Gottfried Wilhelm Leibniz: an Intellectual Portrait
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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. -
Stanislaw Piatkiewicz and the Beginnings of Mathematical Logic in Poland
HISTORIA MATHEMATICA 23 (1996), 68±73 ARTICLE NO. 0005 Stanisøaw PiaËtkiewicz and the Beginnings of Mathematical Logic in Poland TADEUSZ BATO G AND ROMAN MURAWSKI View metadata, citation and similar papers at core.ac.uk brought to you by CORE Department of Mathematics and Computer Science, Adam Mickiewicz University, ul. Matejki 48/49, 60-769 PoznanÂ, Poland provided by Elsevier - Publisher Connector This paper presents information on the life and work of Stanisøaw PiaËtkiewicz (1849±?). His Algebra w logice (Algebra in Logic) of 1888 contains an exposition of the algebra of logic and its use in representing syllogisms. This was the ®rst original Polish publication on symbolic logic. It appeared 20 years before analogous works by èukasiewicz and Stamm. 1996 Academic Press, Inc. In dem Aufsatz werden Informationen zu Leben und Werk von Stanisøaw PiaËtkiewicz (1849±?) gegeben. Sein Algebra w logice (Algebra in der Logik) von 1888 enthaÈlt eine Darstel- lung der Algebra der Logik und ihre Anwendung auf die Syllogistik. PiaËtkiewicz' Schrift war die erste polnische Publikation uÈ ber symbolische Logik. Sie erschien 20 Jahre vor aÈhnlichen Arbeiten von èukasiewicz und Stamm. 1996 Academic Press, Inc. W pracy przedstawiono osobeË i dzieøo Stanisøawa PiaËtkiewicza (1849±?). W szczego lnosÂci analizuje sieË jego rozpraweË Algebra w logice z roku 1888, w kto rej zajmowaø sieË on nowymi no wczas ideami algebry logiki oraz ich zastosowaniami do sylogistyki. Praca ta jest pierwszaË oryginalnaË polskaË publikacjaË z zakresu logiki symbolicznej. Ukazaøa sieË 20 lat przed analog- icznymi pracami èukasiewicza i Stamma. 1996 Academic Press, Inc. MSC 1991 subject classi®cations: 03-03, 01A55. -
Beauty on Display Plato and the Concept of the Kalon
BEAUTY ON DISPLAY PLATO AND THE CONCEPT OF THE KALON JONATHAN FINE Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Graduate School of Arts and Sciences COLUMBIA UNIVERSITY 2018 © 2018 Jonathan Fine All rights reserved ABSTRACT BEAUTY ON DISPLAY: PLATO AND THE CONCEPT OF THE KALON JONATHAN FINE A central concept for Plato is the kalon – often translated as the beautiful, fine, admirable, or noble. This dissertation shows that only by prioritizing dimensions of beauty in the concept can we understand the nature, use, and insights of the kalon in Plato. The concept of the kalon organizes aspirations to appear and be admired as beautiful for one’s virtue. We may consider beauty superficial and concern for it vain – but what if it were also indispensable to living well? By analyzing how Plato uses the concept of the kalon to contest cultural practices of shame and honour regulated by ideals of beauty, we come to see not only the tensions within the concept but also how attractions to beauty steer, but can subvert, our attempts to live well. TABLE OF CONTENTS Acknowledgements ii 1 Coordinating the Kalon: A Critical Introduction 1 1 The Kalon and the Dominant Approach 2 2 A Conceptual Problem 10 3 Overview 24 2 Beauty, Shame, and the Appearance of Virtue 29 1 Our Ancient Contemporaries 29 2 The Cultural Imagination 34 3 Spirit and the Social Dimension of the Kalon 55 4 Before the Eyes of Others 82 3 Glory, Grief, and the Problem of Achilles 100 1 A Tragic Worldview 103 2 The Heroic Ideal 110 3 Disgracing Achilles 125 4 Putting Poikilia in its Place 135 1 Some Ambivalences 135 2 The Aesthetics of Poikilia 138 3 The Taste of Democracy 148 4 Lovers of Sights and Sounds 173 5 The Possibility of Wonder 182 5 The Guise of the Beautiful 188 1 A Psychological Distinction 190 2 From Disinterested Admiration to Agency 202 3 The Opacity of Love 212 4 Looking Good? 218 Bibliography 234 i ACKNOWLEDGEMENTS “To do philosophy is to explore one’s own temperament,” Iris Murdoch suggested at the outset of “Of ‘God’ and ‘Good’”. -
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 -
The Role of Simplicity in Science and Theory. C
East Tennessee State University Digital Commons @ East Tennessee State University Undergraduate Honors Theses Student Works 5-2013 It's Not So Simple: The Role of Simplicity in Science and Theory. C. R. Gregg East Tennessee State University Follow this and additional works at: https://dc.etsu.edu/honors Part of the Theory and Philosophy Commons Recommended Citation Gregg, C. R., "It's Not So Simple: The Role of Simplicity in Science and Theory." (2013). Undergraduate Honors Theses. Paper 97. https://dc.etsu.edu/honors/97 This Honors Thesis - Withheld is brought to you for free and open access by the Student Works at Digital Commons @ East Tennessee State University. It has been accepted for inclusion in Undergraduate Honors Theses by an authorized administrator of Digital Commons @ East Tennessee State University. For more information, please contact [email protected]. IT’S NOT SO SIMPLE: THE ROLE OF SIMPLICITY IN SCIENCE AND THEORY Thesis submitted in partial fulfillment of Honors By C. R. Gregg Philosophy Honors In Discipline Program East Tennessee State University May 3, 2013 (Updated) May 7, 2013 Dr. David Harker, Faculty Mentor Dr. Jeffrey Gold, Honors Coordinator Dr. Gary Henson, Faculty Reader Dr. Allen Coates, Faculty Reader Paul Tudico, Faculty Reader ACKNOWLEDGMENTS I would like to sincerely thank: David Harker, my mentor and friend. Paul Tudico, who is largely responsible for my choice to pursue Philosophy. Leslie MacAvoy, without whom I would not be an HID student. Karen Kornweibel, for believing in me. Rebecca Pyles, for believing in me. Gary Henson and Allen Coates, for offering their time to serve as readers. -
BY PLATO• ARISTOTLE • .AND AQUINAS I
i / REF1,l!;CTit.>NS ON ECONOMIC PROBLEMS / BY PLATO• ARISTOTLE • .AND AQUINAS ii ~FLECTIONS ON ECONO:MIC PROBLEMS 1 BY PLA'I'O, ARISTOTLE, JJJD AQUINAS, By EUGENE LAIDIBEL ,,SWEARINGEN Bachelor of Science Oklahoma Agricultural and Mechanical Collage Stillwater, Oklahoma 1941 Submitted to the Depertmeut of Economics Oklahoma Agricultural and Mechanical College In Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE 1948 iii f.. 'I. I ···· i·: ,\ H.: :. :· ··: ! • • ~ ' , ~ • • !·:.· : i_ ·, 1r 1i1. cr~~rJ3t L l: i{ ,\ I~ Y , '•T •)() 1 0 ,1 8 API-'HOV~D BY: .J ,.· 1.., J l.;"t .. ---- -··- - ·- ______.,.. I 7 -.. JI J ~ L / \ l v·~~ u ' ~) (;_,LA { 7 {- ' r ~ (\.7 __\ _. ...A'_ ..;f_ ../-_" ...._!)_.... ..." ___ ......._ ·;...;;; ··-----/ 1--.,i-----' ~-.._.._ :_..(__,,---- ....... Member of the Report Committee 1..j lj:,;7 (\ - . "'·- -· _ .,. ·--'--C. r, .~-}, .~- Q_ · -~ Q.- 1Head of the Department . · ~ Dean of the Graduate School 502 04 0 .~ -,. iv . r l Preface The purpose and plan of this report are set out in the Introduction. Here, I only wish to express my gratitude to Professor Russell H. Baugh who has helped me greatly in the preparation of this report by discussing the various subjects as they were in the process of being prepared. I am very much indebted to Dr. Harold D. Hantz for his commentaries on the report and for the inspiration which his classes in Philosophy have furnished me as I attempted to correlate some of the material found in these two fields, Ecor!.Omics and Philosophy. I should like also to acknowledge that I owe my first introduction into the relationships of Economics and Philosophy to Dean Raymond Thomas, and his com~ents on this report have been of great value. -
Plato, Philo, and the Author of Hebrews
Plato, Philo, and the Author of Hebrews BY JAMES H. BURTNESS INCE the first centuries of the Christian church, there have been serious ques S tions concerning the origin of the Epistle to the Hebrews. It is primarily to the modern period, however, that we owe the view that the author of this epistle was deeply influenced by Platone idealism and by the philosophy of the Alexandrian School, particularly the writings of Philo. Hugo Grotius was perhaps the first, in 1644, to point out the close connection between Philo and Hebrews 4:10. In 1750, Carpzov published a volume of Sacrae Exercitationes in S. Paulli Epistolam ad Hebraeos ex Philone Alexandrine. J. J. Wettstein, in his Novum Testamentum Graecum of 1752, also pointed out these parallels. The rationalistic critics of the nineteenth century saw Alexandrianism written all over the epistle. Baur regarded it as a Judeo-Christian product inter mixed with Paulinism and spiritualized by an Alexandrian mentality. Ménégoz, in his La Theologie de L'Epitre aux Hébreux of 1894, concluded that the author was a Philonian converted to Christianity. At the end of the last century the de pendence of the epistle upon the religious philosophy of Philo was considered to be a secured result of literary criticism. Typical of this period are the following statements by Pfleiderer and von Soden: The Hellenistic basis of the Epistle to the Hebrews, its dependence in thought and word upon the Book of Wisdom, and especially upon Philo, is so obvious that there is not the smallest room for doubt upon the matter.1 It marks the definite entrance of Alexandrianism into the sphere of Christianity. -
Greek and Latin Roots, Prefixes, and Suffixes
GREEK AND LATIN ROOTS, PREFIXES, AND SUFFIXES This is a resource pack that I put together for myself to teach roots, prefixes, and suffixes as part of a separate vocabulary class (short weekly sessions). It is a combination of helpful resources that I have found on the web as well as some tips of my own (such as the simple lesson plan). Lesson Plan Ideas ........................................................................................................... 3 Simple Lesson Plan for Word Study: ........................................................................... 3 Lesson Plan Idea 2 ...................................................................................................... 3 Background Information .................................................................................................. 5 Why Study Word Roots, Prefixes, and Suffixes? ......................................................... 6 Latin and Greek Word Elements .............................................................................. 6 Latin Roots, Prefixes, and Suffixes .......................................................................... 6 Root, Prefix, and Suffix Lists ........................................................................................... 8 List 1: MEGA root list ................................................................................................... 9 List 2: Roots, Prefixes, and Suffixes .......................................................................... 32 List 3: Prefix List ...................................................................................................... -
Phil 252S Seminar on Meta-Metaphysics
Phil 252S Seminar on Meta-metaphysics Professor: Sara Bernstein ([email protected]) Special Guest: Peter van Inwagen Metaphysics concerns questions about what exists: for example, do chairs really exist, or are there merely particles arranged chair-wise? What are the criteria for their existence? Meta-metaphysics concerns questions about the methodology and substantivity of metaphysics. For example, does reality furnish answers to metaphysical questions? If so, do we have epistemic access to the answers? Or is it our language and social conventions that give us answers to metaphysical questions? Do answers to these questions determine the substantivity of metaphysical debates? Required Texts: Metametaphysics (ed. Wasserman and Chalmers) Requirements: For undergraduate students: weekly well-formed questions due on Tuesdays at 6pm (20%) one in-class presentations on a course reading (20%) one 6-8 page term paper (40%) class participation (20%) For graduate students: weekly well-formed questions due on Tuesdays at 6pm (10%) one in-class presentation on a course reading (10%) one presentation on your own term paper and term paper (60%) class participation (20%) Schedule: Wednesday, January 19: Introduction to Metametaphysics Ted Sider, “Ontology” (chapter 9) and “Metametaphysics” (chapter 5) from Writing the Book of the World (unpublished draft) (Blackboard) 1 January 26: First-Order Ontological Debates Peter van Inwagen, Material Beings, Chapters 2 and 3 (Blackboard) David Lewis and Stephanie Lewis, “Holes” (Blackboard) February 2: -
Epistemology As a Foundation for Epicurean Thought Emma E
Florida State University Libraries Electronic Theses, Treatises and Dissertations The Graduate School 2012 Epistemology as a Foundation for Epicurean Thought Emma E. Hughes Follow this and additional works at the FSU Digital Library. For more information, please contact [email protected] THE FLORIDA STATE UNIVERSITY COLLEGE OF ARTS AND SCIENCES EPISTEMOLOGY AS A FOUNDATION FOR EPICUREAN THOUGHT By EMMA E. HUGHES A Thesis submitted to the Department of Classics in partial fulfillment of the requirements for the degree of Master of Arts Degree Awarded: Spring Semester, 2012 Emma E. Hughes defended this thesis on March 26th, 2012. The members of the supervisory committee were: Svetla Slaveva-Griffin Professor Directing Thesis Timothy Stover Committee Member Nathanael Stein Committee Member The Graduate School has verified and approved the above-named committee members, and certifies that the thesis has been approved in accordance with university requirements. ii TABLE OF CONTENTS Abstract.......................................................................................................................................... iv INTRODUCTION...................................................................................................................1 CHAPTER ONE: A NEW LOOK AT AN OLD SCHOOL ..................................................5 CHAPTER TWO: PROBLEMS IN EPICUREAN EPISTEMOLOGY ...............................18 CHAPTER THREE: AN EPISTEMOLOGICAL FOUNDATION......................................30 CHAPTER FOUR: CONCLUSION .....................................................................................38 -
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. -
Origen in the Likeness of Philo: Eusebius of Caesarea's Portrait Of
SCJR 12, no. 1 (2017): 1-13 Origen in the Likeness of Philo: Eusebius of Caesarea’s Portrait of the Model Scholar JUSTIN M. ROGERS [email protected] Freed-Hardeman University, Henderson, TN 38340 The name of Philo of Alexandria occurs more in the writings of Eusebius of Caesarea than in those of any other ancient author. Philo’s name can be located over 20 times in the surviving literary corpus of Eusebius,1 and there is strong ev- idence that Eusebius’ Caesarean library is the very reason Philo’s works exist today.2 In all probability, the core of this library can be traced to the personal col- lection of Origen when he settled in Caesarea in 232 CE.3 Eusebius’ own teacher Pamphilus expanded the library, and took great pains to copy and preserve Ori- gen’s own works. What we have, then, is a literary union between Philo and Origen, Alexandrians within the same exegetical tradition. But we can go further. Ilaria Ramelli has argued that Eusebius’ accounts of Philo and Origen in the Ecclesiastical History are strikingly similar, picking up Robert Grant’s stress on the similarity between Origen and the Philonic Therapeutae.4 Here, I further Ramelli’s work by noting additional similarities in the Eusebian biographical presentations. I also point to the tension Eusebius felt between Philo Christianus and Philo Judaeus, a tension detectible in his presentation of the Therapeutae, a group about whom Philo reported and whom Eusebius considered to be the first Egyptian Christians.5 The result is that Eusebius recognized Philo to be exegeti- cally closer to Christianity, and religiously closer to Judaism.