We analyze the cognitive strategies underlying performance in the Number task, a Math game that requires both arithmetic fluency and mathematical creativity. In this game all elements in a set of numbers have to be used precisely once to create a target number with basic arithmetic operations. We argue that some instances of this game are NP complete, by showing its relation to the well-known Partition problem. We propose heuristics based on the distinction in forward and backward reasoning. The Number (...) Game is part of Math Garden, a popular online educational platform for practicing and monitoring math skills using innovations in computerized adaptive testing. These educational games generate enormous amounts of rich data on children's cognitive development. We found converging evidence for the use of forward proximity heuristics in the data of Math Garden, consisting of more than 20 million answers to 1,700 items. Item difficulties and the structure of correct answers were analyzed. (shrink)

We analyze the cognitive strategies underlying performance in the Number task, a Math game that requires both arithmetic fluency and mathematical creativity. In this game all elements in a set of numbers have to be used precisely once to create a target number with basic arithmetic operations. We argue that some instances of this game are NP complete, by showing its relation to the well-known Partition problem. We propose heuristics based on the distinction in forward and backward reasoning. The Number (...) Game is part of Math Garden, a popular online educational platform for practicing and monitoring math skills using innovations in computerized adaptive testing. These educational games generate enormous amounts of rich data on children's cognitive development. We found converging evidence for the use of forward proximity heuristics in the data of Math Garden, consisting of more than 20 million answers to 1,700 items. Item difficulties and the structure of correct answers were analyzed. (shrink)

The paper is concerned with the psychological relevance of a logical model for deductive reasoning. We propose a new way to analyze logical reasoning in a deductive version of the Mastermind game implemented within a popular Dutch online educational learning system (Math Garden). Our main goal is to derive predictions about the difficulty of Deductive Mastermind tasks. By means of a logical analysis we derive the number of steps needed for solving these tasks (a proxy for working memory load). Our (...) model is based on the analytic tableaux method, known from proof theory. We associate the difficulty of Deductive Mastermind game-items with the size of the corresponding logical trees obtained by the tableaux method. We derive empirical hypotheses from this model. A large group of students (over 37 thousand children, 5–12 years of age) played the Deductive Mastermind game, which gave empirical difficulty ratings of all 321 game-items. The results show that our logical approach predicts these item ratings well, which supports the psychological relevance of our model. (shrink)

The pivotal problem of comorbidity research lies in the psychometric foundation it rests on, that is, latent variable theory, in which a mental disorder is viewed as a latent variable that causes a constellation of symptoms. From this perspective, comorbidity is a (bi)directional relationship between multiple latent variables. We argue that such a latent variable perspective encounters serious problems in the study of comorbidity, and offer a radically different conceptualization in terms of a network approach, where comorbidity is hypothesized to (...) arise from direct relations between symptoms of multiple disorders. We propose a method to visualize comorbidity networks and, based on an empirical network for major depression and generalized anxiety, we argue that this approach generates realistic hypotheses about pathways to comorbidity, overlapping symptoms, and diagnostic boundaries, that are not naturally accommodated by latent variable models: Some pathways to comorbidity through the symptom space are more likely than others; those pathways generally have the same direction (i.e., from symptoms of one disorder to symptoms of the other); overlapping symptoms play an important role in comorbidity; and boundaries between diagnostic categories are necessarily fuzzy. (shrink)

After more than 15 years of study, the 1/f noise or complex-systems approach to cognitive science has delivered promises of progress, colorful verbiage, and statistical analyses of phenomena whose relevance for cognition remains unclear. What the complex-systems approach has arguably failed to deliver are concrete insights about how people perceive, think, decide, and act. Without formal models that implement the proposed abstract concepts, the complex-systems approach to cognitive science runs the danger of becoming a philosophical exercise in futility. The complex-systems (...) approach can be informative and innovative, but only if it is implemented as a formal model that allows concrete prediction, falsification, and comparison against more traditional approaches. (shrink)

Most models of response time (RT) in elementary cognitive tasks implicitly assume that the speed-accuracy trade-off is continuous: When payoffs or instructions gradually increase the level of speed stress, people are assumed to gradually sacrifice response accuracy in exchange for gradual increases in response speed. This trade-off presumably operates over the entire range from accurate but slow responding to fast but chance-level responding (i.e., guessing). In this article, we challenge the assumption of continuity and propose a phase transition model for (...) RTs and accuracy. Analogous to the fast guess model (Ollman, 1966), our model postulates two modes of processing: a guess mode and a stimulus-controlled mode. From catastrophe theory, we derive two important predictions that allow us to test our model against the fast guess model and against the popular class of sequential sampling models. The first prediction—hysteresis in the transitions between guessing and stimulus-controlled behavior—was confirmed in an experiment that gradually changed the reward for speed versus accuracy. The second prediction—bimodal RT distributions—was confirmed in an experiment that required participants to respond in a way that is intermediate between guessing and accurate responding. (shrink)

The majority of commentators agree on one thing: Our network approach might be the prime candidate for offering a new perspective on the origins of mental disorders. In our response, we elaborate on refinements (e.g., cognitive and genetic levels) and extensions (e.g., to Axis II disorders) of the network model, as well as discuss ways to test its validity.

Three arguments are given to show that neural constructivism lacks an essential ingredient to explain cognitive development. Based on results in the theory of adaptive signal analysis, adaptive biological pattern information and self-organization in nonlinear systems of information processing, it is concluded that neural constructivism should be further extended to accommodate the occurrence of phase transitions generating qualitative development in the sense of Piaget.

Recent developments in music as well as in the debate on present-day transformations of religion, call for a renewal of the question of ‘sacred music.’ This article poses the question, and suggests a direction in which theory could move in order to understand the ways in which the ancient idea of sacred music remains important for present-day music and for religious reflection. Starting from the observation that theological thinkers tend to have a preference for the music of Mozart, the question (...) is raised how they theoretically substantiate the theological privilege of a music like Mozart’s. As it turns out, the key figure relating music to the sacred is the figure of form, often exemplified by musical melody. The music theology of Hans Urs von Balthasar, who has had a significant influence on Jean-Luc Marion, is a case in point. However, as is shown with reference to the musical aesthetics of the early 19th century, this figure is also central to the diametrical opposites of sacred music, being the musically sublime and the ‘religion of music.’ This observation leads to the question how, on a theoretical level, one could distinguish between sacred music and its obverse. As is shown, Marion suggests a new way of understanding the possibility of sacred music, starting from the ideas of the gift and the ‘saturated phenomenon.’ Analysing a key passage from Etant donné, it is argued that the implied shift the from form to the gift does not entirely annul the undecidability of sacred music. But also, it is argues that is does indeed show the importance and challenge that the notion of sacred music implies for both theological-philosophical and musical reflection. (shrink)

Hans Albert ist der Hauptvertreter des Kritischen Rationalismus und einer der einflussreichsten Wissenschaftslehrer im deutschen Sprachraum. Seine interdisziplinar angelegten Arbeiten beschaftigen sich mit den Grundlagen der Sozialwissenschaften und der Bedeutung kritisch-rationalen Denkens fur die sozialwissenschaftliche Theorie und Praxis. Der vorliegende Band enthalt Texte fuhrender Vertreter aus Philosophie, Soziologie, Religionswissenschaft und Jurisprudenz, die sich mit den Positionen Alberts im Kontext ihres eigenen Fachgebiets beschaftigen.

Hans Reichenbach, a philosopher of science who was one of five students in Einstein's first seminar on the general theory of relativity, became Einstein's bulldog, defending the theory against criticism from philosophers, physicists, and popular commentators. This book chronicles the development of Reichenbach's reconstruction of Einstein's theory in a way that clearly sets out all of its philosophical commitments and its physical predictions as well as the battles that Reichenbach fought on its behalf, in both the academic and popular press. (...) The essays include reviews and responses to philosophical colleagues, such as Moritz Schlick and Hugo Dingler; polemical discussions with physicists Max Born and D. C. Miller; as well as popular articles meant to clarify aspects of Einstein's theories and set out their philosophical ramifications for the layperson. At a time when physics and philosophy were both undergoing revolutionary changes in content and method, this book is a window into the development of scientific philosophy and the role of the philosopher. (shrink)

The Hans Reichenbach Papers comprise published and unpublished manuscripts, lectures, correspondence, photographs, drawings, and related materials from his early student days until his death. The correspondence contains about 9000 pages to and from Reichenbach; it ranges over his entire career. Those with whom Reichenbach maintained lifelong contact include Rudolf Carnap, Ernst Cassirer, Herbert Feigl, Philip Frank, Carl Hempel, Sidney Hook, Paul Oppenheim and Wolfgang Pauli. In addition, there is significant correspondence with von Astor, Bergmann, Bertalanffy, Dingler, Dubislav, Einstein, Fraenkel, Frank, (...) Freundlich, Grelling, Grünbaum, Paul Hertz, Hutten, Jordan, Landé, von Laue, Lewin, C.I. Lewis, Charles Morris, Nagel, Neurath, Northrop, Planck, Quine, Regener, Rougier, Salmon, Schillp, Schlick, Scholz, Schrödinger, Martin Strauss, Tarski, Vaihinger, Weiss, Williams, Zawarski, and Zilsel. The correspondence provides a valuable source of information about Reichenbach’s personal and philosophical development. It also provides primary source material for research into one of the 20th century most influential philosophical movements. Reichenbach’s manuscripts include many of his own notes as a student. Some go as far back as his university days in science and mathematics. Some of the most significant of these notes are those taken by him as a student of Albert Einstein on the special and general theories of relativity. There are four such notebooks dating from 1918. In addition there are his student notes on astronomy, Planck and electricity, Hilbert’s “Statistical Mechanics” and “Problems and Principles.” He also kept many of his lecture notes from Germany, Turkey, and the United States. The number of lectures runs to over 100 and provides a glimpse into the problems of philosophy and how he presented them to his students. Many of his lectures discussed principles of radio and issues in philosophy and modern science, often in form of popularizations of questions in relativity and quantum theory delivered on radio programs for a wider audiences. In addition to this there are an abundance of notes, calculations, and diagrams used to draft both published and unpublished papers. (shrink)

In the late 1830s and early 1840s Hans. L. Martensen helped to introduce the thought of G.W.F. Hegel to the intellectual world of Copenhagen. Between Hegel and Kierkegaard offers the first English translations of three important early writings of Martensen in the philsophy of religion. These treatises evidence an original and critical interpretation of Hegel's thought from a speculative theological point of view. The heart of Martensen's philosophy of religion is the idea of freedom or personality grounded in its relation (...) to the divine. These writings exercised an important and formative influence on the young Kierkegaard, Martensen's student, even though Kierkegaard later became a formidable opponent and critic of Martensen. (shrink)