Search results for 'Structuralism' (try it on Scholar)

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  1. P. Lorenzano, W. Balzer, C. U. Moulines & J. Sneed (2000). Structuralist Knowledge Representation: Paradigmatic Examples. In Joseph D. Sneed, Wolfgang Balzer & C.-U. Moulines (eds.), Structuralist Knowledge Representation: Paradigmatic Examples. Rodopi
    Contents: Foreword. Wolfgang BALZER and C. ULISES MOULINES: Introduction. José A. DÍEZ CALZADA: Structuralist Analysis of Theories of Fundamental Measurement. Adolfo GARCÍA DE LA SIENRA and Pedro REYES: The Theory of Finite Games in Extensive Form. Hans Joachim BURSCHEID und Horst STRUVE: The Theory of Stochastic Fairness - its Historical Development, Formulation and Justification. Wolfgang BALZER and Richard MATTESSICH: Formalizing the Basis of Accounting. Werner DIEDERICH: A Reconstruction of Marxian Economics. Bert HAMMINGA and Wolfgang BALZER: The Basic (...)
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  2. Hannes Leitgeb & James Ladyman (2008). Criteria of Identity and Structuralist Ontology. Philosophia Mathematica 16 (3):388-396.
    In discussions about whether the Principle of the Identity of Indiscernibles is compatible with structuralist ontologies of mathematics, it is usually assumed that individual objects are subject to criteria of identity which somehow account for the identity of the individuals. Much of this debate concerns structures that admit of non-trivial automorphisms. We consider cases from graph theory that violate even weak formulations of PII. We argue that (i) the identity or difference of places in a structure is not to be (...)
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  3. Stewart Shapiro (2008). Identity, Indiscernibility, and Ante Rem Structuralism: The Tale of I and –I. Philosophia Mathematica 16 (3):285-309.
    Some authors have claimed that ante rem structuralism has problems with structures that have indiscernible places. In response, I argue that there is no requirement that mathematical objects be individuated in a non-trivial way. Metaphysical principles and intuitions to the contrary do not stand up to ordinary mathematical practice, which presupposes an identity relation that, in a sense, cannot be defined. In complex analysis, the two square roots of –1 are indiscernible: anything true of one of (...)
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  4. Øystein Linnebo (2008). Structuralism and the Notion of Dependence. Philosophical Quarterly 58 (230):59-79.
    This paper has two goals. The first goal is to show that the structuralists’ claims about dependence are more significant to their view than is generally recognized. I argue that these dependence claims play an essential role in the most interesting and plausible characterization of this brand of structuralism. The second goal is to defend a compromise view concerning the dependence relations that obtain between mathematical objects. Two extreme views have tended to dominate the debate, namely the view that (...)
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  5.  55
    J. Keranen (2001). The Identity Problem for Realist Structuralism. Philosophia Mathematica 9 (3):308--330.
    According to realist structuralism, mathematical objects are places in abstract structures. We argue that in spite of its many attractions, realist structuralism must be rejected. For, first, mathematical structures typically contain intra-structurally indiscernible places. Second, any account of place-identity available to the realist structuralist entails that intra-structurally indiscernible places are identical. Since for her mathematical singular terms denote places in structures, she would have to say, for example, that 1 = − 1 in the group (...)
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  6.  48
    Nora Berenstain (2016). What a Structuralist Theory of Properties Could Not Be. In Anna Marmodoro & David Yates (ed.), The Metaphysics of Relations. OUP. Oxford University Press
    Causal structuralism is the view that, for each natural, non-mathematical, non-Cambridge property, there is a causal profile that exhausts its individual essence. On this view, having a property’s causal profile is both necessary and sufficient for being that property. It is generally contrasted with the Humean or quidditistic view of properties, which states that having a property’s causal profile is neither necessary nor sufficient for being that property, and with the double-aspect view, which states that causal profile is necessary (...)
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  7. Hubert L. Dreyfus & Paul Rabinow (2014). Michel Foucault: Beyond Structuralism and Hermeneutics. Routledge.
    This book is the first to provide a sustained, coherent analysis of Foucault's work as a whole. To demonstrate the sense in which Foucault's work is beyond structuralism and hermeneutics, the authors unfold a careful, analytical exposition of his oeuvre. They argue that during the of Foucault's work became a sustained and largely successful effort to develop a new method - "interpretative analytics" - capable of explaining both the logic of structuralism's claim to be an objective science and (...)
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  8. Tim Button (2006). Realistic Structuralism's Identity Crisis: A Hybrid Solution. Analysis 66 (3):216–222.
    Keränen (2001) raises an argument against realistic (ante rem) structuralism: where a mathematical structure has a non-trivial automorphism, distinct indiscernible positions within the structure cannot be shown to be non-identical using only the properties and relations of that structure. Ladyman (2005) responds by allowing our identity criterion to include 'irreflexive two-place relations'. I note that this does not solve the problem for structures with indistinguishable positions, i.e. positions that have all the same properties as each other and exactly (...)
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  9. Geoffrey Hellman (2001). Three Varieties of Mathematical Structuralism. Philosophia Mathematica 9 (2):184-211.
    Three principal varieties of mathematical structuralism are compared: set-theoretic structuralism (‘STS’) using model theory, Shapiro's ante rem structuralism invoking sui generis universals (‘SGS’), and the author's modal-structuralism (‘MS’) invoking logical possibility. Several problems affecting STS are discussed concerning, e.g., multiplicity of universes. SGS overcomes these; but it faces further problems of its own, concerning, e.g., the very intelligibility of purely structural objects and relations. MS, in contrast, overcomes or avoids both sets of problems. Finally, it is (...)
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  10. Marc Gasser (2015). Structuralism and Its Ontology. Ergo, an Open Access Journal of Philosophy 2 (1):1-26.
    A prominent version of mathematical structuralism holds that mathematical objects are at bottom nothing but "positions in structures," purely relational entities without any sort of nature independent of the structure to which they belong. Such an ontology is often presented as a response to Benacerraf's "multiple reductions" problem, or motivated on hermeneutic grounds, as a faithful representation of the discourse and practice of mathematics. In this paper I argue that there are serious difficulties with this kind of view: its (...)
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  11.  33
    Holger Andreas (2010). New Account of Empirical Claims in Structuralism. Synthese 176 (3):311 - 332.
    In this paper, a new account of empirical claims in structuralism is developed. Its novelty derives from the use that is made of the linguistic approach to scientific theories despite the presumed incompatibility of structuralism with that approach. It is shown how the linguistic approach can be applied to the framework of structuralism if the semantic foundations of that approach are refined to do justice to the doctrine of indirect interpretation of theoretical terms. This doctrine goes back (...)
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  12.  54
    Holger Andreas & Frank Zenker (2014). Basic Concepts of Structuralism. Erkenntnis 79 (S8):1367-1372.
    Primarily addressed to readers unfamiliar with the structuralist approach in philosophy of science, we introduce the basic concepts that the contributions to this special issue presuppose. By means of examples, we briefly review set-theoretic structures and predicates, the potential and actual models of an empirical theory, intended applications, as well as links and specializations that are applied, among others, in reconstructing the empirical claim associated with a theory element.
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  13.  24
    Holger Andreas (2011). A Structuralist Theory of Belief Revision. Journal of Logic, Language and Information 20 (2):205-232.
    The present paper aims at a synthesis of belief revision theory with the Sneed formalism known as the structuralist theory of science. This synthesis is brought about by a dynamisation of classical structuralism, with an abductive inference rule and base generated revisions in the style of Rott (2001). The formalism of prioritised default logic (PDL) serves as the medium of the synthesis. Why seek to integrate the Sneed formalism into belief revision theory? With the hybrid system of the present (...)
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  14. Uri Nodelman & Edward N. Zalta (2014). Foundations for Mathematical Structuralism. Mind 123 (489):39-78.
    We investigate the form of mathematical structuralism that acknowledges the existence of structures and their distinctive structural elements. This form of structuralism has been subject to criticisms recently, and our view is that the problems raised are resolved by proper, mathematics-free theoretical foundations. Starting with an axiomatic theory of abstract objects, we identify a mathematical structure as an abstract object encoding the truths of a mathematical theory. From such foundations, we derive consequences that address the main questions and (...)
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  15. Elaine Landry (2011). How to Be a Structuralist All the Way Down. Synthese 179 (3):435 - 454.
    This paper considers the nature and role of axioms from the point of view of the current debates about the status of category theory and, in particular, in relation to the "algebraic" approach to mathematical structuralism. My aim is to show that category theory has as much to say about an algebraic consideration of meta-mathematical analyses of logical structure as it does about mathematical analyses of mathematical structure, without either requiring an assertory mathematical or meta-mathematical background theory as a (...)
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  16. Russell Marcus (2007). Structuralism, Indispensability, and the Access Problem. Facta Philosophica 9 (1):203-211.
    The access problem for mathematics arises from the supposition that the referents of mathematical terms inhabit a realm separate from us. Quine’s approach in the philosophy of mathematics dissolves the access problem, though his solution sometimes goes unrecognized, even by those who rely on his framework. This paper highlights both Quine’s position and its neglect. I argue that Michael Resnik’s structuralist, for example, has no access problem for the so-called mathematical objects he posits, despite recent criticism, since he relies on (...)
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  17.  43
    Jessica Carter (2005). Individuation of Objects – a Problem for Structuralism? Synthese 143 (3):291 - 307.
    . This paper identifies two aspects of the structuralist position of S. Shapiro which are in conflict with the actual practice of mathematics. The first problem follows from Shapiros identification of isomorphic structures. Here I consider the so called K-group, as defined by A. Grothendieck in algebraic geometry, and a group which is isomorphic to the K-group, and I argue that these are not equal. The second problem concerns Shapiros claim that it is not possible to identify objects in a (...)
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  18.  44
    Holger Andreas (2013). Deductive Reasoning in the Structuralist Approach. Studia Logica 101 (5):1093-1113.
    The distinction between the syntactic and the semantic approach to scientific theories emerged in formal philosophy of science. The semantic approach is commonly considered more advanced and more successful than the syntactic one, but the transition from the one approach to the other was not brought about without any loss. In essence, it is the formal analysis of atomic propositions and the analysis of deductive reasoning that dropped out of consideration in at least some of the elaborated versions of the (...)
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  19.  75
    Simon Friederich (2010). Structuralism and Meta-Mathematics. Erkenntnis 73 (1):67 - 81.
    The debate on structuralism in the philosophy of mathematics has brought into focus a question about the status of meta-mathematics. It has been raised by Shapiro (2005), where he compares the ongoing discussion on structuralism in category theory to the Frege-Hilbert controversy on axiomatic systems. Shapiro outlines an answer according to which meta-mathematics is understood in structural terms and one according to which it is not. He finds both options viable and does not seem to prefer one over (...)
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  20. Fraser MacBride (2008). Can Ante Rem Structuralism Solve the Access Problem? Philosophical Quarterly 58 (230):155-164.
    Ante rem structuralism is the doctnne that mathematics descubes a realm of abstract (structural) universab. According to its proponents, appeal to the exutence of these universab provides a source distinctive insight into the epistemology of mathematics, in particular insight into the so-called 'access problem' of explaining how mathematicians can reliably access truths about an abstract realm to which they cannot travel andfiom which they recave no signab. Stewart Shapiro offers the most developed version of this view to date. Through (...)
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  21. Nicholas Shackel (2011). The World as a Graph: Defending Metaphysical Graphical Structuralism. Analysis 71 (1):10-21.
    Metaphysical graphical structuralism is the view that at some fundamental level the world is a mathematical graph of nodes and edges. Randall Dipert has advanced a graphical structuralist theory of fundamental particulars and Alexander Bird has advanced a graphical structuralist theory of fundamental properties. David Oderberg has posed a powerful challenge to graphical structuralism: that it entails the absurd inexistence of the world or the absurd cessation of all change. In this paper I defend (...)
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  22. Julian C. Cole (2010). Mathematical Structuralism Today. Philosophy Compass 5 (8):689-699.
    Two topics figure prominently in recent discussions of mathematical structuralism: challenges to the purported metaphysical insight provided by sui generis structuralism and the significance of category theory for understanding and articulating mathematical structuralism. This article presents an overview of central themes related to these topics.
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  23.  57
    Christian Damböck (2014). Kuhn's Notion of Scientific Progress: “Reduction” Between Incommensurable Theories in a Rigid Structuralist Framework. Synthese 191 (10):2195-2213.
    In the last two sections of Structure, Thomas Kuhn first develops his famous threefold conception of the incommensurability of scientific paradigms and, subsequently, a conception of scientific progress as growth of empirical strength. The latter conception seems to be at odds with the former in that semantic incommensurability appears to imply the existence of situations where scientific progress in Kuhns sense can no longer exist. In contrast to this seeming inconsistency of Kuhns conception, we will try to show in this (...)
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  24.  35
    Ronald P. Endicott (2001). Post-Structuralist Angst - Critical Notice: John Bickle, Psychoneural Reduction: The New Wave. Philosophy of Science 68 (3):377-393.
    I critically evaluate Bickle’s version of scientific theory reduction. I press three main points. First, a small point, Bickle modifies the new wave account of reduction developed by Paul Churchland and Clifford Hooker by treating theories as set-theoretic structures. But that structuralist gloss seems to lose what was distinctive about the Churchland-Hooker account, namely, that a corrected theory must be specified entirely by terms and concepts drawn from the basic reducing theory. Set-theoretic structures are not terms or concepts but the (...)
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  25.  24
    Juha Saatsi (forthcoming). Structuralism with and Without Causation. Synthese:1-17.
    This paper explores the status of causation in structuralist metaphysics of physics. What role (if any) does causation play in understanding ‘structure’ in ontological structural realism? I address this question by examining, in a structuralist setting, arguments for and against the idea that fundamental physics deals, perhaps exclusively, with causal properties. I will argue (against Esfeld, Dorato and others) that a structuralist interpretation of fundamental physics should diverge from ‘causal structuralism’. Nevertheless, causation outside fundamental physics, and the basic motivation (...)
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  26.  51
    C. U. Moulines (2010). Metatheoretical Structuralism: A General Program for Analyzing Science. [REVIEW] Axiomathes 20 (2-3):255-268.
    In spite of the ‘experimental turn’ now fashionable in the philosophy of science, the question of the structure and identity criteria of scientific theories continues to be a central issue for the philosophical analysis of empirical science. We need a precise metatheory of empirical theories to deal with this issue. Metatheoretical structuralism appears to offer the most adequate approach in this sense so far. First, some basic intuitions about what empirical theories are, and how they are structured, are laid (...)
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  27.  12
    Christian Damböck (2012). Theory Structuralism in a Rigid Framework. Synthese 187 (2):693-713.
    This paper develops the first parts of a logical framework for the empirical sciences, by means of a redefinition of theory structuralism as originally developed by Joseph Sneed, Wolfgang Stegmüller, and others, in the context of a ‘rigid’ logic as based on a fixed (therefore rigid) ontology. The paper defends a formal conception of the empirical sciences that has an irreducible ontological basis and is unable, in general, to provide purely structural characterizations of the domain of a theory. The (...)
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  28.  58
    Makmiller Pedroso (2009). On Three Arguments Against Categorical Structuralism. Synthese 170 (1):21 - 31.
    Some mathematicians and philosophers contend that set theory plays a foundational role in mathematics. However, the development of category theory during the second half of the twentieth century has encouraged the view that this theory can provide a structuralist alternative to set-theoretical foundations. Against this tendency, criticisms have been made that category theory depends on set-theoretical notions and, because of this, category theory fails to show that set-theoretical foundations are dispensable. The goal of this paper is to show that these (...)
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  29.  31
    Bob Hale (1996). Structuralism's Unpaid Epistemological Debts. Philosophia Mathematica 4 (2):124--47.
    One kind of structuralism holds that mathematics is about structures, conceived as a type of abstract entity. Another denies that it is about any distinctively mathematical entities at all—even abstract structures; rather it gives purely general information about what holds of any collection of entities conforming to the axioms of the theory. Of these, pure structuralism is most plausibly taken to enjoy significant advantages over platonism. But in what appears to be its most plausible—modalised—version, even restricted to elementary (...)
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  30.  23
    Sandy C. Boucher (2015). Functionalism and Structuralism as Philosophical Stances: Van Fraassen Meets the Philosophy of Biology. Biology and Philosophy 30 (3):383-403.
    I consider the broad perspectives in biology known as ‘functionalism’ and ‘structuralism’, as well as a modern version of functionalism, ‘adaptationism’. I do not take a position on which of these perspectives is preferable; my concern is with the prior question, how should they be understood? Adapting van Fraassen’s argument for treating materialism as a stance, rather than a factual belief with propositional content, in the first part of the paper I offer an argument for construing functionalism and (...) as stances also. The argument draws especially on Gould’s insights concerning functionalism and structuralism, in particular their apparent historical continuity from the pre-Darwinian period through to today. In the second part of the paper I consider Godfrey-Smith’s distinction between empirical and explanatory adaptationism, and suggest that while the former is an empirical scientific hypothesis, the latter is closely related to the functionalist stance. (shrink)
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  31.  24
    Jairo José da Silva (2010). Structuralism and the Applicability of Mathematics. Axiomathes 20 (2-3):229-253.
    In this paper I argue for the view that structuralism offers the best perspective for an acceptable account of the applicability of mathematics in the empirical sciences. Structuralism, as I understand it, is the view that mathematics is not the science of a particular type of objects, but of structural properties of arbitrary domains of entities, regardless of whether they are actually existing, merely presupposed or only intentionally intended.
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    John Lechte (ed.) (1994). Fifty Key Contemporary Thinkers: From Structuralism to Postmodernity. Routledge.
    Fifty Key Contemporary Thinkers surveys the most important figures who have influenced post-war thought. The reader is guided through structuralism, semiotics, post-Marxism and Annales history, on to modernity and postmodernity. With its comprehensive biographical and bibliographical information, this book provides a vital reference work of the last fifty years.
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  33.  53
    Ricardo Restrepo Echavarria (2009). Russell's Structuralism and the Supposed Death of Computational Cognitive Science. Minds and Machines 19 (2):181-197.
    John Searle believes that computational properties are purely formal and that consequently, computational properties are not intrinsic, empirically discoverable, nor causal; and therefore, that an entity’s having certain computational properties could not be sufficient for its having certain mental properties. To make his case, Searle’s employs an argument that had been used before him by Max Newman, against Russell’s structuralism; one that Russell himself considered fatal to his own position. This paper formulates a not-so-explored version of Searle’s problem with (...)
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  34.  45
    Jairo José Silvdaa (forthcoming). Structuralism and the Applicability of Mathematics. Axiomathes.
    In this paper I argue for the view that structuralism offers the best perspective for an acceptable account of the applicability of mathematics in the empirical sciences. Structuralism, as I understand it, is the view that mathematics is not the science of a particular type of objects, but of structural properties of arbitrary domains of entities, regardless of whether they are actually existing, merely presupposed or only intentionally intended.
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  35.  13
    Pablo Lorenzano (2013). The Semantic Conception and the Structuralist View of Theories: A Critique of Suppe’s Criticisms. Studies in History and Philosophy of Science Part A 44 (4):600-607.
    Different conceptions of scientific theories, such as the state spaces approach of Bas van Fraassen, the phase spaces approach of Frederick Suppe, the set-theoretical approach of Patrick Suppes, and the structuralist view of Joseph Sneed et al. are usually put together into one big family. In addition, the definite article is normally used, and thus we speak of the semantic conception of theories and of its different approaches . However, in The Semantic Conception of Theories and Scientific Realism , starting (...)
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  36.  12
    Jonathan P. Seldin (2011). Curry's Formalism as Structuralism. Logica Universalis 5 (1):91-100.
    In 1939, Curry proposed a philosophy of mathematics he called formalism. He made this proposal in two works originally written then, although one of them was not published until 1951. These are the two philosophical works for which Curry is known, and they have left a false impression of his views. In this article, I propose to clarify Curry’s views by referring to some of his later writings on the subject. I claim that Curry’s philosophy was not what is now (...)
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  37.  9
    Ricardo Restrepo Echavarria (2009). Russell's Structuralism and the Supposed Death of Computational Cognitive Science. Minds and Machines 19 (2):181-197.
    John Searle believes that computational properties are purely formal and that consequently, computational properties are not intrinsic, empirically discoverable, nor causal; and therefore, that an entity’s having certain computational properties could not be sufficient for its having certain mental properties. To make his case, Searle’s employs an argument that had been used before him by Max Newman, against Russell’s structuralism; one that Russell himself considered fatal to his own position. This paper formulates a not-so-explored version of Searle’s problem with (...)
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  38.  3
    Ricardo Restrepo (2009). Russell's Structuralism and the Supposed Death of Computational Cognitive Science. Minds and Machines 19 (2):181-197.
    John Searle believes that computational properties are purely formal and that consequently, computational properties are not intrinsic, empirically discoverable, nor causal; and therefore, that an entity’s having certain computational properties could not be sufficient for its having certain mental properties. To make his case, Searle employs an argument that had been used before him by Max Newman, against Russell’s structuralism; one that Russell himself considered fatal to his own position. This paper formulates a not-so-explored version of Searle’s problem with (...)
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  39. Jonathan D. Culler (ed.) (2006). Structuralism: Critical Concepts in Literary and Cultural Studies. Routledge.
    Organized thematically, this four-volume collection explores the key areas of structuralism - and with a new introduction by the editor to guide the reader through the work, this is an essential collection of secondary sources that provides a valuable tool for research. Taking as their methodological model the successes of the structural linguistics inaugurated by Ferdinand de Saussure, a group of thinkers in such fields as anthropology, literary and cultural studies, sociology and philosophy developed ambitious programs for the interdisciplinary (...)
     
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  40.  5
    Martti Kuokkanen (1995). Idealization Vii: Structuralism, Idealization and Approximation. Rodopi.
    Contents: IDEALIZATION, APPROXIMATION AND COUNTERFACTUALS IN THE STRUCTURALIST FRAMEWORK. Theo A.F. KUIPERS: The Refined Structure of Theories. C. ULISES and Reinhold STRAUB: Approximation and Idealization from the Structuralist Point of View. Ilkka A. KIESEPPÄ: A Note on the Structuralist Account of Approximation. C. ULISES MOULINES and Reinhold STRAUB: A Reply to Kieseppä. Wolfgang BALZER and Gerhard ZOUBEK: Structuralist Aspects of Idealization. Andoni IBARRA and Thomas MORMANN: Counterfactual Deformation and Idealization in a Structuralist Framework. Ilkka A. KIESEPPÄ: Assessing the Structuralist Theory (...)
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  41. Donald Palmer (1997/2007). Structuralism and Poststructuralism for Beginners. For Beginners Llc.
    “In its less dramatic versions,” writes author Dan Palmer, “structuralism is just a method of studying language, society, and the works of artists and novelists. But in its most exuberant form, it is a philosophy, an overall worldview that provides an account of reality and knowledge.” Poststructuralism is a loosely knit intellectual movement, comprised mainly of ex-structuralists who either became dissatisfied with the theory or felt they could improve it. Structuralism and Poststructuralism For Beginners is an illustrated tour (...)
     
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  42.  2
    Jean Piaget (1970). Structuralism. New York,Basic Books.
  43.  64
    Wolfgang Stegmüller (1979). The Structuralist View of Theories: A Possible Analogue of the Bourbaki Programme in Physical Science. Springer-Verlag.
    This is the basis of the first part of the book.
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  44. Wolfgang Balzer, Carles Ulises Moulines & Joseph D. Sneed (1987). An Architectonic for Science the Structuralist Program. Monograph Collection (Matt - Pseudo).
     
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  45. Charles Parsons (1990). The Structuralist View of Mathematical Objects. Synthese 84 (3):303 - 346.
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  46.  10
    Benjamin Eva (2016). Category Theory and Physical Structuralism. European Journal for Philosophy of Science 6 (2):231-246.
    As a metaphysical theory, radical ontic structural realism is characterised mainly in terms of the ontological primacy it places on relations and structures, as opposed to the individual relata and objects that inhabit these relations/structures. The most popular criticism of ROSR is that its central thesis is incoherent. Bain attempts to address this criticism by arguing that the mathematical language of category theory allows for a coherent articulation of ROSR’s key thesis. Subsequently, Wüthrich and Lam and Lal and Teh have (...)
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    Arnold Koslow (1992/2005). A Structuralist Theory of Logic. Cambridge University Press.
    Professor Koslow advances a new account of the basic concepts of logic. A central feature of the theory is that it does not require the elements of logic to be based on a formal language. Rather, it uses a general notion of implication as a way of organizing the formal results of various systems of logic in a simple, but insightful way. The study has four parts. In the first two parts the various sources of the general concept of an (...)
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  48. Andoni Ibarra & Thomas Mormann (2010). Appropriating Kuhn’s Philosophical Legacy. Three Attempts: Logical Empiricism, Structuralism, and Neokantianism. Cadernos de Filosofia Das Ciencias 8:65 - 102.
    In this paper we discuss three examples of the appropriation of Kuhn’s ideas in philosophy of science. First we deal with classical logical empiricism. Perhaps somewhat surprisingly, the arch-logical empiricist Carnap considered Kuhn’s socio-historical account as a useful complementation, and not as a threat of the philosophy of science of logical empiricism. As a second example we consider the attempt of the so-called struc- turalist philosophy of science to provide a “rational reconstruction” of Kuhn’s approach. Finally, we will deal with (...)
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  49.  82
    Jessica Carter (2008). Structuralism as a Philosophy of Mathematical Practice. Synthese 163 (2):119 - 131.
    This paper compares the statement ‘Mathematics is the study of structure’ with the actual practice of mathematics. We present two examples from contemporary mathematical practice where the notion of structure plays different roles. In the first case a structure is defined over a certain set. It is argued firstly that this set may not be regarded as a structure and secondly that what is important to mathematical practice is the relation that exists between the structure and the set. In the (...)
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    Øystein Linnebo & Richard Pettigrew (2014). Two Types of Abstraction for Structuralism. Philosophical Quarterly 64 (255):267-283.
    If numbers were identified with any of their standard set-theoretic realizations, then they would have various non-arithmetical properties that mathematicians are reluctant to ascribe to them. Dedekind and later structuralists conclude that we should refrain from ascribing to numbers such ‘foreign’ properties. We first rehearse why it is hard to provide an acceptable formulation of this conclusion. Then we investigate some forms of abstraction meant to purge mathematical objects of all ‘foreign’ properties. One form is inspired by Frege; the other (...)
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