Related papers: Uncomputability and free will
Thermodynamics provides a transparent definition of the free energy of density functional theory (DFT), and of its derivatives - the potentials, at finite temperatures T. By taking the T to 0 limit, it is shown here that both DFT and…
Baroque questions of set-theoretic foundations are widely assumed to be irrelevant to physics. In this article, I demonstrate that this assumption is incorrect. I show that the fundamental physical question of whether a theory is…
Since Descartes' dualism, with his res extensa and res cogitans, six fundamental problems in the philosophy and natural history of mind are these: 1. how does mind act on matter? 2. If mind does not act on matter is mind a mere…
It is argued that any possible definition of a realistic physics theory -- i.e., a mathematical model representing the real world -- cannot be considered comprehensive unless it is supplemented with requirement of being computationally…
Artificial Intelligence (AI) provides many opportunities to improve private and public life. Discovering patterns and structures in large troves of data in an automated manner is a core component of data science, and currently drives…
A number of examples have been given of physical systems (both classical and quantum mechanical) which when provided with a (continuously variable) computable input will give a non-computable output. It has been suggested that these systems…
The gap between classical mechanics and quantum mechanics has an important interpretive implication: the Universe must have an irreducible fundamental level, which determines the properties of matter at higher levels of organization. We…
The before-before experiment demonstrates that quantum randomness can be controlled by influences from outside spacetime, and therefore by immaterial free will. Rather than looking at quantum physics as the model for explaining free will,…
In this paper we present a discussion of the basic aspects of the well-known problem of prediction and inference in physics, with specific attention to the role of models, the use of data and the application of recent developments in…
One of quantum theory's salient features is its apparent indeterminism, i.e. measurement outcomes are typically probabilistic. We formally define and address whether this uncertainty is unavoidable or whether post-quantum theories can offer…
In this paper the theory of flexibly-bounded rationality which is an extension to the theory of bounded rationality is revisited. Rational decision making involves using information which is almost always imperfect and incomplete together…
Building on work by Alfonseca et al. (2021), we study the conditions necessary for it to be logically possible to prove that an arbitrary artificially intelligent machine will exhibit certain behavior. To do this, we develop a formalism…
In this PhD thesis the ancient question of determinism ('Does every event have a cause ?') will be re-examined. In the philosophy of science and physics communities the orthodox position states that the physical world is indeterministic:…
It is the matter of fact that quantum mechanics operates with notions that are not determined in the frame of the mechanics' formalism. Among them we can call the notion of "wave-particle" (that, however, does not appear in both classical…
In honor of Alan Turing's hundredth birthday, I unwisely set out some thoughts about one of Turing's obsessions throughout his life, the question of physics and free will. I focus relatively narrowly on a notion that I call "Knightian…
Many different definitions of computational universality for various types of dynamical systems have flourished since Turing's work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical…
In this paper a conditional logic is defined and studied. This conditional logic, Deterministic Bayesian Logic, is constructed as a deterministic counterpart to the (probabilistic) Bayesian conditional. The logic is unrestricted, so that…
Physical laws are a set of rules in the relationship between observations made by the experimenter. All these observations are made through a mechanism that links the external world to the experimenter's awareness, a mechanism which is not…
The major conceptual difficulties of quantum mechanics are analyzed. They are: the notion "wave-particle", the probabilistic interpretation of the Schroedinger wave \psi-function and hence the probability amplitude and its phase, long-range…
Conway and Kochen have presented a "free will theorem" (Notices of the AMS 56, pgs. 226-232 (2009)) which they claim shows that "if indeed we humans have free will, then [so do] elementary particles." In a more precise fashion, they claim…