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  1. Karl-Georg Niebergall (2009). Calculi of Individuals and Some Extensions: An Overview'. In. In Hieke Alexander & Leitgeb Hannes (eds.), Reduction, Abstraction, Analysis. Ontos Verlag. 11--335.
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  2. Karl-Georg Niebergall (2009). On “About”: Definitions and Principles. In G. Ernst, J. Steinbrenner & O. Scholz (eds.), From Logic to Art: Themes From Nelson Goodman. Ontos. 7--137.
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  3. Karl-Georg Niebergall (2009). On 2nd Order Calculi of Individuals. Theoria 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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  4. Karl-Georg Niebergall (2005). Zur nominalistischen Behandlung der Mathematik. In Nelson Goodman, Jakob Steinbrenner, Oliver R. Scholz & Gerhard Ernst (eds.), Symbole, Systeme, Welten: Studien Zur Philosophie Nelson Goodmans. Synchron. 235--260.
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  5. 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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  6. 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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  7. Karl-Georg Niebergall (2002). Structuralism, Model Theory and Reduction. 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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  8. Karl-Georg Niebergall & Matthias Schirn (2002). Hilbert's Programme and Gödel's Theorems. Dialectica 56 (4):347–370.
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  9. 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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  10. Karl-Georg Niebergall (2000). On the Logic of Reducibility: Axioms and Examples. [REVIEW] 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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  11. Karl-Georg Niebergall (1999). Nonmonotonicity in (the Metamathematics of) Arithmetic. 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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