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  1.  20
    Frege: importance and legacy.Matthias Schirn (ed.) - 1996 - New York: Walter de Gruyter.
  2. The Philosophy of Mathematics Today.Matthias Schirn - 2000 - Tijdschrift Voor Filosofie 62 (1):180-181.
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  3.  44
    Frege’s philosophy of geometry.Matthias Schirn - 2019 - Synthese 196 (3):929-971.
    In this paper, I critically discuss Frege’s philosophy of geometry with special emphasis on his position in The Foundations of Arithmetic of 1884. In Sect. 2, I argue that that what Frege calls faculty of intuition in his dissertation is probably meant to refer to a capacity of visualizing geometrical configurations structurally in a way which is essentially the same for most Western educated human beings. I further suggest that according to his Habilitationsschrift it is through spatial intuition that we (...)
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  4. The Philosophy of mathematics today.Matthias Schirn (ed.) - 1998 - New York: Clarendon Press.
    This comprehensive volume gives a panorama of the best current work in this lively field, through twenty specially written essays by the leading figures in the field. All essays deal with foundational issues, from the nature of mathematical knowledge and mathematical existence to logical consequence, abstraction, and the notions of set and natural number. The contributors also represent and criticize a variety of prominent approaches to the philosophy of mathematics, including platonism, realism, nomalism, constructivism, and formalism.
  5.  28
    Frege's Approach to the Foundations of Analysis (1874–1903).Matthias Schirn - 2013 - History and Philosophy of Logic 34 (3):266-292.
    The concept of quantity (Größe) plays a key role in Frege's theory of real numbers. Typically enough, he refers to this theory as ?theory of quantity? (?Größenlehre?) in the second volume of his opus magnum Grundgesetze der Arithmetik (Frege 1903). In this essay, I deal, in a critical way, with Frege's treatment of the concept of quantity and his approach to analysis from the beginning of his academic career until Frege 1903. I begin with a few introductory remarks. In Section (...)
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  6. Hume’s Principle and Axiom V Reconsidered: Critical Reflections on Frege and His Interpreters.Matthias Schirn - 2006 - Synthese 148 (1):171 - 227.
    In this paper, I shall discuss several topics related to Frege’s paradigms of second-order abstraction principles and his logicism. The discussion includes a critical examination of some controversial views put forward mainly by Robin Jeshion, Tyler Burge, Crispin Wright, Richard Heck and John MacFarlane. In the introductory section, I try to shed light on the connection between logical abstraction and logical objects. The second section contains a critical appraisal of Frege’s notion of evidence and its interpretation by Jeshion, the introduction (...)
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  7. Hilbert's Finitism and the Notion of Infinity.Karl-Georg Niebergall & Matthias Schirn - 1998 - In Matthias Schirn (ed.), The Philosophy of Mathematics Today. Clarendon Press.
  8.  32
    Frege's objects of a quite special kind.Matthias Schirn - 1990 - Erkenntnis 32 (1):27 - 60.
  9.  15
    The Philosophy of Mathematics Today: Papers From a Conference Held in Munich From June 28 to July 4,1993.Matthias Schirn (ed.) - 1998 - Oxford, England: Clarendon Press.
    The Philosophy of Mathematics Today gives a panorama of the best current work in this lively field, through twenty essays specially written for this collection by leading figures. The topics include indeterminacy, logical consequence, mathematical methodology, abstraction, and both Hilbert's and Frege's foundational programmes. The collection will be an important source for research in the philosophy of mathematics for years to come. Contributors Paul Benacerraf, George Boolos, John P. Burgess, Charles S. Chihara, Michael Detlefsen, Michael Dummett, Hartry Field, Kit Fine, (...)
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  10.  40
    Hume’s Principle and Axiom V Reconsidered: Critical Reflections on Frege and His Interpreters.Matthias Schirn - 2006 - Synthese 148 (1):171-227.
    In this paper, I shall discuss several topics related to Frege's paradigms of second-order abstraction principles and his logicism. The discussion includes a critical examination of some controversial views put forward mainly by Robin Jeshion, Tyler Burge, Crispin Wright, Richard Heck and John MacFarlane. In the introductory section, I try to shed light on the connection between logical abstraction and logical objects. The second section contains a critical appraisal of Frege's notion of evidence and its interpretation by Jeshion, the introduction (...)
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  11.  47
    On Translating Frege's Die Grundlagen der Arithmetik.Matthias Schirn - 2010 - History and Philosophy of Logic 31 (1):47-72.
    In this essay, I critically discuss Dale Jacquette's new English translation of Frege's work Die Grundlagen der Arithmetik as well as his Introduction and Critical Commentary (Frege, G. 2007. The Foundations of Arithmetic. A Logical-Mathematical Investigation into the Concept of Number . Translated with an Introduction and Critical Commentary by Dale Jacquette. New York: Longman. xxxii + 112 pp.). I begin with a short assessment of Frege's book. In sections 2 and 3, I examine several claims that Jacquette makes in (...)
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  12.  26
    Die Dichotomie analytisch-synthetisch bei Frege unter Berücksichtigung von Kant.Matthias Schirn - 2019 - Kant Studien 110 (1):74-125.
  13.  11
    Frege on Quantities and Real Numbers in Consideration of the Theories of Cantor, Russell and Others.Matthias Schirn - 2014 - In Godehard Link (ed.), Formalism and Beyond: On the Nature of Mathematical Discourse. De Gruyter. pp. 25-95.
  14.  72
    Concepts, extensions, and Frege's logicist project.Matthias Schirn - 2006 - Mind 115 (460):983-1006.
    Although the notion of logical object plays a key role in Frege's foundational project, it has hardly been analyzed in depth so far. I argue that Marco Ruffino's attempt to fill this gap by establishing a close link between Frege's treatment of expressions of the form ‘the concept F’ and the privileged status Frege assigns to extensions of concepts as logical objects is bound to fail. I argue, in particular, that Frege's principal motive for introducing extensions into his logical theory (...)
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  15.  20
    Kants Theorie der geometrischen Erkenntnis und die nichteuklidische Geometrie.Matthias Schirn - 1991 - Kant Studien 82 (1):1-28.
  16.  18
    On the Nature, Status, and Proof of Hume’s Principle in Frege’s Logicist Project.Matthias Schirn - 2016 - In Sorin Costreie (ed.), Early Analytic Philosophy – New Perspectives on the Tradition. Springer Verlag.
    Sections “Introduction: Hume’s Principle, Basic Law V and Cardinal Arithmetic” and “The Julius Caesar Problem in Grundlagen—A Brief Characterization” are peparatory. In Section “Analyticity”, I consider the options that Frege might have had to establish the analyticity of Hume’s Principle, bearing in mind that with its analytic or non-analytic status the intended logical foundation of cardinal arithmetic stands or falls. Section “Thought Identity and Hume’s Principle” is concerned with the two criteria of thought identity that Frege states in 1906 and (...)
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  17.  70
    Fregean abstraction, referential indeterminacy and the logical foundations of arithmetic.Matthias Schirn - 2003 - Erkenntnis 59 (2):203 - 232.
    In Die Grundlagen der Arithmetik, Frege attempted to introduce cardinalnumbers as logical objects by means of a second-order abstraction principlewhich is now widely known as ``Hume's Principle'' (HP): The number of Fsis identical with the number of Gs if and only if F and G are equinumerous.The attempt miscarried, because in its role as a contextual definition HP fails tofix uniquely the reference of the cardinality operator ``the number of Fs''. Thisproblem of referential indeterminacy is usually called ``the Julius Caesar (...)
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  18.  44
    Extensions of the Finitist Point of View.Matthias Schirn & Karl-Georg Niebergall - 2001 - History and Philosophy of Logic 22 (3):135-161.
    Hilbert developed his famous finitist point of view in several essays in the 1920s. In this paper, we discuss various extensions of it, with particular emphasis on those suggested by Hilbert and Bernays in Grundlagen der Mathematik (vol. I 1934, vol. II 1939). The paper is in three sections. The first deals with Hilbert's introduction of a restricted ? -rule in his 1931 paper ?Die Grundlegung der elementaren Zahlenlehre?. The main question we discuss here is whether the finitist (meta-)mathematician would (...)
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  19.  62
    What Finitism Could Not Be.Matthias Schirn & Karl-Georg Niebergall - 2003 - Critica 35 (103):43-68.
    In his paper "Finitism", W.W. Tait maintains that the chief difficulty for everyone who wishes to understand Hilbert's conception of finitist mathematics is this: to specify the sense of the provability of general statements about the natural numbers without presupposing infinite totalities. Tait further argues that all finitist reasoning is essentially primitive recursive. In this paper, we attempt to show that his thesis "The finitist functions are precisely the primitive recursive functions" is disputable and that another, likewise defended by him, (...)
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  20.  88
    Frege’s Logicism and the Neo-Fregean Project.Matthias Schirn - 2014 - Axiomathes 24 (2):207-243.
    Neo-logicism is, not least in the light of Frege’s logicist programme, an important topic in the current philosophy of mathematics. In this essay, I critically discuss a number of issues that I consider to be relevant for both Frege’s logicism and neo-logicism. I begin with a brief introduction into Wright’s neo-Fregean project and mention the main objections that he faces. In Sect. 2, I discuss the Julius Caesar problem and its possible Fregean and neo-Fregean solution. In Sect. 3, I raise (...)
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  21.  15
    Gottlob Frege: Wissenschaftlicher Briefwechsel. [REVIEW]Matthias Schirn - 1978 - Philosophical Review 87 (3):490-493.
  22. Studien Zu Frege = Studies on Frege.Matthias Schirn - 1976
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  23.  34
    Axiom V and Hume's principle in Frege's foundational project.Matthias Schirn - 1995 - Diálogos. Revista de Filosofía de la Universidad de Puerto Rico 30 (66):7-20.
  24.  86
    Consistency, Models, and Soundness.Matthias Schirn - 2010 - Global Philosophy 20 (2-3):153-207.
    This essay consists of two parts. In the first part, I focus my attention on the remarks that Frege makes on consistency when he sets about criticizing the method of creating new numbers through definition or abstraction. This gives me the opportunity to comment also a little on H. Hankel, J. Thomae—Frege’s main targets when he comes to criticize “formal theories of arithmetic” in Die Grundlagen der Arithmetik (1884) and the second volume of Grundgesetze der Arithmetik (1903)—G. Cantor, L. E. (...)
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  25.  30
    Gottlob Frege. Die Grundlagen der Arithmetik. Eine logisch mathematische Untersuchung über den Begriff der Zahl. Centenary edition of 495. With supplementary text critically edited by Christian Thiel. Felix Meiner Verlag, Hamburg1986, LXIII + 187 pp. - Christian Thiel. Einleitung des Herausgebers. Therein, pp. XXI–LXIII. - Ernst Reinhold Eduard Hoppe. Review of Frege's Die Grundlagen der Arithmetik . Therein, pp. 109–117. , Litterarischer Bericht VII, pp. 28–35.) - Georg Cantor. Review of the same. A reprint of 651. Therein, pp. 117–119. - Ernst Zermelo. Anmerkung. A reprint of 1257. Therein, p. 119. - Gottlob Frege. Erwiderung. Therein, p. 120. , col. 1030.) - Anonymous. Review of the same. Therein, pp. 120–121. , cols. 1514–1515.) - Rudolf Eucken. Review of the same. Therein, pp. 122–123. , pp. 421–422.) - Kurd Laßwitz. Review of the same. Therein, pp. 123–128. , pp. 143–148.) - Ernst Schröder. Stellungnahme. A reprint of p. 704 of 427. Therein, pp. 128–129. - Edmund Husserl. Frege's. [REVIEW]Matthias Schirn - 1988 - Journal of Symbolic Logic 53 (3):993-999.
  26.  29
    Franz von Kutschera. Gottlob Frege. Eine Einführung in sein Werk. Walter de Gruyter, Berlin and New York1989, x + 207 pp. [REVIEW]Matthias Schirn - 1993 - Journal of Symbolic Logic 58 (1):366-368.
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  27.  60
    Frege Y Los nombres de cursos de valores.Matthias Schirn - 1994 - Theoria 9 (2):109-133.
    Frege’s method of introducing abstract singular terms by transforming an equivalence statement into an identity statement suffers from one major defect: it is haunted by a pervasive indeterminacy of putative reference. In this paper, I. discuss mainly Frege’s introduction of courses-of-values in his magnum opus Grundgesetze der Arithmetik (Volume I, 1893, Volume 11, 1903). More specifically, I want to assesscritically, with respect to course-of-values names, what I call Frege’s indeterminacy problem. In the first part, I sketch the nature of this (...)
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  28. Cdd: 149.9 4 sobre algumas ideias fundamentais da filosofia da linguagem de Gottlob frege1.Matthias Schirn - 1997 - Manuscrito 20.
     
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  29. Cdd: 149.94 cuestiones fundamentales de Una teoría Del significado.Matthias Schirn - 1992 - Manuscrito 15:37.
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  30. Frege: Importance and Legacy.Matthias Schirn (ed.) - 1996 - De Gruyter.
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  31. Hans Sluga: Gottlob Frege.Matthias Schirn - 1984 - Philosophische Rundschau 31:74.
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  32. On translating Frege's die Grundlagen der Arithmetik. History and Philosophy of Logic, vol. 31.Matthias Schirn - 2010 - Bulletin of Symbolic Logic 16 (3):428-429.
     
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  33.  2
    Philosophy Mathematics Today.Matthias Schirn (ed.) - 2003 - Oxford University Press UK.
    The Philosophy of Mathematics Today gives a panorama of the best current work in this lively field, through twenty essays specially written for this collection by leading figures. The topics include indeterminacy, logical consequence, mathematical methodology, abstraction, and both Hilbert's and Frege's foundational programmes. The collection will be an important source for research in the philosophy of mathematics for years to come.
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  34. Second-order abstraction, logicism and Julius Caesar.Matthias Schirn - 2002 - Diálogos. Revista de Filosofía de la Universidad de Puerto Rico 37 (79):319-372.
     
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  35. Sprachhandlung, Existenz, Wahrheit Hauptthemen der Sprachanalytischen Philosophie. Hrsg. Von Matthias Schirn.Matthias Schirn - 1974
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  36. Sprachhandlung -Existenz -Wahrheit -Hauptthemen der sprachanalytischen Philosophie.Matthias Schirn - 1975 - Tijdschrift Voor Filosofie 37 (1):150-150.
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  37. Sobre la semántica de los nombres propios.Matthias Schirn - 1990 - Diálogos. Revista de Filosofía de la Universidad de Puerto Rico 25 (56):7.
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  38. Studien zu Frege / Studies on Frege III.Matthias Schirn (ed.) - 1976 - frommann-holzboog.
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  39. Wahrheit und semantische Struktur.Matthias Schirn - 1991 - Allgemeine Zeitschrift für Philosophie 16 (2):27-38.
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  40.  33
    O principio do contexto nas Grundgesetze de Frege.Matthias Schirn - 1996 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 11 (3):177-201.
    Pretendo usar o exemplo dos nomes de percursos de valores como prova de que, contrariamente ao que Michael Resnik e Michael Dummett sustentam, Frege nunca abandonou o seu princípio do contexto: “Apenas no contexto de uma sentenya tem uma palavra significado”. Em particular, pretendo mostrar que a prova da completude com relação ao significado, que Frege tentou introduzir na linguagem formal das Grundgesetze der Arithmetik, baseia-se em uma aplicação do principio do contexto, e que, em consequencia, tambem nomes de percursos (...)
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  41.  20
    Christian Thiel. Einleitung. Frege und die moderne Grundlagenforschung, Symposium, gehalten in Bad Homburg im Dezember 1973, edited by Christian Thiel, Studien zur Wissenschaftstheorie, vol. 9, Verlag Anton Hain, Meisenheim am Glan1975, pp. 1–4. - Ignacio Angelelli. Freges Ort in der Begriffsgeschichte. Frege und die moderne Grundlagenforschung, Symposium, gehalten in Bad Homburg im Dezember 1973, edited by Christian Thiel, Studien zur Wissenschaftstheorie, vol. 9, Verlag Anton Hain, Meisenheim am Glan1975, pp. 9–22. - Egon Börger. Das Problem der Begründung der Mathematik bei Frege im Lichte des gegenwartigen Standes der mathematischen Grundlagenforschung. Frege und die moderne Grundlagenforschung, Symposium, gehalten in Bad Homburg im Dezember 1973, edited by Christian Thiel, Studien zur Wissenschaftstheorie, vol. 9, Verlag Anton Hain, Meisenheim am Glan1975, pp. 23–32. - Peter Hinst. Hätte Frege ohne Wertverlaufsfunktion auskommen können?Frege und die moderne Grundlagenforschung, Sy. [REVIEW]Matthias Schirn - 1979 - Journal of Symbolic Logic 44 (1):119-121.
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  42.  55
    O principio do contexto nas grundgesetze de Frege (the context principle in Frege's grundgesetze).Matthias Schirn - 1996 - Theoria 11 (3):177-201.
    Pretendo usar o exemplo dos nomes de percursos de valores como prova de que, contrariamente ao que Michael Resnik e Michael Dummett sustentam, Frege nunca abandonou o seu princípio do contexto: “Apenas no contexto de uma sentenya tem uma palavra significado”. Em particular, pretendo mostrar que a prova da completude com relação ao significado, que Frege tentou introduzir na linguagem formal das Grundgesetze der Arithmetik, baseia-se em uma aplicação do principio do contexto, e que, em consequencia, tambem nomes de percursos (...)
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  43.  25
    The semantics of value-range names and frege’s proof of referentiality.Matthias Schirn - 2018 - Review of Symbolic Logic 11 (2):224-278.
    In this article, I try to shed some new light onGrundgesetze§10, §29–§31 with special emphasis on Frege’s criteria and proof of referentiality and his treatment of the semantics of canonical value-range names. I begin by arguing against the claim, recently defended by several Frege scholars, that the first-order domain inGrundgesetzeis restricted to value-ranges, but conclude that there is an irresolvable tension in Frege’s view. The tension has a direct impact on the semantics of the concept-script, not least on the semantics (...)
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  44.  18
    Begriff und begriffsumfang. zu freges anzahldefinition in den grundlagen der arithmetik.Matthias Schirn - 1983 - History and Philosophy of Logic 4 (1-2):117-143.
    (1983). Begriff und begriffsumfang. zu freges anzahldefinition in den grundlagen der arithmetik. History and Philosophy of Logic: Vol. 4, No. 1-2, pp. 117-143.
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  45.  48
    Frege y los nombres de cursos de valores.Matthias Schirn - 1995 - Theoria 10 (1):109-133.
    Frege’s method of introducing abstract singular terms by transforming an equivalence statement into an identity statement suffers from one major defect: it is haunted by a pervasive indeterminacy of putative reference. In this paper, I. discuss mainly Frege’s introduction of courses-of-values in his magnum opus Grundgesetze der Arithmetik (Volume I, 1893, Volume 11, 1903). More specifically, I want to assesscritically, with respect to course-of-values names, what I call Frege’s indeterminacy problem. In the first part, I sketch the nature of this (...)
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  46.  8
    Sematische Vollständigkeit, Wertverlaufsnamen und Freges Kontextprinzip.Matthias Schirn - 1985 - Grazer Philosophische Studien 23 (1):79-104.
    Freges Kontextprinzip "Nur im Zusammenhange eines Satzes bedeuten die Wörter etwas" hat auch nach der von ihm vollzogenen Angleichung von Behauptungssätzen an Eigennamen Gültigkeit für die formale Sprache der "Grundgesetze". Der Bedeutungsvollständigkcitsbeweis, den er für sein Logiksystem anstrebt, schließt eine unmittelbare Anwendung dieses Prinzips nicht nur auf die unvollständigen Funktionsausdrücke, sondern auch auf die leerstellenfreien Wertverlaufsnamen ein. Wahrheitsnamen (Sätze) zeichnen sich vor anderen symbolsprachlichen Eigennamen in mehrfacher Hinsicht, insbesondere durch ihre semantische Selbständigkeit aus. Wertverlaufsnamen haben nur im Zusammenhang eines Wahrheitswertnamens (...)
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  47. Finitism = PRA? On a Thesis of W.W. Tait.Matthias Schirn & Karl-Georg Niebergall - 2005 - Reports on Mathematical Logic:3-24.
    In his paper `Finitism', W.W.~Tait maintained that the chief difficulty for everyone who wishes to understand Hilbert's conception of finitist mathematics is this: to specify the sense of the provability of general statements about the natural numbers without presupposing infinite totalities. Tait further argued that all finitist reasoning is essentially primitive recursive. In our paper, we attempt to show that his thesis ``The finitist functions are precisely the primitive recursive functions'' is disputable and that another, likewise defended by him, is (...)
     
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  48. Kant theory on geometrical knowledge and non-euclidean geometry.Matthias Schirn - 1991 - Kant Studien 82 (1):1-28.
     
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  49.  33
    Sobre la teoría Fregeana de las oraciones no extensionales (on Frege's theory of non-extensional sentences).Matthias Schirn - 1999 - Theoria 14 (1):131-156.
    En este articulo quiero discutir algunos temas centrales deI tratamiento fregeano de los contextos no extensionales. Limitaré mi discusión al análisis de oraciones de creencia y de la oratio obliqua. En la primera parte, voy a describir dos tipos de teoría dentro deI marco de la semántica de Frege. En particular, compararé y evaluaré los análisis de oraciones no extensionales de primer y segundo nivel que se pueden llevar a cabo en las teorías de ambos tipos. En la segunda parte, (...)
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  50.  22
    Gottlob Frege, Basic Laws of Arithmetic. Derived Using Concept-Script. [REVIEW]Matthias Schirn - forthcoming - Philosophical Quarterly:pqv096.
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