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Erich Reck
University of California, Riverside
  1.  3
    The Pre-History of Mathematical Structuralism.Erich H. Reck & Georg Schiemer (eds.) - 2020 - Oxford: Oxford University Press.
    This edited volume explores the previously underacknowledged 'pre-history' of mathematical structuralism, showing that structuralism has deep roots in the history of modern mathematics. The contributors explore this history along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics. Second, they re-examine a range of philosophical reflections from mathematically-inclinded philosophers like Russell, Carnap, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysic.
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  2. Completeness and Categoricity. Part I: Nineteenth-Century Axiomatics to Twentieth-Century Metalogic.Steve Awodey & Erich H. Reck - 2002 - History and Philosophy of Logic 23 (1):1-30.
    This paper is the first in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins in the development of the axiomatic method. We argue that, both from historical and logical points of view, higher-order logic is an appropriate framework for considering such notions, and we consider some open questions in higher-order axiomatics. In addition, we indicate how one can fruitfully extend the usual set-theoretic semantics (...)
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  3. Dedekind's Structuralism: An Interpretation and Partial Defense.Erich H. Reck - 2003 - Synthese 137 (3):369 - 419.
    Various contributors to recent philosophy of mathematics havetaken Richard Dedekind to be the founder of structuralismin mathematics. In this paper I examine whether Dedekind did, in fact, hold structuralist views and, insofar as that is the case, how they relate to the main contemporary variants. In addition, I argue that his writings contain philosophical insights that are worth reexamining and reviving. The discussion focusses on Dedekind''s classic essay Was sind und was sollen die Zahlen?, supplemented by evidence from Stetigkeit und (...)
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  4. Structures and Structuralism in Contemporary Philosophy of Mathematics.Erich H. Reck & Michael P. Price - 2000 - Synthese 125 (3):341-383.
    In recent philosophy of mathematics avariety of writers have presented ``structuralist''views and arguments. There are, however, a number ofsubstantive differences in what their proponents take``structuralism'' to be. In this paper we make explicitthese differences, as well as some underlyingsimilarities and common roots. We thus identifysystematically and in detail, several main variants ofstructuralism, including some not often recognized assuch. As a result the relations between thesevariants, and between the respective problems theyface, become manifest. Throughout our focus is onsemantic and metaphysical issues, (...)
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  5.  2
    The Historical Turn in Analytic Philosophy.Erich H. Reck (ed.) - 2013 - Palgrave-Macmillan.
    During the last 25 years, a large number of publications on the history of analytic philosophy have appeared, significantly more than in the preceding period. As most of these works are by analytically trained authors, it is tempting to speak of a 'historical turn' in analytic philosophy. The present volume constitutes both a contribution to this body of work and a reflection on what is, or might be, achieved in it. The twelve new essays, by an international group of contributors, (...)
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  6.  88
    From Frege to Wittgenstein: Perspectives on Early Analytic Philosophy.Erich H. Reck (ed.) - 2001 - Oxford University Press.
    Analytic philosophy--arguably one of the most important philosophical movements in the twentieth century--has gained a new historical self-consciousness, particularly about its own origins. Between 1880 and 1930, the most important work of its founding figures (Frege, Russell, Moore, Wittgenstein) not only gained attention but flourished. In this collection, fifteen previously unpublished essays explore different facets of this period, with an emphasis on the vital intellectual relationship between Frege and the early Wittgenstein.
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  7. Frege or Dedekind? Towards a Reevalaution of Their Legacies.Erich H. Reck - 2013 - In The Historical Turn in Analytic Philosophy. London: Palgrave-Macmillan. pp. 139-170.
    The philosophy of mathematics has long been an important part of philosophy in the analytic tradition, ever since the pioneering works of Frege and Russell. Richard Dedekind was roughly Frege's contemporary, and his contributions to the foundations of mathematics are widely acknowledged as well. The philosophical aspects of those contributions have been received more critically, however. In the present essay, Dedekind's philosophical reception is reconsidered. At the essay’s core lies a comparison of Frege's and Dedekind's legacies, within and outside of (...)
     
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  8. Introduction : Analytic Philosophy and Philosophical History.Erich H. Reck - 2013 - In The Historical Turn in Analytic Philosophy. London: Palgrave-Macmillan. pp. 1-36.
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  9. Frege on Truth, Judgment, and Objectivity.Erich H. Reck - 2007 - Grazer Philosophische Studien 75 (1):149-173.
    In Frege's writings, the notions of truth, judgment, and objectivity are all prominent and important. This paper explores the close connections between them, together with their ties to further cognate notions, such as those of thought, assertion, inference, logical law, and reason. It is argued that, according to Frege, these notions can only be understood properly together, in their inter-relations. Along the way, interpretations of some especially cryptic Fregean remarks, about objectivity, laws of truth, and reason, are offered, and seemingly (...)
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  10.  69
    Completeness and Categoricity, Part II: Twentieth-Century Metalogic to Twenty-First-Century Semantics.Steve Awodey & Erich H. Reck - 2002 - History and Philosophy of Logic 23 (2):77-94.
    This paper is the second in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins in the development of the axiomatic method. We argue that, both from historical and logical points of view, higher-order logic is an appropriate framework for considering such notions, and we consider some open questions in higher-order axiomatics. In addition, we indicate how one can fruitfully extend the usual set-theoretic semantics (...)
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  11.  56
    Logic in the 1930s: Type Theory and Model Theory.Georg Schiemer & Erich H. Reck - 2013 - Bulletin of Symbolic Logic 19 (4):433-472.
    In historical discussions of twentieth-century logic, it is typically assumed that model theory emerged within the tradition that adopted first-order logic as the standard framework. Work within the type-theoretic tradition, in the style of Principia Mathematica, tends to be downplayed or ignored in this connection. Indeed, the shift from type theory to first-order logic is sometimes seen as involving a radical break that first made possible the rise of modern model theory. While comparing several early attempts to develop the semantics (...)
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  12.  55
    Frege, Dedekind, and the Origins of Logicism.Erich H. Reck - 2013 - History and Philosophy of Logic 34 (3):242-265.
    This paper has a two-fold objective: to provide a balanced, multi-faceted account of the origins of logicism; to rehabilitate Richard Dedekind as a main logicist. Logicism should be seen as more deeply rooted in the development of modern mathematics than typically assumed, and this becomes evident by reconsidering Dedekind's writings in relation to Frege's. Especially in its Dedekindian and Fregean versions, logicism constitutes the culmination of the rise of ?pure mathematics? in the nineteenth century; and this rise brought with it (...)
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  13.  10
    Gottlob Frege: Critical Assessments of Leading Philosophers, Vol. II.Michael Beaney & Erich H. Reck (eds.) - 2005 - London: Routledge.
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  14. Frege on Numbers: Beyond the Platonist Picture.Erich H. Reck - 2005 - The Harvard Review of Philosophy 13 (2):25-40.
    Gottlob Frege is often called a "platonist". In connection with his philosophy we can talk about platonism concerning three kinds of entities: numbers, or logical objects more generally; concepts, or functions more generally; thoughts, or senses more generally. I will only be concerned about the first of these three kinds here, in particular about the natural numbers. I will also focus mostly on Frege's corresponding remarks in The Foundations of Arithmetic (1884), supplemented by a few asides on Basic Laws of (...)
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  15.  20
    Logic in the 1930s: Type Theory and Model Theory.Georg Schiemer & Erich H. Reck - 2013 - Bulletin of Symbolic Logic 19 (4):433-472.
    In historical discussions of twentieth-century logic, it is typically assumed that model theory emerged within the tradition that adopted first-order logic as the standard framework. Work within the type-theoretic tradition, in the style ofPrincipia Mathematica, tends to be downplayed or ignored in this connection. Indeed, the shift from type theory to first-order logic is sometimes seen as involving a radical break that first made possible the rise of modern model theory. While comparing several early attempts to develop the semantics of (...)
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  16. Frege's Lectures on Logic: Carnap's Student Notes, 1910-1914.Erich H. Reck & Steve Awodey - 2005 - Bulletin of Symbolic Logic 11 (3):445-447.
  17.  89
    Completeness and Categoricity, Part I: 19th Century Axiomatics to 20th Century Metalogic.Steve Awodey & Erich H. Reck - unknown
    This paper is the first in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins in the development of the axiomatic method. We argue that, both from historical and logical points of view, higher-order logic is an appropriate framework for considering such notions, and we consider some open questions in higher-order axiomatics. In addition, we indicate how one can fruitfully extend the usual set-theoretic semantics (...)
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  18.  95
    Dedekind, Structural Reasoning, and Mathematical Understanding.Erich H. Reck - 2009 - In Bart Van Kerkhove (ed.), New Perspectives on Mathematical Practices: Essays in Philosophy and History of Mathematics. World Scientific. pp. 150--173.
  19. Developments in Logic: Carnap, Gödel, and Tarski.Erich H. Reck - 2013 - In Michael Beaney (ed.), Oxford Handbook of the History of Analytic Philosophy. Oxford: Oxford University Press. pp. 546-571.
    Analytic philosophy and modern logic are intimately connected, both historically and systematically. Thinkers such as Frege, Russell, and Wittgenstein were major contributors to the early development of both; and the fruitful use of modern logic in addressing philosophical problems was, and still is, definitive for large parts of the analytic tradition. More specifically, Frege's analysis of the concept of number, Russell's theory of descriptions, and Wittgenstein's notion of tautology have long been seen as paradigmatic pieces of philosophy in this tradition. (...)
     
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  20.  33
    Completeness and Categoricity: 19th Century Axiomatics to 21st Century Senatics.Steve Awodey & Erich H. Reck - 2002 - History and Philosophy of Logic 23:1-30.
    Steve Awodey and Erich H. Reck. Completeness and Categoricity: 19th Century Axiomatics to 21st Century Senatics.
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  21.  41
    Completeness and Categoricty, Part II: 20th Century Metalogic to 21st Century Semantics.Steve Awodey & Erich H. Reck - 2002 - History and Philosophy of Logic 23:77-92.
    This paper is the second in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins in the development of the axiomatic method. We argue that, both from historical and logical points of view, higher-order logic is an appropriate framework for considering such notions, and we consider some open questions in higher-order axiomatics. In addition, we indicate how one can fruitfully extend the usual set-theoretic semantics (...)
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  22. Hempel, Carnap, and the Covering Law Model.Erich H. Reck - 2013 - In Nikolay Milkov & Volker Peckhaus (eds.), The Berlin Group and the Philosophy of Logical Empiricism. Springer. pp. 311--324.
  23. Frege, Wittgenstein, and Platonism in Mathematics.Erich H. Reck - 1992 - Dissertation, University of Chicago
  24. Logic, Philosophy of Mathematics, and Their History: Essays in Honor of W. W. Tait.Erich H. Reck (ed.) - 2018 - College Publications.
    In a career that spans 60 years so far, W.W. Tait has made many highly influential contributions to logic, the philosophy of mathematics, and their history. The present collection of new essays - contributed by former students, colleagues, and friends - is a Festschrift, i.e., a celebration of his life and work. The essays address a variety of themes prominent in his work or related to it. The collection starts with an introduction in which Tait's contributions are sketched and put (...)
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  25. Wittgenstein's “Great Debt” to Frege; Biographical Traces and Philosophical Themes.Erich H. Reck - 2002 - In From Frege to Wittgenstein: Perspectives on Early Analytic Philosophy. Oxford University Press. pp. 3--38.
  26. Frege-Russell Numbers: Analysis or Explication?Erich H. Reck - 2007 - In Michael Beaney (ed.), The Analytic Turn. London: Routledge. pp. 33-50.
    For both Gottlob Frege and Bertrand Russell, providing a philosophical account of the concept of number was a central goal, pursued along similar logicist lines. In the present paper, I want to focus on a particular aspect of their accounts: their definitions, or re-constructions, of the natural numbers as equivalence classes of equinumerous classes. In other words, I want to examine what is often called the ‘Frege-Russell conception of the natural numbers’ or, more briefly, the Frege-Russell numbers. My main concern (...)
     
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  27.  23
    Introduction to Special Issue: Reconsidering Frege's Conception of Number.Erich H. Reck & Roy T. Cook - 2016 - Philosophia Mathematica 24 (1):1-8.
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