In the past decade, there has been a sudden and vigorous development in a number of research areas in mathematics and mathematical physics, such as theory of operator algebras, knot theory, theory of manifolds, infinite dimensional Lie algebras and quantum groups (as a new topics), etc. on the side of mathematics, quantum field theory and statistical mechanics on the side of mathematical physics. The new development is characterized by very strong relations and interactions between different research areas which were hitherto considered as remotely related. Focussing on these new developments...

Constructibility and complexity play central roles in recent research in computer science, mathematics and physics. For example, scientists are investigating the complexity of computer programs, constructive proofs in mathematics and the randomness of physical processes. But there are different approaches to the explication of these concepts. This volume presents important research on the state of this discussion, especially as it refers to quantum mechanics.
This foundational debate' in computer science, mathematics and physics was already fully developed in 1930 in the Vienna Circle....

When von Neumann's and Morgenstern's Theory of Games and Economic Behavior appeared in 1944, one thought that a complete theory of strategic social behavior had appeared out of nowhere. However, game theory has, to this very day, remained a fast-growing assemblage of models which have gradually been united in a new social theory - a theory that is far from being completed even after recent advances in game theory, as evidenced by the work of the three Nobel Prize winners, John F. Nash, John C. Harsanyi, and Reinhard Selten. Two of them, Harsanyi and Selten, have contributed important articles...

This work is for scholars, researchers and students in history and philosophy of science focusing on Logical Empiricism and analytic philosophy (of science). It provides historical and systematic research and deals with the influence and impact of the Vienna Circle/Logical Empiricism on today's philosophy of science. It also explores the intellectual context of this scientific philosophy and focuses on main figures and peripheral adherents.

The articles in this volume deal with the main inferential methods that can be applied to different kinds of experimental evidence. These contributions - accompanied with critical comments - by renowned scholars in the field of philosophy of science aim at removing the traditional opposition between inductivists and deductivists. They explore the different methods of explanation and justification in the sciences in different contexts and with different objectives.
The volume contains contributions on methods of the sciences, especially on induction, deduction, abduction, laws, probability...

The present Volume 4 of the Vienna Circle Yearbook is dedicated to Otto Neurath, one of the leading figures of the Vienna Circle and one of last polymaths representative of the vanished culture from which the Circle emerged. Situating Neurath's work between the topoi of Encyclopedism - as a theoretical, scientific tool of the unfinished' project of (post-) enlightenment - and Utopianism - as the resolve to work for the systematic improvement of society and science - this volume presents the most recent research as well as critical and updated surveys and assessments of Neurath's...

Mathematical morphology (MM) is a theory for the analysis of spatial structures. It is called morphology since it aims at analyzing the shape and form of objects, and it is mathematical in the sense that the analysis is based on set theory, topology, lattice algebra, random functions, and so on.