular, it focuses on his theory of parallel lines and his attempts to prove the famous Parallel Postulate. Furthermore it explains the role that Leibniz’s work played in the development of non-Euclidean geometry. The first part is an overview of his epistemology of geometry and a few of his geometrical findings, which puts them in the context of the seventeenth-century studies on the foundations of geometry. It also provides a detailed mathematical and philosophical commentary on his writings on the theory of parallels, and discusses how the...
Mathematizing Space
This book collects the papers of the conference held in Berlin, Germany, 27-29 August 2012, on 'Space, Geometry and the Imagination from Antiquity to the Modern Age'. The conference was a joint effort by the Max Planck Institute for the History of Science (Berlin) and the Centro die Ricerca Matematica Ennio De Giorgi (Pisa).
Thinking and Calculating
This volume collects 22 essays on the history of logic written by outstanding specialists in the field. The book was originally prompted by the 2018-2019 celebrations in honor of Massimo Mugnai, a world-renowned historian of logic, whose contributions on Medieval and Modern logic, and to the understanding of the logical writings of Leibniz in particular, have shaped the field in the last four decades. Given the large number of recent contributions in the history of logic that have some connections or debts with Mugnai’s work, the editors have attempted to produce a volume showing the vastness of the development of logic throughout the centuries. We hope that such a volume may help both the...
Leibniz's Science of the Rational
This book explicates Leibnizian analysis as a search for conditions of intelligibility, and reconsiders his use of principles and methods as well as his account of truth in this way. Via careful reading of well-known, lesser known, and previously unedited texts, it gives a more accurate picture of his philosophical intentions, as well as the relevance of his project to contemporary debate. Two case studies are included, one concerning logic and the other arithmetic; they illustrate a theory of intelligibility that takes as its central notion "possibility for thought", a notion which allows Leibniz to escape certain traps of psychologism, the pseudo-ontology of empiricism, and the empty forms of logicism, and suggests new approaches for contemporary philosophy. "In this remarkable study, Grosholz and Yakira offer a fresh interpretive and conceptual angle on Leibniz's metaphysics. [...] this study deserves high marks for its subtlety, novelty, and creative insight into Leibniz's modes of inquiry as well as for its philosophical acumen." Annals of Science
Handbook of Research on Advanced Research Methodologies for a Digital Society
Doing research is an ever-changing challenge for social scientists. This challenge is harder than ever today as current societies are changing quickly and in many, sometimes conflicting, directions. Social phenomena, personal interactions, and formal and informal relationships are becoming more borderless and disconnected from the anchors of the offline “reality.” These dynamics are heavily marking our time and are suggesting evolutionary challenges in the ways we know, interpret, and analyze the world. Internet and computer-mediated communication (CMC) is being incorporated into every aspect of daily life, and social life has been deeply penetrated by the internet. This is due to recent...
Leibniz on Time, Space, and Relativity
In this book, Arthur gives fresh interpretations of Gottfried Leibniz's theories of time, space, and the relativity of motion, based on a thorough examination of Leibniz's manuscripts as well as his published papers. These are analysed in historical context, but also with an eye to their contemporary relevance. Leibniz's views on relativity have been extremely influential, first on Mach, and then on Einstein, while his novel approach to geometry in his analysis situs inspired many later developments in geometry. Arthur expounds the latter in some detail, explaining its relationship to Leibniz's metaphysics of space and the grounding of motion, and defending Leibniz's views on the relativity ...
