Structures and Structuralism in Contemporary Philosophy of Mathematics
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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. -
Perceptual Variation and Structuralism
NOUSˆ 54:2 (2020) 290–326 doi: 10.1111/nous.12245 Perceptual Variation and Structuralism JOHN MORRISON Barnard College, Columbia University Abstract I use an old challenge to motivate a new view. The old challenge is due to variation in our perceptions of secondary qualities. The challenge is to say whose percep- tions are accurate. The new view is about how we manage to perceive secondary qualities, and thus manage to perceive them accurately or inaccurately. I call it perceptual structuralism. I first introduce the challenge and point out drawbacks with traditional responses. I spend the rest of the paper motivating and defending a structuralist response. While I focus on color, both the challenge and the view generalize to the other secondary qualities. 1. Perceptual Variation Our perceptual experiences tell us that lemons are yellow and sour. It’s natural to infer that lemons really are yellow and sour. But perceptions vary, even among ordinary observers. Some perceive lemons as slightly greener and sweeter. This gives rise to a challenge that forces us to rethink the nature of perception and the objectivity of what we perceive. For concreteness, I’ll focus on the perceptions of two ordinary observers, Miriam and Aaron. I’ll also focus on their perceptions of a particular lemon’s color. These restrictions will make the challenge easier to understand and the responses easier to compare. But the challenge and responses are perfectly general. Toward the end of the paper I’ll return to sourness and the other secondary qualities. When Miriam and Aaron look at the same lemon, their perceptions differ. -
The Meanings of Structuralism : Considerations on Structures and Gestalten, with Particular Attention to the Masks of Levi-Strauss
The meanings of structuralism : considerations on structures and Gestalten, with particular attention to the masks of Levi-Strauss Sonesson, Göran Published in: Segni e comprensione 2012 Link to publication Citation for published version (APA): Sonesson, G. (2012). The meanings of structuralism : considerations on structures and Gestalten, with particular attention to the masks of Levi-Strauss. Segni e comprensione, XXVI(78), 84-101. Total number of authors: 1 General rights Unless other specific re-use rights are stated the following general rights apply: Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal Read more about Creative commons licenses: https://creativecommons.org/licenses/ Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. LUND UNIVERSITY PO Box 117 221 00 Lund +46 46-222 00 00 International RIVISTA TELEMATICA QUADRIMESTRALE - ANNO XXVI NUOVA SERIE - N. 78 – SETTEMBRE-DICEMBRE 2012 1 This Review is submitted to international peer review Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf.com) Segni e comprensione International Pubblicazione promossa nel 1987 dal Dipartimento di Filosofia e Scienze sociali dell’Università degli Studi di Lecce, oggi Università del Salento, con la collaborazione del “Centro Italiano di Ricerche fenomenologiche” con sede in Roma, diretto da Angela Ales Bello. -
Structure and Perspective: Philosophical Perplexity and Paradox Published: Pp
Structure and Perspective: Philosophical Perplexity and Paradox published: pp. 511-530 in M. L. Dalla Chiara et al. (eds.) Logic and Scientific Methods. Vol 1. Dordrecht: Kluwer, 1997. Bas C. van Fraassen, Princeton University 1. Science as representation ..................................................................................... 1 1.1 The philosophical consensus ca. 1900 .............................................................. 2 1.2 The problem of multiple geometries ................................................................. 3 1.3 Relativity of representation ............................................................................... 5 2. Structuralism, its initial (mis)fortunes ................................................................. 6 2.1 Russell's structuralist turn ................................................................................. 6 2.2 The collapse of structuralism? .......................................................................... 8 2.3 Putnam's model-theoretic argument -- a paradox? .......................................... 11 3. Structuralism: the semantic approach ............................................................... 15 3.1 Structural description of nature ....................................................................... 15 3.2 Adequacy to the phenomena ........................................................................... 16 3.3 Structuralism lost after all? ............................................................................. 18 3.4 Truth -
Structuralism 1. the Nature of Meaning Or Understanding
Structuralism 1. The nature of meaning or understanding. A. The role of structure as the system of relationships Something can only be understood (i.e., a meaning can be constructed) within a certain system of relationships (or structure). For example, a word which is a linguistic sign (something that stands for something else) can only be understood within a certain conventional system of signs, which is language, and not by itself (cf. the word / sound and “shark” in English and Arabic). A particular relationship within a شرق combination society (e.g., between a male offspring and his maternal uncle) can only be understood in the context of the whole system of kinship (e.g., matrilineal or patrilineal). Structuralism holds that, according to the human way of understanding things, particular elements have no absolute meaning or value: their meaning or value is relative to other elements. Everything makes sense only in relation to something else. An element cannot be perceived by itself. In order to understand a particular element we need to study the whole system of relationships or structure (this approach is also exactly the same as Malinowski’s: one cannot understand particular elements of culture out of the context of that culture). A particular element can only be studied as part of a greater structure. In fact, the only thing that can be studied is not particular elements or objects but relationships within a system. Our human world, so to speak, is made up of relationships, which make up permanent structures of the human mind. B. The role of oppositions / pairs of binary oppositions Structuralism holds that understanding can only happen if clearly defined or “significant” (= essential) differences are present which are called oppositions (or binary oppositions since they come in pairs). -
Putting Structuralism Back Into Structural Inequality Anders Walker Saint Louis University School of Law
Saint Louis University School of Law Scholarship Commons All Faculty Scholarship 2019 Freedom and Prison: Putting Structuralism Back into Structural Inequality Anders Walker Saint Louis University School of Law Follow this and additional works at: https://scholarship.law.slu.edu/faculty Part of the Civil Rights and Discrimination Commons, Criminal Law Commons, Criminal Procedure Commons, and the Criminology and Criminal Justice Commons Recommended Citation Walker, Anders, Freedom and Prison: Putting Structuralism Back into Structural Inequality (January 4, 2019). University of Louisville Law Review, Vol. 49, No. 267, 2019. This Article is brought to you for free and open access by Scholarship Commons. It has been accepted for inclusion in All Faculty Scholarship by an authorized administrator of Scholarship Commons. For more information, please contact [email protected], [email protected]. FREEDOM AND PRISON: PUTTING STRUCTURALISM BACK INTO STRUCTURAL INEQUALITY Anders Walker* ABSTRACT Critics of structural racism frequently miss structuralism as a field of historical inquiry. This essay reviews the rise of structuralism as a mode of historical analysis and applies it to the mass incarceration debate in the United States, arguing that it enriches the work of prevailing scholars in the field. I. INTRODUCTION Structuralism has become a prominent frame for discussions of race and inequality in the United States, part of a larger trend that began in the wake of Barack Obama’s presidential victory in 2008. This victory was a moment -
Effectiveness of Mathematics in Empirical Science
The (reasonable) effectiveness of mathematics in empirical science Jairo José da Silva Universidade Estadual Paulista Júlio de Mesquita Filho, UNESP, Brazil e–mail: [email protected] ABSTRACT WORK TYPE I discuss here the pragmatic problem in the philosophy of mathematics, that is, Article the applicability of mathematics, particularly in empirical science, in its many variants. My point of depart is that all sciences are formal, descriptions of formal– ARTICLE HISTORY structural properties instantiated in their domain of interest regardless of their Received: material specificity. It is, then, possible and methodologically justified as far as 27–April–2018 science is concerned to substitute scientific domains proper by whatever domains Accepted: —mathematical domains in particular— whose formal structures bear relevant 30–November–2018 formal similarities with them. I also discuss the consequences to the ontology of mathematics and empirical science of this structuralist approach. ARTICLE LANGUAGE English KEYWORDS Philosophy of Mathematics Domains Formal Structures Ontology © Studia Humanitatis – Universidad de Salamanca 2018 NOTES ON CONTRIBUTOR Jairo José da Silva is a Professor of Mathematics (retired) at the State University of São Paulo and a Researcher at the National Council of Scientific and Technological Development (CNPq) of the Brazilian Ministry of Science and Technology. PhD in Mathematics at the University of California – Berkeley, USA, and a PhD in Philosophy at the Universidade Estadual de Campinas, Brazil. His main interests are the philosophy of formal and empirical sciences, phenomenology and the foundations of mathematics. He is co–author, together with Claire Ortiz Hill, of the book The Road Not Taken – On Husserl’s Philosophy of Logic and Mathematics (London: College Publications, 2013); and author of Mathematics and Its Applications. -
Foundations for Mathematical Structuralism This Philosophical View Comes in a Variety of Forms
Uri Nodelman and Edward N. Zalta 2 1 Introduction Mathematical structuralism is the view that pure mathematics is about 1 ∗ abstract structure or structures (see, e.g., Hellman 1989, Shapiro 1997). Foundations for Mathematical Structuralism This philosophical view comes in a variety of forms. In this paper, we investigate, and restrict our use of the term `structuralism' to the form that acknowledges that abstract structures exist, that the pure objects of Uri Nodelman mathematics are in some sense elements of, or places in, those structures, and and that there is nothing more to the pure objects of mathematics than Edward N. Zalta can be described by the basic relations of their corresponding structure (e.g., Dedekind 1888 [1963], Resnik 1981, 1997, Parsons 1990, and Shapiro Center for the Study of Language and Information 1997).2 We shall not suppose that structures are sets nor assume any Stanford University set theory; our goal is to give an analysis of mathematics that doesn't presuppose any mathematics. Our work is motivated by two insights. First, as we discuss in Section 2.1, abstract objects are connected to the properties that define them in a different way than ordinary objects are connected to the properties they bear. Second, as we discuss in Section 3.1, theorems and truths about abstract relations are more important in Abstract defining mathematical structures than mathematical entities. Recently, the literature on structuralism has centered on a variety of questions and problems. These issues arise, in part, because the philo- sophical view has not been given proper, mathematics-free theoretical We investigate the form of mathematical structuralism that ac- foundations.3 We shall show how to view mathematical structures as knowledges the existence of structures and their distinctive struc- tural elements. -
CURRICULUM VITAE MICHAEL DAVID RESNIK Born: March 20, 1938, New Haven, Connecticut Education
CURRICULUM VITAE MICHAEL DAVID RESNIK Born: March 20, 1938, New Haven, Connecticut Education: Yale University, New Haven, Connecticut, B.A. as a Scholar of the House in Mathematics and Philosophy, 1960 Harvard University, Cambridge, Massachusetts, M.A. in Philosophy, 1962; Ph.D. in Philosophy, 1964 Academic Experience: University Distinguished Professor, The University of North Carolina at Chapel Hill, 1988- Professor, The University of North Carolina at Chapel Hill, 1975-1988 Member, Social Science Research Institute, The University of North Carolina at Chapel Hill, 1985-present; Fellow of the UNC Institute of Arts and Humanities, 1988- Visiting Fellow, Center for The Study of Science in Society, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, Spring, 1984 Chairman, The University of North Carolina at Chapel Hill, 1975-1983 Associate Professor, The University of North Carolina at Chapel Hill, 1967- 1975 Visiting Assistant Professor, Washington University, St. Louis, Missouri, 1966-1967 Assistant Professor, The University of Hawaii, Honolulu, 1964-1967; Member, Social Science Research Institute, 1966-1967 Memberships: American Philosophical Association Association for Symbolic Logic Philosophy of Science Association Grants: Co-principal investigator with C. Y. Cheng on N.S.F. Grant G.S. 835,"Classical Chinese Logic and Scientific Methodology", 1965-1966 Director, National Endowment for the Humanities Summer Seminar for College Teachers, "Frege and the Philosophy of Mathematics", 1980 Participant in a Sloan Foundation -
What Is Structuralism?
What Is Structuralism? M. S. Lourenço LanCog, Universidade de Lisboa Disputatio Vol. 3, No. 27 November 2009 DOI: 10.2478/disp-2009-0012 ISSN: 0873-626X © 2009 Lourenço. Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License What is structuralism?* M. S. Lourenço University of Lisbon I. Introduction Good afternoon, ladies and gentlemen. Let me start by saying how I interpret this meeting, because that does determine what I am going to say next. I think about this meeting as a kind of technology fair, where products are for the first time shown and tested. The purpose of this meeting, as I see it, is to bring together professional philoso- phers doing analytic philosophy and ask them to show their products, so that hopefully we end up not only with a map of who is doing what but also with an increased pride in having given an old profession a distinctly new profile. I would like to say why I think this is important and for that purpose I will revert to my technology metaphor. The practice of analytic philosophy requires such an intensive training and such a peculiar skill that each philosopher becomes by its practice a specialist, in Taylor’s sense of the word. This is a reversal of a long-standing tradition of the philosopher as a generalist and, as we all know, anybody who wants to do analytic philosophy has to give up any claims to being a generalist. However, this is not to be seen as unfortunate in any way, because it is simply a by-product, on one hand, of the size of the literature in each of the traditional philosophical domains and, on the other, of the modern diversity of methods used in each of them. -
Introduction to Developmental and Historical Structuralism
RB-72-53 INTRODUCTION TO DEVELOPMENTAL AND HISTORICAL STRUCTURALISM Klaus F. Riegel University of Michigan 1 To appear as a chapter in K. F. Riegel (Ed.), I Structure, Transformation, Interaction: Develop mental and Historical Aspects (Vol. I. Topics in Human Development). Basel: Karger, 1973. Educational Testing Service Princeton, New Jersey November 1972 Introduction to Developmental and Historical Structuralism Klaus F. Riegel The following essay introduces structuralism from several different angles. In the first section of this introduction, the concept of structure (and in extension those of schema, pattern, gestalt, etc.) will be contrasted with that of function (and in extension those of activity, interaction, transforma tion, etc.). Such a comparison will not merely reconfirm the old dichotomy as introduced into psychology by James and Titchner, but will emphasize the mutual dependency of structure and functions. In this attempt we rely on Piaget's interpretations and, thus, emphasize genetic aspects. Reference will also be given to recent trends in linguistics, especially to Chomsky's transformational grammar. In the second section, we trace the origin of these ideas to some reformu lations in mathematics proposed during the second half of the 19th century by Dedekind, Frege, Russell and others. The new emphasis stressed the analysis of relational orders and classes and thus contributed to the foundation for structural interpretations. Further steps in this direction were taken in Carnap's early work, which is represented in the third section. Carnap provides explicit descriptions of structural interpretations, by relying on some positivists of the late 19th century, especially Mach, Poincare and Avenarius. whose contributions- unfortunately--have frequently been viewed in clear antithesis to structural descriptions. -
Saussurian Structuralism in Linguistics
Journal of Literature, Languages and Linguistics www.iiste.org ISSN 2422-8435 An International Peer-reviewed Journal Vol.20, 2016 Saussurian Structuralism in Linguistics Tanveer Ahmed Muhammadi MS Scholar, Mehran University Of Engineering and Technology, Jamshoro, Sindh, Pakistan Abstract This research article focuses on the basic assumptions about structuralism as proposed by Ferdinand Saussure through his ideas of structure, language signs, synchronic and diachronic study of language and langue and parole. It also incorporates the criticism on Saussurean thought from different intellectual quarters. The background view of the life of Saussure and his intellectual legacy and attempts have been attempted to explain in simple terms before indulging into the technicalities of the topic. Introduction Structuralism, since its inception has extended itself to the various other fields and disciplines due to its wider applicability. However, this article only covers its relation to the field of Linguistics where it was born. The work undertaken here is aimed at focusing the interpretation of structuralism theory as proposed and discussed by Saussure and his school of thought as well as the emergent new concepts about structuralism. The sign system in language, langue and parole and other related concepts would be taken into consideration. Structuralism owes its origin to Ferdinand Saussure (26 November 1857 – 22 February 1913). He is renowned for his revolutionary ideas about the fields of linguistics and semiology. His founding role in semiology is only compared with the role of Charles Sanders Peirce. Saussure gave a new status to the understanding of language. He believed that language should be approached not from the view of rules and regulations for correct or incorrect expressions rather it should be looked from the angle of how people actually use it.