The concept of free will as an infinite metatheoretic recursion

It is argued that the concept of free will, like the concept of truth in formal languages, requires a separation between an object level and a meta-level for being consistently defined. The Jamesian two-stage model, which deconstructs free will into the causally open "free" stage with its closure in the "will" stage, is implicitly a move in this direction. However, to avoid the dilemma of determinism, free will additionally requires an infinite regress of causal meta-stages, making free choice a hypertask. We use this model to define free will of the rationalist-compatibilist type. This is shown to provide a natural three-way distinction between quantum indeterminism, freedom and free will, applicable respectively to artificial intelligence (AI), animal agents and human agents. We propose that the causal hierarchy in our model corresponds to a hierarchy of Turing uncomputability. Possible neurobiological and behavioral tests to demonstrate free will experimentally are suggested. Ramifications of the model for physics, evolutionary biology, neuroscience, neuropathological medicine and moral philosophy are briefly outlined.Comment: Accepted in INDECS (close to the accepted version

The Grin of Schrödinger's Cat; Quantum Photography and the limits of Representation

The famous quantum physics experiment 'Schrödinger's cat' suggests that some situations are undecidable, i.e. they exist outside of the normative distinctions between 'truth' and 'false' because both states can co-exist under certain conditions. This paper suggests that photography has very close links with this state of affairs, because photography allows one to move from the world of certainty into the quantum dimension of undecidability and indeterminate states

Scale-invariant cellular automata and self-similar Petri nets

Two novel computing models based on an infinite tessellation of space-time are introduced. They consist of recursively coupled primitive building blocks. The first model is a scale-invariant generalization of cellular automata, whereas the second one utilizes self-similar Petri nets. Both models are capable of hypercomputations and can, for instance, "solve" the halting problem for Turing machines. These two models are closely related, as they exhibit a step-by-step equivalence for finite computations. On the other hand, they differ greatly for computations that involve an infinite number of building blocks: the first one shows indeterministic behavior whereas the second one halts. Both models are capable of challenging our understanding of computability, causality, and space-time.Comment: 35 pages, 5 figure

Free will and (in)determinism in the brain: a case for naturalized philosophy

In this article we study the question of free will from an interdisciplinary angle, drawing on philosophy, neurobiology and physics. We start by reviewing relevant neurobiological findings on the functioning of the brain, notably as presented in (Koch 2009); we assess these against the physics of (in)determinism. These biophysics findings seem to indicate that neuronal processes are not quantum but classical in nature. We conclude from this that there is little support for the existence of an immaterial ‘mind’, capable of ruling over matter independently of the causal past. But what, then, can free will be ? We propose a compatibilist account that resonates well with neurobiology and physics, and that highlights that free will comes in degrees – degrees which vary with the conscious grasp the ‘free’ agent has over his actions. Finally, we analyze the well-known Libet experiment on free will through the lens of our model. We submit this interdisciplinary investigation as a typical case of naturalized philosophy: in our theorizing we privilege assumptions that find evidence in science, but our conceptual work also suggests new avenues for research in a few scientific disciplines

Being and Change: Foundations of a Realistic Operational Formalism

The aim of this article is to represent the general description of an entity by means of its states, contexts and properties. The entity that we want to describe does not necessarily have to be a physical entity, but can also be an entity of a more abstract nature, for example a concept, or a cultural artifact, or the mind of a person, etc..., which means that we aim at very general description. The effect that a context has on the state of the entity plays a fundamental role, which means that our approach is intrinsically contextual. The approach is inspired by the mathematical formalisms that have been developed in axiomatic quantum mechanics, where a specific type of quantum contextuality is modelled. However, because in general states also influence context -- which is not the case in quantum mechanics -- we need a more general setting than the one used there. Our focus on context as a fundamental concept makes it possible to unify `dynamical change' and `change under influence of measurement', which makes our approach also more general and more powerful than the traditional quantum axiomatic approaches. For this reason an experiment (or measurement) is introduced as a specific kind of context. Mathematically we introduce a state context property system as the structure to describe an entity by means of its states, contexts and properties. We also strive from the start to a categorical setting and derive the morphisms between state context property systems from a merological covariance principle. We introduce the category SCOP with as elements the state context property systems and as morphisms the ones that we derived from this merological covariance principle. We introduce property completeness and state completeness and study the operational foundation of the formalismComment: 44 page