Nietzsche’s 1873 fragment, the Zeitatomenlehre, posits a temporal conception of action at a distance where space is reduced to a single point and time consists only in a series of discrete atoms. Taken as a physical doctrine that destroys all spatial difference, this conception raises serious conflicts with the rest of his work. I describe and situate this theory within the historical context of debates over action at a distance in nineteenth-century physics, distinguish it from physical theories influential on Nietzsche, (...) and argue that these conflicts can be resolved only by viewing it in the anti-metaphysical phenomenalist and representational terms that he also expressed in his early work. (shrink)

This paper investigates mathematical ideas found in a Jaina non-mathematical text, by which I mean a work not dedicated to mathematics as a separate scholarly discipline. The Aṇuogaddārāiṃ, a Prakrit text from the Śvetāmbara Āgamas, explains the methods a Jaina monk should use in investigating a scriptural text. This work shows a remarkable ability to deal with numerical concepts and quantitative descriptions of all kinds. I shall often compare its mathematical content with texts from different Sanskrit bodies of knowledge. This (...) paper demonstrates that the Aṇuogaddārāiṃ, as well as presenting a wealth of mathematical information, expounds a Jaina theory of numbers that has been so far disregarded by historiography. In order to understand this formulation, I shall propose an analytical-interpretative model to then improve the English translation by Hanaki 1970. In Jainism, the knowledge of the true nature of the universe was a requisite to progressing towards a full awareness of the human condition and hence towards the path of liberation. Numerical data and detailed calculations provide minute descriptions of the universe and matters related to karma and liberation. I shall argue that the Aṇuogaddārāiṃ testifies that mathematics was a perfect, functional instrument for representing Jaina cosmological and soteriological models. (shrink)

Before the discovery of the expanding universe, one of the challenges faced in early relativistic cosmology was the determination of the finite and constant curvature radius of space-time by using astronomical observations. Great interest in this specific question was shown by de Sitter, Silberstein, and Lundmark. Their ideas and methods for measuring the cosmic curvature radius, at that time interpreted as equivalent to the size of the universe, contributed to the development of the empirical approach to relativistic (...) class='Hi'>cosmology. Their works are a noteworthy example of the efforts made by modern cosmologists toward the understanding of the universe as a whole, its properties, and its content. (shrink)

This work focuses on the conception of God of the medieval Jewish philosopher and legal scholar, Hasdai Crescas (1340-1410/11). It demonstrates that Crescas’ God is infinitely creative and good and explores the parallel that Crescas implicitly draws between God as creator and legislator.

pt. 1. Chapters 1-10 and 27-28 -- pt. 2. Chapters 11-26.

This volume presents a critical edition of the final parts of Bate's Speculum, which constitute the culmination of his Platonic-Aristotelian encyclopedia.

In lieu of an abstract, here is a brief excerpt of the content:Transitions to a Modern Cosmology: Meister Eckhart and Nicholas of Cusa on the Intensive InfiniteElizabeth BrientThe Epochal Transition from the late medieval to the early modern world has long been thought in terms of the gradual “infinitization” of the cosmos. Traditionally this process has been studied by focusing on the pre-history and the aftermath of the Copernican revolution, that is, by describing the transition from the finite, (...) hierarchically ordered medieval cosmos to the infinite and homogeneous universe of the new astronomy. I would like to situate this paper within the context of a more general reading of the process of the infinitization of the medieval cosmos. That is, I want to argue that this process of “infinitization” must be understood intensively as well as extensively. Nature, in the modern age, is thought of not only as infinitely extended in space, but also as exhibiting an infinite richness in all of its parts. Each particular, each individual being is grasped as utterly unique, as infinitely rich and consequently as conceptually inexponable. Thus the infinitization of the real leads to an infinitization of the knowable—the radical shift in ontology grounds a corresponding shift in epistemology, so that the progress of human knowledge is understood as an unending project infinitely extended over time. In order to underscore both aspects of the infinitization of the medieval cosmos (intensive as well as extensive) I will focus on the way in which a single metaphor (that of the infinite sphere) is unfolded historically in the thought of Meister Eckhart and Nicholas of Cusa.1 This paper may thus be viewed as a case study of [End Page 575] the way in which the modern notion of “intensive infinity” may be traced back to late medieval speculation on the nature of God’s omnipresence in the world.1. EARLY SOURCES OF THE INFINITE SPHERE METAPHORThe metaphor of the infinite sphere makes its first appearance in the pseudo-Hermetic Liber XXIV philosophorum, a small book in the literary form of an “opus propositionum” which, in twenty-four propositions, describes the ineffable essence of God in the mystical language of Neoplatonic theology. It is in the second proposition of this book that we find for the first time the formulation, “God is an infinite sphere, whose center is everywhere, whose circumference is nowhere.”2 This formulation represents a significant development in the history of the Neoplatonic conception of intensive unity, and in the Christian understanding of divine infinity. The Neoplatonic One is here identified with God as infinite being. As a result the relationship between the One and the many, between God and the world, comes to be viewed in a new light, through the lens of “infinite unity.” The metaphor of the infinite sphere is a paradoxical formulation which pictures the coincidence of divine immanence with divine transcendence. That is, it expresses a double infinity: both intensive and extensive. God’s center is located at every point, as it were, indicating the plenitude and infinite richness of God’s being, while there is no limit, no boundary to the extent of God’s all-encompassing reach. The infinite sphere figures the divine nature as an intensive plenitude without end or bounds. The third and next proposition in this same work goes on to strengthen this sense of divine intensity, by asserting that God in his entirety is present in every part (Deus est totus in quolibet sui). The divine nature is not spread out compositionally, as it were, but is wholly present throughout. Proposition 18 describes God as a sphere which has just as many circumferences as points (Deus est sphaera cuius tot sunt circumferentiae, quot sunt puncta), once again, an exploding image which can only make sense in the case of an infinite sphere. These three propositions taken together provide us with a springboard for considering the nature of infinite unity. The exploding paradox of the infinite sphere [End Page 576] provides a rubric for thinking the coincidence of transcendence and immanence, a way of conceptualizing infinite unity, which cannot be “grasped” with finite concepts or through discursive reasoning. The metaphor of the infinite sphere finds its meaning precisely in the way... (shrink)

Kant’s early essay, Universal Natural History and Theory of the Heavens, is commonly regarded as an original contribution to the development of Newtonian cosmological ideas, and as a step in the evolution of Kant’s own thought. In this paper I try to show, firstly, that despite the recognised debt to Newton’s Principia, the young German thinker makes a personal philosophical synthesis of several ancient and modern sources of cosmological thought; secondly, that besides the novelty of the exposed conjectures about (...) the mechanical production and systematic constitution of the Universe as a whole, and beyond the boldness of the proposed perspectives on the origins and continuous formation or creation of the Cosmos, this essay is also an interesting example of the manner how the young Kant works in such matters as cosmology and cosmogony. There, we can perceive and identify the epistemic presuppositions he puts in action, which are founded in the principle of analogy, used largely as a heuristic principle when the direct observation of phenomena is not possible or the propositions of natural philosophy cannot reach the mathematical precision and geometrical rigour. (shrink)

abstract: In Kephalaia Gnostika, the third part of his great trilogy on the ascetic and contemplative life, the early Christian desert monk Evagrios of Pontus made a statement that resonates with the story told by the Buddha in the Aggañña Sutta. Evagrios declared that there had been a time when evil did not exist, and from this premise, he extrapolated that there will come a time when evil will not exist anymore. Both Evagrios and the Buddha, it seems, were (...) essentially optimistic in their teaching, convinced that despite being subject to a "fall," human beings have agency and can work toward establishing virtue in their lives and experiencing the fruits of this labor. In order to do this, a sophisticated understanding of how the mind works is key, and the two teachers, within the lineaments of the thought worlds of their respective backgrounds, explore what contemplation and meditation offer to this end. They also discuss other qualities that contribute to the development of a "gentle warrior," a character recognizable in both traditions and notable for the level to which they have erased subjectivity and their dedication to the achievement of good outcomes. Evidence can be found in both Buddhist and Christian writings of the recognition of correlations between the structure of the cosmos and spiritual or religious experience. (shrink)

Ian Hacking has defined himself as a philosopher in the analytic tradition. However, he has also recognized the profound influence that Michel Foucault had on much of his work. In this article I analyse the specific imprint of certain works by Foucault—in particular Les mots et les choses—in two of Hacking’s early works: Why Does Language Matter to Philosophy? and The Emergence of Probability. I propose that these texts not only share a debt of Foucauldian thought, but (...) also are part of what I believe is Hacking’s central project: the analysis of the historical and situated conditions of possibility for the emergence of concepts and of objects, inspired also by the French philosopher’s thought. (shrink)

In this volume, noted philosopher Lenn E. Goodman shares the insights gained over a lifetime of pondering the meaning and purpose of Maimonides' celebrated Guide to the Perplexed. Written in the late twelfth century, Maimonides' Guide aims to help religiously committed readers who are alive to the challenges posed by reason and the natural sciences to biblical and rabbinic tradition. Keyed to the new translation and commentary by Lenn E. Goodman and Phillip I. Lieberman, this volume follows Maimonides' life and (...) learning and delves into the text of the Guide, clearly explaining just what Maimonides means by identifying the Talmudic Ma'aseh Bereshit and Ma'aseh Merkavah with physics and metaphysics (to Maimonides, biblical cosmology and theology). Exploring Maimonides' treatments of revelation, religious practice and experience, law and ritual, the problem of evil, and the rational purposes of the commandments, this guide to the Guide explains the tactics Maimonides deployed to ensure that readers not get in over their heads when venturing into philosophical deep waters. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:A Tenth-Century Arabic Interpretation of Plato's Cosmology MAJID FAKIIRY OF PLATO'STHIRTY-SIXDIALOG~Y~Sonly the Timaeus is devoted entirely to cosmological questions. The influence of this dialogue on the development of cosmological ideas in antiquity and the Middle Ages was very great. At a time when the knowledge of Greek philosophy and science in Western Europe had almost vanished, the Timaeus was the only Greek cosmological work to circulate freely in (...) learned circles. The translation and commentary of Chalcidius (c. 350) made the Timaeus available to Latin scholars, at least up to c. 53. But interest in the Timae~s was sustained for a long time before that. The lost commentary of Posidonius of Apamea (d. 51 B.C.), the De animae procreatione in Timeo of Plutarch (d. A.D. 125), the commentary of Proclus (d. 485), extant up to 44d,1 are the most important links in this continuous chain of Platonic cosmological exegesis in antiquity. In the Arabic tradition, the Timaeus had a decisive impact on the development of cosmological ideas also. Plutarch and Proclus were familiar names in the history of Platonic and post-Platonic thought, but I am not aware that the Stoic Posidonius, whom Zeller has described as ".the most universal mind that Greece had seen since the time of Aristotle," 2 was known to the Arabs, or that any mention of his commentary on the Timaeus is to be found in the Arabic sources. General interest in Platonism was an early feature of the philosophical wave which swept the Islamic learned world in the 8th century, and Zeller may be right in saying that it was the Platonic School of Athens which gave Muslim Neoplatonism its peculiar stamp. 3 One of the earliest translators of philosophical texts into Arabic, Yah.ia (b. al-Bit.riq) who flourished in the 2rid half of the 8th century, is credited with the translation of the Timaeus, later retranslated or revised by Hunain (b. Ish~q; d. 873) and Yahia (b. 'Adi and not, as Sarton has it, b. 'Ali; d. 974).~ In addition, the following Platonic dialogues appear to have been translated into Arabic: The Sophistes, the Parmenides, the Cratylus, the Euthydemus, the Republic, the Statesman, the Laws and the Crito. The determination of the actual translator of each work poses serious difficulties. In an autobiographical tract, Hunain simply reports that either he or his disciple Is~ (b. Yahia) translated these works for his patron Muhammad (b. Cf. A. E. Taylor, A Commentary on Plata's Timaeu~ (Oxford, 1928),pp. 34f., and George Sarton, History o] Science (Cambridge, Mass., 1959),I, 428f. Cf. E. Zeller,OutEnesof the History oSGreek Philosophy (N.Y., 1955),p. 268. sIbid., p. 329. ' Cf. al-Fihrist (Cairo, N~D.),p. 358. [15] 16 HISTORY OF PHILOSOPHY Musa), the astrologer.~ Other writers corroborate or supplement this account. Thus Ibn al-Nadim (d. 997), ascribes to Hunain the interpretation (tarsi'r) of the Republic, to him and to Ibn 'Adi the translation of the Laws, and to his son Ish.iq the translation of the Sophistes, together with the commentary of Olympiodorus2 The Crito appears to have been translated also by Yahia (b. Adi), and extensive excerpts from it and the Phaedo are often quoted in the Arabic sources in connection with the trial and execution of Socrates. Another difficulty is raised by the fact that none of the Arabic versions of these dialogues which have come down to us, either as separate works or parts of general commentaries such as the Laws, the Timaeus and the Republic, are complete, so that the inference is inescapable that, as borne out by Hunain's own testimony, it was Galen's paraphrases or compendia of these works, or at any rate those which were translated into Arabic within the School of Hunain, that are actually referred to in our sources.7 It is not, however, with the general diffusion of Platonism in the Muslim world that I am primarily concerned here, but rather with the impact of Platonic cosmological theory as illustrated in the writings of Abu Bakr Muhammad (b. Zakariya al-Razi; d., c. 932), the Rhases of Latin authors, the greatest... (shrink)

This article aims to present a detailed analysis of the “Christian natural philosophy” elaborated by the German humanist philosopher and theologian Otto Casmann (1562–1607) in his various works. To this end, Casmann’s general idea of philosophia Christiana is discussed and critically evaluated. Regarding natural philosophy, or physics, attention is paid mainly to topics such as cosmogony and cosmology, which Casmann promised to have developed biblically and independently of the pagan (namely Aristotelian) tradition. However, when Casmann’s natural philosophy is (...) analyzed in detail, his resolute emphasis on the literal reading of the Bible, the cornerstone of his entire concept, turns out to be problematic. Similarly, despite his resolutions, his natural‑philosophical views are, to a considerable extent, still dependent on Aristotelian terms and concepts. (shrink)

John McTaggart was a Cambridge philosopher, famous for his metaphysical theory that time is not real and that temporal order is an illusion. Although best known for his contributions to the philosophy of time, McTaggart also spent a large part of his career expounding Hegel's work. In this book, first published in 1901, he discusses which views on a range of topics in metaphysics and ethics are compatible with Hegel's logic and idea of 'the Absolute'. Some early work on (...) theories for which McTaggart later became well known can be found in this work, such as his beliefs that humans are immortal, that the Absolute is not in any sense a person, and that love is the relation that binds people together. In this book he also discusses punishment, sin, morality and whether Hegel could be considered a Christian. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Cambridge Companion to Early Greek PhilosophyPatricia CurdA. A. Long, editor. The Cambridge Companion to Early Greek Philosophy. Cambridge: Cambridge University Press, 1999. Pp. xxxii + 427. Cloth, $54.95. Paper, $19.95.The Cambridge Companions are designed both to introduce and to survey, aims that anyone who teaches introductory courses knows are not fully compatible. The Cambridge Companion to Early Greek Philosophy is successful because its contributors (...) have kept to a uniform tone of mostly introduction, with some reference to recent developments and controversies in the field. There are sixteen essays, with a judicious mix of chapters on particular figures and on general topics.A. A. Long provides a helpful introduction, discussing the problems of dealing with the fragmentary evidence for these philosophers, and giving an account of the nature and scope of early Greek thought. (He also argues—not entirely persuasively—that we should give up the nineteenth century name "Presocratics" for these thinkers.) Jaap Mansfeld explains the problems of sources and doxography (the chapter is quite compressed and could be rather overwhelming for the newcomer to the area), while Keimpe Algra surveys Ionian cosmology. Carl Huffman provides a masterful discussion of early Pythagoreanism, attempting to sort out what we can and cannot be justified in claiming about Pre-Platonic Pythagoreanism. The chapters on individual thinkers mostly provide systematic overviews. Edward Hussey contributes an exemplary chapter on Heraclitus, and David Sedley one on Parmenides and Melissus (it is good to see Melissus treated seriously), with Richard McKirahan weighing in on Zeno (mostly on the paradoxes of motion but with some attention to the arguments against plurality). The discussions of individual Presocratics are rounded out with Daniel Graham's treatment of Empedocles' and Anaxagoras' responses to Parmenides, and C. C. W. Taylor on the Atomists. Sarah Broadie considers rational theology and James Lesher early Greek epistemology, while André Laks surveys ancient theories of soul, sensation, and thought. Paul Woodruff and Fernanda Decleva Caizzi provide chapters on the Sophists, the former discussing Protagoras and Gorgias, the latter, Protagoras and Antiphon. Mario Vegetti undertakes an examination of the notion of causation in early Greek thought, and Diskin Clay explores the poetics of the Presocratic philosophers. The book opens with short discussions—three paragraphs devoted to life, sources, and works for each of the thinkers who figure in the period (in alphabetical rather than even roughly chronological order), a chronological chart, and a map. There is a large and useful—though necessarily selective— bibliography (supplemented in the notes to some chapters by references to articles that are not included in the main bibliography), an index locorum, and an index of names and subjects that [End Page 429] includes modern scholars "only if their views are cited in the main text or discussed in footnotes" (which makes it difficult to use in tracking down references). Unfortunately, as in all the Cambridge Companions, notes are at the end of articles rather than at the foot of the page, making necessary a fair bit of flipping while reading.How well do the contributors succeed in meeting the needs of the intended readers of the series? For the most part, very well; the novice reader will find this an accessible guide to Early Greek philosophy. The various discussions are solid and well-informed, and the authors have indicated issues and interpretations that are controversial (for example, Taylor takes time to consider objections to his earlier criticism of Vlastos on the connection between atomistic metaphysics and ethics, and Hussey is careful to note the traditional flashpoints of disagreement in Heraclitus interpretation). It is also good that some of the Sophists are included (it is worth considering how viable the traditional distinction between the Sophists and the Philosophers really is), and inclusion of both the medical tradition and the issue of poetics is very welcome. Further chapters considering in more detail the cosmologies of post-Milesians (including Parmenides) and on the philosophical uses made of the early Greek thinkers by Plato and Aristotle would have rounded things out, but these would have made an already big book bigger. As perhaps befits an introductory survey, most of the interpretations lean to the traditional - someone looking for... (shrink)

John McTaggart was a Cambridge philosopher, famous for his metaphysical theory that time is not real and that temporal order is an illusion. Although best known for his contributions to the philosophy of time, McTaggart also spent a large part of his career expounding Hegel's work. In this book, first published in 1901, he discusses which views on a range of topics in metaphysics and ethics are compatible with Hegel's logic and idea of 'the Absolute'. Some early work on (...) theories for which McTaggart later became well known can be found in this work, such as his beliefs that humans are immortal, that the Absolute is not in any sense a person, and that love is the relation that binds people together. In this book he also discusses punishment, sin, morality and whether Hegel could be considered a Christian. (shrink)

Proofs of God in Early Modern Europe offers a fascinating window into early modern efforts to prove God’s existence. Assembled here are twenty-two key texts, many translated into English for the first time, which illustrate the variety of arguments that philosophers of the seventeenth and eighteenth centuries offered for God. These selections feature traditional proofs—such as various ontological, cosmological, and design arguments—but also introduce more exotic proofs, such as the argument from eternal truths, the argument from universal aseity, (...) and the argument ex consensu gentium. Drawn from the work of eighteen philosophers, this book includes both canonical figures (such as Descartes, Spinoza, Newton, Leibniz, Locke, and Berkeley) and noncanonical thinkers (such as Norris, Fontenelle, Voltaire, Wolff, Du Châtelet, and Maupertuis). -/- Lloyd Strickland provides fresh translations of all selections not originally written in English and updates the spelling and grammar of those that were. Each selection is prefaced by a lengthy headnote, giving a biographical account of its author, an analysis of the main argument(s), and important details about the historical context. Strickland’s introductory essay provides further context, focusing on the various reasons that led so many thinkers of early modernity to develop proofs of God’s existence. -/- Proofs of God is perfect for both students and scholars of early modern philosophy and philosophy of religion. (shrink)

During the nineteenth and early twentieth centuries, a wide variety of American writers proposed the existence of energies connecting human beings to cosmic processes. From varying points of view--scientific, philosophical, religious, and literary--they suggested that such energies would eventually result in the perfection of individual and collective bodies, assuming that assimilation into larger networks of being meant the expansion of humanity's powers and potentialities--a belief that continues to inform much posthumanist theory today. Universes without Us explores a lesser-known countertradition (...) in American literature. As Matthew A. Taylor's incisive readings reveal, the heterodox cosmologies of Edgar Allan Poe, Henry Adams, Charles Chesnutt, and Zora Neale Hurston reject the anthropocentric fantasy that sees the universe as a kind of reservoir of self-realization. For these authors, the world can be made neither "other" nor "mirror." Instead, humans are enmeshed with "alien" processes that are both constitutive and destructive of "us." By envisioning universes no longer our own, these cosmologies picture a form of interconnectedness that denies any human ability to master it. Universes without Us demonstrates how the questions, possibilities, and dangers raised by the posthuman appeared nearly two centuries ago. Taylor finds in these works an untimely engagement with posthumanism, particularly in their imagining of universes in which humans are only one category of heterogeneous thing in a vast array of species, objects, and forces. He shows how posthumanist theory can illuminate American literary texts and how those texts might, in turn, prompt a reassessment of posthumanist theory. By understanding the posthuman as a materialist cosmology rather than a technological innovation, Taylor extends the range of thinkers who can be included in contemporary conversations about the posthuman. (shrink)

Scholars of early Chinese philosophy frequently point to the non transcendent, organismic conception of the cosmos in early China as the source of China's unique perspective and distinctive values. One would expect recent works in Confucian ethics to capitalize on this idea. Reviewing recent works in Confucian ethics by P. J. Ivanhoe, David Nivison, R. P. Peerenboom, Henry Rosemont, and Tu Wei‐Ming, the author analyzes these new studies in termsof the extent to which their representation of (...) Confucian ethics reflects and is consistent with the view that in early China the cosmos was conceived to be organismic, nontranscendent, and nondualistic. (shrink)

In his first major publication, the Mysterium Cosmographicum, Johann Kepler undertook to answer several questions--most notably why there are six planets and why their orbits have a particular relative spacing. Neither Kepler's answers to these questions nor the questions themselves survived the transition to Newtonian physics. Kepler's conviction about the importance of his questions, and his early answers to them, provided the foundation for his subsequent scientific work, including the discovery of the laws of planetary motion for which he (...) is now chiefly remembered. Near the end of his career, in 1621, Kepler produced a second edition of the Mysterium, differing from the first only in the addition of copious notes; in it he refers to his Harmonice Mundi as a vindication of the insights of the Mysterium. J. V. Field's new book systematically examines the mathematical cosmology presented in these three volumes. (shrink)

This volume provides a much needed, historically accurate narrative of the development of theories of space up to the beginning of the eighteenth century. It studies conceptions of space that were implicitly or explicitly entailed by ancient, medieval and early modern representations of the cosmos. The authors reassess Alexandre Koyré’s groundbreaking work From the Closed World to the Infinite Universe and they trace the permanence of arguments to be found throughout the Middle Ages and beyond. By adopting a long (...) timescale, this book sheds new light on the continuity between various cosmological representations and their impact on the ontology and epistemology of space. Readers may explore the work of a variety of authors including Aristotle, Epicurus, Henry of Ghent, John Duns Scotus, John Wyclif, Peter Auriol, Nicholas Bonet, Francisco Suárez, Francesco Patrizi, Giordano Bruno, Libert Froidmont, Marin Mersenne, Pierre Gassendi, Gottfried Wilhelm Leibniz and Samuel Clarke. We see how reflections on space, imagination and the cosmos were the product of a plurality of philosophical traditions that found themselves confronted with, and enriched by, various scientific and theological challenges which induced multiple conceptual adaptations and innovations. This volume is a useful resource for historians of philosophy, those with an interest in the history of science, and particularly those seeking to understand the historical background of the philosophy of space. (shrink)

In the range of his intellectual interests and the profundity of his mathematical thought Hermann Weyl towered above his contemporaries, many of whom viewed him with awe. This volume, the most ambitious study to date of Weyl's singular contributions to mathematics, physics, and philosophy, looks at the man and his work from a variety of perspectives, though its gaze remains fairly steadily fixed on Weyl the geometer and space‐time theorist. Structurally, the book falls into two parts, described in the general (...) introduction by the editor: Part 1 contains four essays on particular aspects of Weyl's work, highlighting ideas he developed in various editions of his classic Raum‐Zeit‐Materie. Part 2 presents a lengthy study by Robert Coleman and Herbert Korté covering nearly the whole gamut of Weyl's mathematical research, an impressive feat. Both in the introduction as well as in footnotes to the articles Erhard Scholz's editorial voice chimes in discreetly, helping tie all five studies together.Coleman and Korté begin chronologically with Weyl's early work in analysis and the modern theory of Riemann surfaces before turning to differential geometry, unified field theory, and the space problem, a topic they use as a springboard for a discussion of their own recent work on the foundations of space‐time. They then take up Weyl's shift to group representation theory and its applications to quantum mechanics, ending with his much earlier research on the structure of the continuum. All of these topics are well handled, but the authors' own agendas coupled with their penchant for overlooking chronology in order to package Weyl's work into neat little bundles leave one feeling rather stranded and far removed from the sources of Weyl's inspiration. Moreover, the narrative style makes this part of the volume read like a technical appendix, albeit a most informative one. Readers who tackle Scholz's far more contextualized essay will be amply rewarded by comparing his views with the opinions set forth by Coleman and Korté in Part 2.Scholz gives a masterful account of Weyl's intellectual journeys from 1917 to 1925 in a study that serves as a fulcrum for the entire volume. Drawing on a number of recently published studies, including his own, on the interplay between mathematics and physics inspired by Einstein's theory of general relativity, Scholz describes how Weyl responded to this challenge by developing a truly infinitesimal space‐time geometry that generalized classical Riemannian geometry. Although unconvinced by Einstein's critique of his unified field theory, Weyl shifted his focus from this realm to the classical space problem, analyzed earlier with more primitive techniques by Hermann Helmholtz and Sophus Lie. In this connection, it should be mentioned that Thomas Hawkins has given a probing analysis of Weyl's related work on the representation of Lie groups in his tour‐de‐force work, Emergence of the Theory of Lie Groups . Scholz argues that Weyl's struggle to tame his modernized version of the space problem stemmed from a deep‐seated belief in his geometrical ideas, which in turn were nourished by philosophical musings. By demonstrating the closely related conceptual links that motivated Weyl's research in infinitesimal geometry, space‐time physics, and the foundations of mathematics, Scholz nicely illuminates the underlying fabric of epistemological concerns that occupied Weyl's attention during this fertile period.The three remaining essays in Part 1 focus on other aspects of Weyl's work in mathematical physics and cosmology. Skuli Sigurdsson's “Journeys in Spacetime” offers a broad interpretation of Weyl's career, one that emphasizes Weyl's sensitivity to cultural tensions as reflected in his philosophical roots, which combined phenomenology with facets of German idealism. Shaken by the annihilation of cultural values in Nazi Germany, Weyl became deeply aware of the gulf that separated his earlier life in Göttingen and Zurich from the one he took up at Princeton's Institute for Advanced Study in 1933. He tried to adapt, but felt out of place in an Anglo‐American scientific culture openly hostile toward metaphysics and speculative philosophy. Sigurdsson stresses these tensions, contrasting the introspective, creative individual against the backdrop of the collective in the age of the machine, but without spelling out which collective were most important for him. Wolfgang Pauli thought he knew and, like Einstein before him, he had no compunction about bluntly telling Weyl he was a mathematician, not a physicist.Pauli's opinions notwithstanding, Weyl did far more than just dabble around the mathematical edges of the new physics. If Coleman and Korté perhaps press their case for his visionary accomplishments too far, Norbert Straumann's essay “Ursprünge der Eichtheorien” suggests why Weyl's reputation among physicists has risen steadily ever since the advent of Yang‐Mills theory in the 1950s. In the course of describing Weyl's adaptation of his gauge transformation formalism to Dirac's electron theory, Straumann sheds considerable light on Pauli's role as self‐appointed watchman guarding the disciplinary boundary that separated theoretical physics from physical mathematics . He further suggests that disciplinary jealousy was a major reason why Pauli dismissed Weyl's two‐component formalism for spinors out of hand.In the realm of cosmology, on the other hand, Weyl's work has long since passed into the dustbins of history, as Hubert Goenner remarks in recounting a fascinating chapter in the infancy of space‐time physics. While doing so, Goenner shows how initially Weyl almost slavishly adopted what Einstein called Mach's principle, which asserts that the metric structure of space‐time is solely determined by the distribution of matter in the universe. This notion was quickly challenged by Willem De Sitter, who showed that Einstein's matter‐free field equations admitted a global solution with non‐zero constant curvature. Both Einstein and Weyl tried to argue that invisible masses must be present just over the “spatial horizon” of De Sitter's world in order to account for its curvature. Goenner meticulously analyzes the physical and mathematical issues at stake in this debate, stressing how Weyl gradually moved away from a strong physical interpretation to one in which mathematics models rather than physics models simply reveal natural phenomena. He argues further that Weyl's cosmological principle arose as the final expression of his search for a deeper physical meaning.Given the quality of these essays, it is regrettable that this book contains so little about Weyl's professional career, a weakness the editor could have redressed at least partially in his general introduction. This omission is all the more unfortunate given the dearth of readily accessible information about Weyl's life available elsewhere. For however mundane his outward existence may have been, the reader cannot be expected to appreciate the interplay between the world Weyl knew and his creative responses to it without fairly detailed knowledge of his biography. Shorn from these contexts, it becomes difficult to form a flesh‐and‐blood image of Weyl beyond the cliché‐ridden stereotype that sees him as a “heroic thinker in the grand German tradition.” While none of the authors falls into this trap, the collective impression they leave suggests a most enigmatic figure. Either Weyl the man tends to get lost in the shadows of his collected scientific output or he appears as a mystic loner, an outcast who abhorred the machine age in which he lived. Closer attention to the people in his life would no doubt produce a very different picture of the man and his interests. This major lacuna notwithstanding, the present volume will surely remain an indispensable resource for any future investigations of Weyl's staggering intellectual achievements. (shrink)

pars 1. Quaestiones super librum topicorum.--pars 2. Opuscula: De aeternitate mundi. De summo bono. De somnis.

The author claims that parts of the De Caelo comprise a distinct work of Aristotle and can be taken as an early composition, earlier than the De Philosophia. The book is a careful philological and philosophical analysis of this text, and takes a position in regard to the authors who have commented on it. The doctrine of the text is contrasted to Plato’s cosmology, especially concerning the concepts of physics and aether. The text is also compared to Aristotle’s (...) later teaching and many differences are noted: hylomorphism, entelechy, and the unmoved mover, are conspicuously absent. Besides analyzing the relevant parts of De Caelo, the author has remarks about such works as the Protreptic, De Philosophia, and Physics I and II.—R.S. (shrink)

Professor Sir Roger Penrose's work, spanning fifty years of science, with over five thousand pages and more than three hundred papers, has been collected together for the first time and arranged chronologically over six volumes, each with an introduction from the author. Where relevant, individual papers also come with specific introductions or notes. The first volume covers the beginnings of a career that is ground-breaking from the outset. Inspired by courses given by Dirac and Bondi, much of the early (...) published work involves linking general relativity with tensor systems. Among his early works is the seminal 1955 paper, 'A Generalized Inverse for Matrices', his previously unpublished PhD and St John's College Fellowship theses, and from 1967, his Adam's Prize-winning essay on the structure of space-time. Add to this his 1965 paper, 'Gravitational collapse and space-time singularities', and the 1967 paper that introduced a remarkable new theory, 'Twistor algebra', and this becomes a truly stellar procession of works on mathematics and cosmology. (shrink)

Cosmological narratives like the creation story in the book of Genesis or the modern Big Bang are popularly understood to be descriptions of how the universe was created. However, cosmologies also say a great deal more. Indeed, the majority of cosmologies, ancient and modern, explore not simply how the world was made but how humans relate to their surrounding environment and the often thin line which separates humans from gods and animals. Combining approaches from classical studies, anthropology, and philosophy, this (...) book studies three competing cosmologies of the early Greek world: Hesiod's Theogony; the Orphic Derveni theogony; and Protagoras' creation myth in Plato's eponymous dialogue. Although all three cosmologies are part of a single mythic tradition and feature a number of similar events and characters, Olaf Almqvist argues they offer very different answers to an ongoing debate on what it is to be human. Engaging closely with the ontological turn in anthropology and in particular with the work of Philippe Descola, this book outlines three key sets of ontological assumptions - analogism, pantheism, and naturalism - found in early Greek literature and explores how these competing ontological assumptions result in contrasting attitudes to rituals such as prayer and sacrifice. (shrink)

This volume is the first systematic presentation of the work of Albert Einstein, comprising fourteen essays by leading historians and philosophers of science that introduce readers to his work. Following an introduction that places Einstein's work in the context of his life and times, the book opens with essays on the papers of Einstein's 'miracle year', 1905, covering Brownian motion, light quanta, and special relativity, as well as his contributions to early quantum theory and the opposition to his light (...) quantum hypothesis. Further essays relate Einstein's path to the general theory of relativity (1915) and the beginnings of two fields it spawned, relativistic cosmology and gravitational waves. Essays on Einstein's later years examine his unified field theory program and his critique of quantum mechanics. The closing essays explore the relation between Einstein's work and twentieth-century philosophy, as well as his political writings. (shrink)

A study of problems, all revolving around the subject of intellect in the philosophies of Alfarabi, Avicenna, and Averroes, this book starts by reviewing discussions in Greek and early Arabic philosophy which served as the background for the three Arabic thinkers. Davidson examines the cosmologies and theories of human and active intellect in the three philosophers and covers such subjects as: the emanation of the supernal realm from the First Cause; the emanation of the lower world from the transcendent (...) active intellect; stages of human intellect; illumination of the human intellect by the transcendent active intellect; conjunction of the human intellect with the transcendent active intellect; prophecy; and human immortality. Davidson shows that medieval Jewish philosophers and the Latin Scholastics had differing perceptions of Averroes because they happened to use works belonging to different periods of his philosophic career. (shrink)

Recent works by Fabienne Jourdan, Luc Brisson and Francesc Casadesús emphasize the importance of the similarities between the Derveni papyrus and early Stoicism. The paper examines the se parallelisms – focusing on the method of allegorical interpretation, the cosmological roles of air, fire and pneuma and cosmic teleology – and argues that the similarities, although non-negligible, are not such that would require us to re-interpret the Derveni papyrus against the background of Stoicism. Moreover, the relevant features of the (...) papyrus may be explained from the internal dynamics of the Derveni author’s system, and there is thus no need to modify the date of the papyrus to allow Stoic influence. (shrink)

In the early twenty-first century, we often ask whether there is life (intelligent or otherwise) in the cosmos, but almost never whether the heavens themselves are actually alive or animated, that is, infused somehow with a soul, the anima mundi, or some such entity. This was not the case in the Middle Ages, the Renaissance, or the early modern period. Although Aristotelians normally answered no to this question, Marsilio Ficino (1433–99) took a decidedly Platonic turn when he answered (...) the question positively, insistently, and consistently in a broad range of works over his entire philosophical career. By contrast, Giovanni Pico della Mirandola (1463–94), Ficino’s younger contemporary, began by embracing the new Platonic position but joined the Aristotelian fold in his later works. In this essay, I will briefly compare and contrast Ficino’s solid and consistent position with the changing trajectory of Pico’s views over the course of his short but intense career. This essay is an exploration of central themes and some preliminary reflections thereon. These essentially Platonic views of a living universe provide the conceptual and literary foundations for understanding this issue in the early modern period. (shrink)

This work traces the theory of Radical Dependence through its various forms in Berkeleys philosophical works. It shows that a desire to establish a theory of Radical Dependence underlies all of these works and that this theory unifies Berkeleys various phases of philosophical development. The work begins by establishing the meaning of Radical Dependence and examining the influence of Greek, Early Christian and Mediaeval philosophers and theologians on the development of the concept. Subsequently, the deism of the (...) seventeenth-century philosophers is examined; the influence of science and rationalism on the development of deism is traced, with particular attention being given to Berkeleys personal milieu. With a view to showing that Berkeley wishes to re-establish the waning Christian cosmology, his philosophical works are examined in chronological order, particular attention being paid to his final work Siris. It is shown that, although Berkeley moves from a philosophy based on the immaterialist hypothesis in his early works, to one based on the doctrine of participation in his last work, each phase is a variation of the doctrine of Radical Dependence. In the final chapter some of the shortcomings of Berkeleys various philosophical systems are discussed and alternatives are examined. The direction of his thought is found to be guided more by piety than by common-sense and reason: he suffers from a pious pragmatism which leads him to hold doctrines as true on the grounds that they corroborate Christian doctrines. His firm belief in the providence of God leads him to affirm an almost pantheistic worldview which he never fully manages to reconcile with traditional Christian theology, and the doctrine of creation ex nihilo in particular. (shrink)

In this work, we reconstruct the cosmological unified dark fluid model proposed previously by Elkhateeb (Astrophys Space Sci 363(1):7, 2018) in the framework of _f_(_R_) gravity. Utilizing the equivalence between the scalar-tensor theory and the _f_(_R_) gravity theory, the scalar field for the dark fluid is obtained, whence the _f_(_R_) function is extracted and its viability is discussed. The _f_(_R_) functions and the scalar field potentials have then been extracted in the early and late times of asymptotically de Sitter (...) spacetime. The ability of our function to describe early time inflation is also tested. The early time scalar field potential is used to derive the slow roll inflation parameters. Our results of the tensor-to-scalar ratio _r_ and the scalar spectral index \(n_s\) are in good agreement with results from Planck-2018 TT+TE+EE+lowE data for the model parameter \(n > 2\). (shrink)

Vernünfftige Gedancken von Gott, der Welt und der Seele des Menschen, auch allen Dingen überhaupt -- Christian Freyherrn von Wolf Erinnerung, wie er es künftig mit den Einwürfen halten will, die wider seine Schriften gemacht werden.

Scholars of early Chinese philosophy frequently point to the nontranscendent, organismic conception of the cosmos in early China as the source of China's unique perspective and distinctive values. One would expect recent works in Confucian ethics to capitalize on this idea. Reviewing recent works in Confucian ethics by P. J. Ivanhoe, David Nivison, R. P. Peerenboom, Henry Rosemont, and Tu Wei-Ming, the author analyzes these new studies in terms of the extent to which their representation of (...) Confucian ethics reflects and is consistent with the view that in early China the cosmos was conceived to be organismic, nontranscendent, and nondualistic. (shrink)

A study of problems, all revolving around the subject of intellect in the philosophies of Alfarabi, Avicenna, and Averroes, this book starts by reviewing discussions in Greek and early Arabic philosophy which served as the background for the three Arabic thinkers. Davidson examines the cosmologies and theories of human and active intellect in the three philosophers and covers such subjects as: the emanation of the supernal realm from the First Cause; the emanation of the lower world from the transcendent (...) active intellect; stages of human intellect; illumination of the human intellect by the transcendent active intellect; conjunction of the human intellect with the transcendent active intellect; prophecy; and human immortality. Davidson shows that medieval Jewish philosophers and the Latin Scholastics had differing perceptions of Averroes because they happened to use works belonging to different periods of his philosophic career. (shrink)

In a 1967 article, A. C. Graham made the claim that 情 qing should never be translated as "emotions" in rendering early Chinese texts into English. Over time, sophisticated translators and interpreters have taken this advice to heart, and qing has come to be interpreted as "the facts" or "what is genuine in one." In these English terms all sense of interrelationality is gone, leaving us with a wooden, objective stasis. But we also know, again partly through the work (...) of Graham, that interrelationality was of fundamental importance in the early Chinese cosmology and that qing, by later carrying the meaning of "emotions," expressed that interrelationality. I take as my project in this article the recovery of an emotional adumbration in the qing of early Chinese texts, notably the Mencius, from which Graham begins his discussion. With an eye to explicating qing in the Mencius, and with a sensitivity to an implied notion of interrelationality in early texts, I survey early literature from the Shu Jing to late commentaries on the Yi Jing. I find that usages of qing and contexts in which qing is used inevitably illuminate it as key term in the evocation of interrelationality, shading it with emotional overtones. Emotions, of course, are inherently interrelational, and even more so in a Chinese world in which the internal and the external are in constant communication by way of a cosmic interchange of arousal and response among all things. That qing, as a term which later comes to explicitly mean "emotions," should have a centuries old convention of emotional connotation prior to its explicit definition should come as no surprise. The corroboration of this supposition entails a complex investigation and analysis, however, and it is a preliminary step in this investigation and analysis that I undertake here. (shrink)