The problem of free will
Free will is a familiar stranger! We think that we have it, but can't define it. The difficulty lies in its paradoxical nature: free will simultaneously incorporates two opposing notions: freedom and control.
One might think that free will is the freedom to do what one wants, but do we have the control to choose what we want? If not, then obviously we are unfree. If we have the control, it simply means we have higher-order intentions, determined by our individual nature, and are able to align our wants to those intentions. Do we have the power the control those intentions?
Clearly,one can continue this chain and invoke higher order choices, but cannot quite escape the paradox in the end.
No wonder, its existence and nature have been debated for over two thousand years by philosophers, scientists and theologians.
There are some easy questions to ask about it that are hard to answer. First among them: What is free will? Physicists typically treat it as unpredictability or uncorrelatedness with past data. This would entail that the drunkard, given to random behavior, is free, while the saint, marked by predictable goodness, lacks free will!
Free will is thus a causal primitive that is neither deterministic nor indeterministic. The viewpoint developed here is that free will, like Tarski's concept of truth, is meta-theoretic. This allows us to define free will relative to a theory, without committing ourselves to its ultimate nature.
Actions are random in a given theory because their algorithmic complexity is greater than all causes in the theory. However, it can be deterministic according to the laws of a more complex meta-theory.
A free agent, such as a human being, is causally open. The brain is not a computable input-output machine. The AI premise is basically flawed if we remain within the Turing machine paradigm.
Interestingly, essentially this idea is used in the study of quantum nonlocality, where free will is defined as the independence of action of observers from the variables underlying the property of the observed nonlocal system (Hall 2010). Formulated as a meta-theoretic construct, the observers live in the meta-theory and study a physical quantum system located in the base theory.
To develop this meta-theoretic viewpoint, we need to combine ideas from ideas from mathematical logic and algorithmic complexity theory (Chaitin 2000). This is n ongoing effort in this program. Perhaps this will help us to prove that free will exists using method of transfinite induction.
Thus free will indeed combines the contradictory qualities of control and freedom, but is saved from becoming a paradox because they occur at two different levels of theory or uncomputability. The other basic questions are: Does it exist is the world? If it does, how do we demonstrate the existence of free will? What is its neurological basis?
- Gödel, Tarski, Turing and the conundrum of free will
- On a neurological basis for free will: In search of the Gödel oracle
- External references
Gödel, Tarski, Turing and the conundrum of free will
The problem of defining and locating free will (FW) in physics is studied. On basis of logical paradoxes, we argue that FW has a meta-theoretic character, like the concept of truth in Tarski's undefinability theorem. Free will exists relative to a base theory if there is freedom to deviate from the deterministic or indeterministic dynamics in the theory, with the deviations caused by parameters (representing will) in the meta-theory. By contrast, determinism and indeterminism do not require meta-theoretic considerations in their formalization, making FW a fundamentally new causal primitive. FW exists relative to the meta-theory if there is freedom for deviation, due to higher-order causes. Absolute free will, which corresponds to our intuitive introspective notion of free will, exists if this meta-theoretic hierarchy is infinite. We argue that this hierarchy corresponds to higher levels of uncomputability. In other words, at any finitely high order in the hierarchy, there are uncomputable deviations from the law at that order. Applied to the human condition, the hierarchy corresponds to deeper levels of the subconscious or unconscious mind. Possible ramifications of our model for physics, neuroscience and artificial intelligence (AI) are briefly considered.
- Gödel, Tarski, Turing and the conundrum of free will. Chetan S. Mandayam Nayakar, R. Srikanth. To appear as a chapter in "Nature's Longest Threads: New Frontiers in the Mathematics and Physics of Information in Biology", eds: J. Balakrishnan and B.V. Sreekantan, to be published under book series: "World Scientific Lecture Notes in Complex Systems".
- Consciousness, libertarian free will and quantum indeterminism: Chetan S. Mandayam Nayakar, S. Omkar, R. Srikanth. Ch. 23 in "Looking Within: Interdisciplinary Approaches to Consciousness" (eds. Sangeetha Menon, Anindya Sinha, B. V. Sreekantan) (Springer 2014).
-- R. Srikanth
On a neurological basis for free will: In search of the Gödel oracle
In a recently proposed model of volition, physical causality does not encompass the full behavior of free-willed agents like humans. Free will is posited to exist in the sense that there is freedom to deviate from the deterministic or indeterministic brain dynamics determined by neurological, genetic and other instinctual factors, with the deviations produced by causally higher parameters of will. We argue that this causal hierarchy corresponds to a higher level of uncomputability. Applied to the human condition, the hierarchy corresponds to deeper levels of the subconscious or unconscious mind. From a computational perspective, this higher level is proposed to be accessed through an oracle. Here we attempt to pin down the neurological basis of the oracle. Possible ramifications of our model for physics, neuroscience and artificial intelligence (AI) are briefly considered
--H. Hanaan and R. Srikanth
- Gödel's incompleteness theorems, free will and mathematical thought by S. Feferman. Accessible here.
- Local deterministic model of singlet state correlations based on relaxing measurement independence -- M. J. W. Hall (2010).
- 13 Things that don't make sense-- The Most Intriguing Mysteries of
our Times -- M. Brooks, chap. 11 (Hachette 2010).
Last updated: March 11, 2014.