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  1.  67
    Logic and philosophy of mathematics in the early Husserl.Stefania Centrone - 2010 - New York: Springer.
    This volume will be of particular interest to researchers working in the history, and in the philosophy, of logic and mathematics, and more generally, to ...
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  2.  53
    Essays on Husserl’s Logic and Philosophy of Mathematics.Stefania Centrone (ed.) - 2017 - Dordrecht, Netherland: Springer Verlag.
    Essays on Husserl’s Logic and Philosophy of Mathematics sets out to fill up a lacuna in the present research on Husserl by presenting a precise account of Husserl’s work in the field of logic, of the philosophy of logic and of the philosophy of mathematics. The aim is to provide an in-depth reconstruction and analysis of the discussion between Husserl and his most important interlocutors, and to clarify pivotal ideas of Husserl’s by considering their reception and elaboration by some of (...)
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  3.  64
    Begründungen bei Bolzano und beim frühen Husserl.Stefania Centrone - 2011 - Zeitschrift für Philosophische Forschung 65 (1):5-27.
    Two hundred years ago Bernard Bolzano published a booklet on the philosophy of mathematics that is the first major step forward in this area since Pascal’s De l’esprit géométrique. Following Aristotelian lines Bolzano distinguishes in his opusculum two kinds of proofs, those that simply show that something is the case, and those that explain why something is the case. In his Wissenschaftslehre this contrast reappears as that between derivability and consecutivity . Husserl takes up some of Bolzano’s key concepts in (...)
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  4.  31
    Der Reziprozitätskanon in den Beyträgen_ und in der _Wissenschaftslehre.Stefania Centrone - 2010 - Zeitschrift für Philosophische Forschung 64 (3):310-330.
    Two centuries ago Bernard Bolzano published his Contributions to a more well-founded presentation of mathematics which Goethe praised as “an opusculum of very high value”. Bolzano still seems to accept the traditional principle that that intension and extension of a concept stand in an inverse relation . In particular he claims that the concept of a genus proximum is always a component of the concept of the species which are subordinated to it. However, this does not harmonize with his simultaneous (...)
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  5.  45
    Early Bolzano on ground-consequence proofs.Stefania Centrone - 2016 - Bulletin of Symbolic Logic 22 (2):215-237.
    In his earlyContributions to a Better-Grounded Presentation of Mathematics Bernard Bolzano tries to characterizerigorous proofs.Rigorousis,prima facie, any proof that indicates the grounds for its conclusion. Bolzano lists a number of methodological constraints all rigorous proofs should comply with, and tests them systematically against a specific collection of elementary inference schemata that, according to him, are evidently of ground-consequence-kind. This paper intends to give a detailed and critical account of the fragmentary logic of theContributions, and to point out as well some (...)
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  6.  34
    Relational Theories of Intentionality and the Problem of Non-Existents.Stefania Centrone - 2016 - In Marian David & Mauro Antonelli (eds.), Existence, Fiction, Assumption: Meinongian Themes and the History of Austrian Philosophy. Boston: De Gruyter. pp. 1-26.
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  7.  30
    Das Problem der apagogischen Beweise in Bolzanos Beyträgen und seiner Wissenschaftslehre.Stefania Centrone - 2012 - History and Philosophy of Logic 33 (2):127 - 157.
    This paper analyzes and evaluates Bolzano's remarks on the apagogic method of proof with reference to his juvenile booklet "Contributions to a better founded presentation of mathematics" of 1810 and to his ?Theory of science? (1837). I shall try to defend the following contentions: (1) Bolzanos vain attempt to transform all indirect proofs into direct proofs becomes comprehensible as soon as one recognizes the following facts: (1.1) his attitude towards indirect proofs with an affirmative conclusion differs from his stance to (...)
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  8.  31
    Bolzano und Leibniz über Klarheit und Deutlichkeit.Stefania Centrone - 2010 - Archiv für Geschichte der Philosophie 92 (3):256-289.
    At a time when they had largely fallen into disrepute Bolzano reactivated the distinctions between ‚clear‘ and ‚obscure‘, ‚distinct‘ and ‚confused‘ ideas. In the central sections of this paper I offer a critical reconstruction of the explanations of these pairs of opposita which are to be found in vol. III of Bolzano's monumental Wissenschaftslehre . I then provide a detailed account of its Leibnizian counterparts that were well-known to the ‚Bohemian Leibniz‘, and finally I evaluate Bolzano's criticism thereof.
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  9.  9
    Der Reziprozitätskanon in den Beyträgen_ und in der _Wissenschaftslehre.Stefania Centrone - 2010 - Zeitschrift für Philosophische Forschung 64 (3):310-330.
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  10.  41
    Husserl on the 'Totality of all conceivable arithmetical operations'.Stefania Centrone - 2006 - History and Philosophy of Logic 27 (3):211-228.
    In the present paper, we discuss Husserl's deep account of the notions of ?calculation? and of arithmetical ?operation? which is found in the final chapter of the Philosophy of Arithmetic, arguing that Husserl is as far as we know the first scholar to reflect seriously on and to investigate the problem of circumscribing the totality of computable numerical operations. We pursue two complementary goals, namely: (i) to provide a formal reconstruction of Husserl's intuitions, and (ii) to demonstrate on the basis (...)
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  11.  33
    Strenge Beweise und das Verbot der metábasis eis állo génos : Eine Untersuchung zu Bernard Bolzanos Beyträgen zu einer begründeteren Darstellung der Mathematik.Stefania Centrone - 2012 - History and Philosophy of Logic 33 (1):1 - 31.
    In his booklet "Contributions to a better founded presentation of mathematics" of 1810 Bernard Bolzano made his first serious attempt to explain the notion of a rigorous proof. Although the system of logic he employed at that stage is in various respects far below the level of the achievements in his later Wissenschaftslehre, there is a striking continuity between his earlier and later work as regards the methodological constraints on rigorous proofs. This paper tries to give a perspicuous and critical (...)
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  12. Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts.Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.) - 2019 - Springer Verlag.
    This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives. The first two sections focus on the two most prominent candidate theories for a foundation of mathematics. Readers may trace current research in set theory, (...)
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  13. Functions in Frege, Bolzano and Husserl.Stefania Centrone - 2010 - History and Philosophy of Logic 31 (4):315-336.
    This explorative article is organized around a set of questions concerning the concept of a function. First, a summary of certain general facts about functions that are a common coin in contemporary logic is given. Then Frege's attempt at clarifying the nature of functions in his famous paper Function and Concept and in his Grundgesetze is discussed along with some questions which Freges' approach gave rise to in the literature. Finally, some characteristic uses of functional notions to be found in (...)
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  14. Husserls Doppelvortrag in der Mathematischen Gesellschaft in Göttingen 1901.Stefania Centrone - 2011 - In C. Beyer & K. Cramer (eds.), Edmund Husserl 1859-2009. Beiträge aus Anlass der 150. Wiederkehr des Geburtstages des Philosophen, Abhandlungsreihe der Akademie der Wissenschaften zu Göttingen ADW 14. pp. 107-128.
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  15.  13
    Husserl and Boole.Pierluigi Minari & Stefania Centrone - 2017 - In Stefania Centrone (ed.), Essays on Husserl’s Logic and Philosophy of Mathematics. Dordrecht, Netherland: Springer Verlag.
    We aim at clarifying to what extent the work of the English mathematician George Boole on the algebra of logic is taken into consideration and discussed in the work of early Husserl, focusing in particular on Husserl’s lecture “Über die neueren Forschungen zur deduktiven Logik” of 1895, in which an entire section is devoted to Boole. We confront Husserl’s representation of the problem-solving processes with the analysis of “symbolic reasoning” proposed by George Boole in the Laws of Thought and try (...)
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  16. Studien zu Bolzano.Stefania Centrone (ed.) - 2015 - Sankt Augustin: Academia Verlag.
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  17.  20
    Husserls Zeichentheorie. Bemerkungen zur Ersten Logischen Untersuchung.Stefania Centrone - 2015 - Archiv für Geschichte der Philosophie 97 (1):66-96.
    Name der Zeitschrift: Archiv für Geschichte der Philosophie Jahrgang: 97 Heft: 1 Seiten: 66-96.
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  18. Collections in Early Bolzano.Stefania Centrone & Mark Siebel - 2018 - Journal for the History of Analytical Philosophy 6 (7).
    There are quite a few studies on late Bolzano’s notion of a collection (Inbegriff). We try to broaden the perspective by introducing the forerunner of collections in Bolzano’s early writings, namely the entities referred to by expressions with the technical term ‘et’. Special emphasis is laid on the question whether these entities are set-theoretical or mereological plenties. Moreover, similarities and differences to Bolzano’s mature conception are pointed out.
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  19.  7
    Versuche über Husserl.Stefania Centrone (ed.) - 2013 - Hamburg: Meiner Felix.
    Der Band versammelt neue Beiträge namhafter Husserl-Forscher und eröffnet analytische und phänomenologische Interpretationsperspektiven auf Husserls Werk. Zugleich versuchen die Autoren, die Diskussionsgrundlagen zwischen Husserl und einigen seiner wichtigsten und einflußreichsten Gesprächspartner wiederherzustellen: Bernard Bolzano, Franz Brentano, Gottlob Frege, Martin Heidegger und Ludwig Wittgenstein. Mit Beiträgen von: Christian Beyer, Stefania Centrone, Dagfinn Føllesdal, George Heffernan, Wolfgang Künne, Eduard Marbach und Markus Stepanians.
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  20.  4
    Strenge Beweise und das Verbot der metábasis eis állo génos : Eine Untersuchung zu Bernard Bolzanos Beyträgen zu einer begründeteren Darstellung der Mathematik.Stefania Centrone - 2012 - History and Philosophy of Logic 33 (1):1-31.
    In his booklet ‘Contributions to a better founded presentation of mathematics’ of 1810 Bernard Bolzano made his first serious attempt to explain the notion of a rigorous proof. Although the system of logic he employed at that stage is in various respects far below the level of the achievements in his later Wissenschaftslehre, there is a striking continuity between his earlier and later work as regards the methodological constraints on rigorous proofs. This paper tries to give a perspicuous and critical (...)
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  21.  7
    Das Problem der apagogischen Beweise in Bolzanos Beyträgen_ und seiner _Wissenschaftslehre.Stefania Centrone - 2012 - History and Philosophy of Logic 33 (2):127-157.
    This paper analyzes and evaluates Bolzano's remarks on the apagogic method of proof with reference to his juvenile booklet ‘Contributions to a better founded presentation of mathematics’ of 1810 and to his ‘Theory of science’ (1837). I shall try to defend the following contentions: (1) Bolzanos’ vain attempt to transform all indirect proofs into direct proofs becomes comprehensible as soon as one recognizes the following facts: (1.1) his attitude towards indirect proofs with an affirmative conclusion differs from his stance to (...)
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  22. Aspekte des Psychologismus-Streits: Husserl und Frege über Anzahlen und logische Gesetze.Stefania Centrone - 2013 - In Versuche über Husserl. Hamburg: Meiner Felix. pp. 65-96.
  23. A note on the logic of distributed knowledge.Stefania Centrone & P. Minari - 2019 - In Luca Bellotti, Luca Gili, Enrico Moriconi & Giacomo Turbanti (eds.), Third Pisa Colloquium in Logic, Language and Epistemology. Essays in Honour of Mauro Mariani and Carlo Marletti. Pisa: Edizioni ETS. pp. 263-274.
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  24. Ableitbarkeit, Verträglichkeit und Enthymem.Stefania Centrone - 2015 - In Studien zu Bolzano. Sankt Augustin: Academia Verlag. pp. 1-64.
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  25.  9
    Bolzanos Zeichentheorie. Eine Untersuchung zu § 285 der Wissenschaftslehre.Stefania Centrone & Wolfgang Künne - 2011 - Grazer Philosophische Studien 83 (1):171-198.
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  26.  25
    Consequentia Mirabilis, Antiskeptizismus und Antinomien Über Bolzanos Beweis, daß es wenigstens eine Wahrheit an sich, daß es der Wahrheiten mehre, ja unendlich viele gebe.Stefania Centrone - 2012 - Zeitschrift für Philosophische Forschung 66 (4):539-565.
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  27.  7
    Der junge Leibniz und Gott. Der Beweis der Existenz Gottes in der Dissertatio de Arte Combinatoria.Stefania Centrone - 2018 - Studia Leibnitiana 50 (2):146-162.
    The present paper analyses the proof of the existence of God given by Leibniz in his early work, the Dissertatio de arte combinatoria of 1666. Leibniz delivers a proof by an (infinite) distinction of cases that has not always been recognized by his translators and critics.
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  28. Husserl and Leibniz on Symbolical Thinking.Stefania Centrone - 2014 - In Proceedings of the 45th Annual Meeting of the Husserl Circle. Hanover, New Hampshire, USA:
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  29.  4
    Husserls Doppelvortrag in der Mathematischen Gesellschaft in Göttingen 1901.Stefania Centrone - 2011 - In Konrad Cramer & Christian Beyer (eds.), Edmund Husserl, 1859-2009: Beiträge Aus Anlass der 150. Wiederkehr des Geburtstages des Philosophen : Internationales Symposium, Im November 2009 Veranstaltet von der Akademie der Wissenschaften Zu Göttingen in Verbindung Mit Dem Philosophischen Seminar d. De Gruyter. pp. 103-124.
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  30. Husserl on Schröder's View of Logic.Stefania Centrone & P. Minari - 2014 - In E. Moriconi & L. Tesconi (eds.), Second Pisa Colloquium in Logic, Epistemology and Philosophy of Language. pp. 138-161.
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  31. Husserl secondo Casari.Stefania Centrone - 2020 - Rivista di Filosofia 111 (2).
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  32. Introduction.Stefania Centrone - 2019 - In Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.), Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Springer Verlag.
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  33. Introduction.Stefania Centrone - 2017 - In Essays on Husserl’s Logic and Philosophy of Mathematics. Dordrecht, Netherland: Springer Verlag.
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  34. Infinito matematico e soggettività: Notazioni sulla sezione “quantità” della “Scienza della logica” di Hegel.Stefania Centrone - 2002 - Giornale Critico Della Filosofia Italiana 22 (3):430-448.
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  35. Introduction: Mathesis Universalis, Proof and Computation.Stefania Centrone - 2019 - In Stefania Centrone, Sara Negri, Deniz Sarikaya & Peter M. Schuster (eds.), Mathesis Universalis, Computability and Proof. Cham, Switzerland: Springer Verlag.
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  36. Mathematical Existence, Mathematical Fictions, Etiological Proofs and Other Matters: Replies to M. Hartimo and R. Tragesser.Stefania Centrone - 2012 - The New Yearbook for Phenomenology and Phenomenological Philosophy 12:336-369.
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  37.  35
    Notes on Mally’s Deontic Logic and the Collapse of Modalities.Stefania Centrone - 2013 - Synthese 190 (18):4095-4116.
    This paper analyzes Mally’s system of deontic logic, introduced in his The Basic Laws of Ought: Elements of the Logic of Willing (1926). We discuss Mally’s text against the background of some contributions in the literature which show that Mally’s axiomatic system for deontic logic is flawed, in so far as it derives, for an arbitrary A, the theorem “A ought to be the case if and only if A is the case”, which represents a collapse of obligation. We then (...)
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  38. Oskar Becker on Modalities.Stefania Centrone & P. Minari - 2019 - Berlin: Logos.
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  39. Proceedings of the 45th Annual Meeting of the Husserl Circle.Stefania Centrone (ed.) - 2014 - Hanover, New Hampshire, USA:
     
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  40. Reply to M. van Atten: On Husserl-Computable Functions.Stefania Centrone - 2012 - The New Yearbook for Phenomenology and Phenomenological Philosophy 12:377-383.
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  41.  16
    Theory of Science, written by Bernard Bolzano.Stefania Centrone - 2017 - Grazer Philosophische Studien 94 (4):625-637.
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  42.  12
    Husserl and Schröder.Pierluigi Minari & Stefania Centrone - 2017 - In Stefania Centrone (ed.), Essays on Husserl’s Logic and Philosophy of Mathematics. Dordrecht, Netherland: Springer Verlag.
    We aim at clarifying to what extent the work of the German mathematician Ernst Schröder on the algebra of logic is taken into consideration and rehashed in the work of the early Husserl, focusing on Husserl’s 1891 Review of the first volume of Schröder’s monumental Vorlesungen über die Algebra der Logik and on Husserl’s text Der Folgerungskalkül und die Inhaltslogik written in the same year. We will try to show how and why Husserl, while praising Schröder’s calculus, strongly criticizes Schröder’s (...)
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  43.  43
    Mathesis Universalis, Computability and Proof.Stefania Centrone, Sara Negri, Deniz Sarikaya & Peter M. Schuster (eds.) - 2019 - Cham, Switzerland: Springer Verlag.
    In a fragment entitled Elementa Nova Matheseos Universalis Leibniz writes “the mathesis [...] shall deliver the method through which things that are conceivable can be exactly determined”; in another fragment he takes the mathesis to be “the science of all things that are conceivable.” Leibniz considers all mathematical disciplines as branches of the mathesis and conceives the mathesis as a general science of forms applicable not only to magnitudes but to every object that exists in our imagination, i.e. that is (...)
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  44.  30
    Husserl and Leibniz: Notes on the Mathesis Universalis.Jairo Silva & Stefania Centrone - 2017 - In Stefania Centrone (ed.), Essays on Husserl’s Logic and Philosophy of Mathematics. Dordrecht, Netherland: Springer Verlag. pp. 1-24.
    The notion of mathesis universalis appears in many of Edmund Husserl’s works, where it corresponds essentially to “a universal a priori ontology”. This paper has two purposes; one, largely exegetical, of clarifying how Husserl elaborates on Leibniz’ concept of mathesis universalis and associated notions like symbolic thinking and symbolic knowledge filtering them through the lesson of the so called “bohemian Leibniz”, Bernard Bolzano; another, more properly philosophical, of examining the role that the universal mathesis is allowed to play, and the (...)
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  45.  9
    Edgar Morscher, Normenlogik. Grundlagen – Systeme – Anwendungen. Paderborn, Mentis, 2012. 309 pp., ISBN-13: 978-3897857841. [REVIEW]Stefania Centrone - 2014 - Bulletin of Symbolic Logic 20 (1):97-98.
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  46.  41
    Review of M. Hartimo (ed.), Phenomenology and Mathematics[REVIEW]Stefania Centrone - 2014 - Philosophia Mathematica 22 (1):126-129.
  47.  16
    Mirja Hartimo ed. Phenomenology and Mathematics. Phaenomenologia; 195. Dordrecht: Springer, 2010. ISBN 978-90-481-3728-2 ; 978-90-481-3728-2 ; 978-94-007-3196-7 . Pp. xxv + 222†: Critical Studies/Book Reviews. [REVIEW]Stefania Centrone - 2014 - Philosophia Mathematica 22 (1):126-129.
  48.  94
    Richard Tieszen, After Gödel. Platonism and Rationalism in Mathematics and Logic.: Oxford University Press, Oxford, 2011. [REVIEW]Stefania Centrone - 2014 - Husserl Studies 30 (2):153-162.
    It is well known that Husserl, together with Plato and Leibniz, counted among Gödel’s favorite philosophers and was, in fact, an important source and reference point for the elaboration of Gödel’s own philosophical thought. Among the scholars who emphasized this connection we find, as Richard Tieszen reminds us, Gian-Carlo Rota, George Kreisel, Charles Parsons, Heinz Pagels and, especially, Hao Wang. Right at the beginning of After Gödel we read: “The logician who conducted and recorded the most extensive philosophical discussions with (...)
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  49.  36
    The Origin of the Logic of Symbolic Mathematics. Edmund Husserl and Jacob Klein. [REVIEW]Stefania Centrone - 2013 - History and Philosophy of Logic 34 (2):187-193.
    Burt C. Hopkins, The Origin of the Logic of Symbolic Mathematics. Edmund Husserl and Jacob Klein. Bloomington and Indianapolis: Indiana University Press. 2011. 592 pp. $49.95. ISBN 978-0-253-35671-...
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