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.
The year 2012 marks the 50th anniversary of the publication of Thomas S. Kuhn’s The Structure of Scientific Revolutions. Up until recently, the book’s philosophical reception has been shaped, for the most part, by the debates and the climate in philosophy of science in the 1960s and 1970s; this new collection of essays takes a renewed look at this work. This volume concentrates on particular issues addressed or raised in light of recent scholarship and without the pressure of the immediate concerns scholars had at the time of the Structure’s publication. There has been extensive research on all of the major issues concerning the development of science which are discussed in Structure, work in which the scholars contributing to this volume have all been actively involved. In recent years they have pursued novel research on a number of topics relevant to Structure’s concerns, such as the nature and function of concepts, the complexity of logical positivism and its legacy, the relation of history to philosophy of science, the character of scientific progress and rationality, and scientific realism, all of which are brought together and given new light in this text. In this way, our book makes new connections and undertakes new approaches in an effort to understand the Structure’s significance in the canon of philosophy of science.
Leibniz Algebras: Structure and Classification is designed to introduce the reader to the theory of Leibniz algebras. Leibniz algebra is the generalization of Lie algebras. These algebras preserve a unique property of Lie algebras that the right multiplication operators are derivations. They first appeared in papers of A.M Blokh in the 1960s, under the name D-algebras, emphasizing their close relationship with derivations. The theory of D-algebras did not get as thorough an examination as it deserved immediately after its introduction. Later, the same algebras were introduced in 1993 by Jean-Louis Loday , who called them Leibniz algebras due to the identity they satisfy. The main motivation for the introduction of Leibniz algebras was to study the periodicity phenomena in algebraic K-theory. Nowadays, the theory of Leibniz algebras is one of the more actively developing areas of modern algebra. Along with (co)homological, structural and classification results on Leibniz algebras, some papers with various applications of the Leibniz algebras also appear now. However, the focus of this book is mainly on the classification problems of Leibniz algebras. Particularly, the authors propose a method of classification of a subclass of Leibniz algebras based on algebraic invariants. The method is applicable in the Lie algebras case as well. Features: Provides a systematic exposition of the theory of Leibniz algebras and recent results on Leibniz algebras Suitable for final year bachelor's students, master's students and PhD students going into research in the structural theory of finite-dimensional algebras, particularly, Lie and Leibniz algebras Covers important and more general parts of the structural theory of Leibniz algebras that are not addressed in other texts
In recent decades, there has been much scholarly controversy as to the basic ontological commitments of the philosopher Gottfried Wilhelm Leibniz (1646-1716). The old picture of his thought as strictly idealistic, or committed to the ultimate reduction of bodies to the activity of mind, has come under attack, but Leibniz's precise conceptualization of bodies, and the role they play in his system as a whole, is still the subject of much controversy. One thing that has become clear is that in order to understand the nature of body in Leibniz, and the role body plays in his philosophy, it is crucial to pay attention to the related concepts of organism and of corporeal substance, the former being Leibniz's account of the structure of living bodies (which turn out, for him, to be the only sort of bodies there are), and the latter being an inheritance from the Aristotelian hylomorphic tradition which Leibniz appropriates for his own ends. This volume brings together papers from many of the leading scholars of Leibniz's thought, all of which deal with the cluster of questions surrounding Leibniz's philosophy of body.
In his well-known Discourse on Metaphysics, Leibniz puts individual substance at the basis of metaphysical building. In so doing, he connects himself to a venerable tradition. His theory of individual concept, however, breaks with another idea of the same tradition, that no account of the individual as such can be given. Contrary to what has been commonly accepted, Leibniz’s intuitions are not the mere result of the transcription of subject-predicate logic, nor of the uncritical persistence of some old metaphysical assumptions. They grow, instead, from an unprejudiced inquiry about our basic ontological framework, where logic of truth, linguistic analysis, and phenomenological experience of the mind’s life are tightly interwoven. Leibniz’s struggle for a concept capable of grasping concrete individuals as such is pursued in an age of great paradigm changes – from the Scholastic background to Hobbes’s nominalism to the Cartesian ‘way of ideas’ or Spinoza’s substance metaphysics – when the relationships among words, ideas and things are intensively discussed and wholly reshaped. This is the context where the genesis and significance of Leibniz’s theory of ‘complete being’ and its concept are reconstrued. The result is a fresh look at some of the most perplexing issues in Leibniz scholarship, like his ideas about individual identity and the thesis that all its properties are essential to an individual. The questions Leibniz faces, and to which his theory of individual substance aims to answer, are yet, to a large extent, those of contemporary metaphysics: how to trace a categorial framework? How to distinguish concrete and abstract items? What is the metaphysical basis of linguistic predication? How is trans-temporal sameness assured? How to make sense of essential attributions? In this ontological framework Leibniz’s further questions about the destiny of human individuals and their history are spelt out. Maybe his answers also have something to tell us. This book is aimed at all who are interested in Leibniz’s philosophy, history of early modern philosophy and metaphysical issues in their historical development.
Leibniz’s metaphysics of space and time stands at the centre of his philosophy and is one of the high-water marks in the history of the philosophy of science. In this work, Futch provides the first systematic and comprehensive examination of Leibniz’s thought on this subject. In addition to elucidating the nature of Leibniz’s relationalism, the book fills a lacuna in existing scholarship by examining his views on the topological structure of space and time, including the unity and unboundedness of space and time. It is shown that, like many of his more recent counterparts, Leibniz adopts a causal theory of time where temporal facts are grounded on causal facts, and that his approach to time represents a precursor to non-tensed theories of time. Futch then goes on to situate Leibniz’s philosophy of space and time within the broader context of his idealistic metaphysics and natural theology. Emphasizing the historical background of Leibniz’s thought, the book also places him in dialogue with contemporary philosophy of science, underscoring the enduring philosophical interest of Leibniz’s metaphysics of time and space.
Professor Pandit, working among the admirable group of philosophers at the University of Delhi, has written a fundamental criticism and a constructive re-interpretation of all that has been preserved as serious epistemological and methodological reflections on the sciences in modern Western philosoph- from the times of Galileo, Newton, Descartes and Leibniz to those of Russell and Wittgenstein, Carnap and Popper, and, we need hardly add, onward to the troubling relativisms and reconstructions of historical epistemologies in the works of Hanson, Kuhn, Lakatos and Feyerabend. His themes are intrigu ing, set forth as they are with masterly case studies of physics and the life sciences, and within an original conceptual framework for philosophical analysis of the processes, functions, and structures of scientific knowing. Pandit's contributions deserve thoughtful examination. For our part, we wish to point to some among them: (1) an interactive articulation of subjective and objective factors of both problems and theories in the course of scientific development; (2) a striking contrast between the explanatory power of a scientific theory and its 'resolving power', i. e.
The selections contained in these volumes from the papers and letters of Leibniz are intended to serve the student in two ways: first, by providing a more adequate and balanced conception of the full range and penetration of Leibniz's creative intellectual powers; second, by inviting a fresher approach to his intellectual growth and a clearer perception of the internal strains in his thinking, through a chronological arrangement. Much confusion has arisen in the past through a neglect of the develop ment of Leibniz's ideas, and Couturat's impressive plea, in his edition of the Opuscu/es et fragments (p. xii), for such an arrangement is valid even for incomplete editions. The beginning student will do well, however, to read the maturer writings of Parts II, III, and IV first, leaving Part I, from a period too largely neglected by Leibniz criticism, for a later study of the still obscure sources and motives of his thought. The Introduction aims primarily to provide cultural orientation and an exposition of the structure and the underlying assumptions of the philosophical system rather than a critical evaluation. I hope that together with the notes and the Index, it will provide those aids to the understanding which the originality of Leibniz's scientific, ethical, and metaphysical efforts deserve.
Identifies the philosophical problems that science raises through an examination of questions about its nature, methods and justification. A valuable introduction for science and philosophy students alike.
The philosophy of science has lost its self-confidence, witness the lack of advanced textbooks in contrast to the abundance of elementary textbooks. Structures in Science is an advanced textbook that explicates, updates, accommodates, and integrates the best insights of logical-empiricism and its main critics. This `neo-classical approach' aims at providing heuristic patterns for research. The book introduces four ideal types of research programs (descriptive, explanatory, design, and explicative) and reanimates the distinction between observational laws and proper theories. It explicates various patterns of explanation by subsumption and specification as well as structures in reductive and other types of interlevel research. Its analysis of theory evaluation leads to new characterizations of confirmation, empirical progress, and pseudoscience. Partial analogies between progress in nomological research (i.e. observational, referential, and theoretical truth approximation, presented in detail in From Instrumentalism to Constructive Realism, 2000) and progress in explicative and design research emerge. Finally, special chapters are devoted to design research programs, computational philosophy of science, the structuralist approach to theories, and research ethics.
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
Anapolitanos critically examines and evaluates three basic characteristics of the Leibnizian metaphysical system: Leibniz's version of representation; the principle of continuity; and space, time, and the phenomenally spatio-temporal. Chapter I discusses representation, especially as it refers to the connection between the real and the phenomenal levels of Leibniz's system. Chapter II examines the principle of continuity, including continuity as a general feature of every level of Leibniz's metaphysics. The position adopted is that the problem of the composition of the continuum played a central role on the development of Leibniz's non-spatial and non-temporal monadic metaphysics. The machinery developed is then used to offer a new interpretation of Leibniz' metaphysics of space and time. The notion of indirect representation is used to construct appropriate models that clarify the nature of the correspondence between the real and the phenomenal levels in the case of the relations `spatially between' and `temporally between', as well as in the cases of spatial and temporal density. Finally, Leibniz's solution to the problem of the continuum is discussed, arguing that it is not entirely satisfactory. A non-anachronistic alternative is proposed, compatible with Leibniz's metaphysics of substance.
This addresses the transformations of metaphysics as a discipline, the emergence of analytical mechanics, the diverging avenues of 18th-century Newtonianism, the body-mind problem, and philosophical principles of classification in the life sciences. An appendix contains a critical edition and first translation into English of Newton's scholia from David Gregory's Estate on the Propositions IV through IX Book III of his Principia.
The present volume advances a recent historiographical turn towards the intersection of early modern philosophy and the life sciences by bringing together many of its leading scholars to present the contributions of important but often neglected figures, such as Ralph Cudworth, Nehemiah Grew, Francis Glisson, Hieronymus Fabricius ab Aquapendente, Georg Ernst Stahl, Juan Gallego de la Serna, Nicholas Hartsoeker, Henry More, as well as more familiar figures such as Descartes, Spinoza, Leibniz, Malebranche, and Kant. The contributions to this volume are organized in accordance with the particular problems that living beings and living nature posed for early modern philosophy: the problem of life in general, whether it constitutes something ontologically distinct at all, or whether it can ultimately be exhaustively comprehended "in the same manner as the rest"; the problem of the structure of living beings, by which we understand not just bare anatomy but also physiological processes such as irritability, motion, digestion, and so on; the problem of generation, which might be included alongside digestion and other vital processes, were it not for the fact that it presented such an exceptional riddle to philosophers since antiquity, namely, the riddle of coming-into-being out of -- apparent or real -- non-being; and, finally, the problem of natural order.
The Bloomsbury Companion to Leibniz presents a comprehensive and authoritative introduction to the life, thought and work of one of the great polymaths of the modern world, G.W. Leibniz. This guide enriches the reader's understanding of Leibniz by establishing the philosophies of, and Leibniz's reactions to, his most important philosophical contemporaries from Descartes to Malebranche. While addressing current philosophical research in Leibniz studies such as his metaphysics, logic and theory of free will, a leading team of experts in the field demonstrate that Leibniz's work was wider in scope. Examining new directions in this field they cover a number of Leibniz's concerns outside of philosophy including mathematics, physics, and the life sciences. The Companion concludes by offering analysis of Leibniz's legacy; his impact on further study, particularly on his successor Immanuel Kant, and how he has subsequently been understood. Together with extended biographical sketches and an up-to-date and fully comprehensive bibliography, The Bloomsbury Companion to Leibniz is an extremely valuable study tool for students and scholars interested in Leibniz and the era in which he wrote.
The impressive record of Italian philosophical research since the end of Fascism thirty-two years ago is shown in many fields: esthetics, social and" personal ethics, history and sociology of philosophy, and magnificently, perhaps above all, in logic, foundations of mathematics and the philosophY, methodology, and intellectual history ofthe empirical sciences. To our pleasure, Maria Luisa Dalla Chiara of the University of Florence gladly agreed to assemble a 'sampler' of recent Italian logical and analytical work on the philosophical foundations of mathematics and physics, along with a number of historical studies of epistemological and mathematical concepts. The twenty-five essays that form this volume will, we expect, encourage English-reading philosophers and scientists to seek further works by these authors and by their teachers, colleagues, and students; and, we hope, to look for those other Italian currents of thought in the philosophy of science for which points of departure are not wholly analytic, and which also deserve study and recognition in the world wide philosophical community. Of course, Italy has long been related to that world community in scien titlc matters.
While we are commonly told that the distinctive method of mathematics is rigorous proof, and that the special topic of mathematics is abstract structure, there has been no agreement among mathematicians, logicians, or philosophers as to just what either of these assertions means. John P. Burgess clarifies the nature of mathematical rigor and of mathematical structure, and above all of the relation between the two, taking into account some of the latest developments in mathematics, including the rise of experimental mathematics on the one hand and computerized formal proofs on the other hand. The main theses of Rigor and Structure are that the features of mathematical practice that a large group of philosophers of mathematics, the structuralists, have attributed to the peculiar nature of mathematical objects are better explained in a different way, as artefacts of the manner in which the ancient ideal of rigor is realized in modern mathematics. Notably, the mathematician must be very careful in deriving new results from the previous literature, but may remain largely indifferent to just how the results in the previous literature were obtained from first principles. Indeed, the working mathematician may remain largely indifferent to just what the first principles are supposed to be, and whether they are set-theoretic or category-theoretic or something else. Along the way to these conclusions, a great many historical developments in mathematics, philosophy, and logic are surveyed. Yet very little in the way of background knowledge on the part of the reader is presupposed.
The traditional topics of the "philosophy of nature" — space, time, causality, the structure of the universe — are overwhelmingly present in our modern scientific theories. This book traces the complex paths that discussion of these topics has followed, from Plato and Aristotle, through Descartes, Leibniz, Kant and other great thinkers, right up to the relativistic cosmologies and the grand unified theories of contemporary science. In the light of this historical development, it becomes clear that modern science gives us not only a technological power over the world, but also a deeper understanding of physical reality. In this sense, science could be regarded as an heir to the traditional "philosophy of nature". Moreover, the reader will learn why science itself deserves to be the subject of philosophical reflection.
Philonous: You see, Hylas, the water of yonder fountain, how it is forced upwards, in a round column, to a certain height, at which it breaks and falls back into the basin from whence it rose, its ascent as well as descent proceeding from the same uniform law or principle of gravitation. Just so, the same principles which at first view, lead to skepticism, pursued to a certain point, bring men back to common 1 sense. Although major works on Berkeley have considered his Philosophy of 1 George Berkeley, Three Dialogues Between Hylas and Philonous, ed. Colin Murray Turbayne, (third and final edition; London 1734); (New York: The Bobbs Merrill Company, Inc., Library of Liberal Arts, 1965), p. 211. Berkeley, in general, conveniently numbered sections in his works, and in the text of the essay, we will refer if possible to the title and section number. References to the Three Dialogues Between Hylas and Philonous will be also made in the text and refer to the dialogue number and page in the Turbayne edition cited above.
Remembered mainly as a logician and mathematician, Leibniz also endeavored to resolve political and religious conflicts of his day by bringing opponents into negotiation. The dialectical Leibniz who emerges from the texts here translated, commented, and interpreted is certainly not the familiar one. The book sheds new light on the familiar, yet incomplete image of Leibniz, providing further reason for cherishing and cultivating the heritage of a truly great man.