Prof. Dr. Karl-Georg Niebergall
Profil
Forschungsthemen3
Cluster Topoi II: Formale Theorien zu Körper und Raum D-3-4
Quelle ↗Förderer: DFG Exzellenzinitiative Cluster Zeitraum: 11/2012 - 10/2017 Projektleitung: Prof. Dr. Karl-Georg Niebergall
GRK 1939/2: Philosophie, Wissenschaft und die Wissenschaften: Der Dialog zwischen Formen und Modellen des Wissens im antiken griechischen, römischen und arabischen Denken
Quelle ↗Förderer: DFG Graduiertenkolleg Zeitraum: 04/2019 - 06/2024 Projektleitung: Prof. Dr. Jonathan Beere
GRK 1939: Philosophie, Wissenschaft und die Wissenschaften: Der Dialog zwischen Formen und Modellen des Wissens im antiken griechischen, römischen und arabischen Denken
Quelle ↗Förderer: DFG Graduiertenkolleg Zeitraum: 10/2014 - 06/2024 Projektleitung: Prof. Dr. Jonathan Beere
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Publikationen18
Top 25 nach Zitationen — Quelle: OpenAlex (BAAI/bge-m3 embedded für Matching).
Erkenntnis · 36 Zitationen · DOI
Synthese · 19 Zitationen · DOI
6 Zitationen · DOI
Abstract When Hilbert set about developing his foundational programme in the l 920s, proof theory was still enjoying a state of pre-Gödelian innocence. The principal objective of the programme was to establish once and for all the entire heritage of classical mathematics by means of a finitist metamathematical consistency proof.
dialectica · 5 Zitationen · DOI
In this paper, we attempt to show that a weak version of Hilbert's metamathematics is compatible with Gödel's Incompleteness Theorems by employing only what are clearly natural prov- ability predicates. Defining first “T proves the consistency of a theory S indirectly in one step”, we subsequently prove (i) “PA proves its own consistency indirectly in one step” and sketch the proof for (ii) “If S is a recursively enumerable extension of (QF-IA), S proves its own consistency indirectly in one step”. The formalizations of the metatheoretical consistency assertions that occur in these theorems are clearly the natural ones. We conclude the paper with reflections on indirect consistency proofs and soundness proofs.
4 Zitationen · DOI
THEORIA An International Journal for Theory History and Foundations of Science · 4 Zitationen · DOI
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 definitions and distinctions and some metatheorems, to the development of a general metatheory of such theories.
4 Zitationen · DOI
History and Philosophy of Logic · 4 Zitationen · DOI
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 ω -rule in his 1931 paper ‘Die Grundlegung der elementaren Zahlenlehre’. The main question we discuss here is whether the finitist (meta-)mathematician would be entitled to accept this rule as a finitary rule of inference. In the second section, we assess the strength of finitist metamathematics in Hilbert and Bernays 1934. The third and final section is devoted to the second volume of Grundlagen der Mathematik. For preparatory reasons, we first discuss Gentzen's proposal of expanding the range of what can be admitted as finitary in his esssay ‘Die Widerspruchsfreiheit der reinen Zahlentheorie’ (1936). As to Hilbert and Bernays 1939, we end on a ‘critical’ note: however considerable the impact of this work may have been on subsequent developments in metamathematics, there can be no doubt that in it the ideals of Hilbert's original finitism have fallen victim to sheer proof-theoretic pragmatism.
Cambridge University Press eBooks · 2 Zitationen · DOI
. The relation between intensionality as understood in philosophy and in metamathematics (in particular in early writings of S. Feferman) is explored in this paper. It investigates whether the latter can be interpreted as an instance of the former and presents metamathematical examples of "serious intensionality".
Cambridge University Press eBooks · 2 Zitationen · DOI
2 Zitationen · DOI
and Hannes Leitgeb, and the sterreichische Ludwig Wittgenstein Gesellschaft for the invitation, and the participants of the talk for comments. 1 For Goodman (1951), the calculus of individuals was a specific theory in L 1 [o]; it is called "CI + FUS 1 " below. In the meantime, "calculus of individuals" has become a predicate which is now ascribed to many theories.
2 Zitationen
... that the chief difficulty for everyone who wishes to un-derstand 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 re-cursive. 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 unten-able. The second thesis is that the finitist theorems are precisely those Π0 1-sentences that can be proved in (QF-IA).
Crítica (México D F En línea) · 2 Zitationen · DOI
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 him, is untenable. The second thesis is that the finitist theorems are precisely the universal closures of the equations that can be proved in PRA.
1 Zitationen · DOI
This paper contains: (i) a list of adequacy conditions for the use of the phrase " is about a"; (ii) arguments that Goodman's definition of " is absolutely about a" is unacceptable both from his viewpoint and from the perspective of that list; (iii) general reflections on related topics: on principles vs. definitions, on semantic vocabulary and on free logic. 1 1. Intuitive basis and simple definitions
Logic and Logical Philosophy · DOI
This paper deals with the treatment of infinity and finiteness in mereology. After an overview of some first-order mereological theories, finiteness axioms are introduced along with a mereological definition of “x is finite” in terms of which the axioms themselves are derivable in each of those theories. The finiteness axioms also provide the background for definitions of “(mereological theory) T makes an assumption of infinity”. In addition, extensions of mereological theories by the axioms are investigated for their own sake. In the final part, a definition of “x is finite” stated in a second-order language is also presented, followed by some concluding remarks on the motivation for the study of the (first-order) extensions of mereological theories dealt with in the paper.
Deutsches Jahrbuch Philosophie · DOI
Erkenntnis · DOI
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GRK 1939/2: Philosophie, Wissenschaft und die Wissenschaften: Der Dialog zwischen Formen und Modellen des Wissens im antiken griechischen, römischen und arabischen Denken
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GRK 1939/2: Philosophie, Wissenschaft und die Wissenschaften: Der Dialog zwischen Formen und Modellen des Wissens im antiken griechischen, römischen und arabischen Denken
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Identität, Organisation und Kontakt aus HU-FIS.
- Name
- Prof. Dr. Karl-Georg Niebergall
- Titel
- Prof. Dr.
- Fakultät
- Philosophische Fakultät
- Institut
- Institut für Philosophie
- Arbeitsgruppe
- Logik / Sprachphilosophie
- Telefon
- +49 30 2093-70476
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- 26.4.2026, 01:09:52