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This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled ‘The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,’ reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity,’ discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincaré, Brouwer, and Weyl. Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry. No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal.
The aim of this book is to critically examine whether it is methodologically possible to combine mathematical rigor – topology with a systematic dialectical methodology in Hegel, and if so, to provide as result of my interpretation the outline of Hegel’s Analysis Situs, also with the proposed models (build on the topological manifold, cobordism, topological data analysis, persistent homology, simplicial complexes and graph theory, to provide an indication of how the merger of Hegel’s dialectical logic and topology may be instrumental to a systematic logician and of how a systematic dialectical logic perspective may help mathematical model builders.
Value pluralism is the idea, most prominently endorsed by Isaiah Berlin, that fundamental human values are universal, plural, conflicting, and incommensurable with one another. Incommensurability is the key component of pluralism, undermining familiar monist philosophies such as utilitarianism. But if values are incommensurable, how do we decide between them when they conflict? George Crowder assesses a range of responses to this problem proposed by Berlin and developed by his successors. Three broad approaches are especially important: universalism, contextualism, and conceptualism. Crowder argues that the conceptual approach is the most fruitful, yielding norms of value diversity, personal autonomy, and inclusive democracy. Historical context must also be taken into account. Together these approaches indicate a liberal politics of redistribution, multiculturalism, and constitutionalism, and a public policy in which basic values are carefully balanced. The Problem of Value Pluralism: Isaiah Berlin and Beyond is a uniquely comprehensive survey of the political theory of value pluralism and also an original contribution by a leading voice in the pluralist literature. Scholars and researchers interested in the work of Berlin, liberalism, value pluralism, and related ideas will find this a stimulating and valuable source.
This volume features the complete text of the material presented at the Twentieth Annual Conference of the Cognitive Science Society. As in previous years, the symposium included an interesting mixture of papers on many topics from researchers with diverse backgrounds and different goals, presenting a multifaceted view of cognitive science. This volume contains papers, posters, and summaries of symposia presented at the leading conference that brings cognitive scientists together to discuss issues of theoretical and applied concern. Submitted presentations are represented in these proceedings as "long papers" (those presented as spoken presentations and "full posters" at the conference) and "short papers" (those presented as "abstract posters" by members of the Cognitive Science Society).
Architectural Philosophy is the first book to outline a philosophical account of architecture and to establish the singularity of architectural practice and theory. This dazzling sequence of essays opens out the subject of architecture, touching on issues as wide ranging as the problem of memory and the dystopias of science fiction. Arguing for the indissolubility of form and function, Architectural Philosophy explores both the definition of the site and the possibility of alterity. The analysis of the nature of the present and the complex sructure of repetition allows for the possibility of judgement, a judgement that arises from a reworked politics of architecture.
What is "Chinese philosophy?" What is "philosophy" itself? How can one understand unfamiliar philosophical stances? How can comparison become a prominent philosophical tool? In this book, Massimiliano Lacertosa examines these questions by proposing an ethical understanding of the aesthetic encounter with the other and the world. Through the analysis of the works of Laozi, Zhuangzi, Nietzsche, and Heidegger, among others, this book explores the possibilities of stepping out of the anthropocentric standpoint and seeing the relation of objects in the world under a different light. This implies a shift from the metaphysical representation of the world divided between the sensible and the supersensible to an aesthetic and undivided experience of the world in which one partakes in the constant transformation of the myriad things. Approachable yet rigorous, this book is essential reading for anyone interested in the most fundamental issues of philosophy and in the challenges of doing philosophy in a multicultural context.
Jean-Luc Nancy is one of the leading voices in European philosophy of the last thirty years, and he has influenced a range of fields, including theology, aesthetics, and political theory. This volume offers the widest and most up-to-date responses to his work, oriented by the themes of world, finitude, and sense, with attention also given to his recent project on the "deconstruction of Christianity." Focusing on Nancy's writings on globalization, Christianity, the plurality of art forms, his materialist ontology, as well as a range of contemporary issues, an international group of scholars provides not just inventive interpretations of Nancy's work but also essays taking on the most pressing issues of today. The collection brings to the fore the originality of his thinking and points to the future of continental philosophy. A previously unpublished interview with Nancy concludes the volume.
This book examines the birth of the scientific understanding of motion. It investigates which logical tools and methodological principles had to be in place to give a consistent account of motion, and which mathematical notions were introduced to gain control over conceptual problems of motion. It shows how the idea of motion raised two fundamental problems in the 5th and 4th century BCE: bringing together being and non-being, and bringing together time and space. The first problem leads to the exclusion of motion from the realm of rational investigation in Parmenides, the second to Zeno's paradoxes of motion. Methodological and logical developments reacting to these puzzles are shown to be present implicitly in the atomists, and explicitly in Plato who also employs mathematical structures to make motion intelligible. With Aristotle we finally see the first outline of the fundamental framework with which we conceptualise motion today.
This book explores the constitutive role alterity plays in identity formation in Western and Eastern traditions. It examines the significance of difference in conceptions of identity across major philosophical and religious traditions in a global and comparative context, considering Ancient Greek and Egyptian, Chinese, Islamic, European and Japanese philosophies. In addition, the book opens up discussion of less dominant trends in philosophical thinking, particularly the spaces between self-same existence and otherness in the histories of philosophical and religious thought. Chapters critique both essentialist and postmodern understandings of self-constitution by questioning the ordinary narrative of identity construction across Western and non-Western traditions. The book also explores the construction of selfhood from a wide range of perspectives, drawing upon individual philosophers (including Plotinus, Descartes, Geulincx, Hume, de Beauvoir and Ueda) as well as religious and philosophical movements, including Confucian philosophy, Zen Buddhism, Protestantism and Post-Phenomenology. Differences in Identity in Philosophy and Religion represents a landmark study, drawing together a range of approaches, perspectives and traditions to explore how identity is constructed across the world.