The aim of the present research was to develop a difficulty model for logical reasoning problems involving complex ordered arrays used in the Graduate Record Examination. The approach used involved breaking down the problems into their basic cognitive elements such as the complexity of the rules used, the number of mental models required to represent the problem, and question type. Weightings for these different elements were derived from two experimental studies and from the reasoning literature. Based on these weights, difficulty (...) models were developed which were then tested against new data. The models had excellent predictive validity and showed the relative influence of rule based factors and factors relating to the number of underlying models. Different difficulty models were needed for different question types, suggesting that people used a variety of approaches and, at a wider level, that both mental models and mental rules may be used in reasoning. (shrink)
The early twentieth century was a lively time for the foundations of mathematics. This ensuing debates were, in large part, a reaction to the settheoretic and nonconstructive methods that had begun making their way into mathematical practice around the turn of the twentieth century. The controversy was exacerbated by the discovery that overly na¨ıve formulations of the fundamental principles governing the use of sets could result in contradictions. Many of the leading mathematicians of the day, including Hilbert, Henri Poincar´e, ´.
_Mini-set E: Radical Politics/The Socialist Tradition_ re-issues works by H B Acton, George Brenkert, Tom Campbell, Antony Cutler, Barry Hindess, Paul Hirst, Athar Hussain, Amlan Datta, J Jupp, Dennis Kavanagh, Norman MacKenzie, Patricia Pugh and Paul Thomas among others which discuss the history of socialism and the marxist and anarchist traditions.
This paper examines E. W. Beth's work in the philosophy of physics, both from a historical and a systematic point of view. Beth saw the philosophy of physics first of all as an opportunity to illustrate and promulgate a new and modern general approach to the philosophy of nature and to philosophy tout court: an approach characterized negatively by its rejection of all traditional metaphysics and positively by its firm orientation towards science. Beth was successful in defending this new ideology, (...) and became its leading Dutch representative in the first two decades after the second world war. Beth also contributed importantly to the method of the philosophy of physics in a narrower sense, by proposing and promoting the semantic approach in the formal analysis of physical theories. Finally, he worked on several specific foundational questions; but he was probably too much of a logician to leave his mark in this area. (shrink)