This volume is a critical edition of the ten-year correspondence between Gottfried Wilhelm Leibniz, one of Europe’s most influential early modern thinkers, and Bartholomew Des Bosses, a Jesuit theologian who was keen to bring together Leibniz’s philosophy and the Aristotelian philosophy and religious doctrines accepted by his order. The letters offer crucial insights into Leibniz’s final metaphysics and into the intellectual life of the eighteenth century. Brandon C. Look and Donald Rutherford present seventy-one of Leibniz’s and Des Bosses’s letters in (...) the original Latin and in careful English translation. Few of the letters have been translated into English before. The editors also provide extensive annotations, deletions, and marginalia from Leibniz’s various drafts, and a substantial introduction setting the context for the correspondence and analyzing the main philosophical issues. (shrink)

This brief paper shows how an exact analogue of Einstein's original hole argument can be constructed in the loop representation of quantum gravity. The new argument is based on the embedding of spin-networks in a manifold and the action of the diffeomorphism constraint on them. The implications of this result are then discussed. I argue that the conclusions of many physicists working on loop quantum gravity---Rovelli and Smolin in particular---that the loop representation uniquely supports relationalism are unfounded.

In the New Essays on Human Understanding, Leibniz argues chapter by chapter with John Locke's Essay Concerning Human Understanding, challenging his views about knowledge, personal identity, God, morality, mind and matter, nature versus nurture, logic and language, and a host of other topics. The work is a series of sharp, deep discussions by one great philosopher of the work of another. Leibniz's references to his contemporaries and his discussions of the ideas and institutions of the age make this a fascinating (...) and valuable document in the history of ideas. The work was originally written in French, and the version by Peter Remnant and Jonathan Bennett, based on the only reliable French edition (published in 1962), first appeared in 1981 and has become the standard English translation. It has been thoroughly revised for this series and provided with a new and longer introduction, a chronology on Leibniz's life and career and a guide to further reading. (shrink)

The procedures of canonical quantization of the gravitational field apparently lead to entities for which any interpretation in terms of spatio-temporal localization or spatio-temporal extension seems difficult. This fact is the main ground for the suggestion that can often be found in the physics literature on canonical quantum gravity according to which spacetime may not be fundamental in some sense. This paper aims to investigate this radical suggestion from an ontologically serious point of view in the cases of two standard (...) forms of canonical quantum gravity, quantum geometrodynamics and loop quantum gravity. We start by discussing the physical features of the quantum wave functional of quantum geometrodynamics and of the spin networks of loop quantum gravity that motivate the view according to which spacetime is not fundamental. We then point out that, by contrast, for any known ontologically serious understanding of quantum entanglement, the commitment to spacetime seems indispensable. Against this background, we then critically discuss the idea that spacetime may emerge from more fundamental entities. As a consequence, we finally suggest that the emergence of classical spacetime in canonical quantum gravity faces a dilemma: either spacetime ontologically emerges from more fundamental non-spatio-temporal entities or it already belongs to the fundamental quantum gravitational level and the emergence of the classical picture is merely a matter of levels of description. On the first horn of the dilemma, it is unclear how to make sense of concrete physical entities that are not in spacetime and of the notion of ontological emergence that is involved. The second horn runs into the difficulties raised by the physics of canonical quantum gravity. (shrink)

The procedures of canonical quantization of the gravitational field apparently lead to entities for which any interpretation in terms of spatio-temporal localization or spatio-temporal extension seems difficult. This fact is the main ground for the suggestion that can often be found in the physics literature on canonical quantum gravity according to which spacetime may not be fundamental in some sense. This paper aims to investigate this radical suggestion from an ontologically serious point of view in the cases of two standard (...) forms of canonical quantum gravity, quantum geometrodynamics and loop quantum gravity. We start by discussing the physical features of the quantum wave functional of quantum geometrodynamics and of the spin networks of loop quantum gravity that motivate the view according to which spacetime is not fundamental. We then point out that, by contrast, for any known ontologically serious understanding of quantum entanglement, the commitment to spacetime seems indispensable. Against this background, we then critically discuss the idea that spacetime may emerge from more fundamental entities. As a consequence, we finally suggest that the emergence of classical spacetime in canonical quantum gravity faces a dilemma: either spacetime ontologically emerges from more fundamental non-spatio-temporal entities or it already belongs to the fundamental quantum gravitational level and the emergence of the classical picture is merely a matter of levels of description. On the first horn of the dilemma, it is unclear how to make sense of concrete physical entities that are not in spacetime and of the notion of ontological emergence that is involved. The second horn runs into the difficulties raised by the physics of canonical quantum gravity. (shrink)

Spacetime substantivalism leads to a radical form of indeterminism within a very broad class of spacetime theories which include our best spacetime theory, general relativity. Extending an argument from Einstein, we show that spacetime substantivalists are committed to very many more distinct physical states than these theories' equations can determine, even with the most extensive boundary conditions.

Debates about the ontological implications of the general theory of relativity have long oscillated between spacetime substantivalism and relationism. I evaluate such debates by claiming that we need a third option, which I refer to as “structural spacetime realism.” Such a tertium quid sides with the relationists in defending the relational nature of the spacetime structure, but joins the substantivalists in arguing that spacetime exists, at least in part, independently of particular physical objects and events, the degree of “independence” being (...) given by the extent to which geometrical laws exist “over and above” physical events exemplifying them. By showing that structural spacetime realism is the natural outcome of a semantic, model-theoretic approach to the nature of scientific theories, I conclude by arguing that the notion of partial isomorphic representation is the most plausible candidate to connect spacetime models with reality. (shrink)

Adams presents an in-depth interpretation of three important parts of Leibniz's metaphysics, thoroughly grounded in the texts as well as in philosophical analysis and critique. The three areas discussed are the metaphysical part of Leibniz's philosophy of logic, his essentially theological treatment of the central issues of ontology, and his theory of substance. Adams' work helps make sense of one of the great classic systems of modern philosophy.

The most obvious thing about the universe in which we find ourselves is its structure. Before the scientific revolution, the instinctive reaction of thinkers to the existence of perceived structure was to find a direct reason for that structure. This is reflected above all in the Pythagorean notion of the well-ordered cosmos: the cosmos has the structure it does because that is the best structure it could have. In fact, that is what the word cosmos really means—primarily order, but also (...) decoration, embellishment, or dress. Kepler and Galileo were no less entranced by the beauty of the world than was Pythagoras, and they formulated their ideas in the overall conceptual framework of the well-ordered cosmos. However, both studied the world so intently that they actually identified aspects of motion that fairly soon led to the complete overthrow of such a notion of cosmos. The laws of the new physics were found to determine not the actual structure of the universe, but the way in which structure changes from instant to instant. Ultimately, no explanation is provided for the currently observed structure; it is simply attributed to an initial structure that was never fashioned by the laws of nature but merely continually refashioned thereafter. The initial and boundary conditions for our universe lie outside the purview of science. But all of the structure we observe around us must ultimately be traced back to those mysterious initial and boundary conditions. (shrink)

Although Leibniz's writing forms an enormous corpus, no single work stands as a canonical expression of his whole philosophy. In addition, the wide range of Leibniz's work--letters, published papers, and fragments on a variety of philosophical, religious, mathematical, and scientific questions over a fifty-year period--heightens the challenge of preparing an edition of his writings in English translation from the French and Latin.

These are just some of the fundamental questions addressed in Time and Space. Writing for a primary readership of advanced undergraduate and graduate philosophy students, Barry Dainton introduces the central ideas and arguments that make space and time such philosophically challenging topics. Although recognising that many issues in the philosophy of time and space involve technical features of physics, Dainton has been careful to keep the conceptual issues accessible to students with little scientific or mathematical training. Surveying historical debates and (...) ideas at the forefront of contemporary thinking, the book is unrivaled in its coverage. Topics include McTaggart's argument for the unreality of change; static, tensed, and dynamic time; time travel and causal arrows; space as void, motion, and curved spac; as well as a non-technical introduction to the special theory of relativity and the key features of general relativity, spacetime, and strings. Dainton also addresses the relationship between the philosophy of time and broader human concerns involving actions, ethics, fatalism, and death. (shrink)

Volumes I and II provided a completely new translation of the philosophical works of Descartes, based on the best available Latin and French texts. Volume III contains 207 of Descartes' letters, over half of which have previously not been translated into English. It incorporates, in its entirety, Anthony Kenny's celebrated translation of selected philosophical letters, first published in 1970. In conjunction with Volumes I and II it is designed to meet the widespread demand for a comprehensive, authoritative and accurate edition (...) of Descartes' philosophical writings in clear and readable modern English. (shrink)

Quantum gravity poses the problem of merging quantum mechanics and general relativity, the two great conceptual revolutions in the physics of the twentieth century. The loop and spinfoam approach, presented in this book, is one of the leading research programs in the field. The first part of the book discusses the reformulation of the basis of classical and quantum Hamiltonian physics required by general relativity. The second part covers the basic technical research directions. Appendices include a detailed history of the (...) subject of quantum gravity, hard-to-find mathematical material, and a discussion of some philosophical issues raised by the subject. This fascinating text is ideal for graduate students entering the field, as well as researchers already working in quantum gravity. It will also appeal to philosophers and other scholars interested in the nature of space and time. (shrink)

Sir Isaac Newton (1642-1727) left a voluminous legacy of writings. Despite his influence on the early modern period, his correspondence, manuscripts, and publications in natural philosophy remain scattered throughout many disparate editions. In this volume, Newton's principal philosophical writings are for the first time collected in a single place. They include excerpts from the Principia and the Opticks, his famous correspondence with Boyle and with Bentley, and his equally significant correspondence with Leibniz, which is often ignored in favor of Leibniz's (...) later debate with Samuel Clarke. Newton's exchanges with Leibniz place their different understandings of natural philosophy in sharp relief. The volume also includes 'De Gravitatione', offered here in a corrected translation, which is crucial for understanding Newton's relation to his great predecessor Descartes. In a historical and philosophical introduction, Andrew Janiak examines Newton's philosophical positions and his relations to canonical figures in early modern philosophy. (shrink)

Gordon Belot investigates the distinctive notion of geometric possibility that relationalists rely upon. He examines the prospects for adapting to the geometric case the standard philosophical accounts of the related notion of physical possibility, with particular emphasis on Humean, primitivist, and necessitarian accounts of physical and geometric possibility. This contribution to the debate concerning the nature of space will be of interest not only to philosophers and metaphysicians concerned with space and time, but also to those interested in laws of (...) nature, modal notions, or more general issues in ontology. (shrink)

The Philosophical Writings of Descartes VOLUME 3. Volumes 1 and 2 provide a completely new translation of many of the major works in metaphysics, epistemology, and natural philosophy.

Daniel Garber presents a study of Leibniz's conception of the physical world, elucidating his puzzling metaphysics of monads, mind-like simple substances.

This is the most up-to-date and comprehensive interpretation of the philosophy of Gottfried Wilhelm Leibniz. Amongst its other virtues, it makes considerable use of unpublished manuscript sources. The book seeks to demonstrate the systematic unity of Leibniz's thought, in which theodicy, ethics, metaphysics and natural philosophy cohere. The key, underlying idea of the system is the conception of nature as an order designed by God to maximise the opportunities for the exercise of reason. From this idea emerges the view that (...) this world is the best of all possible worlds, and an ethical ideal in which the well-being of human beings is promoted through the gradual extension of intellectual enlightenment. (shrink)

The primary objective of this study is to provide a description of the major ideas about void space within and beyond the world that were formulated between the fourteenth and early eighteenth centuries. The second part of the book - on infinite, extracosmic void space - is of special significance. The significance of Professor Grant's account is twofold: it provides the first comprehensive and detailed description of the scholastic Aristotelian arguments for and against the existence of void space; and it (...) presents (again for the first time) an analysis of the possible influence of scholastic ideas and arguments on the interpretations of space proposed by the nonscholastic authors who made the Scientific Revolution possible. The concluding chapter of the book is unique in not only describing the conceptualizations of space proposed by the makers of the Scientific Revolution, but in assessing the role of readily available scholastic ideas on the conception of space adopted for the Newtonian world. (shrink)

Letter to du Faur de Pibrac, 1621.--Exercises against the Aristotelians, 1624.--Letter to Diodati, 1634.--De motu, 1642.--The rebuttals against Descartes, 1644.--The syntagma, 1658.

It generally agreed that the requirement of formal general covariance is a condition of the well-formedness of a spacetime theory and not a restriction on its content. Physicists commonly take the substantive requirement of general covariance to mean that the laws exhibit diffeomorphism invariance and that this invariance is a gauge symmetry. This latter requirement does place restrictions on the content of a spacetime theory. The present paper explores the implications of these restrictions for interpreting the ideology and ontology of (...) classical general relativity theory and loop quantum gravity. (shrink)

The conceptual incompatibility between General Relativity and Quantum Mechanics is generally seen as a sufficient motivation for the development of a theory of Quantum Gravity. If - so a typical argumentation - Quantum Mechanics gives a universally valid basis for the description of the dynamical behavior of all natural systems, then the gravitational field should have quantum properties, like all other fundamental interaction fields. And, if General Relativity can be seen as an adequate description of the classical aspects of gravity (...) and spacetime - and their mutual relation -, this leads, together with the rather convincing arguments against semi-classical theories of gravity, to a strategy which takes a quantization of General Relativity as the natural avenue to a theory of Quantum Gravity. And, because in General Relativity the gravitational field is represented by the spacetime metric, a quantization of the gravitational field would in some sense correspond to a quantization of geometry. Spacetime would have quantum properties. But, this direct quantization strategy to Quantum Gravity will only be successful, if gravity is indeed a fundamental interaction. Only if it is a fundamental interaction, the given argumentation is valid, and the gravitational field, as well as spacetime, should have quantum properties. - What, if gravity is instead an intrinsically classical phenomenon? Then, if Quantum Mechanics is nevertheless fundamentally valid, gravity can not be a fundamental interaction; a classical and at the same time fundamental gravity is excluded by the arguments against semi-classical theories of gravity. An intrinsically classical gravity in a quantum world would have to be an emergent, induced or residual, macroscopic effect, caused by a quantum substrate dominated by other interactions, not by gravity. Then, the gravitational field (as well as spacetime) would not have any quantum properties. And then, a quantization of gravity (i.e. of General Relativity) would lead to artifacts without any relation to nature. The serious problems of all approaches to Quantum Gravity that start from a direct quantization of General Relativity (e.g. non-perturbative canonical quantization approaches like Loop Quantum Gravity) or try to capture the quantum properties of gravity in form of a 'graviton' dynamics (e.g. Covariant Quantization, String Theory) - together with the, meanwhile, rich spectrum of (more or less advanced) theoretical approaches to an emergent gravity and/or spacetime - make this latter option more and more interesting for the development of a theory of Quantum Gravity. The most advanced emergent gravity (and spacetime) scenarios are of an information-theoretical, quantum-computational type. A paradigmatic model for the emergence of gravity and spacetime comes from the Pregeometric Quantum Causal Histories approach. (shrink)

We survey some philosophical aspects of the search for a quantum theory of gravity, emphasising how quantum gravity throws into doubt the treatment of spacetime common to the two `ingredient theories' (quantum theory and general relativity), as a 4-dimensional manifold equipped with a Lorentzian metric. After an introduction (Section 1), we briefly review the conceptual problems of the ingredient theories (Section 2) and introduce the enterprise of quantum gravity (Section 3). We then describe how three main research programmes in quantum (...) gravity treat four topics of particular importance: the scope of standard quantum theory; the nature of spacetime; spacetime diffeomorphisms, and the so-called `problem of time' (Section 4). These programmes are the old particle-physics approach, superstring theory, and canonical quantum gravity. By and large, these programmes accept most of the ingredient theories' treatment of spacetime, albeit with a metric with some type of quantum nature; but they also suggest that the treatment has fundamental limitations. This prompts the idea of going further: either by quantizing structures other than the metric, such as the topology; or by regarding such structures as phenomenological. We discuss this in Section 5. (shrink)

This is a contribution to a book on quantum gravity and philosophy. I discuss nature and origin of the problem of quantum gravity. I examine the knowledge that may guide us in addressing this problem, and the reliability of such knowledge. In particular, I discuss the subtle modification of the notions of space and time engendered by general relativity, and how these might merge into quantum theory. I also present some reflections on methodological questions, and on some general issues in (...) philosophy of science which are are raised by, or a relevant for, the research on quantum gravity. (shrink)