CURRICULUM VITAE MICHAEL DAVID RESNIK Born: March 20, 1938, New Haven, Connecticut Education
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Pluralisms About Truth and Logic Nathan Kellen University of Connecticut - Storrs, [email protected]
University of Connecticut OpenCommons@UConn Doctoral Dissertations University of Connecticut Graduate School 8-9-2019 Pluralisms about Truth and Logic Nathan Kellen University of Connecticut - Storrs, [email protected] Follow this and additional works at: https://opencommons.uconn.edu/dissertations Recommended Citation Kellen, Nathan, "Pluralisms about Truth and Logic" (2019). Doctoral Dissertations. 2263. https://opencommons.uconn.edu/dissertations/2263 Pluralisms about Truth and Logic Nathan Kellen, PhD University of Connecticut, 2019 Abstract: In this dissertation I analyze two theories, truth pluralism and logical pluralism, as well as the theoretical connections between them, including whether they can be combined into a single, coherent framework. I begin by arguing that truth pluralism is a combination of realist and anti-realist intuitions, and that we should recognize these motivations when categorizing and formulating truth pluralist views. I then introduce logical functionalism, which analyzes logical consequence as a functional concept. I show how one can both build theories from the ground up and analyze existing views within the functionalist framework. One upshot of logical functionalism is a unified account of logical monism, pluralism and nihilism. I conclude with two negative arguments. First, I argue that the most prominent form of logical pluralism faces a serious dilemma: it either must give up on one of the core principles of logical consequence, and thus fail to be a theory of logic at all, or it must give up on pluralism itself. I call this \The Normative Problem for Logical Pluralism", and argue that it is unsolvable for the most prominent form of logical pluralism. Second, I examine an argument given by multiple truth pluralists that purports to show that truth pluralists must also be logical pluralists. -
Cassirer's Reception of Dedekind and the Structuralist Transformation Of
13 Cassirer’s Reception of Dedekind and the Structuralist Transformation of Mathematics Erich H. Reck For much of the 20th century, Ernst Cassirer was seen as an intellectual historian, besides being the last member of Marburg Neo-Kantianism. More recently, he has been rediscovered as an original, substantive philosopher in his own right, perhaps even one of the great philosophers of the 20th century. This concerns his contributions to the philosophy of science (relativity theory, quantum me- chanics, etc.), his mature, wide- ranging philosophy of symbolic forms (leading to a “philosophy of culture”), and the ways in which his views position him, in potentially fruitful ways, at the intersection of “analytic” and “continental” phi- losophy.1 In addition, Cassirer was a keen observer of developments in pure mathematics, especially of their philosophical significance. There are two sep- arable, though not unrelated, strands on that topic in his writings. The first concerns his reflections on revolutionary changes in geometry during the 19th century, culminating in David Hilbert’s and Felix Klein’s works. The second strand involves parallel changes in algebra, arithmetic, and set theory, where Evariste Galois, Richard Dedekind, and Georg Cantor played key roles. In this essay the main focus will be on the second of the strands just mentioned, and in particular, on Cassirer’s reception of Dedekind, which still deserves more attention.2 As we will see, Cassirer was a perceptive reader of Dedekind, arguably still his subtlest philosophical interpreter. What he was concerned about with 1 For the philosophy of physics, cf. Ryckman (2005) and French (2014), more generally also Ihmig (2001) and Part I of Friedman and Luft (2017); for the philosophy of culture, cf. -
Jeremy Wyatt: Curriculum Vitae
Jeremy Wyatt Philosophy Programme School of Social Sciences Website: https://jeremywyatt.net The University of Waikato Email: [email protected] Private Bag 3105 Hamilton, New Zealand 3240 Areas of specialization: Truth, philosophy of language, metaphysics Areas of competence: Philosophy of logic, epistemology, Asian philosophy Education Ph.D. Philosophy; University of Connecticut; 2014 M.A., Philosophy; University of Connecticut, 2011 B.A. summa cum laude; Major: Philosophy; Minors: Political Science, Classical Studies; Texas Christian University, 2008 Employment Lecturer, Philosophy Programme, University of Waikato; February 2020-present Assistant Professor, Underwood International College, Yonsei University; September 2016-February 2020 Postdoctoral Researcher, Pluralisms Global Research Network, Yonsei University (principal investiga- tor: Nikolaj Pedersen); May 2014-August 2016 Publications Edited volumes and special issues The Nature of Truth: Classic and Contemporary Perspectives, 2nd edition, co-edited with Michael P. Lynch, Junyeol Kim, and Nathan Kellen. Forthcoming with MIT Press in 2020. Truth: Concept Meets Property, a special issue of Synthese. Contributions from Jamin Asay, Robert Barnard and Joseph Ulatowski, Douglas Edwards, Matti Eklund, Friederike Moltmann, and Kevin Scharp. Forthcoming in 2020. Pluralisms in Truth and Logic, co-edited with Nikolaj Pedersen and Nathan Kellen. Palgrave Macmillan, 2018. Jeremy Wyatt 2 Articles and book chapters Truth and insubstantiality: the metaphysics of deflationism. To appear in The Nature of Truth: Classic and Contemporary Perspectives, 2nd edition. Deflationary theories of truth. To appear in The Nature of Truth: Classic and Contemporary Perspectives, 2nd edition. Truth in English and elsewhere: an empirically-informed functionalism. In Wyatt, Pedersen, and Kellen, eds. Pluralisms in Truth and Logic. New York: Palgrave Macmillan. -
Complete Dissertation with Proper Pagination 4-12-14
The Logiphro Dilemma: An Examination of the Relationship between God and Logic Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By James C. McGlothlin, M.A. Graduate Program in Philosophy The Ohio State University 2014 Dissertation Committee: Stewart Shapiro, Advisor Tamar Rudavsky Chris Pincock Copyright James C. McGlothlin 2014 Abstract In this dissertation I set out to answer the following main question: What is the relationship between God and logic? I argue for an answer to this question by first examining two possible options and then give my own philosophical explanation that I believe overcomes the problems associated with the prior investigated options. In Chapter 1 I first define and clarify the desiderata of my main question. I understand God to be the divine being of classical theism shared by Jews, Christians and Muslims. I understand logic as primarily about the logical consequence relation. I characterize this relation in terms of necessity and universal applicability (or form), which captures various popular intuitions. Therefore, my main question is refined to: What is the relationship between the God of classical theism and logical consequence? In Chapter 2 I investigate an ancient question and dilemma presented by Plato in his Euthyphro dialogue, known popularly as the Euthyphro Dilemma. I suggest that the structure of this question naturally lends itself to the investigation of my question—what I call the Logiphro Dilemma, or the Logical Euthyphro Dilemma. As the name suggests, this dilemma gives us at least two options for thinking about the relationship between God and logic: (1) logical voluntarism: the view that claims the logical consequence relation is the result of God’s commands or will; and (2) logical non-voluntarism: the view that the logical consequence relation is completely independent of God’s commands ii or will in the sense of being independent of his creating or sustaining power. -
Structures and Structuralism in Contemporary Philosophy of Mathematics
ERICH H. RECK and MICHAEL P. PRICE STRUCTURES AND STRUCTURALISM IN CONTEMPORARY PHILOSOPHY OF MATHEMATICS ABSTRACT. In recent philosophy of mathematics a variety of writers have presented “structuralist” views and arguments. There are, however, a number of substantive differ- ences in what their proponents take “structuralism” to be. In this paper we make explicit these differences, as well as some underlying similarities and common roots. We thus identify systematically and in detail, several main variants of structuralism, including some not often recognized as such. As a result the relations between these variants, and between the respective problems they face, become manifest. Throughout our focus is on semantic and metaphysical issues, including what is or could be meant by “structure” in this connection. 1. INTRODUCTION In recent philosophy of mathematics a variety of writers – including Geoffrey Hellman, Charles Parsons, Michael Resnik, Stewart Shapiro, and earlier Paul Benacerraf – have presented “structuralist” views and arguments.1As a result “structuralism”, or a “structuralist approach”, is increasingly recognized as one of the main positions in the philosophy of mathematics today. But what exactly is structuralism in this connection? Geoffrey Hellman’s discussion starts with the following basic idea: [M]athematics is concerned principally with the investigation of structures of various types in complete abstraction from the nature of individual objects making up those structures. (Hellman 1989, vii) Charles Parsons gives us this initial characterization: By the “structuralist view” of mathematical objects, I mean the view that reference to mathematical objects is always in the context of some background structure, and that the objects have no more to them than can be expressed in terms of the basic relations of the structure. -
Experiment Month: Helping Philosophers to Engage Empirically June 30, 2009
Experiment Month: Helping Philosophers to Engage Empirically June 30, 2009 Overview: Although there has been a growing interest in experimental research among young philosophers, especially undergraduate and graduate students, many find that they don’t have the resources or expertise required to conduct rigorous experimental research. These budding philosophers often have exciting and original ideas; they simply lack the support they would need to turn those visions into real philosophical research. The aim of the proposed Experiment Month program is to provide these philosophers with resources, encouragement and technical assistance to realize the potential of their own ideas. To attain these objectives, we propose, in conjunction with a consortium of prominent philosophers and under the auspices of the Yale University Program in Cognitive Science, to implement a program that will provide philosophers (especially students) with: x ‘Experiment buddies’ who can help them to correctly design studies and think through the implications of their data x On-line educational videos that guide them through the process of developing philosophically relevant experiments x The resources necessary to put together online studies, attract a large sample of subjects, and analyze the resulting data. Above all, we aim to encourage and inspire young philosophers through the organization of a community-wide event that will enable broad participation in a friendly and supportive atmosphere. Summary of Project: Fall 2010 Proposals for experiments due. Winter 2010 Team of volunteers select the most viable proposals for inclusion in the Experiment Month and provide helpful comments on selected submissions. Winter 2010— Each winning project is assigned an ‘experiment buddy’ who works Spring 2011 with the philosopher to help refine the proposed study, enabling research that successfully engages with the key philosophical questions in the relevant area. -
Stewart Shapiro's Complete Publication List
PUBLICATIONS Books: Vagueness in context, Oxford, Oxford University Press, 2006; reissued in paperback, March, 2008. Thinking about mathematics: The philosophy of mathematics, Oxford, Oxford University Press, 2000. Philosophy of mathematics: Structure and ontology, Oxford, Oxford University Press, 1997; reissued in paperback, Autumn 2000. Foundations without foundationalism: A case for second-order logic, Oxford Logic Guides 17, Oxford, Oxford University Press, 1991, reissued in paperback, Summer 2000. Editorships: Oxford handbook of the philosophy of logic and mathematics, Oxford University Press, 2005. Special issue of History and Philosophy of Logic 20 (2000), a Festschrift for John Corcoran (edited with Michael Scanlan). Special issue of Philosophia Mathematica (3) 8 (2000), devoted to abstraction and neo-logicism. Two special issues of Philosophia Mathematica (3) 7 (1999), 9 (2001), devoted to the proceedings of a conference in memory of George Boolos, held at Notre Dame, during the April of 1998. The limits of logic: Second-order logic and the Skolem paradox, The international research library of philosophy, Dartmouth Publishing Company, 1996. Special issue of Philosophia Mathematica (3) 4 (1996), devoted to structuralism. Contributors: P. Benacerraf, G. Hellman, B. Hale, C. Parsons, M. Resnik, S. Shapiro. Intensional Mathematics, Studies in Logic and the Foundations of Mathematics 113, Amsterdam, North Holland Publishing Company, 1985, Contributors: S. Shapiro, J. Myhill, N. D. Goodman, A. Scedrov, V. Lifschitz, R. Flagg, R. Smullyan. Articles: “Towards a point-free account of the continuous” (with Geoffrey Hellman), Iyyun 61, 2012, 263- 287. “Revising logic in light of paradox”, in Insolubles and consequences: essays in honor of Stephen Read, Tributes 18, edited by Catarina Dutilh and Ole Hjortland, College Publications, 2012, 213-237. -
Shapiro's and Hellman's Structuralism
Shapiro’s and Hellman’s Structuralism Christopher von Bulow¨ ∗ Trends in the Philosophy of Mathematics Frankfurt/Main, September 4, 2009 Abstract I give brief descriptions of and motivations for Stewart Shapiro’s and Geoffrey Hellman’s positions in mathematical structuralism and criticize each position in turn. Shapiro explains mathematical objects as ‘places in structures’, conceived as akin to offices, occupiable by arbitrary things and individuated by their interrela- tions. I argue that while places as occupiables are much like the ‘places’ of relations and thus not too worrisome, the two aspects of places – occupiability and what I call ‘relational essence’ – don’t go well together. Therefore Shapiro’s structuralism doesn’t constitute a substantial advance over traditional platonism. Furthermore, mathematical practice indicates that mathematical objects aren’t needed anyway to account for the information content of mathematics. Accordingly, in Hellman’s version of structuralism mathematical propositions do not refer to mathematical objects; rather, they are implicit generalizations over logically possible systems. Statements P of a mathematical theory have to be analyzed as “Necessarily, for all systems of type so-and-so, P”, where the theory also says that it is logically possible that there be systems of type so-and-so. I claim, however, that the logical possibility of structural conditions isn’t required for mathematical reasoning about them. Thus Hellman’s structuralism isn’t adequate as an account of mathematics. Finally, I hint at my own half-baked views on what mathematics is about. 1 Introduction I am a structuralist. I find myself situated somewhere between Stewart Shapiro and Two versions of Geoffrey Hellman – which is a nice place to be, I guess. -
Philosophy Lectures Prospectus Hilary Term 2019
F A C U L T Y O F P HILOSOPHY U NIVERSITY OF O XFORD PHILOSOPHY LECTURES PROSPECTUS HILARY TERM 2019 1 The Philosophy Centre is found at the Radcliffe Humanities Building, on Woodstock Road, which is also the site of the Philosophy and Theology Faculties Library. NOTES: - “CL” means the lecture is a Core Lecture for one of the Honour Schools papers. - The normal duration of an event is one hour. Where the class or lecture lasts longer than an hour, the start time and end time will be given. - Unless otherwise specified, the lectures and classes are given for all of weeks 1 to 8. - Lectures and classes begin at five minutes past the hour, and end five minutes before. (E.g: a lecture listed as “M. 10” will start on Mondays at 10.05am, and finish at 10.55am.) - Students registered on Philosophy courses, and Faculty members, will need their University card to enter the Philosophy Centre at Radcliffe Humanities. Visitors should use the intercom on the front door to ask for access. - There are several rooms used as lecture/class spaces at Radcliffe Humanities. The main rooms are: the Ryle Room (1st floor), the Lecture Room (2nd floor), and the Seminar Room (3rd floor). Other rooms sometimes used are the Colin Matthew Room (ground floor) and Meeting Room 4 (ground floor). - There is lift and stair access to all floors. A list of rooms is found by the stairwell and lift on each floor. - “Schools” refers to the Examination Schools (75 – 81 High Street), one of the main lecturing facilities in the University. -
Philosophy of Mathematics and Its Logic: Introduction
Philosophy of Mathematics and Its Logic: Introduction Oxford Handbooks Online Philosophy of Mathematics and Its Logic: Introduction Stewart Shapiro The Oxford Handbook of Philosophy of Mathematics and Logic Edited by Stewart Shapiro Print Publication Date: Jun Subject: Philosophy, Philosophy of Mathematics and Logic 2007 Online Publication Date: Sep DOI: 10.1093/oxfordhb/9780195325928.003.0001 2009 Abstract and Keywords Mathematics plays an important role in virtually every scientific effort, no matter what part of the world it is aimed at. There is scarcely a natural or a social science that does not have substantial mathematics prerequisites. The burden on any complete philosophy of mathematics is to show how mathematics is applied to the material world, and to show how the methodology of mathematics (whatever it may be) fits into the methodology of the sciences (whatever it may be). In addition to its role in science, mathematics itself seems to be a knowledge-gathering activity. The philosophy of mathematics is, at least in part, a branch of epistemology. However, mathematics is at least prima facie different from other epistemic endeavors. Keywords: mathematics, philosophy of mathematics, methodology of mathematics, epistemology, material world, logic 1. Motivation, or What We Are Up to From the beginning, Western philosophy has had a fascination with mathematics. The entrance to Plato's Academy is said to have been marked with the words “Let no one ignorant of geometry enter here.” Some major historical mathematicians, such as René Descartes, Gottfried Leibniz, and Blaise Pascal, were also major philosophers. In more recent times, there are Bernard Bolzano, Alfred North Whitehead, David Hilbert, Gottlob Frege, Alonzo Church, Kurt Gödel, and Alfred Tarski. -
Michael D. RESNIK (Ed.): Mathemati- Cal Objects and Mathematical
Michael D. RESNIK (Ed.): Mathemati dispensability argument), Gödel (mathe cal Objects and Mathematical Know matical reaIism) and the (later) Witttgen ledge. Aldershot / Broockfield, USA / stein (his ideas were transmitted largely Singapore / Sydney: Dartmouth 1995, through the work ofM. Dummett who ap xxi + 647 pp. (= The International Re plied them to intuitionistic logic) began to search Library of Philosophy 13). influence the course ofthe contemporary philosophy of mathematics. The book under review is an anthology of The papers collected in the volume texts in the contemporary philosophy of concentrate on two fundamental ques mathematics. It was published in the se tions wh ich have been in fact considered ries ofbooks "The International Research since Plato: What are mathematical ob Library of Philosophy". The aim of this jects? and How can we know them? series is to collect "in book form a wide Resnik claims that most of the collected range of important and influential essays essays were strongly influenced by arti in philosophy, drawn predominantly cles by Paul Benacerraf and Hilary Put from English-language journals" (p. xi). nam which had appeared in the decade Each volume deals with a field of inquiry 1965-1975, especially by Benacerrafs which has received significant attention "What Numbers Could Not Be" and in philosophy in the last 25 years. The Li "Mathematical Truth" and Putnam' s brary is divided into four series of vol "Mathematics without Foundations". umes: (1) Metaphysics and Epistemol The texts in the first part of the book ogy, (2) The Philosophy ofMathematics are collected under the label "Field's re and Science, (3) The Philosophy of sponse" and are devoted to Hartry Field's Logic, Language and Mind, (4) The Phi anti-realist ideas claiming that there are losophy ofValue. -
Frege's Rationalist Epistemology
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