Game theory is usually considered applied mathematics, but a few game‐theoretic results, such as Borel determinacy, were developed by mathematicians for mathematics in a broad sense. These results usually state determinacy, i.e., the existence of a winning strategy in games that involve two players and two outcomes saying who wins. In a multi‐outcome setting, the notion of winning strategy is irrelevant yet usually replaced faithfully with the notion of (pure) Nash equilibrium. This article shows that every determinacy result over an (...) arbitrary game structure, e.g., a tree, is transferable into existence of multi‐outcome (pure) Nash equilibrium over the same game structure. The equilibrium‐transfer theorem requires cardinal or order‐theoretic conditions on the strategy sets and the preferences, respectively, whereas counter‐examples show that every requirement is relevant, albeit possibly improvable. When the outcomes are finitely many, the proof provides an algorithm computing a Nash equilibrium without significant complexity loss compared to the two‐outcome case. As examples of application, this article generalises Borel determinacy, positional determinacy of parity games, and finite‐memory determinacy of Muller games. (shrink)

Previously conducted structural magnetic resonance imaging (MRI) studies on the neuroanatomical correlates of mathematical abilities and competencies have a number of methodological limitations. Besides small sample sizes, the majority of these studies have employed voxel-based morphometry (VBM) – a method that, although it is easily to implement, has some major drawbacks. Taking this into account, the current study is the first to investigate in a large sample of typically developed adults the associations between mathematical abilities and variations in brain surface (...) structure by using surface-based morphometry (SBM). SBM is a method that also allows the investigation of brain morphometry by avoiding the pitfalls of VBM. Eighty-nine young adults were tested with a large battery of psychometric tests to measure mathematical competencies in four different areas: (1) simple arithmetic, (2) complex arithmetic, (3) higher-order mathematics and (4) numerical intelligence. In addition, we asked participants for their mathematics grade of their final school exam. Inside the MRI scanner, we collected high-resolution T1-weighted anatomical images from each subject. SBM analyses were performed with the computational anatomy toolbox (CAT12) and indices for cortical thickness, for cortical surface complexity, for gyrification and for sulcal depth were calculated. Further analyses revealed associations between (1) the cortical surface complexity of the right superior temporal gyrus and numerical intelligence, (2) the depth of the right central sulcus and adults’ ability to solve complex arithmetic problems and (3) the depth of the left parieto-occipital sulcus and adults’ higher-order mathematics competence. Interestingly, no relationships with previously reported brain regions were observed, thus, suggesting the importance of similar research to confirm the role of the brain regions found in this study. (shrink)

Originally presented as the author's thesis (doctoral--Technische Universit'at Berlin, 1988).

Using Sneed's metatheory an attempt is made to reconstruct Hodgkin and Huxley's theory of excitation of cell membranes. The structure of this theory is uncovered by defining set-theoretical predicates for the partial potential models, potential models, and models of the theory. The function of permeability is said to be the only theoretical function with respect to this theory. The main underlying assumptions of the theory are briefly outlined.

The Repugnant Conclusion served an important purpose in catalyzing and inspiring the pioneering stage of population ethics research. We believe, however, that the Repugnant Conclusion now receives too much focus. Avoiding the Repugnant Conclusion should no longer be the central goal driving population ethics research, despite its importance to the fundamental accomplishments of the existing literature.

Am 14. Juli 1995 berichteten die angesehene Wissenschaftszeitschrift Science sowie die berühmte amerikanische Tageszeitung New York Times – auf dem Titelblatt – gleichzeitig über die erstmalige experimentelle Erzeugung eines Bose-Einstein-Kondensates aus einem Gas schwach wechselwirkender Alkaliatome am Joint Institute for Laboratory Astrophy- sics (JILA) in Boulder/Colorado (USA). Was war an dieser Leistung so bedeutsam, dass man sich entschloss, sie auf jene Weise bekannt zu geben?

Der bedeutende amerikanische Logiker und Philosoph W.V.O. Quine hat die folgende Frage ins Zentrum seines Schaffens gestellt: "Wie kommen wir von unseren Sinnesdaten zu Theorien über die Welt?“ Bei der Beantwortung dieser Frage tritt ein grundlegendes Problem auf, das damit zusammenhängt, dass uns immer nur ein endlicher Satz an Informationen über die Welt zugänglich ist. Jedes Experiment liefert z. B. nur eine endliche Anzahl von Messpunkten.

Using Sneed''s metatheory an attempt is made to reconstruct Hodgkin and Huxley''s theory of excitation of cell membranes. The structure of this theory is uncovered by defining set-theoretical predicates for the partial potential models, potential models, and models of the theory. The function of permeability is said to be the only theoretical function with respect to this theory. The main underlying assumptions of the theory are briefly outlined.

There is a deeply entrenched view in philosophy and physics, the closed systems view, according to which isolated systems are conceived of as fundamental. On this view, when a system is under the influence of its environment this is described in terms of a coupling between it and a separate system which taken together are isolated. We argue against this view, and in favor of the alternative open systems view, for which systems interacting with their environment are conceived of as (...) fundamental, and the environment's influence is represented via the dynamical equations that govern the system's evolution. Taking quantum theories of closed and open systems as our case study, and considering three alternative notions of fundamentality: (i) ontic fundamentality, (ii) epistemic fundamentality, and (iii) explanatory fundamentality, we argue that the open systems view is fundamental, and that this has important implications for the philosophy of physics, the philosophy of science, and for metaphysics. (shrink)

We argue that the economic evaluation of health care (cost–benefit analysis) should respect individual preferences and should incorporate distributional considerations. Relying on individual preferences does not imply subjective welfarism. We propose a particular non-welfarist approach, based on the concept of equivalent income, and show how it helps to define distributional weights. We illustrate the feasibility of our approach with empirical results from a pilot survey.

We say that A≤LRB if every B-random set is A-random with respect to Martin–Löf randomness. We study this relation and its interactions with Turing reducibility, classes, hyperimmunity and other recursion theoretic notions.

Background Genuine uncertainty on superiority of one intervention over the other is called equipoise. Physician-investigators in randomized controlled trials need equipoise at least in studies with more than minimal risks. Ideally, this equipoise is also present in patient-participants. In pediatrics, data on equipoise are lacking. We hypothesize that 1) lack of equipoise at enrolment among parents may reduce recruitment; 2) lack of equipoise during participation may reduce retention in patients assigned to a less favoured treatment-strategy. Methods We compared preferences of (...) parents/patients at enrolment, documented by a questionnaire, with preferences developed during follow-up by an interview-study to investigate equipoise of child-participants and parents in the BeSt-for-Kids-study. This trial in new-onset Juvenile Idiopathic Arthritis-patients consists of three strategies. One strategy comprises initial treatment with a biological disease-modifying-antirheumatic-drug, currently not standard-of-care. Semi-structured interviews were conducted with 23 parents and 7 patients, median 11 months after enrolment. Results Initially most parents and children were not in equipoise. Parents/patients who refused participation, regularly declined due to specific preferences. Many participating families preferred the biological-first-strategy. They participated to have a chance for this initial treatment, and would even consider stopping trial-participation when not randomized for it. Their conviction of superiority of the biological-first strategy was based on knowledge from internet and close relations. According to four parents, the physician-investigator preferred the biological-first-strategy, but the majority stated that she had no preferred strategy. In phase 2, preferences tended to change to the treatment actually received. Conclusions Lack of equipoise during enrolment did not reduce study recruitment, mainly due to the fact that preferred treatment was only available within the study. Still, when developing a trial it is important to evaluate whether the physicians’ research question is in line with preferences of the patient-group. By exploring so-called ‘informed patient-group’-equipoise, successful recruitment may be enhanced and bias avoided. In our study, lack of equipoise during trial-participation did not reduce retention in those assigned to a less favoured option. We observed a change for preference towards treatment actually received, possibly explained by comparable outcomes in all three arms. (shrink)

It is argued that those who defend the Everett, or ‘many-worlds’, interpretation of quantum mechanics should embrace what we call the general quantum theory of open systems (GT) as the proper framework in which to conduct foundational and philosophical investigations in quantum physics. GT is a wider dynamical framework than its alternative, standard quantum theory (ST). This is true even though GT makes no modifications to the quantum formalism. GT rather takes a different view, what we call the open systems (...) view, of the formalism; i.e., in GT, the dynamics of systems whose physical states are fundamentally represented by density operators are represented as fundamentally open as specified by an in general non-unitary dynamical map. This includes, in principle, the dynamics of the universe as a whole. We argue that the more general dynamics describable in GT can be physically motivated, that there is as much prima facie empirical support for GT as there is for ST, and that GT could be fully in the spirit of the Everett interpretation—that there might, in short, be little reason for an Everettian not to embrace the more general theoretical landscape that GT allows one to explore. (shrink)

If one formulates Helmholtz's ideas about perception in terms of modern-day theories one arrives at a model of perceptual inference and learning that can explain a remarkable range of neurobiological facts. Using constructs from statistical physics it can be shown that the problems of inferring what cause our sensory inputs and learning causal regularities in the sensorium can be resolved using exactly the same principles. Furthermore, inference and learning can proceed in a biologically plausible fashion. The ensuing scheme rests on (...) Empirical Bayes and hierarchical models of how sensory information is generated. The use of hierarchical models enables the brain to construct prior expectations in a dynamic and context-sensitive fashion. This scheme provides a principled way to understand many aspects of the brain's organisation and responses. In this paper, we suggest that these perceptual processes are just one emergent property of systems that conform to a free-energy principle. The free-energy considered here represents a bound on the surprise inherent in any exchange with the environment, under expectations encoded by its state or configuration. A system can minimise free-energy by changing its configuration to change the way it samples the environment, or to change its expectations. These changes correspond to action and perception, respectively, and lead to an adaptive exchange with the environment that is characteristic of biological systems. This treatment implies that the system's state and structure encode an implicit and probabilistic model of the environment. We will look at models entailed by the brain and how minimisation of free-energy can explain its dynamics and structure. (shrink)

This thought-provoking book discusses the concept of progress in economics and investigates whether any advance has been made in its different spheres of research. The authors look back at the history, successes and failures of their respective fields and thoroughly examine the notion of progress from an epistemological and methodological perspective. The idea of progress is particularly significant as the authors regard it as an essentially contested concept which can be defined in many ways – theoretically or empirically; locally or (...) globally; or as encouraging or impeding the existence of other research traditions. The authors discuss the idea that for progress to make any sense there must be an accumulation of knowledge built up over time rather than the replacement of ideas by each successive generation. Accordingly, they are not concerned with estimating the price of progress, reminiscing in the past, or assessing what has been lost. Instead they apply the complex mechanisms and machinery of the discipline to sub-fields such as normative economics, monetary economics, trade and location theory, Austrian economics and classical economics to critically assess whether progress has been made in these areas of research. -/- Bringing together authoritative and wide-ranging contributions by leading scholars, this book will challenge and engage those interested in philosophy, economic methodology and the history of economic thought. It will also appeal to economists in general who are interested in the advancement of their profession. (shrink)

Dondeyne, A. Pluriformiteit en eenheid van de filosofie.--Peperzak, A. Wegwijzers naar een dialogiek?--Boer, T. de. De eindigheid van de mens en de oneindigheid van de waarheid.--Hollak, J. Wijsgerige reflecties over de scheppingsidee : St. Thomas, Hegel en de Grieken.--Plat, J. Kants kritiek op de rationele psychologie.--Melsen, A. van. Wijsgerige antropologie en de ontwikkeling van natuurwetenschap en techniek.--Buytendijk, F. Het pathisch aspect van de eindigheid.--Struyker Boudier, H. 's Bergbeklimmers einder.

A number of distinct definitions ofsustainable agriculture have been proposed. In this paper we criticize two such definitions, primarily for conflating sustainability with other objectives such as economic viability and ecological integrity. Finally, we propose and defend a definition which avoids our objections to the other definitions.