In 2000, Rüdiger Thiele [1] found in a notebook of David Hilbert, kept in Hilbert's Nachlass at the University of Göttingen, a small note concerning a 24th problem. As Hilbert wrote, he had considered including this problem in his famous problem list for the International Congress of Mathematicians in Paris in 1900.

Bd. 1. 1791-1794.--Bd. 2. 1793-1795.--Bd. 3.--1794-1796.--Bd. 4. 1797-1798.--Bd. 5. 1798-1799.--Bd. 6. 1799-1800.--Bd. 7. 1800-1801.--Bd. 8. 1801-1806.--Bd. 9. 1806-1807.--Bd. 10. 1808-1812.

Bd. 1. 1791-1794.--Bd. 2. 1793-1795.--Bd. 3.--1794-1796.--Bd. 4. 1797-1798.--Bd. 5. 1798-1799.--Bd. 6. 1799-1800.--Bd. 7. 1800-1801.--Bd. 8. 1801-1806.--Bd. 9. 1806-1807.--Bd. 10. 1808-1812.

In 2000, a draft note of David Hilbert was found in his Nachlass concerning a 24th problem he had consider to include in the his famous problem list of the talk at the International Congress of Mathematicians in 1900 in Paris. This problem concerns simplicity of proofs. In this paper we review the traces of this problem which one can find in the work of Hilbert and his school, as well as modern research started on it after its publication. We (...) stress, in particular, the mathematical nature of the problem.1. (shrink)

The market seems to have substituted politics as a coordination model in modern societies. While philosophy's complementarity to politics is well-acknowledged, its importance for economic markets can be questioned. Economics deals with optimization, but as markets are constituted by real persons with individual beliefs and normative values the economic tool box is not sufficient to describe market behavior. This is especially true whenever technologicalinnovations challenge established market rules. Philosophy supplies analytical instruments for a better, more complete description of markets including (...) theirnormative aspects. For this complementary function philosophy should be placed at the core of any theory of markets. (shrink)

ObjectiveDropout rates are a prominent problem in youth psychotherapy. An important determinant of dropouts is the quality of the therapeutic relationship. This study aimed to evaluate the association between the therapeutic relationship and dropouts in an intensive mentalization-based treatment for adolescents with personality disorders.MethodsPatients included were either dropouts or completers of an intensive MBT. The therapeutic relationship was measured with the child version of the Session Rating Scale, which was completed by the patient after each group therapy session. For each (...) patient, the treatment termination status was indicated by the treatment staff. The reliable change index was calculated for the C-SRS to determine significant changes in the therapeutic relationship.ResultsWhile both groups started with similar scores on the C-SRS, the scores between dropouts and completers differed significantly at the end of the treatment period. On average, during therapy, an increase was seen in the scores of completers, and a decrease was seen in the scores of dropouts. While dropouts could not be predicted based on the C-SRS scores, a significant decrease in C-SRS scores during the last two sessions occurred more often for dropouts than for completers.ConclusionOur findings show that to prevent dropouts, the patient’s judgment of the quality of the therapeutic relationship should be monitored continuously, and decreases discussed with the patient and the group. (shrink)

This paper shows how the dynamic interpretation of natural language introduced in work by Hans Kamp and Irene Heim can be modeled in classical type logic. This provides a synthesis between Richard Montague's theory of natural language semantics and the work by Kamp and Heim.

In this note, we review paradoxes like Russell’s, the Liar, and Curry’s in the context of intuitionistic logic. One may observe that one cannot blame the underlying logic for the paradoxes, but has to take into account the particular concept formations. For proof-theoretic semantics, however, this comes with the challenge to block some forms of direct axiomatizations of the Liar. A proper answer to this challenge might be given by Schroeder-Heister’s definitional freedom.

This paper embeds the core part of Discourse Representation Theory in the classical theory of types plus a few simple axioms that allow the theory to express key facts about variables and assignments on the object level of the logic. It is shown how the embedding can be used to combine core analyses of natural language phenomena in Discourse Representation Theory with analyses that can be obtained in Montague Semantics.

We explore the different meanings of “quantum uncertainty” contained in Heisenberg’s seminal paper from 1927, and also some of the precise definitions that were developed later. We recount the controversy about “Anschaulichkeit”, visualizability of the theory, which Heisenberg claims to resolve. Moreover, we consider Heisenberg’s programme of operational analysis of concepts, in which he sees himself as following Einstein. Heisenberg’s work is marked by the tensions between semiclassical arguments and the emerging modern quantum theory, between intuition and rigour, and between (...) shaky arguments and overarching claims. Nevertheless, the main message can be taken into the new quantum theory, and can be brought into the form of general theorems. They come in two kinds, not distinguished by Heisenberg. These are, on one hand, constraints on preparations, like the usual textbook uncertainty relation, and, on the other, constraints on joint measurability, including trade-offs between accuracy and disturbance. (shrink)

Name der Zeitschrift: Kant-Studien Jahrgang: 109 Heft: 3 Seiten: 447-472.

The idea of complementarity is one of the key concepts of quantum mechanics. Yet, the idea was originally developed in William James’ psychology of consciousness. Recently, it was re-applied to the humanities and forms one of the pillars of modern quantum cognition. I will explain two different concepts of complementarity: Niels Bohr’s ontic conception and Werner Heisenberg’s epistemic conception. Furthermore, I will give an independent motivation of the epistemic conception based on the so-called operational interpretation of quantum theory, which has (...) powerfully been applied in the domain of quantum cognition. Finally, I will give examples illustrating the potency of complementarity in the domains of bounded rationality and survey research. Concerning the broad topic of consciousness, I will focus on the psychological aspects of awareness. This closes the circle spanning complementarity, quantum cognition, the operational interpretation, and consciousness. (shrink)

Name der Zeitschrift: Kant-Studien Jahrgang: 109 Heft: 1 Seiten: 147-169.

In der Reihe werden herausragende monographische Interpretationen von Nietzsches Werk im Ganzen oder von spezifischen Themen und Aspekten aus unterschiedlichen wissenschaftlichen Perspektiven veröffentlicht, vor allem aus philosophischer, literatur- und kommunikationswissenschaftlicher, soziologischer und historischer Sicht. Die Publikationen repräsentieren den aktuellen Stand. Jeder Band ist peer-reviewed.