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  1. Matthias Schirn (2014). Erratum To: Frege's Logicism and the Neo-Fregean Project. 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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  2. Matthias Schirn (2014). Frege's Logicism and the Neo-Fregean Project. 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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  3. Matthias Schirn (2013). Frege's Approach to the Foundations of Analysis (1874–1903). 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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  4. Matthias Schirn (2011). On Translating Frege's Die Grundlagen der Arithmetik. 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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  5. Matthias Schirn (2010). Consistency, Models, and Soundness. 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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  6. Matthias Schirn (2010). Percursos de Valores e Indeterminação da Referência. Princípios 8 (9):36-48.
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  7. Matthias Schirn (2006). Concepts, Extensions, and Frege's Logicist Project. 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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  8. Matthias Schirn (2006). Hume's Principle and Axiom V Reconsidered: Critical Reflections on Frege and His Interpreters. 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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  9. Karl-Georg Niebergall & Matthias Schirn (2003). Hilbert's Finitism and the Notion of Infinity. In Matthias Schirn (ed.), The Philosophy of Mathematics Today. Clarendon Press.
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  10. Matthias Schirn (2003). Fregean Abstraction, Referential Indeterminacy and the Logical Foundations of Arithmetic. 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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  11. Matthias Schirn & Karl-Georg Niebergall (2003). What Finitism Could Not Be (Lo Que El Finitismo No Podría Ser). Crítica 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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  12. Karl-Georg Niebergall & Matthias Schirn (2002). Hilbert's Programme and Gödel's Theorems. Dialectica 56 (4):347–370.
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  13. Matthias Schirn & Karl-Georg Niebergall (2001). Extensions of the Finitist Point of View. 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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  14. Matthias Schirn (1999). Sobre la Teoría Fregeana de Las Oraciones No Extensionales (on Frege's Theory of Non-Extensional Sentences). 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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  15. Matthias Schirn (ed.) (1998). The Philosophy of Mathematics Today. 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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  16. Matthias Schirn (1997). Cdd: 149.9 4 Sobre Algumas Ideias Fundamentais da Filosofia da Linguagem de Gottlob Frege1. Manuscrito 20.
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  17. Matthias Schirn (ed.) (1996). Frege: Importance and Legacy. Walter De Gruyter.
  18. Matthias Schirn (1996). O Principio Do Contexto Nas Grundgesetze de Frege (the Context Principle in Frege's Grundgesetze). 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. Matthias Schirn (1995). Axiom V and Hume¿ s Principle in Frege¿ s Foundational Project. Dialogos 30 (66):7-20.
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  20. Matthias Schirn (1995). Book Review. [REVIEW] Erkenntnis 42 (1):113-118.
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  21. Matthias Schirn (1995). Frege y los nombres de cursos de valores. 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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  22. Matthias Schirn (1994). Frege Y Los Nombres de Cursos de Valores. 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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  23. Matthias Schirn (1993). Review: Franz von Kutschera, Gottlob Frege. Eine Einfuhrung in Sein Werk. [REVIEW] Journal of Symbolic Logic 58 (1):366-368.
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  24. Matthias Schirn (1992). Cdd: 149.94 cuestiones fundamentales de Una teoría Del significado. Manuscrito 15:37.
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  25. Matthias Schirn (1991). Kants Theorie der geometrischen Erkenntnis und die nichteuklidische Geometrie. Kant-Studien 82 (1):1-28.
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  26. Matthias Schirn (1990). Frege's Objects of a Quite Special Kind. Erkenntnis 32 (1):27 - 60.
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  27. Matthias Schirn (1988). Review: Gottlob Frege, Christian Thiel, Die Grundlagen der Arithmetik. Eine Logisch Mathematische Untersuchung uber den Begriff der Zahl. [REVIEW] Journal of Symbolic Logic 53 (3):993-999.
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  28. Matthias Schirn (1985). Sematische Vollständigkeit, Wertverlaufsnamen und Freges Kontextprinzip. 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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  29. Matthias Schirn (1984). Sluga über Freges These der Priorität von Urteilen gegenüber Begriffen. Archiv für Geschichte der Philosophie 66 (2):194-215.
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  30. B. Peppinghaus & Matthias Schirn (1983). Review. [REVIEW] Erkenntnis 20 (2):233-251.
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  31. Matthias Schirn (1983). Begriff Und Begriffsumfang. Zu Freges Anzahldefinition in Dengrundlagen der Arithmetik. 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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  32. Matthias Schirn (1982). Wahrheitsbedingungen und Verifikation. Zeitschrift für Philosophische Forschung 36 (3):378 - 391.
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  33. Matthias Schirn (1981). Reviews. [REVIEW] British Journal for the Philosophy of Science 32 (4):419-425.
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  34. Matthias Schirn (1979). Review: Christian Thiel, Frege und die moclerne. [REVIEW] Journal of Symbolic Logic 44 (1):119-121.
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