Nominalism and Constructivism in Seventeenth-Century Mathematical Philosophy
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On the Infinite in Leibniz's Philosophy
On the Infinite in Leibniz's Philosophy Elad Lison Interdisciplinary Studies Unit Science, Technology and Society Ph.D. Thesis Submitted to the Senate of Bar-Ilan University Ramat-Gan, Israel August 2010 This work was carried out under the supervision of Dr. Ohad Nachtomy (Department of Philosophy), Bar-Ilan University. Contents א.……………………………….…………………………………………Hebrew Abstract Prologue…………………………………………………………...………………………1 Part A: Historic Survey Methodological Introduction…………………………………………………………..15 1. Aristotle: Potential Infinite………………………………………………………….16 2. Thomas Aquinas: God and the Infinite………………………………………..…….27 3. William of Ockham: Syncategorematic and Actual Infinite……………………..….32 4. Rabbi Abraham Cohen Herrera: Between Absolute Unity and Unbounded Multitude………………………………………………………………………..….42 5. Galileo Galilei: Continuum Constructed from Infinite Zero's………………………49 6. René Descartes: Infinite as Indefinite…………………………………………….…58 7. Pierre Gassendi: Rejection of the Infinite…………………………………………...69 8. Baruch Spinoza: Infinite Unity…………………………………………………...…73 9. General Background: Leibniz and the History of the Infinite……………………....81 Summary…………………………………………………………………………….…94 Part B: Mathematics Introduction…………………………………………………………………………….99 1. 'De Arte Combinatoria' as a Formal Basis for Thought: Retrospective on Leibniz's 1666 Dissertation………………………………………………………………....102 2. Leibniz and the Infinitesimal Calculus……………………………………….……111 2.1. Mathematical Background: Mathematical Works in 16th-17th Centuries…..111 2.2. Leibniz's Mathematical Development…………………………………….…127 -
The Search for the Historical Gassendi
The Search for the Historical Gassendi Margaret J. Osler University of Calgary Writing about the history of science and the history of philosophy in- volves assumptions about the role of context and about the relationships between past and present ideas. Some historians emphasize the context, concentrating on the intellectual, personal, and social factors that affect the way earlier thinkers have approached their subject. Analytic philoso- phers take a critical approach, considering the logic and merit of the arguments of past thinkers almost as though they are engaging in contem- porary debates. Some philosophers use the ideas of historical ªgures to support their own philosophical agendas. Scholarly studies of the French natural philosopher Pierre Gassendi (1592–1655) exemplify many of these approaches. What, then, is context? At the most basic level, the context is the text itself. The most acontextual scholars examine only snippets of the text. In- terested in ideas about necessity, arguments for the existence of God, or ideas about matter and gravity, they mine the writings of historical ªgures for their views on these questions without considering the author’s aim for the book or project as a whole. This approach has frequently characterized discussions of Gassendi’s philosophy. His major work, the Syntagma Philo- sophicum, is a massive treatise in difªcult neo-Latin, daunting to all but the hardiest (or most foolish) of scholars. Consequently, of those philosophers and historians who deal with Gassendi at all, many rely on the bits that have been translated into English or French or those that deal with speciªc topics and seldom consider the entirety of his work, but the work as a whole gives the parts their meaning. -
Pierre Gassendi's Animals
[Intellectual History Archive 3, 2018] Begley, Pierre Gassendi’s Animals PIERRE GASSENDI’S ANIMALS: A CASE OF EXCLUSION Justin Begley1 University of Helsinki I. Introduction: A Learned Vegetarian The French priest, professor of mathematics, historian, and philosopher, Pierre Gassendi, was perhaps the most influential and well-respected thinkers of his day. 2 While the linguistic and conceptual complexity of his Latin tomes excluded him from the philosophical canon that was formed during the late eighteenth, historians are now beginning to appreciate just how central his ideas were to the development of early modern intellectual life. But recent studies of Gassendi have consistently bypassed a major component of his thought: his defense of a vegetarian diet.3 Conversely, because it is no small task to identify and translate the relevant passages from Gassendi’s oeuvre, historical surveys of vegetarianism have mostly neglected his arguments. Indeed, in the history of vegetarianism, emphasis has been placed on religious sectarians or intellectual outsiders such as Thomas Bushnell and Roger Crab, while figures such as Gassendi who were, historically speaking, intellectual insiders have paradoxically been neglected. 4 Proponents of vegetarianism have thus been shaped teleologically as progressive or even “radical” thinkers. But Gassendi remained thoroughly embedded in the institutions of his day, and channeled the full gamut of humanist apparatuses in his endeavor to integrate the philosophy of the ancient Greek atomist, Epicurus, into the university curriculum. For this purpose, he sought to cleanse Epicurean philosophy of its popular associations with excess, atheism, and debauchery 1 [email protected] 2 Meric Casaubon, Generall Learning: A Seventeenth-Century Treatise on the Formation of the General Scholar, ed. -
Seventeenth-Century News
131 seventeenth-century news Michael Edwards. Time and The Science of The Soul In Early Modern Philosophy. Brill’s Studies in Intellectual History 224. Leiden: Brill, 2013. x + 224 pp. $128.00. Review by Karin Susan Fester, Independent Scholar. This is a book for philosophers who are not only interested in the concept of time, but who seek new perspectives on this intriguing and problematical philosophical concept as well as appreciate what René Descartes and Thomas Hobbes have to say about it. Michael Edwards’ book is distinctive because it focuses attention on the numerous late Aristotelian thinkers who assumed that the soul’s diverse functions played an active role in the concept of time. More precisely, it is de- voted to the aspects of time which have either not been thoroughly examined or omitted by other historians of early modern philosophy; instead, these other scholars have shown how Aristotelian natural philosophy was concentrated on “space” rather than “time.” Edwards argues that time is somehow intimately connected to the human ra- tional soul—“‘relative’ or as dependent on motion and the soul”—and this, of course, contrasts with Isaac Newton’s (1642–1727) concept of time as something ‘absolute’ (6). The author seems to achieve a persuasive argument, and he invokes elements from early modern commentaries and textbooks concerning Aristotle’s Physics and De Anima and attempts to find connections and influential elements to the natural and political philosophy of Descartes and Hobbes in the seventeenth century. The in-depth Introduction begins with delineating distinct ways of conceptualizing time: absolute and relative. -
Empiricism, Stances, and the Problem of Voluntarism
Swarthmore College Works Philosophy Faculty Works Philosophy 1-1-2011 Empiricism, Stances, And The Problem Of Voluntarism Peter Baumann Swarthmore College, [email protected] Follow this and additional works at: https://works.swarthmore.edu/fac-philosophy Part of the Philosophy Commons Let us know how access to these works benefits ouy Recommended Citation Peter Baumann. (2011). "Empiricism, Stances, And The Problem Of Voluntarism". Synthese. Volume 178, Issue 1. 27-36. DOI: 10.1007/s11229-009-9519-7 https://works.swarthmore.edu/fac-philosophy/13 This work is brought to you for free by Swarthmore College Libraries' Works. It has been accepted for inclusion in Philosophy Faculty Works by an authorized administrator of Works. For more information, please contact [email protected]. Empiricism, Stances and the Problem of Voluntarism Peter Baumann Synthese 178, 2011, 207-224 Empiricism can be very roughly characterized as the view that our knowledge about the world is based on sensory experience. Our knowledge about the world is "based" on sensory experience in the sense that we could not know what we know without relying on sense experience. This leaves open the possibility that sense experience is only necessary but not sufficient for the knowledge based upon it1-as long as the non-empirical elements are not themselves sufficient for the relevant piece of knowledge.2 The basing relation is not just a genetic one but also a justificatory one: Sense experience does not only lead to beliefs which happen to count as knowledge but also qualifies them as knowledge. In his important book The Empirical Stance Bas van Fraassen characterizes traditional empiricism at one point in a more negative way-as involving the rejection of "metaphysical" explanations which proceed by postulating the existence of something not 1 "But although all our cognition commences with experience, yet it does not on that account all arise from experience." (Kant, CpR, B1). -
FROM Foundations to Spirals the Final Stage of the Puzzle Will
CHAPTER EIGHT From fouNDatioNS to spiraLS The final stage of the puzzle will therefore be to answer the following question: if as Feyerabend says, knowledge is now ‘without founda- tions’, does that therefore also entail the epistemic anarchy which Feyerabend advocates, or is it possible to salvage the rather more ordered construction which is theological science? Enlightenment foundationalism and reductionism Logical positivism represented the most systematic formulation of enlightenment (and empiricist) foundationalism,1 and Feyerabend’s correct critique (theory ladenness/determinedness of observations) of this particular form of foundationalism is over-stretched to rather shaky conclusions (theoretical pluralism, counter-inductivism, relativ- ism, voluntarism), not shared by other more moderate critics of logical positivism. Torrance for instance, like most theologians, rejects logical positivism, welcoming a renewed ‘dynamic integration’2 between the theoretic and empirical components of modern physics. It is not obvious, at least from a developmental psychological or cog- nitive point of view, why foundationalism provides an ideal metaphor for knowledge or the methods of its acquisition. The two features of foundationalism which were attractive to enlightenment thought were 1 See Oberdan in The British Journal for the Philosophy of Science, “The Vienna Circle’s ‘anti-foundationalism’ ”. Vol. 49/2, p. 297–308, for a ‘traditional’ account of Schlick’s work as foundational against the ‘anti-foundational’ interpretation of Uebel. For another anti-foundationalist account of logical positivism see M. Friedman, Reconsidering logical positivism, CUP, Cambridge, 1999. Here we have adopted a more conventional account of logical positivism, firstly because it is beyond the scope of this book to weigh arguments within the philosophy of science regarding traditional and revisionist accounts of logical positivism – but more importantly because our major players Feyerabend, in particular, Torrance, McGrath (e.g. -
Letting Scotus Speak for Himself
View metadata, citation and similar papers at core.ac.uk brought to you by CORE Medieval Philosophy and Theology 10 (2001), 173–216. Printed in the United States of America. provided by eCommons@Cornell Copyright C 2003 Cambridge University Press 1057-0608 DOI: 10.1017.S1057060801010076 Letting Scotus Speak for Himself MARY BETH INGHAM Loyola Marymount University In “The Unmitigated Scotus,” Thomas Williams calls for another, better reading of the Subtle Doctor: one in which he is able to “speak for himself.”1 In this and other articles, Williams criticizes recent Scotist scholarship for its misguided attempt to save Scotus from “the unpalatable position” he actually held, that is, a libertarian voluntarist divine command moral philosophy.2 He presents his position as one that, finally, allows Scotus to speak for himself. Williams’s position involves three distinct claims. First, that Scotus’s voluntarism is not moderate. Second, that he defends a libertarian notion of freedom, both in the divine and human wills. Third, that, as a result of the first two claims, natural reason is unable to know moral truths without some sort of supernatural revelation or immediate moral intuition. While these are clearly related, they must be argued for independently of one another. For example, Scotus could be a moderate voluntarist about the human will and a libertarian about the divine will. Additionally, he might be both a moderate voluntarist and nonlibertarian who defends some sort of supernatural requirement for moral judgment. So, even if the radical voluntarist, libertarian divine command claim in its most extreme form is unwarranted, one might defend it in a more nuanced formulation. -
Introduction
Cambridge University Press 978-0-521-86613-2 - Pierre Gassendi and the Birth of Early Modern Philosophy Antonia Lolordo Excerpt More information Introduction This book is bothaninterpretation of Gassendi’s central metaphysical, epistemological, and natural philosophical views and an advertisement for their philosophical and historical interest. Historians of seventeenth- century philosophy can usually tell you that Gassendi was an atomist, an empiricist,oramitigated skeptic, as well as an opponent of Aristotle and Descartes. They might add that he attempted to revive Epicureanism. However, few are likely to have any clear conception ofthe theses Gassendi articulates, the argumentsheoffers in their defense, or the systematic connections between them. This is an unfortunatesituation, and I aim to remedy it. There are at leasttwo reasons why those of us who are interested in early modern philosophy and natural philosophy need to know more about Gassendi. The first is widely recognized. Gassendi’s influence and the importance he was accorded by his peers and close contemporaries is unquestionable. Gassendi was a central figure in seventeenth-century philosophy and, as such, very importantfor the development of mod- ern philosophical thought. He knew and was known by such figures as Descartes and Hobbes and is importantfor understanding Leibniz, Locke, and Newton. Were one a seventeenth-century intellectual who found Cartesianism unacceptable, Gassendi’s philosophy was the obvi- ous alternative. Less well known, however, is the philosophical interest -
Calculation and Controversy
calculation and controversy The young Newton owed his greatest intellectual debt to the French mathematician and natural philosopher, René Descartes. He was influ- enced by both English and Continental commentators on Descartes’ work. Problems derived from the writings of the Oxford mathematician, John Wallis, also featured strongly in Newton’s development as a mathe- matician capable of handling infinite series and the complexities of calcula- tions involving curved lines. The ‘Waste Book’ that Newton used for much of his mathematical working in the 1660s demonstrates how quickly his talents surpassed those of most of his contemporaries. Nevertheless, the evolution of Newton’s thought was only possible through consideration of what his immediate predecessors had already achieved. Once Newton had become a public figure, however, he became increasingly concerned to ensure proper recognition for his own ideas. In the quarrels that resulted with mathematicians like Gottfried Wilhelm Leibniz (1646–1716) or Johann Bernoulli (1667–1748), Newton supervised his disciples in the reconstruction of the historical record of his discoveries. One of those followers was William Jones, tutor to the future Earl of Macclesfield, who acquired or copied many letters and papers relating to Newton’s early career. These formed the heart of the Macclesfield Collection, which has recently been purchased by Cambridge University Library. 31 rené descartes, Geometria ed. and trans. frans van schooten 2 parts (Amsterdam, 1659–61) 4o: -2 4, a-3t4, g-3g4; π2, -2 4, a-f4 Trinity* * College, Cambridge,* shelfmark* nq 16/203 Newton acquired this book ‘a little before Christmas’ 1664, having read an earlier edition of Descartes’ Geometry by van Schooten earlier in the year. -
Isaac Barrow
^be ©pen Court A MONTHLY MAGAZINE S>et»otc^ to tbe Science of l^eUdion, tbe l^elfdfon ot Science, anb tbc BXiCnsion ot tbe Itelidioud parliament Ibea Founded by Edwabo C. Hegeuol VOL. XXX. (No. 2) FEBRUARY, 1916 NO. 717 CONTENTS: MM Frontispiece. Isaac Barrow. Isaac Barrow: The Drawer of Tangents. J. M. Child 65 ''Ati Orgy of Cant.'' Paul Carus 70 A Chippewa Tomahawk. An Indian Heirloom with a History (Illus- trated). W. Thornton Parker 80 War Topics. —In Reply to My Critics. Paul Carus 87 Portraits of Isaac Barrow 126 American Bahaism and Persia 126 A Correction 126 A Crucifix After Battle (With Illustration) ^ 128 ^be i^pen Court publiebing CompaniS i CHICAGO Per copy, 10 cents (sixpence). Yearly, $1.00 (in the U.P.U., 5i. 6d). Entered w Secoad-QaM Matter March j6, 1897, at the Post Office at Chicago. III., under Act of Marck 3, \\j% Copyright by The Open Court Publishing Company, 1916 tTbe ©pen Court A MONTHLY MAGAZINE S>et»otc^ to tbe Science ot l^eUdion, tbe l^elfdfon ot Science* anb tbe BXiCndion ot tbe 1{eliaiou0 parliament Ibea Founded by Edwabo C Hegeueb. VOL. XXX. (No. 2) FEBRUARY, 1916 NO. 717 CONTENTS: Frontispiece. Isaac Barrow. Isaa£ Barrow: The Drawer of Tangents. J. M. Child 65 ''A7i Orgy of Cant.'" Paul Carus 70 A Chippewa Totnahawk. An Indian Heirloom with a History (Illus- trated). W. Thornton Parker 80 War Topics. —In Reply to My Critics. Paul Carus 87 Portraits of Isaac Barrow • 126 American Bahaism and Persia 126 A Correction 126 A Crucifix After Battle (With Illustration) 128 ^be ®pen Court publisbino CompaniS I CHICAGO Per copy, 10 cents (sixpence). -
1 1 Forthcoming in Philosophical Studies. Bellingham Conference
1 Forthcoming in Philosophical Studies. Bellingham Conference Issue, 2012 Grounding Practical Normativity: Going Hybrid Ruth Chang In virtue of what is something a reason for an agent to perform some action? In other words, what makes a consideration a reason for an agent to act? This is a prima facie metaphysical (or meta-normative) question about the grounding of reasons for action and not a normative question about the circumstances or conditions under which, normatively speaking, one has a reason to do something. The normative question is answered by normative theory, as when one says that such-and-such feature of an action is a reason to perform that action because bringing about that feature would maximize happiness. The metaphysical question asks instead for the metaphysical determinant of something’s being a reason. When we ask for the ground of a reason’s normativity, we ask what metaphysically makes something have the action-guidingness of a reason: where does the normativity of a practical reason come from? As Christine Korsgaard puts it, somewhat more poetically, what is the ‘source’ of a reason’s normativity? This paper takes a synoptic approach to the question of source and from this broad perspective explores the idea that the source of normativity might best be understood as a hybrid of more traditional views of source. The paper begins with a survey of three leading non-hybrid answers to the question of a reason’s normative ground or source (§1). It then recapitulates one or two of the supposedly most difficult problems for each, suggesting along the way a new objection to one of the leading views (§ 2). -
Doing Hard Time: Is God the Prisoner of the Oldest Dimension?
Doing Hard Time: Is God the Prisoner of the Oldest Dimension? R.T. Mullins University of Notre Dame Abstract: In this paper I shall consider an objection to divine temporality called “The Prisoner of Time” objection. I shall begin by distinguishing divine timelessness from divine temporality in order to clear up common misunderstandings and caricatures of divine temporality. From there I shall examine the prisoner of time objection and explain why the prisoner of time objection fails to be a problem for the Christian divine temporalist. During the 20th Century, various Christian philosophers and theologians have rejected divine timelessness. This is not an entirely new phenomena; one can find philosophers and theologians from the Reformation on rejecting divine timelessness. Thinkers like Pierre Gassendi, Isaac Newton, Samuel Clarke, and John Tillotson all rejected the doctrine of divine timelessness long ago for philosophical, theological, scientific, and biblical reasons.1 For these thinkers, time is a necessary concomitant of God’s eternal nature. Despite the efforts of these thinkers, the doctrine of divine timelessness continued to play a central role in Christian theology until the 20th Century. During the 20th Century, and the beginning of this century, one can find a more wide spread rejection of divine timelessness amongst Christian philosophers and systematic theologians. Some of these rejections have been quite rigorous, while others have been misguided. The more recent widespread rejection of the atemporal God has led many into the loving arms of the temporal God. However, divine temporality is not without its critics. Divine atemporality refuses to lay down and die.