Bridging the Gap : Philosophy, Mathematics and Physics - Lectures on the Foundations of Science

Why is there a general 'malaise' concerning the logical approach to the foundations of mathematics? What is the role of symmetry in physics? To what extent is the transfinite part of mathematics completely trustworthy? This volume discusses some of these questions which collects 14 lectures on the foundation of science.

Part I: Logic, Mathematics and Information. Theory of Deduction; C. Cellucci. An Introduction to Modal Semantics; F. Bellissima. Complexity of Logical Decision Problems: An Introduction; E. Börger. Remarks on Hilbert''s Program for the Foundation of Mathematics; D. Prawitz. Working Foundations; S. Feferman. Minds and Brains, Algorithms and Machines; K. Tahir Shah. Remarks on Information and Mind; G. Longo. Part II: Physics and Probability. Axioms and Paradoxes in Special Relativity; P. Budinicii. The Quantum Worldview: Its Difficulties and An Attempt to Overcome Them; G.C. Ghirardi. Indeterminism, Nonseparability and the Einstein-Podolsky-Rosen Paradox; T. Weber. Sigma-Convex Structures of the Sets of States and Probability Measures in Quantum Mechanics; G. Cassinelli, P.J. Lahti. The `Logical'' Approach to Quantum Theory; G. Cattaneo. Individuals, Kinds and Names in Physics; M.L. Dalla Chiara, G.T. Di Francia. Symmetries of Probability Kinematics; B. van Fraassen.