63 found
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  1.  19
    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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  2.  51
    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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  3.  5
    Frege: Importance and Legacy.Matthias Schirn (ed.) - 1996 - De Gruyter.
  4.  14
    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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  5.  51
    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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  6.  34
    What Finitism Could Not Be (Lo Que El Finitismo No Podría Ser).Matthias Schirn & Karl-Georg Niebergall - 2003 - Critica 35 (103):43 - 68.
    In his paper "Finitism" (1981), 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 (...)
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  7.  36
    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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  8.  40
    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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  9.  12
    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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  10.  88
    Hilbert's Programme and Gödel's Theorems.Karl-Georg Niebergall & Matthias Schirn - 2002 - Dialectica 56 (4):347–370.
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  11.  77
    The Philosophy of Mathematics Today.Matthias Schirn (ed.) - 1998 - 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.
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  12.  27
    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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  13.  52
    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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  14.  11
    Axiom V and Hume¿ s Principle in Frege¿ s Foundational Project.Matthias Schirn - 1995 - Dialogos 30 (66):7-20.
  15.  44
    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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  16.  27
    Consistency, Models, and Soundness.Matthias Schirn - 2010 - Axiomathes 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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  17.  37
    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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  18.  40
    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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  19. Hilbert's Finitism and the Notion of Infinity.Karl-Georg Niebergall & Matthias Schirn - 2003 - In Matthias Schirn (ed.), The Philosophy of Mathematics Today. Clarendon Press.
  20.  7
    Gottlob Frege, Basic Laws of Arithmetic. Derived Using Concept-Script.Matthias Schirn - forthcoming - Philosophical Quarterly:pqv096.
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  21.  15
    Frege's Objects of a Quite Special Kind.Matthias Schirn - 1990 - Erkenntnis 32 (1):27 - 60.
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  22.  24
    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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  23.  6
    Sematische Vollständigkeit, Wertverlaufsnamen und Freges Kontextprinzip.Matthias Schirn - 1985 - Grazer Philosophische Studien 23:79-104.
    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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  24.  15
    Review. [REVIEW]B. Peppinghaus & Matthias Schirn - 1983 - Erkenntnis 20 (2):233-251.
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  25.  14
    Erratum To: Frege's Logicism and the Neo-Fregean Project.Matthias Schirn - 2014 - Axiomathes 24 (2):245-245.
    Erratum to: Axiomathes DOI 10.1007/s10516-013-9222-7In the online publication, page 13, line 27, after the sentence “Hence, neo-logicism is doomed to failure.”, the following two sentences were missing:This argument was developed by Robert Trueman in a draft of his paper ‘Sham Names andion’. A revised version of this paper is forthcoming in Philosophia Mathematica under the tile ‘A Dilemma for Neo-Fregeanism’.
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  26. Studien Zu Frege = Studies on Frege.Matthias Schirn - 1976
     
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  27.  10
    Wahrheitsbedingungen und Verifikation.Matthias Schirn - 1982 - Zeitschrift für Philosophische Forschung 36 (3):378 - 391.
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  28.  10
    Kants Theorie der geometrischen Erkenntnis und die nichteuklidische Geometrie.Matthias Schirn - 1991 - Kant-Studien 82 (1):1-28.
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  29.  6
    Sluga über Freges These der Priorität von Urteilen gegenüber Begriffen.Matthias Schirn - 1984 - Archiv für Geschichte der Philosophie 66 (2):194-215.
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  30. Percursos de Valores e Indeterminação da Referência.Matthias Schirn - 2010 - Princípios 8 (9):36-48.
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  31.  1
    Frege: Importance and Legacy.Peter M. Sullivan & Matthias Schirn - 2000 - Philosophical Review 109 (4):648.
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  32.  8
    Begriff Und Begriffsumfang. Zu Freges Anzahldefinition in Dengrundlagen 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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  33.  4
    Review: Franz von Kutschera, Gottlob Frege. Eine Einfuhrung in Sein Werk. [REVIEW]Matthias Schirn - 1993 - Journal of Symbolic Logic 58 (1):366-368.
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  34.  8
    Book Review. [REVIEW]Matthias Schirn - 1995 - Erkenntnis 42 (1):113-118.
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  35.  3
    Review: Gottlob Frege, Christian Thiel, Die Grundlagen der Arithmetik. Eine Logisch Mathematische Untersuchung uber den Begriff der Zahl. [REVIEW]Matthias Schirn - 1988 - Journal of Symbolic Logic 53 (3):993-999.
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  36.  1
    Frege Gottlob. 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, Hamburg 1986, LXIII + 187 Pp.Thiel Christian. Einleitung des Herausgebers. Therein, Pp. XXI–LXIII.Hoppe Ernst Reinhold Eduard. Review of Frege's Die Grundlagen der Arithmetik . Therein, Pp. 109–117. , Litterarischer Bericht VII, Pp. 28–35.)Cantor Georg. Review of the Same. A Reprint of 651. Therein, Pp. 117–119.Zermelo Ernst. Anmerkung. A Reprint of 1257. Therein, P. 119.Frege Gottlob. Erwiderung. Therein, P. 120. , Col. 1030.)Anonymous. Review of the Same. Therein, Pp. 120–121. , Cols. 1514–1515.)Eucken Rudolf. Review of the Same. Therein, Pp. 122–123. , Pp. 421–422.)Laßwitz Kurd. Review of the Same. Therein, Pp. 123–128. , Pp. 143–148.)Schröder Ernst. Stellungnahme. A Reprint of P. 704 of 427. Therein, Pp. 128–129.Husserl Edmund. Frege's Versuch. A Reprint of VIII 5. [REVIEW]Matthias Schirn - 1988 - Journal of Symbolic Logic 53 (3):993-999.
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  37.  1
    Logica and Philosophy of Mathematics.Matthias Schirn - 1982 - Journal of Symbolic Logic 47 (1):226-229.
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  38.  2
    Reviews. [REVIEW]Matthias Schirn - 1981 - British Journal for the Philosophy of Science 32 (4):419-425.
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  39. Cdd: 149.9 4 Sobre Algumas Ideias Fundamentais da Filosofia da Linguagem de Gottlob Frege1.Matthias Schirn - 1997 - Manuscrito 20.
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  40. Cdd: 149.94 cuestiones fundamentales de Una teoría Del significado.Matthias Schirn - 1992 - Manuscrito 15:37.
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  41. DUMMETT, M.: "Truth and Other Enigmas". [REVIEW]Matthias Schirn - 1981 - British Journal for the Philosophy of Science 32:419.
  42. El método de descomposición de pensamientos en Frege.Matthias Schirn - 1992 - Análisis Filosófico 12 (1):31.
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  43. 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. 25-96.
  44. 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, (...)
     
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  45. Frege y los nombres de cursos de valores.Matthias Schirn - 1995 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 10 (1):211-211.
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  46. Hans Sluga: Gottlob Frege.Matthias Schirn - 1984 - Philosophische Rundschau 31:74.
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  47. Juicio, concepto y curso de valores.Matthias Schirn - 1983 - Dialogos 18 (42):187.
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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. Los números como objetos y el análisis de los enunciados numéricos.Matthias Schirn - 1994 - Análisis Filosófico 14 (1):21.
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  50. 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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