This volume contains essays that examine infinity in early modern philosophy. The essays not only consider the ways that key figures viewed the concept. They also detail how these different beliefs about infinity influenced major philosophical systems throughout the era. These domains include mathematics, metaphysics, epistemology, ethics, science, and theology. Coverage begins with an introduction that outlines the overall importance of infinity to early modern philosophy. It then moves from a general background of infinity (before early modern thought) up through Kant. Readers will learn about the place of infinity in the writings of key early modern thinkers. The contributors profile the work of Descartes, Spinoza, Leibniz, and Kant. Debates over infinity significantly influenced philosophical discussion regarding the human condition and the extent and limits of human knowledge. Questions about the infinity of space, for instance, helped lead to the introduction of a heliocentric solar system as well as the discovery of calculus. This volume offers readers an insightful look into all this and more. It provides a broad perspective that will help advance the present state of knowledge on this important but often overlooked topic.

Philosophy begins with wonder, according to Plato and Aristotle. Yet Plato and Aristotle did not expand a great deal on what precisely wonder is. Does this fact alone not raise curiosity in us as to why this passion or concept is important? What is wonder's role in science, philosophy, or theology except to end thinking or theorizing as soon as one begins? The primary purpose of this book is to show how seventeenth- and eighteenth-century developments in natural theology, metaphysics, epistemology, ethics, aesthetics, and the philosophy of science resulted in a complex history of the passion of wonder-a history in which the elements of continuation, criticism, and reformulation are equally present. Philosophy Begins in Wonder provides the first historical overview of wonder and changes the way we see early modern Europe. It is intended for readers who are curious-who wonder-about how modern philosophy and science were born. The book is for scholars and educated readers alike.

This book offers a comprehensive treatment of the philosophical system of the seventeenth-century philosopher Pierre Gassendi. Gassendi's importance is widely recognized and is essential for understanding early modern philosophers and scientists such as Locke, Leibniz and Newton. Offering a systematic overview of his contributions, LoLordo situates Gassendi's views within the context of sixteenth- and early seventeenth-century natural philosophy as represented by a variety of intellectual traditions, including scholastic Aristotelianism, Renaissance Neo-Platonism, and the emerging mechanical philosophy. LoLordo's work will be essential reading for historians of early modern philosophy and science.

The Actual and the Possible presents new essays by leading specialists on modality and the metaphysics of modality in the history of modern philosophy from the seventeenth to the twentieth centuries. It revisits key moments in the history of modern modal doctrines, and illuminates lesser-known moments of that history. The ultimate purpose of this historical approach is to contextualise and even to offer some alternatives to dominant positions within the contemporary philosophy of modality. Hence the volume contains not only new scholarship on the early-modern doctrines of Baruch Spinoza, G. W. F. Leibniz, Christian Wolff and Immanuel Kant, but also work relating to less familiar nineteenth-century thinkers such as Alexius Meinong and Jan Lukasiewicz, together with essays on celebrated nineteenth- and twentieth-century thinkers such as G. W. F. Hegel, Martin Heidegger and Bertrand Russell, whose modal doctrines have not previously garnered the attention they deserve. The volume thus covers a variety of traditions, and its historical range extends to the end of the twentieth century, addressing the legacy of W. V. Quine's critique of modality within recent analytic philosophy.

"The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite." - David Hilbert This interdisciplinary study of infinity explores the concept through the prism of mathematics and then offers more expansive investigations in areas beyond mathematical boundaries to reflect the broader, deeper implications of infinity for human intellectual thought. More than a dozen world‐renowned researchers in the fields of mathematics, physics, cosmology, philosophy, and theology offer a rich intellectual exchange among various current viewpoints, rather than displaying a static picture of accepted views on infinity. The book starts with a historical examination of the transformation of infinity from a philosophical and theological study to one dominated by mathematics. It then offers technical discussions on the understanding of mathematical infinity. Following this, the book considers the perspectives of physics and cosmology: Can infinity be found in the real universe? Finally, the book returns to questions of philosophical and theological aspects of infinity.

The book contains popular expositions (accessible to readers with no more than a high school mathematics background) on the mathematical theory of infinity, and a number of related topics. These include G?del's incompleteness theorems and their relationship to concepts of artificial intelligence and the human mind, as well as the conceivability of some unconventional cosmological models. The material is approached from a variety of viewpoints, some more conventionally mathematical and others being nearly mystical. There is a brief account of the author's personal contact with Kurt G?del.An appendix contains one of the few popular expositions on set theory research on what are known as "strong axioms of infinity."

Anne Conway, Viscountess Conway (1631-1679), nee Finch, was an English philosopher whose work, in the tradition of the Cambridge Platonists, was an influence on Leibniz. She became interested in the Lurianic Kabbalah, and then in Quakerism, to which she converted in 1677. In England at that time the Quakers were generally disliked and feared, and suffered persecution and even imprisonment. Conway's decision to convert, to make her house a centre for Quaker activity, and to proselytise actively was thus particularly bold and courageous. Her life from the age of twelve (when she suffered a period of fever) was marked by the recurrence of severe migraines. These meant that she was often incapacitated by pain, and she spent much time under medical supervision and trying various cures (at one point even having her "jugular arteries" opened). None of the treatments had any effect, and she died in 1679 at the age of forty-seven.

The Passion of Infinity generates a historical narrative surrounding the concept of the irrational as a threat which rational culture has made a series of attempts to understand and relieve. It begins with a reading of Sophocles' Oedipus as the paradigmatic figure of a reason that, having transgressed its mortal limit, becomes catastrophically reversed. It then moves through Aristotle's ethics, psychology and theory of tragedy, which redefine reason's collapses in moral-psychological rather than religious terms. By changing the way in which the irrational is conceived, and the nature of its relation to reason, Aristotle eliminates the concept of an irrationality which reason cannot in principle dissolve. The book culminates in an extensive reading of Kierkegaard's pseudonyms, who, in a critical retrieval of both Greek tragedy and Aristotle, prescribe their apparently pathological age a paradoxical task: develop a finite form of subjectivity willing to undergo an unthinkable thought ‐ allow the transcendence of a god to enter into the mind as well as the marrow, to make a tragic appearance in which a limit to the immanence of human reason can again be established.

We are all captivated and puzzled by the infinite, in its many varied guises; by the endlessness of space and time; by the thought that between any two points in space, however close, there is always another; by the fact that numbers go on forever; and by the idea of an all-knowing, all-powerful God. In this acclaimed introduction to the infinite, A. W. Moore takes us on a journey back to early Greek thought about the infinite, from its inception to Aristotle. He then examines medieval and early modern conceptions of the infinite, including a brief history of the calculus, before turning to Kant and post-Kantian ideas. He also gives an account of Cantor’s remarkable discovery that some infinities are bigger than others. In the second part of the book, Moore develops his own views, drawing on technical advances in the mathematics of the infinite, including the celebrated theorems of Skolem and Gödel, and deriving inspiration from Wittgenstein. He concludes this part with a discussion of death and human finitude. For this third edition Moore has added a new part, ‘Infinity superseded’, which contains two new chapters refining his own ideas through a re-examination of the ideas of Spinoza, Hegel, and Nietzsche. This new part is heavily influenced by the work of Deleuze. Also new for the third edition are: a technical appendix on still unresolved questions about different infinite sizes; an expanded glossary; and updated references and further reading. The Infinite, Third Edition is ideal reading for anyone interested in an engaging and historically informed account of this fascinating topic, whether from a philosophical point of view, a mathematical point of view, or a religious point of view.

Original anthology features less-technical essays discussing logic, topology, abstract algebra, relativity theory, and the works of David Hilbert. Most have been long unavailable or previously unpublished in book form. 2012 edition.