(I) MATHEMATICAL LECTURES. LECTURE I. Of the Name and general Division of the Mathematical Sciences. BEING about to treat upon the Mathematical Sciences, ...

In lieu of an abstract, here is a brief excerpt of the content:Isaac Barrow on the Mathematization of Nature: Theological Voluntarism and the Rise of Geometrical OpticsAntoni MaletIntroductionIsaac Newton’s Mathematical Principles of Natural Philosophy embodies a strong program of mathematization that departs both from the mechanical philosophy of Cartesian inspiration and from Boyle’s experimental philosophy. The roots of Newton’s mathematization of nature, this paper aims to demonstrate, are to be found in Isaac Barrow’s (1630–77) philosophy of (...) the mathematical sciences.Barrow’s attitude towards natural philosophy evolved from his earnest interest in medicine of around 1650, when a young Cambridge graduate, to natural philosophy (apparently under Henry More’s influence); from his thesis on the insufficiency of the Cartesian hypothesis to geometrical optics and the strong program of mathematization of natural philosophy of the middle 1660s; from Lucasian professor of Mathematics to Chaplain of his Majesty and eminent Restoration divine. Contemporary accounts of Barrow’s life suggest that he grew ever more skeptical about the worth of natural philosophy and mathematics. 1 In his last years he became a prolific [End Page 265] author of sermons and theological works. Published shortly after his death by John Tillotson (1630–94), later archbishop of Canterbury, they occupy over two thousand folio pages. Overloaded with involved philosophical arguments, Barrow’s sermons were apparently not very popular, but they were highly regarded by scholars and the Anglican hierarchy. 2 It is on certain of his sermons, as well as on the philosophical discussions contained in the Mathematical Lectures that our account of Barrow’s philosophy of the mathematical sciences will rest. 3 Barrow’s understanding of the mathematical sciences will allow us to discuss together three issues often analyzed independently: the theological background to English natural philosophy, the changing notion of mixed mathematical sciences during the seventeenth century, and finally the philosophical foundations of modern geometrical optics.It has long been recognized that significant relationships exist between theological voluntarism or intellectualism and views on natural philosophy. In particular Robert Boyle’s theological voluntarism is seen as grounding his experimentalist approach to natural philosophy. It is not quite so clear, however, how well theological voluntarism may relate to a strong program of mathematization such as the one embodied in Newton’s Principia Mathematica. In fact it has been suggested that the relationship is a negative one. This is derived from the necessary character of mathematical laws, which would put unwanted restrictions on God’s absolute dominion over nature, and also from the notion that theological intellectualism is conducive to a deductive, a priori science—the paradigm of which is of course geometry. However, Barrow’s theological voluntarism lead him to heighten the role of mathematics within natural philosophy.During the seventeenth century the so-called mixed or subalternate mathematical sciences changed profoundly. In the Enlightenment mixed mathematics—meaning above all rational mechanics—became one of the most prestigious and influential disciplines. The mixed mathematics of the Enlightenment, however, was markedly different from the Aristotelian [End Page 266] mixed mathematical sciences. The differences are noticeable both in the subject matter and in the substitution of mathematical infinitesimal analysis for geometrical synthesis, but also in the way of grounding mathematical theory on empirical evidence. Barrow’s Mathematical Lectures (delivered at Cambridge from 1664 to 1666) offer a fresh insight into the metamorphosis of these sciences just when Newton’s “mathematical principles” were in the making. Not the least interesting feature of Barrow’s discussion is that God’s omnipotence allows an evaluation of the truth of mathematical theories that do not apply to this world. Therefore, Barrow is led to introduce the distinction between the internal consistency, or mathematical truth, of a mathematical theory and its physical truth. This, in turn, leads him to the notion that theories need testing.Barrow on Matter and GodRecent literature has established significant correlations between theological voluntarism and empiricism, as well as between theological intellectualism and rationalism. As E. B. Davis writes, “the Christian doctrine of creation is a dialogue between God’s unconstrained will, which utterly transcends the bounds of human comprehension, and God’s orderly intellect, which serves as the model for the human mind.” Intellectualist theology considers God’s omniscience His... (shrink)

Published among the posthumous Opuscula of Isaac Barrow in 1687, the Epitome fidei et religionis Turcicae offers an exposition of the main tenets and practices of Islam that is unusually accurate for its time. The Epitome has been noted in passing by Barrow’s biographers and by scholars of seventeenth-century Oriental studies; but it is here firmly identified as the work of the Polish-born Ottoman dragoman and musician Ali Ufki, known in Latin as Albertus Bobovius (Wojciech Bobowski). As (...) the Epitome has never before been studied in detail, this article considers its nature, its importance and its circulation in the European Republic of Letters. The first part treats the evidence of Barrow’s amateur interest in Oriental studies, including his acquisition of the Epitome, and establishes Ufki’s authorship of the treatise. The second part examines the Epitome itself and traces its dissemination and influence through such figures as John Worthington, Samuel Hartlib, William Sancroft, Claes Rålamb and Johan Ulrich von Wallich. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Barrow and Newton E. W. STRONG As E. A. Buxrr HAS ADDUCED,Isaac Barrow (1630-1677) in his philosophy of space, time, and mathematical method strongly influenced the thinking of Newton: The recent publication of an early paper written by Newton (his De gravitatione et aequipondio fluidorum)2 affords evidence not known to Burtt of Newton's indebtedness in philosophy to Barrow, his teacher. Prior to its publication in (...) 1962, this paper was utilized by Alexandre Koyrd in his essay, "Newton and Descartes," 3 a study based on the third Horblit Lecture in the History of Science which he gave at Harvard University, March 8, 1961. Koyr8 maintains that there is a radical opposition in Newton's Principia not only to Descartes' purely scientific theories but also to the Cartesian philosophy. Yet, as he remarks, "we do not find in the Principia an open criticism of the philosophy of Descartes.... " He attributes this fact principally "to the very structure of the Principia: it is essentially a book on rational mechanics, which provides principles for physics and astronomy. In such a book there is a normal place for the discussion of Cartesian optics, but not of the conception of the relations of mind and body, and other such things." Koyrd asserts, nonetheless, that the criticism is not absent. It lurks in Newton's carefully worded definitions of fundamental concepts--those of space, time, motion, and matter--and becomes more apparent in the Optice of 1706 and in the second odition of the Principia. In support of this argument, he makes much of young Newton's unfini.~hed paper. He holds that this essay is of exceptional value "as it enables us to get some insight into the formation of Newton's thought, and to recognize that preoccupation with philosophic problems was not an external additatmentum but an integral dement of his thinking." 4 As concerns "young Newton's conception of space in its being and in its relation to God and time," Koyrd remarks that we learn from this essay The Metaphysical Foundations of Modern Physical Science (New York, 1927), p. 144. A. Rupert Hall and Marie Boas Hall, Unpublished Scientific Papers of Isaac Newton (Cambridge, 1962), Introduction, pp. 75-88; Latin text, pp. 90-121; English translation, pp. 121156. " Newtonian Studies (Harvard University Press, 1965), pp. 53-114. " Newtonian Studies, pp. 82-83. In his De gravitatione et aequipondio fluidorum, Newton is indeed engrossed with philosophic problems. With regard, however, to the announced purpose of his paper, namely, "to treat of the science of gravity and solid bodies in fluids by two methods," does Newton represent kis metaphysical "explanation of the nature of body" as an element of his science essential to its completeness7 He does not do so. At the end of his explanation he remarks: "I have already digressed enough; let us return to the main theme." He proceeds to set forth fifteen more definitions and then turns to the demonstration of two "Propositions on Non-Elastic Fluids." [155] 156 HISTORY OF PHILOSOPHY "that space is necessary, eternal, immutz~ble, and unmovable, that though we can imagine that there is nothing in space we cannot think space is not.., and that if there is no space, God would be nowhere. We learn also that all points of space are simultaneous and that, therefore, the divine omnipresence does not introduce composition in God.... " What we here learn from Newton about space in confutation of Descartes is to be found in Barrow's tenth mathematical lecture, "'Of Space, and Impenetrability." 5 In this lecture, Barrow opposes both Descartes and Hobbes. He objects, as does Newton, to the position taken by Descartes in his Principia Philosophiae, namely, "it is necessary.forMatter to be infinitely extended." He proceeds, as does Newton, to show how "very much Cartesius's great Subtility has failed him in this Case" to conclude that there is space empty of matter and distinct from magnitude from which an infinity of matter cannot be deduced. The correspondence of arguments tendered by Barrow and Newton indicates that the tenth lecture constituted a source from which Newton gleaned principal objections to Descartes' Principia Philosophiae. Although Koyr~ makes reference to Burtt's... (shrink)

SummaryIn 1693, Gottfried Wilhelm Leibniz published in the Acta Eruditorum a geometrical proof of the fundamental theorem of the calculus. It is shown that this proof closely resembles Isaac Barrow's proof in Proposition 11, Lecture 10, of his Lectiones Geometricae, published in 1670. This comparison provides evidence that Leibniz gained substantial help from Barrow's book in formulating and presenting his geometrical formulation of this theorem. The analysis herein also supports the work of J. M. Child, who in (...) 1920 studied the early manuscripts of Leibniz and concluded that he had frequently copied his diagrams from Barrow's book, but without acknowledgement. It is also shown that the diagram of Leibniz associated with his 1693 proof has often been reproduced with errors that make some aspects of his text difficult to comprehend. (shrink)

ABSTRACT Few texts in the history of science and philosophy have achieved the level of interpretative indeterminacy as a short manuscript tract by Isaac Newton, known as ‘De gravitatione’. On the basis of some new evidence, this article argues that it is an introductory fragment of some lectures on hydrostatics delivered in the of spring 1671. Taking seriously the possibility of a pedagogical purpose, it is then argued that the famous digression on space, far from articulating a sophisticated metaphysics (...) that may have owed something to Henry More, was a simple piece of mixed-mathematical prolegomena designed to facilitate the subsequent geometrical argumentation. In this regard, Newton was doing the same as his mentor, Isaac Barrow, had done in his own mathematical lectures; both drew heavily on the explicitly anti-metaphysical approach of Pierre Gassendi. It is shown that More himself would have almost certainly opposed Newton’s approach. The excesses of metaphysical readings of Newton’s intentions are challenged; there is no warrant for reading the digression as directly relevant to the Principia. (shrink)

In ?155 of his New Theory of Vision Berkeley explains that a hypothetical ?unbodied spirit? ?cannot comprehend the manner wherein geometers describe a right line or circle?.1The reason for this, Berkeley continues, is that ?the rule and compass with their use being things of which it is impossible he should have any notion.? This reference to geometrical tools has led virtually all commentators to conclude that at least one reason why the unbodied spirit cannot have knowledge of plane geometry is (...) because it cannot manipulate a ruler or a compass. In this article I will show that such an interpretation is flawed. I will instead argue that Berkeley's understanding of Euclidian geometry was based on Isaac Barrow's account of the foundations of geometry. On this view geometrical objects are conceived in terms of the idealized motion that generates the objects of geometry. Consequently, that what the unbodied spirit cannot do in this context is to form an idea of motion rather than being unable to handle geometrical tools. 1All references to Berkeley are from, A. A. Luce and T. E. Jessop (eds.), The Works of George Berkeley, Bishop of Cloyne (London: Thomas Nelson and Sons, Ltd., 1948) The following abbreviations are used: An Essay Towards A New Theory of Vision, section x = New Theory x; Philosophical Commentaries, entry x = Commentaries x; Part I of A Treatise concerning the Principles of Knowledge, section x = Principles x. All other references to Berkeley's works are of the form The Works of George Berkeley, Bishop of Cloyne, volume x, page y = Works, x, y. (shrink)

This paper discusses the logical space of alternative conceptual engineering projects, with a specific focus on (1) the processes, (2) the targets and goals, and (3) the methods of such projects. We present an overview of how these three aspects interact in the contemporary literature and discuss those alternative projects that have yet to be explored based on our suggested typology. We show how choices about each element in a conceptual engineering project constrain the possibilities for the others, thereby giving (...) rise to distinct groupings of possible projects under the banner of conceptual engineering. We conclude with a critical reflection on the potential ethical issues that arise as a result of effectively putting conceptual engineering into practice. (shrink)

This chapter contains sections titled: I II III IV V VI VII Notes References.

This chapter contains sections titled: I II III IV V Notes References.

Gigant v t︠s︡epi︠a︡kh -- Chelovek protiv mifov -- Mysliteli i kaznachei.

Putting God First: Jewish Humanism after Heidegger tackles the challenge of maintaining Jewish identity in a world dominated by Western humanism. It argues that the Holocaust reflects more broadly on contemporary humanism than the Jewish world has ever dared to acknowledge. It advances the view that the establishment of the State of Israel presents a profound historical opportunity to disentangle Jewish thought from elements of the Western humanist tradition that threaten Jewish survival and conceal from view the plausibility of core (...) Jewish ideas and values. The work proposes that a healthy and peaceful relationship between Westernism and a robust Jewish identity can be achieved only by unraveling the two, and it presents a philosophical path for achieving this. Following a precise analysis of modern and postmodern thought that includes discussions of Immanuel Kant, Jacques Derrida, Michel Foucault, Ludwig Wittgenstein, George Steiner, Bruno Latour, Hannah Arendt, Jonathan Haidt, Daniel Kahneman, and others, the centerpiece of the book offers a close reading of the masterwork Being and Time, which Martin Heidegger composed in the period when his thought was gravitating toward his endorsement of Hitler and Nazism. This deep dive into Heidegger's ontological understanding of how the individual (Dasein) interacts with others in space and time yields a method for articulating the onto-theological meanings of key Jewish concepts such as the Nefesh (psyche), the Neshamah (soul), Tzelem Elohim (human being in God's image), Am Segulah, (Jewish chosenness), Shabbat, the Land of Israel, and more in texts such as the Tanya, the Sefat Emet, the Nefesh HaChayim, the Kedushat Levi, and in the writings of Rav Kook and the Maharal of Prague. Ultimately the book proposes a disentangled spiritual/political vision for a Jewish state that is characterized by the politics of Tikun Olam" -- From the publisher. (shrink)

The works of Hannah Arendt and Albert Camus--two of the most compelling political thinkers of the "resistance generation" that lived through World War II--can still provide penetrating insights for contemporary political reflection. Jeffrey C. Isaac offers new interpretations of these writers, viewing both as engaged intellectuals who grappled with the possibilities of political radicalism in a world in which liberalism and Marxism had revealed their inadequacy by being complicit in the rise of totalitarianism. According to Isaac, self-styled postmodern (...) writers who proclaim the death of grandiose ideologies often fail to recognize that such thinkers as Camus and Arendt had already noted this. But unlike many postmodernists, these two sought to preserve what was worthy in modern humanism--the idea of a common human condition and a commitment to human rights and the dignity of individuals. Isaac shows that both writers advanced the idea of a democratic civil society made up of self-limiting groups. Although they criticized the typical institutions of mass democratic politics, they endorsed alternative forms of local and international organization that defy the principle of state sovereignty. Isaac also shows how Arendt's writings on the Middle East, and Camus's on Algeria, urged the creation of such institutions. The vision of a "rebellious politics" that Arendt and Camus shared is of great relevance to current debates in democratic theory and to the transformations taking place in Europe and the states of the former Soviet Union. (shrink)

When schools react to contemporary events and focus on complex moral problems they commonly fail to make basic distinctions between the morally serious and trivial, the moral and the non-moral, and problems and dilemmas. We need to teach the distinction between moral and other values, and between what is intrinsically good, what is right in practice and what is justifiable. Moral theory seeks to delineate an ideal situation. Different circumstances give rise to different particular practices; but the principles of freedom, (...) fairness, respect for persons, truth and felicity constitute a widely recognized view of the essence of morality. These principles, and the nature of education itself, are often ignored in programs of moral education, which should proceed by providing an understanding of the nature and limits of the moral sphere. (shrink)

In the last book of The Consolation of Philosophy, Boethius develops his solution to the problem of divine foreknowledge and free choice. Interpreters standardly hold that this problem and his solution to it presuppose causal indeterminism. In this paper, I argue that Boethius, following a Neoplatonist view found in Proclus, is a causal determinist and compatibilist and maintains that God’s providential knowledge ensures the occurrence of all the events he knows. This alternative interpretation offers a better fit with Boethius’s text (...) and its historical antecedents and provides resources to address the main criticisms of his solution. (shrink)

In-depth study of the enduring impact of the 1970s debate between state theorists Ralph Miliband and Nicos Poulantzas. We have recently lived through the turmoil of a global financial crisis that originated in the United States and, despite the platitudes of neo-liberal ideology, nation-states were deeply involved in managing this crisis. If “the state” is again a preeminent actor in the global economy, then state theory and the problem of the state should also return to the forefront of political theory. (...) Toward a Critical Theory of States is an intensive analysis of the 1970s debate between state theorists Ralph Miliband and Nicos Poulantzas, including its wider impact on Marxist theories of the state in subsequent decades. Clyde W. Barrow makes unique arguments and contributions to this continuing discussion in state theory and lays the foundation for more theoretically informed empirical and historical research on the state in the age of globalization. He argues that by merely moving past the Poulantzas-Miliband debate, as some have recommended, scholars have abandoned much that is valuable in understanding the state, particularly the need to comprehend the contemporary transformation of the state form and the state apparatuses as part of the new conditions of globalization and transnational capital accumulation. Building upon themes of state restructuring found in Poulantzas and Miliband, Barrow establishes the outlines of an approach that integrates the thought of both to propose a synthetic understanding of the new imperialism. (shrink)

The Routledge Encyclopedia of Films comprises 200 essays by leading film scholars analysing the most important, influential, innovative and interesting films of all time. Arranged alphabetically, each entry explores why each film is significant for those who study film and explores the social, historical and political contexts in which the film was produced. Ranging from Hollywood classics to international bestsellers to lesser-known representations of national cinema, this collection is deliberately broad in scope crossing decades, boundaries and genres. The encyclopedia thus (...) provides an introduction to the historical range and scope of cinema produced throughout the world. (shrink)

We present a novel model of individual people, online posts, and media platforms to explain the online spread of epistemically toxic content such as fake news and suggest possible responses. We argue that a combination of technical features, such as the algorithmically curated feed structure, and social features, such as the absence of stable social-epistemic norms of posting and sharing in social media, is largely responsible for the unchecked spread of epistemically toxic content online. Sharing constitutes a distinctive communicative act, (...) governed by a dedicated norm and motivated to a large extent by social identity maintenance. But confusion about this norm and its lack of inherent epistemic checks lead readers to misunderstand posts, attribute excess or insufficient credibility to posts, and allow posters to evade epistemic accountability—all contributing to the spread of epistemically toxic content online. This spread can be effectively addressed if people and platforms add significantly more context to shared posts and platforms nudge people to develop and follow recognized epistemic norms of posting and sharing. (shrink)

For the past fifty years anxiety over naturalism has driven debates in social theory. One side sees social science as another kind of natural science, while the other rejects the possibility of objective and explanatory knowledge. _Interpretation and Social Knowledge_ suggests a different route, offering a way forward for an antinaturalist sociology that overcomes the opposition between interpretation and explanation and uses theory to build concrete, historically specific causal explanations of social phenomena.

I present and explain the Bohmian account of collapse in quantum mechanics.

Presents Newton's unifying idea of gravitation and explains how he converted physics from a science of explanation into a general mathematical system.

This first critical edition of Isaac Abravanel’s correspondence opens a window into the cultural, political and commercial world of one of the first Jewish humanists of the quattrocento. Jewish leader of the expelled Sephardim after 1492, commentator of the Bible, Abravanel is a legendary figure of the Sephardic history. The edition of the letters along with the introductive essay that reconstructs their cultural background intends to connect the legendary figure of Abravanel to the major reason of his remarkable career: (...) his successful assimilation of Renaissance humanism. (shrink)

My aim in this paper is to give a philosophical analysis of the relationship between contingently available technology and the knowledge that it makes possible. My concern is with what specific subjects can know in practice, given their particular conditions, especially available technology, rather than what can be known “in principle” by a hypothetical entity like Laplace’s Demon. The argument has two parts. In the first, I’ll construct a novel account of epistemic possibility that incorporates two pragmatic conditions: responsibility and (...) practicability. For example, whether subjects can gain knowledge depends in some circumstances on whether they have the capability of gathering relevant evidence. In turn, the possibility of undertaking such investigative activities depends in part on factors like ethical constraints, economical realities, and available technology. In the second part of the paper, I’ll introduce “technological possibility” to analyze the set of actions made possible by available technology. To help motivate the problem and later test my proposal, I’ll focus on a specific historical case, one of the earliest uses of digital electronic computers in a scientific investigation. I conclude that the epistemic possibility of gaining access to scientific knowledge about certain subjects depends (in some cases) on the technological possibility for making responsible investigations. (shrink)