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  1. In praise of replacement.Akihiro Kanamori - 2012 - Bulletin of Symbolic Logic 18 (1):46-90.
    This article serves to present a large mathematical perspective and historical basis for the Axiom of Replacement as well as to affirm its importance as a central axiom of modern set theory.
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  • On arbitrary sets and ZFC.José Ferreirós - 2011 - Bulletin of Symbolic Logic 17 (3):361-393.
    Set theory deals with the most fundamental existence questions in mathematics—questions which affect other areas of mathematics, from the real numbers to structures of all kinds, but which are posed as dealing with the existence of sets. Especially noteworthy are principles establishing the existence of some infinite sets, the so-called “arbitrary sets.” This paper is devoted to an analysis of the motivating goal of studying arbitrary sets, usually referred to under the labels of quasi-combinatorialism or combinatorial maximality. After explaining what (...)
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  • Frege, August Bebel and the Return of Alsace-Lorraine: The dating of the distinction between Sinn and Bedeutung.Göran Sundholm - 2001 - History and Philosophy of Logic 22 (2):57-73.
    A detailed chronology is offered for the writing of Frege's central philosophical essays from the early 1890s. Particular attention is given to (the distinction between) Sinn and Bedeutung. Suggestions are made as to the origin of the examples concerning the Morning Star/Evening Star and August Bebel's views on the return of Alsace-Lorraine. Likely sources are offered for Frege's use of the terms Bestimmungsweise, Art des Gegebenseins and Sinn und Bedeutung.
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  • On the philosophical significance of Frege's theorem.Crispin Wright - 1997 - In Richard G. Heck (ed.), Language, thought, and logic: essays in honour of Michael Dummett. New York: Oxford University Press. pp. 201--44.
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  • The reason's proper study: essays towards a neo-Fregean philosophy of mathematics.Crispin Wright & Bob Hale - 2001 - Oxford: Clarendon Press. Edited by Crispin Wright.
    Here, Bob Hale and Crispin Wright assemble the key writings that lead to their distinctive neo-Fregean approach to the philosophy of mathematics. In addition to fourteen previously published papers, the volume features a new paper on the Julius Caesar problem; a substantial new introduction mapping out the program and the contributions made to it by the various papers; a section explaining which issues most require further attention; and bibliographies of references and further useful sources. It will be recognized as the (...)
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  • Logic, Logic, and Logic.George Boolos - 1998 - Cambridge, Mass: Harvard University Press. Edited by Richard C. Jeffrey.
    This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; ...
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  • (1 other version)The Frege reader.Gottlob Frege & Michael Beaney (eds.) - 1997 - Cambridge: Blackwell.
    This is the first single-volume edition and translation of Frege's philosophical writings to include his seminal papers as well as substantial selections from ...
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  • Frege's philosophy of mathematics.William Demopoulos (ed.) - 1995 - Cambridge: Harvard University Press.
    Widespread interest in Frege's general philosophical writings is, relatively speaking, a fairly recent phenomenon. But it is only very recently that his philosophy of mathematics has begun to attract the attention it now enjoys. This interest has been elicited by the discovery of the remarkable mathematical properties of Frege's contextual definition of number and of the unique character of his proposals for a theory of the real numbers. This collection of essays addresses three main developments in recent work on Frege's (...)
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  • Russell, idealism, and the emergence of analytic philosophy.Peter Hylton - 1990 - New York: Oxford University Press.
    Analytic philosophy has become the dominant philosophical tradition in the English-speaking world. This book illuminates that tradition through a historical examination of a crucial period in its formation: the rejection of Idealism by Bertrand Russell and G.E. Moore at the beginning of the twentieth century, and the subsequent development of Russell's thought in the period before the First World War.
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  • Frege's mathematical setting.Mark Wilson - unknown
    This survey article describes Frege's celebrated foundational work against the context of other late nineteenth century approaches to introducing mathematically novel "extension elements" within both algebra and geometry.
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  • Eudoxos and dedekind: On the ancient greek theory of ratios and its relation to modern mathematics.Howard Stein - 1990 - Synthese 84 (2):163 - 211.
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  • Frege: The Royal road from geometry.Mark Wilson - 1992 - Noûs 26 (2):149-180.
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  • The caesar problem in its historical context: Mathematical background.Jamie Tappenden - 2005 - Dialectica 59 (2):237–264.
    The issues surrounding the Caesar problem are assumed to be inert as far as ongoing mathematics is concerned. This paper aims to correct this impression by spelling out the ways that, in their historical context, Frege's remarks would have had considerable resonance with work that other mathematicians such as Riemann and Dedekind were doing. The search for presentation‐independent characterizations of objects and global definitions was seen as bound up with fundamental methodological questions in complex analysis and number theory.
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  • Russell’s reasons for logicism.Ian Proops - 2006 - Journal of the History of Philosophy 44 (2):267-292.
    What is at stake philosophically for Russell in espousing logicism? I argue that Russell's aims are chiefly epistemological and mathematical in nature. Russell develops logicism in order to give an account of the nature of mathematics and of mathematical knowledge that is compatible with what he takes to be the uncontroversial status of this science as true, certain and exact. I argue for this view against the view of Peter Hylton, according to which Russell uses logicism to defend the unconditional (...)
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  • Labyrinth of Thought. A history of set theory and its role in modern mathematics.Jose Ferreiros - 2001 - Basel, Boston: Birkhäuser Verlag.
    Review by A. Kanamori, Boston University (author of The Higher Infinite), review in The Bulletin of Symbolic Logic: “Notwithstanding and braving the daunting complexities of this labyrinth, José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in (...)
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  • The Reason's Proper Study: Essays toward a Neo-Fregean Philosophy of Mathematics.Bob Hale & Crispin Wright - 2001 - Bulletin of Symbolic Logic 12 (2):291-294.
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  • Kant und die moderne Mathematik. (Mit Bezug auf Bertrand Russells und Louis Couturats Werke über die Prinzipien der Mathematik.).Ernst Cassirer - 1907 - Kant Studien 12 (1-3):1-49.
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  • A Parting of the Ways: Carnap, Cassirer, and Heidegger.Michael Friedman - 2000 - Open Court Publishing.
    In this insightful study of the common origins of analytic and continental philosophy, Friedman looks at how social and political events intertwined and influenced philosophy during the early twentieth century, ultimately giving rise to the two very different schools of thought. He shows how these two approaches, now practiced largely in isolation from one another, were once opposing tendencies within a common discussion. Already polarized by their philosophical disagreements, these approaches were further split apart by the rise of Naziism and (...)
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  • Frege’s Conception of Logic.Patricia Blanchette - 2012 - Oxford, England: Oup Usa.
    In Frege's Conception of Logic Patricia A. Blanchette explores the relationship between Gottlob Frege's understanding of conceptual analysis and his understanding of logic.
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  • Frege, Lotze, and Boole.Jeremy Heis - 2013 - In Erich H. Reck (ed.), The Historical turn in Analytic Philosophy. New York, NY: Palgrave-Macmillan.
    In the ‘analytic tradition’, Hans Sluga wrote thirty years ago in his book Gottlob Frege, there has been a ‘lack of interest in historical questions — even in the question of its own roots. Anti-historicism has been the baggage of the tradition since Frege’ (Sluga, 1980, p. 2). The state of the discussion of Frege among analytic philosophers, Sluga claimed, illustrated well this indifference. Despite the numbers of pages devoted to Frege, there was still, Sluga claimed, little understanding of the (...)
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  • The Historical turn in Analytic Philosophy.Erich H. Reck (ed.) - 2013 - New York, NY: 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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  • Frege's theorem.Richard G. Heck - 2011 - New York: Clarendon Press.
    The book begins with an overview that introduces the Theorem and the issues surrounding it, and explores how the essays that follow contribute to our understanding of those issues.
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  • The Philosophy of Mathematical Practice.Paolo Mancosu (ed.) - 2008 - Oxford, England: Oxford University Press.
    There is an urgent need in philosophy of mathematics for new approaches which pay closer attention to mathematical practice. This book will blaze the trail: it offers philosophical analyses of important characteristics of contemporary mathematics and of many aspects of mathematical activity which escape purely formal logical treatment.
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  • Frege explained: from arithmetic to analytic philosophy.Joan Weiner - 2004 - Chicago: Open Court.
    Frege's life and character -- The project -- Frege's new logic -- Defining the numbers -- The reconception of the logic, I-"Function and concept" -- The reconception of the logic, II- "On sense and meaning" and "on concept and object" -- Basic laws, the great contradiction, and its aftermath -- On the foundations of geometry -- Logical investigations -- Frege's influence on recent philosophy.
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  • How applied mathematics became pure.Penelope Maddy - 2008 - Review of Symbolic Logic 1 (1):16-41.
    My goal here is to explore the relationship between pure and applied mathematics and then, eventually, to draw a few morals for both. In particular, I hope to show that this relationship has not been static, that the historical rise of pure mathematics has coincided with a gradual shift in our understanding of how mathematics works in application to the world. In some circles today, it is held that historical developments of this sort simply represent changes in fashion, or in (...)
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  • (1 other version)Frege versus Cantor and dedekind: On the concept of number.William Tait - manuscript
    There can be no doubt about the value of Frege's contributions to the philosophy of mathematics. First, he invented quantification theory and this was the first step toward making precise the notion of a purely logical deduction. Secondly, he was the first to publish a logical analysis of the ancestral R* of a relation R, which yields a definition of R* in second-order logic.1 Only a narrow and arid conception of philosophy would exclude these two achievements. Thirdly and very importantly, (...)
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  • Logic as Universal Science: Russell's Early Logicism and its Philosophical Context.Anssi Korhonen - 2013 - London, England: Palgrave-Macmillan.
    Logic as Universal Science offers a detailed reconstruction of the underlying philosophy in The Principles of Mathematics showing how Russell sought to deliver a death blow to the dominant Kantian view that formal logic is a concise and dry science and unable to enlarge our understanding.
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  • Russell's Unknown Logicism: A Study in the History and Philosophy of Mathematics.Sébastien Gandon - 2012 - Houndmills, England and New York: Palgrave-Macmillan.
    In this excellent book Sebastien Gandon focuses mainly on Russell's two major texts, Principa Mathematica and Principle of Mathematics, meticulously unpicking the details of these texts and bringing a new interpretation of both the mathematical and the philosophical content. Winner of The Bertrand Russell Society Book Award 2013.
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  • Gottlob Frege: Leben - Werk - Zeit.Lothar Kreiser - 2001 - Hamburg: Meiner.
    Gottlob Frege (1848-1925) und Ludwig Wittgenstein gelten als die geistigen Väter der analytischen Philosophie. Das wissenschaftliche Schaffen Gottlob Freges hat wie kein anderes nach Aristoteles die Logik in ihrer theoretischen Erscheinungsform und in ihrer praktischen Relevanz grundlegend verändert. Seine logisch-semantischen Untersuchungen haben noch immer auf Philosophie und Sprachwissenschaft großen Einfluß. Doch wer war dieser Mann, der die Geistesgeschichte des 20. Jahrhunderts mitgestaltete, dessen Rückführung logischen Schließens auf mechanisch kontrollierte Elementarschritte den Weg zur Logik der elektronischen Datenverarbeitung eröffnete? Zwar gibt es (...)
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  • Russell, Idealism, and the Emergence of Analytic Philosophy by Peter Hylton. [REVIEW]Thomas Baldwin - 1992 - Journal of Philosophy 89 (1):51-55.
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  • Dedekind’s Analysis of Number: Systems and Axioms.Wilfried Sieg & Dirk Schlimm - 2005 - Synthese 147 (1):121-170.
    Wilfred Sieg and Dirk Schlimm. Dedekind's Analysis of Number: Systems and Axioms.
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  • Substanzbegriff und Funktionsbegriff.Ernst Cassirer - 1910 - Revue de Métaphysique et de Morale 18 (6):7-8.
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  • Collected Papers on Mathematics, Logic, and Philosophy.Gottlob Frege - 1991 - Wiley-Blackwell. Edited by Brian McGuinness.
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  • Frege, Dedekind, and the philosophy of mathematics.Philip Kitcher - 1986 - In Leila Haaparanta & Jaakko Hintikka (eds.), Frege Synthesized: Essays on the Philosophical and Foundational Work of Gottlob Frege. Dordrecht, Netherland: Kluwer Academic Publishers. pp. 299--343.
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  • (1 other version)Frege versus Cantor and Dedekind: On the Concept of Number.W. W. Tait - 1996 - In Matthias Schirn (ed.), Frege: Importance and Legacy. New York: De Gruyter. pp. 70-113.
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  • [Omnibus Review].Tyler Burge - 1981 - Journal of Symbolic Logic 46 (2):412-415.
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  • [Omnibus Review].William Demopoulos - 1998 - Journal of Symbolic Logic 63 (4):1598-1602.
    Richard G. Heck, On the Philosophical Significance of Frege's Theorem. Language, Thought, and Logic, Essays in Honour of Michael Dummett.George Boolos, Is Hume's Principle Analytic?.Charles Parsons, Wright onion and Set Theory.Richard G. Heck, The Julius Caesar Objection.
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  • Truth, thought, reason: essays on Frege.Tyler Burge - 2005 - New York: Oxford University Press.
    Tyler Burge presents a collection of his seminal essays on Gottlob Frege (1848-1925), who has a strong claim to be seen as the founder of modern analytic philosophy, and whose work remains at the centre of philosophical debate today. Truth, Thought, Reason gathers some of Burge's most influential work from the last twenty-five years, and also features important new material, including a substantial introduction and postscripts to four of the ten papers. It will be an essential resource for any historian (...)
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  • 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.
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  • 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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  • Frege on extensions of concepts, from 1884 to 1903.Tyler Burge - 1984 - Philosophical Review 93 (1):3-34.
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  • Was Sind und was Sollen Die Zahlen?Richard Dedekind - 1888 - Cambridge University Press.
    This influential 1888 publication explained the real numbers, and their construction and properties, from first principles.
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  • Mathematical concepts: Fruitfulness and naturalness.Jamie Tappenden - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford, England: Oxford University Press. pp. 276--301.
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  • The Logicism of Frege, Dedekind, and Russell.William Demopoulos & Peter Clark - 2005 - In Stewart Shapiro (ed.), Oxford Handbook of Philosophy of Mathematics and Logic. Oxford and New York: Oxford University Press. pp. 129--165.
    The common thread running through the logicism of Frege, Dedekind, and Russell is their opposition to the Kantian thesis that our knowledge of arithmetic rests on spatio-temporal intuition. Our critical exposition of the view proceeds by tracing its answers to three fundamental questions: What is the basis for our knowledge of the infinity of the numbers? How is arithmetic applicable to reality? Why is reasoning by induction justified?
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  • Introduction : Analytic philosophy and philosophical history.Erich H. Reck - 2013 - In The Historical turn in Analytic Philosophy. New York, NY: Palgrave-Macmillan. pp. 1-36.
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  • (1 other version)Frege or Dedekind? Towards a reevalaution of their legacies.Erich H. Reck - 2013 - In The Historical turn in Analytic Philosophy. New York, NY: 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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  • Begriffsschrift: Eine der arithmetischen nachgebildete Formelsprache des reinen Denkens.Gottlob Frege - 1879 - Halle a.d.S.: Louis Nebert.
    Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens / von Dr. Gottlob Frege,...Date de l'edition originale : 1879Ce livre est la reproduction fidele d'une oeuvre publiee avant 1920 et fait partie d'une collection de livres reimprimes a la demande editee par Hachette Livre, dans le cadre d'un partenariat avec la Bibliotheque nationale de France, offrant l'opportunite d'acceder a des ouvrages anciens et souvent rares issus des fonds patrimoniaux de la BnF.Les oeuvres faisant partie de cette collection ont ete numerisees (...)
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  • Frege's conception of numbers as objects.Crispin Wright - 1983 - [Aberdeen]: Aberdeen University Press.
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  • Logicist Responses to Kant.Michael Kremer - 2006 - Philosophical Topics 34 (1-2):163-188.
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  • Frege's natural numbers: Motivations and modifications.Erich Reck - 2005 - In Michael Beaney & Erich Reck (eds.), Gottlob Frege: Critical Assessments of Leading Philosophers, Vol. III. London: Routledge. pp. 270-301.
    Frege's main contributions to logic and the philosophy of mathematics are, on the one hand, his introduction of modern relational and quantificational logic and, on the other, his analysis of the concept of number. My focus in this paper will be on the latter, although the two are closely related, of course, in ways that will also play a role. More specifically, I will discuss Frege's logicist reconceptualization of the natural numbers with the goal of clarifying two aspects: the motivations (...)
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