Discusses the incompatibility of the concepts of free will and determinism and argues that moral responsibility needs the doctrine of free will.

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Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with trajectories in phase space. For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states. Systems with bounded solutions are shown to possess bounded numerical solutions.A simple system representing cellular convection is solved numerically. All (...) of the solutions are found to be unstable, and almost all of them are nonperiodic.The feasibility of very-long-range weather prediction is examined in the light of these results. (shrink)

We prove the existence of hidden variables, or, what we call generalized common causes, for finite sequences of pairwise correlated random variables that do not have a joint probability distribution. The hidden variables constructed have upper probability distributions that are nonmonotonic. The theorem applies directly to quantum mechanical correlations that do not satisfy the Bell inequalities.

One of the cornerstone books of Western philosophy, Critique of Pure Reason is Kant's seminal treatise, where he seeks to define the nature of reason itself and builds his own unique system of philosophical thought with an approach known as transcendental idealism. He argues that human knowledge is limited by the capacity for perception and attempts a logical designation of two varieties of knowledge: a posteriori, the knowledge acquired through experience; and a priori, knowledge not derived through experience. This accurate (...) translation by J. M. D. Meiklejohn offers a simple and direct rendering of Kant's work that is suitable for readers at all levels. (shrink)

This chapter explores some fundamental consequences of the correspondence between physical process and computations. Most physical questions may be answerable only through irreducible amounts of computation. Those that concern idealized limits of infinite time, volume, or numerical precision can require arbitrarily long computations, and so be considered formally undecidable. The behavior of a physical system may always be calculated by simulating explicitly each step in its evolution. Much of theoretical physics has, however, been concerned with devising shorter methods of calculation (...) that reproduce the outcome without tracing each step. Computational irreducibility is common among the systems investigated in mathematics and computation theory, but it may well be the exception rather than the rule, since most physical questions may be answerable only through irreducible amounts of computation. (shrink)