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)

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

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)

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.

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.

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.

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.

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.

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)

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)

The emerging consensus in the philosophy of cognition is that cognition is situated, i.e., dependent upon or co-constituted by the body, the environment, and/or the embodied interaction with it. But what about emotions? If the brain alone cannot do much thinking, can the brain alone do some emoting? If not, what else is needed? Do (some) emotions (sometimes) cross an individual's boundary? If so, what kinds of supra-individual systems can be bearers of affective states, and why? And does that make (...) emotions ?embedded? or ?extended? in the sense cognition is said to be embedded and extended? Section 2 shows why it is important to understand in which sense body, environment, and our embodied interaction with the world contribute to our affective life. Section 3 introduces some key concepts of the debate about situated cognition. Section 4 draws attention to an important disanalogy between cognition and emotion with regard to the role of the body. Section 5 shows under which conditions a contribution by the environment results in non-trivial cases of ?embedded? emotions. Section 6 is concerned with affective phenomena that seem to cross the organismic boundaries of an individual, in particular with the idea that emotions are ?extended? or ?distributed.? (shrink)

Artificial intelligence (AI) and robotics are digital technologies that will have significant impact on the development of humanity in the near future. They have raised fundamental questions about what we should do with these systems, what the systems themselves should do, what risks they involve, and how we can control these. - After the Introduction to the field (§1), the main themes (§2) of this article are: Ethical issues that arise with AI systems as objects, i.e., tools made and used (...) by humans. This includes issues of privacy (§2.1) and manipulation (§2.2), opacity (§2.3) and bias (§2.4), human-robot interaction (§2.5), employment (§2.6), and the effects of autonomy (§2.7). Then AI systems as subjects, i.e., ethics for the AI systems themselves in machine ethics (§2.8) and artificial moral agency (§2.9). Finally, the problem of a possible future AI superintelligence leading to a “singularity” (§2.10). We close with a remark on the vision of AI (§3). - For each section within these themes, we provide a general explanation of the ethical issues, outline existing positions and arguments, then analyse how these play out with current technologies and finally, what policy consequences may be drawn. (shrink)

We maximally extend the quantum‐mechanical results of Muller and Saunders ( 2008 ) establishing the ‘weak discernibility’ of an arbitrary number of similar fermions in finite‐dimensional Hilbert spaces. This confutes the currently dominant view that ( A ) the quantum‐mechanical description of similar particles conflicts with Leibniz’s Principle of the Identity of Indiscernibles (PII); and that ( B ) the only way to save PII is by adopting some heavy metaphysical notion such as Scotusian haecceitas or Adamsian primitive thisness. We (...) take sides with Muller and Saunders ( 2008 ) against this currently dominant view, which has been expounded and defended by many. *Received July 2008; revised May 2009. †To contact the authors, please write to: F. A. Muller, Faculty of Philosophy, Erasmus University Rotterdam, Burg. Oudlaan 50, H5–16, 3062 PA Rotterdam, The Netherlands; e‐mail: [email protected] , and Institute for the History and Foundations of Science, Utrecht University, Budapestlaan 6, IGG–3.08, 3584 CD Utrecht, The Netherlands; e‐mail: [email protected] . M. P. Seevinck, Institute for the History and Foundations of Science, Utrecht University, Budapestlaan 6, IGG–3.08, 3584 CD Utrecht, The Netherlands; e‐mail: [email protected]. (shrink)

Discussions about a replicability crisis in science have been driven by the normative claim that all of science should be replicable and the empirical claim that most of it isn’t. Recently, such crisis talk has been challenged by a new localism, which argues a) that serious problems with replicability are not a general occurrence in science and b) that replicability itself should not be treated as a universal standard. The goal of this article is to introduce this emerging strand of (...) the debate and to discuss some of its implications and limitations. I will in particular highlight the issue of demarcation that localist accounts have to address, i.e. the question of how we can distinguish replicable science from disciplines where replicability does not apply. (shrink)

Causal queries about singular cases, which inquire whether specific events were causally connected, are prevalent in daily life and important in professional disciplines such as the law, medicine, or engineering. Because causal links cannot be directly observed, singular causation judgments require an assessment of whether a co‐occurrence of two events c and e was causal or simply coincidental. How can this decision be made? Building on previous work by Cheng and Novick (2005) and Stephan and Waldmann (2018), we propose (...) a computational model that combines information about the causal strengths of the potential causes with information about their temporal relations to derive answers to singular causation queries. The relative causal strengths of the potential cause factors are relevant because weak causes are more likely to fail to generate effects than strong causes. But even a strong cause factor does not necessarily need to be causal in a singular case because it could have been preempted by an alternative cause. We here show how information about causal strength and about two different temporal parameters, the potential causes' onset times and their causal latencies, can be formalized and integrated into a computational account of singular causation. Four experiments are presented in which we tested the validity of the model. The results showed that people integrate the different types of information as predicted by the new model. (shrink)

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)

Seven unknown letters from 1823 to 1831 are published. The famous discoverer of the mammal's egg and founder of the modern embryology Karl Ernst von Baer (1792–1876), born as a German in Estonia and then anatomist and zoologist at Königsberg University, wrote them to his publisher Ludwig F. Froriep in Weimar and his son and successor. Robert F. Baer offered his co-work with a dictionary of natural history (which he criticized), he proposed a map of all research voyages everywhere in (...) the world, and he sent a few small papers about local birds. To Robert F. Baer gave some recommendations concerning his career; he asked for details of a death elephant, and he told that they were awaiting the cholera. (shrink)