Theodicy and Reason Logic, Metaphysics
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How Dualists Should (Not) Respond to the Objection from Energy
c 2019 Imprint Academic Mind & Matter Vol. 17(1), pp. 95–121 How Dualists Should (Not) Respond to the Objection from Energy Conservation Alin C. Cucu International Academy of Philosophy Mauren, Liechtenstein and J. Brian Pitts Faculty of Philosophy and Trinity College University of Cambridge, United Kingdom Abstract The principle of energy conservation is widely taken to be a se- rious difficulty for interactionist dualism (whether property or sub- stance). Interactionists often have therefore tried to make it satisfy energy conservation. This paper examines several such attempts, especially including E. J. Lowe’s varying constants proposal, show- ing how they all miss their goal due to lack of engagement with the physico-mathematical roots of energy conservation physics: the first Noether theorem (that symmetries imply conservation laws), its converse (that conservation laws imply symmetries), and the locality of continuum/field physics. Thus the “conditionality re- sponse”, which sees conservation as (bi)conditional upon symme- tries and simply accepts energy non-conservation as an aspect of interactionist dualism, is seen to be, perhaps surprisingly, the one most in accord with contemporary physics (apart from quantum mechanics) by not conflicting with mathematical theorems basic to physics. A decent objection to interactionism should be a posteri- ori, based on empirically studying the brain. 1. The Objection from Energy Conservation Formulated Among philosophers of mind and metaphysicians, it is widely believed that the principle of energy conservation poses a serious problem to inter- actionist dualism. Insofar as this objection afflicts interactionist dualisms, it applies to property dualism of that sort (i.e., not epiphenomenalist) as much as to substance dualism (Crane 2001, pp. -
Realizing Monads
anDrás kornai Realizing Monads ABSTrACT We reconstruct monads as cyclic finite state automata whose states are what Leibniz calls perceptions and whose transitions are automatically triggered by the next time tick he calls entelechy. This goes some way toward explaining key as- pects of the Monadology, in particular, the lack of inputs and outputs (§7) and the need for universal harmony (§59). 1. INTrODUCTION Monads are important both in category theory and in programming language de- sign, clearly demonstrating that Leibniz is greatly appreciated as the conceptual forerunner of much of abstract thought both in mathematics and in computer sci- ence. Yet we suspect that Leibniz, the engineer, designer of the Stepped reck- oner, would use the resources of the modern world to build a very different kind of monad. Throughout this paper, we confront Leibniz with our contemporary scientific understanding of the world. This is done to make sure that what we say is not “concretely empty” in the sense of Unger (2014). We are not interested in what we can say about Leibniz, but rather in what Leibniz can say about our cur- rent world model. readers expecting some glib demonstration of how our current scientific theories make Leibniz look like a fool will be sorely disappointed. Looking around, and finding a well-built Calculus ratiocinator in Turing ma- chines, pointer machines, and similar abstract models of computation, Leibniz would no doubt consider his Characteristica Universalis well realized in modern proof checkers such as Mizar, Coq, or Agda to the extent mathematical deduc- tion is concerned, but would be somewhat disappointed in their applicability to natural philosophy in general. -
Orbital Mechanics
Orbital Mechanics These notes provide an alternative and elegant derivation of Kepler's three laws for the motion of two bodies resulting from their gravitational force on each other. Orbit Equation and Kepler I Consider the equation of motion of one of the particles (say, the one with mass m) with respect to the other (with mass M), i.e. the relative motion of m with respect to M: r r = −µ ; (1) r3 with µ given by µ = G(M + m): (2) Let h be the specific angular momentum (i.e. the angular momentum per unit mass) of m, h = r × r:_ (3) The × sign indicates the cross product. Taking the derivative of h with respect to time, t, we can write d (r × r_) = r_ × r_ + r × ¨r dt = 0 + 0 = 0 (4) The first term of the right hand side is zero for obvious reasons; the second term is zero because of Eqn. 1: the vectors r and ¨r are antiparallel. We conclude that h is a constant vector, and its magnitude, h, is constant as well. The vector h is perpendicular to both r and the velocity r_, hence to the plane defined by these two vectors. This plane is the orbital plane. Let us now carry out the cross product of ¨r, given by Eqn. 1, and h, and make use of the vector algebra identity A × (B × C) = (A · C)B − (A · B)C (5) to write µ ¨r × h = − (r · r_)r − r2r_ : (6) r3 { 2 { The r · r_ in this equation can be replaced by rr_ since r · r = r2; and after taking the time derivative of both sides, d d (r · r) = (r2); dt dt 2r · r_ = 2rr;_ r · r_ = rr:_ (7) Substituting Eqn. -
Developments in Neuroscience and Human Freedom: Some Theological and Philosophical Questions
S & CB (2003), 16, 123–137 0954–4194 ALAN TORRANCE Developments in Neuroscience and Human Freedom: Some Theological and Philosophical Questions Christianity suggests that human beings are free and responsible agents. Developments in neuroscience challenge this when wedded with two ‘fideisms’: ‘naturalism’ and ‘nomological monism’ (causality applies exclusively to basic particles). The wedding of Galen Strawson’s denial that anything can be a cause of itself with a physicalist account of brain states highlights the problem neuroscience poses for human freedom. If physicalism is inherently reductionistic (Kim) and dualism struggles to make sense of developments in neuroscience, Cartwright’s pluralist account of causality may offer a way forward. It integrates with thinking about the person from a Christian epistemic base and facilitates response to Strawson. Key Words: God, person, neuroscience, freedom, naturalism, nomological monism, physicalism, dualism, causality. Five years ago, the Ethics and Public Policy Center in Washington, hosted a conference on ‘Neuroscience and the Human Spirit’. In his opening address, the organiser, Dr Frederick Goodwin, asked whether developments in the field do not pose a challenge to the ‘very foundation upon which our civilization rests’, namely, ‘free will and the capacity to make moral choices?’ The question I am seeking to address here raises the same issue with respect to the grounds of the Christian understanding of its message and, indeed, of what it is to be a person. In the light of recent advances in understanding the physical workings of our neural substrate, the electrochemical nature of cerebral processing and so on, does it still make sense to conceive of our minds as the free cause of our actions and the conscious centre of human life? So much suggests that the workings of our minds require to be construed in radically physical and, apparently, imper- sonal terms – as a complex causal series of synaptic firings and the like. -
Leibniz and Monads
Leibniz and Monads The Human Situaon Team Omega, Spring 2010 Dr. Cynthia Freeland Overview • Leibniz’s Life • The Rise of Modernism • Monadology 1‐30 • All about Monads Leibniz 1646‐1716 The Duchess of Orleans said of him: “It's so rare for intellectuals to be smartly dressed, and not to smell, and to understand jokes.” A contemporary descripon of Leibniz “Leibniz was a man of medium height with a stoop, broad‐shouldered but bandy‐legged, as capable of thinking for several days sing in the same chair as of travelling the roads of Europe summer and winter. He was an indefagable worker, a universal leer writer (he had more than 600 correspondents), a patriot and cosmopolitan, a great scienst, and one of the most powerful spirits of Western civilisaon.” Goried Wilhelm von Leibniz “A walking encyclopedia” – King George I Monadology, 1714 Leibniz the Polymath • Studies in university: Law, philosophy, Lan, Greek • Independent: algebra, mathemacs, physics, dynamics, opcs, tried to create a submarine • Secretary of Nuremberg Alchemical Society • Laws of moon, gravity, mechanics, dynamics, topology, geology, linguiscs • Polics, internaonal affairs, economics, coinage, watches, lamps • Traveled to Paris, London, Vienna, Italy, etc. • Invented Infinitesimal calculus, created a notaon for it d(xn) = nxn‐1dx Leibniz’s Calculang Machine Leibniz and the Prince • 1676‐1716, Librarian to the Duke of Hanover • Privy councilor to successive members of the House of Brunswick of Hanover, and friend/correspondent/teacher of successive prominent women in the family -
16.346 Astrodynamics Fall 2008
MIT OpenCourseWare http://ocw.mit.edu 16.346 Astrodynamics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Lecture 2 The Two Body Problem Continued The Eccentricity Vector or The Laplace Vector µ µe = v × h − r r Explicit Form of the Velocity Vector #3.1 Using the expansion of the triple vector product a × (b × c)=(a · c)b − (a · b)c we have µ h × µe = h × (v × h) − h × r = h2v − (h · v)h − µh × i = h2v − µh i × i r r h r since h and v are perpendicular. Therefore: µ h × µe =⇒ v = i × (e + i ) h h r or hv = i × (e i + i )=e i × i + i × i = e i + i µ h e r h e h r p θ Then since ip = sin f ir + cos f iθ we have hv = e sin f i +(1+e cos f) i µ r θ which is the basic relation for representing the velocity vector in the Hodograph Plane. See Page 1 of Lecture 4 Conservation of Energy hv hv p p 2 1 · = v · v = 2(1 + e cos f)+e 2 − 1=2× − (1 − e 2)=p − µ µ µ r r a which can be written in either of two separate forms each having its own name: 1 µ µ 1 Energy Integral v2 − = − = c 2 r 2a 2 3 2 1 Vis-Viva Integral v 2 = µ − r a The constant c3 is used by Forest Ray Moulton, a Professor at the University of Chicago in his 1902 book “An Introduction to Celestial Mechanics” — the first book on the subject written by an American. -
Kant's Doctrine of Religion As Political Philosophy
Kant's Doctrine of Religion as Political Philosophy Author: Phillip David Wodzinski Persistent link: http://hdl.handle.net/2345/987 This work is posted on eScholarship@BC, Boston College University Libraries. Boston College Electronic Thesis or Dissertation, 2009 Copyright is held by the author, with all rights reserved, unless otherwise noted. Boston College The Graduate School of Arts and Sciences Department of Political Science KANT’S DOCTRINE OF RELIGION AS POLITICAL PHILOSOPHY a dissertation by PHILLIP WODZINSKI submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy May 2009 © copyright by PHILLIP DAVID WODZINSKI 2009 ABSTRACT Kant’s Doctrine of Religion as Political Philosophy Phillip Wodzinski Advisor: Susan Shell, Ph.D. Through a close reading of Immanuel Kant’s late book, Religion within the Boundaries of Mere Reason, the dissertation clarifies the political element in Kant’s doctrine of religion and so contributes to a wider conception of his political philosophy. Kant’s political philosophy of religion, in addition to extending and further animating his moral doctrine, interprets religion in such a way as to give the Christian faith a moral grounding that will make possible, and even be an agent of, the improvement of social and political life. The dissertation emphasizes the wholeness and structure of Religion within the Boundaries of Mere Reason as a book, for the teaching of the book is not exhausted by the articulation of its doctrine but also includes both the fact and the manner of its expression: the reader learns most fully from Kant by giving attention to the structure and tone of the book as well as to its stated content and argumentation. -
David Hume, "The Dialogues Concerning Natural Religion," and Religious Tolerance
University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Supervised Undergraduate Student Research Chancellor’s Honors Program Projects and Creative Work 5-2020 David Hume, "The Dialogues Concerning Natural Religion," and Religious Tolerance Jarrett Delozier [email protected] Follow this and additional works at: https://trace.tennessee.edu/utk_chanhonoproj Part of the History of Philosophy Commons, History of Religion Commons, Intellectual History Commons, and the Religious Thought, Theology and Philosophy of Religion Commons Recommended Citation Delozier, Jarrett, "David Hume, "The Dialogues Concerning Natural Religion," and Religious Tolerance" (2020). Chancellor’s Honors Program Projects. https://trace.tennessee.edu/utk_chanhonoproj/2382 This Dissertation/Thesis is brought to you for free and open access by the Supervised Undergraduate Student Research and Creative Work at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Chancellor’s Honors Program Projects by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. DeLozier 1 Introduction In the history of philosophy of religion and natural theology, David Hume is an immensely influential contributor. One of his most important works in the field is his Dialogues Concerning Natural Religion, which contains his greatest treatment of natural theology, specifically the design argument. However, there’s a big problem which the Dialogues present to understanding Hume. Eleven of the twelve parts of the Dialogues contain Hume’s sharp criticisms and attacks on the Design argument. But in the final part, in what is often called “Philo’s Reversal,” he seems to completely reverse course by renouncing his skepticism and endorsing the Design argument. -
Leibniz's Ultimate Theory Soshichi Uchii Abstract
Leibniz’s Ultimate Theory Soshichi Uchii Abstract This is a short summary of my new interpretation of Leibniz’s philosophy, including metaphysics and dynamics. Monadology is the core of his philosophy, but according to my interpretation, this document must be read together with his works on dynamics and geometry Analysis Situs, among others. Monadology describes the reality, the world of monads. But in addition, it also contains a theory of information in terms of the state transition of monads, together with a sketch of how that information is transformed into the phenomena via coding. I will argue that Leibniz’s program has a surprisingly wide range, from classical physics to the theories of relativity (special and general) , and extending even to quantum mechanics. 1. How should we read Monadology? Among Leibniz’s papers he completed in his last years, the one that should be regarded as containing the core of his system of knowledge is Monadology (1714). It is a theory of metaphysics, but I take it that Leibniz thought that it is the foundation of dynamics, and he envisaged that dynamics should be combined with his new geometry, called Analysis Situs. There are two firm grounds for the preceding assertion. The first is that Leibniz sketched the relationship between his metaphysics and dynamics, in the two papers New System and Specimen Dynamicum (both published in 1695; English tr. in Ariew and Garber 1989). If we wish to figure out a reasonable interpretation of Monadology, this ground must be taken very seriously. The second ground is the amazing accomplishments shown in The Metaphysical Foundations of Mathematics (written around the same time as Monadology; English tr. -
Staying Optimistic: the Trials and Tribulations of Leibnizian Optimism
Strickland, Lloyd 2019 Staying Optimistic: The Trials and Tribulations of Leibnizian Optimism. Journal of Modern Philosophy, 1(1): 3, pp. 1–21. DOI: https://doi.org/10.32881/jomp.3 RESEARCH Staying Optimistic: The Trials and Tribulations of Leibnizian Optimism Lloyd Strickland Manchester Metropolitan University, GB [email protected] The oft-told story of Leibniz’s doctrine of the best world, or optimism, is that it enjoyed a great deal of popularity in the eighteenth century until the massive earthquake that struck Lisbon on 1 November 1755 destroyed its support. Despite its long history, this story is nothing more than a commentators’ fiction that has become accepted wisdom not through sheer weight of evidence but through sheer frequency of repetition. In this paper we shall examine the reception of Leibniz’s doctrine of the best world in the eighteenth century in order to get a clearer understanding of what its fate really was. As we shall see, while Leibniz’s doctrine did win a good number of adherents in the 1720s and 1730s, especially in Germany, support for it had largely dried up by the mid-1740s; moreover, while opponents of Leibniz’s doctrine were few and far between in the 1710s and 1720s, they became increasing vocal in the 1730s and afterwards, between them producing an array of objections that served to make Leibnizian optimism both philosophically and theologically toxic years before the Lisbon earthquake struck. Keywords: Leibniz; Optimism; Best world; Lisbon earthquake; Evil; Wolff The oft-told story of Leibniz’s doctrine of the best world, or optimism, is that it enjoyed a great deal of popularity in the eighteenth century until the massive earthquake that struck Lisbon on 1 November 1755 destroyed its support. -
Leibniz' De Arte Combinatoria
Leibniz’ De arte combinatoria John N. Martin Department of Philosophy University of Cincinnati Cincinnati, OH 45221 [email protected] John N. Martin, 2003 Page 1 Leibniz’ De arte combinatoria I. INTRODUCTION Logicians, philosophers and to judge from the Internet even the general public are vaguely aware that Leibniz held views about logic that anticipate modern ideas of proof system and algorithm. Though there are many places in Leibniz’ works that might be cited as evidence for such claims, popular works cite virtually only two of Leibniz’ shorter papers, Characteristica universalis and De arte combinatoria. Curiously, though there are hundreds, maybe thousands, of references to these papers, nothing serious has been written in recent decades about the papers themselves that could be called a professional exegesis or discussion of their logical content. The purpose of this short paper is to remedy that lack by offering a “reconstruction” of the system Leibniz sketches in De arte combinatoria, which of the two essays is the one more focused on the notions of proof and algorithm. A point of caution about method should be made at the outset. Any modern “reconstruction” of views in the history of logic is by its nature a compromise. It is an attempt to preserve as much of the original content, including its terminology and formulas, as is possible while simultaneously meeting the standards of modern metatheory. For example, if it is possible to do justice to the original by observing standard formats, then they should be Page 2 followed. For example, if it is fair to the text, it is desirable to define the syntax inductively, state definitions set theoretically, develop notions of proof within an axiom or natural deduction system, and define semantic ideas in a recursive manner parallel to syntax. -
A Leibnizian Approach to Mathematical Relationships: a New Look at Synthetic Judgments in Mathematics
A Thesis entitled A Leibnizian Approach to Mathematical Relationships: A New Look at Synthetic Judgments in Mathematics by David T. Purser Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Master of Arts Degree in Philosophy ____________________________________ Dr. Madeline M. Muntersbjorn, Committee Chair ____________________________________ Dr. John Sarnecki, Committee Member ____________________________________ Dr. Benjamin S. Pryor, Committee Member ____________________________________ Dr. Patricia Komuniecki, Dean College of Graduate Studies The University of Toledo December 2009 An Abstract of A Leibnizian Approach to Mathematical Relationships: A New Look at Synthetic Judgments in Mathematics by David T. Purser Submitted to the Graduate Faculty in partial fulfillment of the requirements for the Master of Arts Degree in Philosophy The University of Toledo May 2010 I examine the methods of Georg Cantor and Kurt Gödel in order to understand how new symbolic innovations aided in mathematical discoveries during the early 20th Century by looking at the distinction between the lingua characterstica and the calculus ratiocinator in the work of Leibniz. I explore the dynamics of innovative symbolic systems and how arbitrary systems of signification reveal real relationships in possible worlds. Examining the historical articulation of the analytic/synthetic distinction, I argue that mathematics is synthetic in nature. I formulate a moderate version of mathematical realism called modal relationalism. iii Contents Abstract iii Contents iv Preface vi 1 Leibniz and Symbolic Language 1 1.1 Introduction……………………………………………………. 1 1.2 Universal Characteristic……………………………………….. 4 1.2.1 Simple Concepts……………………………………….. 5 1.2.2 Arbitrary Signs………………………………………… 8 1.3 Logical Calculus………………………………………………. 11 1.4 Leibniz’s Legacy……………………………………………… 16 1.5 Leibniz’s Continued Relevance……………………………….