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  1. Structuralism, Model Theory and Reduction.Karl-Georg Niebergall - 2002 - Synthese 130 (1):135 - 162.
    In this paper, the (possible) role of model theory forstructuralism and structuralist definitions of ``reduction'' arediscussed. Whereas it is somewhat undecisive with respect tothe first point – discussing some pro's and con's ofthe model theoretic approach when compared with a syntacticand a structuralist one – it emphasizes that severalstructuralist definitions of ``reducibility'' do not providegenerally acceptable explications of ``reducibility''. This claimrests on some mathematical results proved in this paper.
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  2.  73
    On 2nd Order Calculi of Individuals.Karl-Georg Niebergall - 2009 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 24 (2):169-202.
    From early work of N. Goodman to recent approaches by H. Field and D. Lewis, there have been attempts to combine 2nd order languages with calculi of individuals. This paper is a contribution, containing basic denitions and distinctions and some metatheorems, to the development of a general metatheory of such theories.
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  3.  35
    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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  4.  13
    On 2nd Order Calculi of Individuals.Karl-Georg Niebergall - 2009 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 24 (2):169-202.
    From early work of N. Goodman to recent approaches by H. Field and D. Lewis, there have been attempts to combine 2nd order languages with calculi of individuals. This paper is a contribution, containing basic denitions and distinctions and some metatheorems, to the development of a general metatheory of such theories.
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  5.  90
    Hilbert's Programme and Gödel's Theorems.Karl-Georg Niebergall & Matthias Schirn - 2002 - Dialectica 56 (4):347–370.
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  6.  29
    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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  7.  62
    On the Logic of Reducibility: Axioms and Examples. [REVIEW]Karl-Georg Niebergall - 2000 - Erkenntnis 53 (1-2):27-61.
    This paper is an investigation into what could be a goodexplication of ``theory S is reducible to theory T''''. Ipresent an axiomatic approach to reducibility, which is developedmetamathematically and used to evaluate most of the definitionsof ``reducible'''' found in the relevant literature. Among these,relative interpretability turns out to be most convincing as ageneral reducibility concept, proof-theoreticalreducibility being its only serious competitor left. Thisrelation is analyzed in some detail, both from the point of viewof the reducibility axioms and of modal logic.
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  8. On “About”: Definitions and Principles.Karl-Georg Niebergall - 2009 - In G. Ernst, J. Steinbrenner & O. Scholz (eds.), From Logic to Art: Themes From Nelson Goodman. Ontos. pp. 7--137.
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  9. 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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  10.  5
    Assumptions of Infinity.Karl-Georg Niebergall - 2014 - In Godehard Link (ed.), Formalism and Beyond: On the Nature of Mathematical Discourse. De Gruyter. pp. 229-274.
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  11. 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.
  12.  26
    Nonmonotonicity in (the Metamathematics of) Arithmetic.Karl-Georg Niebergall - 1999 - Erkenntnis 50 (2-3):309-332.
    This paper is an attempt to bring together two separated areas of research: classical mathematics and metamathematics on the one side, non-monotonic reasoning on the other. This is done by simulating nonmonotonic logic through antitonic theory extensions. In the first half, the specific extension procedure proposed here is motivated informally, partly in comparison with some well-known non-monotonic formalisms. Operators V and, more generally, U are obtained which have some plausibility when viewed as giving nonmonotonic theory extensions. In the second half, (...)
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  13.  5
    Calculi of Individuals and Some Extensions: An Overview'.Karl-Georg Niebergall - 2009 - In Hieke Alexander & Leitgeb Hannes (eds.), Reduction, Abstraction, Analysis. Ontos Verlag. pp. 11--335.
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  14. Philosophie der Wissenschaft – Wissenschaft der Philosophie. Festschrift Für C.Ulises Moulines Zum 60. Geburstag.Gerhard Ernst & Karl-Georg Niebergall (eds.) - 2006 - Mentis.
     
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  15. Zur nominalistischen Behandlung der Mathematik.Karl-Georg Niebergall - 2005 - In Nelson Goodman, Jakob Steinbrenner, Oliver R. Scholz & Gerhard Ernst (eds.), Symbole, Systeme, Welten: Studien Zur Philosophie Nelson Goodmans. Synchron. pp. 235--260.
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  16. What Finitism Could Not Be.Matthias Schirn & Karl-Georg Niebergall - 2003 - Crítica: Revista Hispanoamericana de Filosofía 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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