What is Free Will

"nobody ever seems to give me a straight definition".

I do have a straight definition of free will, maybe not containing its full nature (which I don't think can ever be formulated), but at least a negative definition already sufficient to make it rigorously clear that it differs from the case it had no real meaning:

Precise formulation of free will

• In algorithmics (halting problem)
• As demonstrated by Tarski's Truth Undefinability Theorem

Short, logical positivist formulation

Artificial intelligence cannot pass the Turing test

Some necessary details

Reply to his "challenge":

"Across from you are what appear to be two identical twins.  They look the same, they act the same, and in all physical respects, they are as alike as two people can possibly be. However, there is one key distinction that exists between them: one of them has free will, while the other one does not. (...) Your only job is to tell me which is which. Which one has free will and which one does not?"

My answer is simple : if they are physically identical, and one has free will but the one hasn't (is a zombie), then they do not act in the same "human way". They can be distinguished by their behavior (as soon as they are put in such difference circumstances that prevent you from solving the problem of "programming the zombie" by the simple answer "let us program the zombie's behavior by the simple instruction of copying the behavior observed from the real person" in which case "observing the zombie" would be a mere indirect way of observing the real person). The zombie's behavior is best described as obeying the probability law given by quantum mechanics (something usually not observed; still I guess it sometimes happens and is then qualified as a sort of coma); the one with free will is visibly departing from this law.

What can indeterminism bring to free will

Does Free Will violate any physical law (Born's rule) ?

In the article Is Quantum Indeterminism Relevant to Free Will? by Michael Esfeld (2000)
it is stated that the idea of free will is physically unacceptable as it would be a violation of one of the laws of physics : Born's probability rule.
It is compared to some ancient speculations (by Descartes) on how a non-physical mind would act on matter by a "non-physical force" that would violate the conservation laws of classical mechanics:

"Indeterminism in physics in the described sense opens up the possibility of an interactionism which does not have to assume a force over and above those force that are acknowledged in physics. It thereby reduces the ontological burden of interactionism.
(...) instead of having to endorse an additional force for metaphysical reasons, we have to endorse a change to the probabilities that a physical theory indicates for metaphysical reasons.
Within the framework of the positions considered in this paper, the conclusion is as follows: taking everything into account and given the current state of the art, quantum physics does not reduce the price which one has to pay for interactionism."

Visibly, he contradicts himself on the question whether the "burden" or "price" is reduced or not by taking quantum randomness as the place of operation of free will. In his mind, the diverse "laws of physics" seem to be assumed as being all at "the same level" of necessity.
These are quite naive and far from any kind of well-assessed comparisons "given the current state of the art", I would say. By the way, whose "state of the art" is he referring to ? Probably, the one of science philosophers trained with their usual bullshit kind of "reasoning", who pretend to discuss science without having any decent understanding of the needed concepts and theories.

Actually, Born's rule is very far from having a status of "physical law" with a necessity for things to obey it, that can stand any comparison of strength with the the conservation laws of mechanics. These conservation laws (of energy, momentum...) are not mere "postulates" like arbitrary assumptions, axioms or speculations, but come as theorems in either framework of General Relativity and QM. Thus, there is absolutely no way, even for any God, to violate them, as this would contradict a mathematical theorem. It is absolutely impossible, logically unconceivable (the only "conceivable" process that would look like this would be a transformation of ordinary matter into dark matter, but that is still so unlikely....).

• This "rule" only qualifies what happens during "wavefunction collapse", which operates in mysterious circumstances : there is no such a thing as a verified law of physics that describes how this collapse "happens", and it is a matter of interpretation whether it happens at all, when and how.
• There is no such a thing as a possible exact mathematical definition of what it means for phenomena to be "typical", i.e. to "follow a given probability law", as opposed to "deviate from this law". Because, first, laws of physics are local, so that only a finite number of observations can be analyzed at at time. Every possibility getting a "nonzero probability" by some probability law, remains possible according to this law (as, if it wasn't possible then its probability for this law would be 0 by definition !), so that the occurrence of this possibility cannot be said to contradict the law. Therefore, no possible (nonzero probability) outcome can be said to contradict the law if it happens.
  
• Does it make sense to consider as "violation" of a probability law, the occurrence of very unlikely possibilities (with probabilities close to 0) ? Actually, it is not. Indeed, consider the concept of entropy : it is the measure of the average expectable unlikeliness of the specific exact state of a physical system occurring at a given time. Usual values of entropy of macroscopic systems (i.e. typical numbers of possible elementary states across which actual states typically "choose") are VERY big compared to their absolute unit (the Boltzmann constant). So, it is very likely for a physical system to be in a very unlikely specific state.
• Among all possibilities that are similarly very unlikely as each other but globally likely when put together, any claim that some of these are "more unlikely than others" is relative to an arbitrary choice of a "typicality criterion" that would distinguish a specific subset of possibilities as "less typical than others" in the sense that "this is a small set for the probability law" : the "total probability for the outcome to be unlikely according to this criterion", defined as the sum of probabilities on this set, is close to zero. However, there is no such a thing as a fundamental law of physics which naturally comes to specify how this set, to be taken as the definition of "unlikeliness", should be chosen. Ultimately, the choice of an "unlikeliness" concept, can only come as a matter of taste. It is a purely subjective, psychological concept instead a physical one.
• So, if my free will comes to choose the outcome of a "random process", while the physical "probability law" would give it only a small chance of happening in this way, then we might say that the physical probability law only gives a small chance for my will to be satisfied. In this sense, the satisfaction of my will by the outcome is an "untypical event". However, this untypicality concept is only defined in relation to the subjective preference of my thoughts and will, which is of an unphysical nature. The definition of which outcome I happen to prefer, is only a matter of taste ! This preference or untypicality concept cannot be mathematically formalized to be used in the expression of any self-contained mathematical law of physics. We cannot mathematically define any precise concept of "typicality" to be used in any additional "physical typicality law", from the viewpoint of which the satisfaction of my will by the outcome of "random events" can be said to "break that physical typicality law" by its untypicality.
• Of course, what did you imagine ? This is no news to say that, on a deep level, no conceivable "physical law" defined by any kind of mathematical theory can ever succeed to give to the concept of "probability" any "real sense" that fits with its intended metaphysical idea that "only one possibility will become real but the choice is not determined yet", but that it requires an appeal to a metaphysical source of randomness with a metaphysical interpretation of probability instead. Otherwise, supporters of the different interpretations would not spend that time criticizing each other's troubles in properly explaining the sense of probabilities and justifying the Born rule, as an excuse for their own inability to do so themselves.
• Assume for a moment that the presence of immaterial conscious beings with their mathematically indescribable free will able to act on matter, was a metaphysical precondition for some material universe to possibly exist. Assume also the universe still needs some mathematical structures to give it a shape, but that would have to be compatible with both kinds of circumstances:
  
• Providing a plurality a possibilities available for the intervention of a choice by a non-physical free will ;
• For the outcomes of those physical processes that the mathematical structure would happen to leave undetermined (as it must for the provision of the previous case), but that do not happen to be influenced by anybody's preference, some kind of trends still have to be given ;
then what kind of mathematical structure do you expect to fit, describing and leading the way things go, if not the structure of a "probability law" ?
• In conclusion, as the theory only postulates randomness with given values of probabilities but clearly no way to find any explanation by any known "natural cause", of what could make the universe pick particular results there, not even any explanation what it may mean to claim that a result was actually picked up rather than things staying in an undetermined state, thus, if a result was picked, no explanation either of what can actually force these results to remain "typical" for this law nor to make sense of the very claim it did, then it makes no sense to theoretically refer to this "probability law" as if it could ever contradict any more precise claim on the cause of the result such as the idea that the result is actually picked by the free will of an immaterial mind not subject to any physical law; the only meaningful argument is a matter of checking the statistics of observations and how they fit the "law". And the fact is that significant deviations from the physical "probability law" by the influence of free will have been observed (see references below).

Explanation by Robert Lipschitz

The "no" answers are wrong. In the free will versus determinism debate, you have to understand context.
Historically (pre industrial revolution), western societies believed in free will. More importantly, intuitively (based on simple reflection), our starting assumption is also that we have free will. After all, if I knew not a whiff about science, I would say that you, right now, have absolute control over whether to move your hand up or down. I can chose absolutely whether my next key will be an A or a Z:.......Z!
Enter science. It says: don't buy this notion about free will and inherent responsibility; everything is deterministic and every direction of every molecule (including those in your brain) were in fact predetermined at the moment of the big bang. Throw in the apparent success of Newton and Darwin, and it seemed convincing. If materialism is true, then everything was determined at big bang including that I would type...Z!
Many argued against these base assumptions. They refused to accept that materialism (notion that there is nothing non-physical) was true without evidence. Core to this position was the historical religious basis to our societies, as well as our relentless experience of free will, which seemed so...obvious that it could not be doubted (that's certainly my view.....A! Ha!)
Then came quantum physics and showed that determinism was false. So that means that the main argument against free will fell away. That makes the argument for free will as stronger, much much stronger. Why not resort back to our intuitive observations?

                          I'm am alive, I'm in the forest, I'm thinking, I'm choosing

But that could be an illusion. Yes, it could be. So could the fact that I'm in the forest. Or that Im typing. Those type of sceptical arguments are boring and unconvincing 
So then the die hard materialists come back and say, well QM may not show determinism but it does show Randomness and Randomness does not admit free will.
"That's all, Randomness does not admit Free Will, so on your way, nothing to see here... "
What! What the heck is Randomness? How does Randomness actually "choose" in any given instance for object to go up or down.
"It does not choose, it just happens, and nothing causes it to happen (nothing material anyway), it just happens. Thank you, please move on."
It just happens! Nothing causes it to happen!
"Yes, nothing. It just 'pop' does it, no explanation, no cause at all - certainly not free will, certainly not the free will choice of God or man. Please now, move along."
All we know from QM experiments is that what material objects do cannot be determined, but we can come up with reasonable odds whether it will go up or down. Then these guys come and say that a magical thing called Mr Randomness comes and makes the "choice" in any given instance. Only that Mr Random does not chose. Nothing chooses. And nothing causes it to happen. It just happens.
So here is the rub. There is NO evidence that Randomness as opposed to Free Will is responsible for movements of physical molecules. Both ask you to come up with an interpretation of what is going on - and if you ask me, Randomness is a far, far greater stretch: a magical force that causes things to happen without any cause at all.
Its far simpler to say that a force called Free Will causes it to happen as I can attest to every single moment....Z! Simpler, that is, if you don't have any metaphysical pre-commitments (e.g. that everything is physical and there cannot, simple cannot be anything non-physical...except of course our dear Mr Random who happens to determine the direction of every single object in the universe!)
But finally, and critically, even if you don't like the free will explanation, nothing about science precludes it now that determinism has been debunked. Certainly not unfounded calls to mysterious things called randomness - forces which causes things to happen without actually causing anything at all.
(Note, randomness used in statistics is a epistemological (knowledge based) stance; it never relied on things being random in actuality)
My answers employs the classical interpretation of quantum physics, the Copenhagen Interpretation. While there are many interpretations for many different things, that does not make them all equally valid. In any event, I do not want to get into that debate here. Suffice to say, I was relying on what is (or at least what has been) the most scientifically accepted interpretation.
Now, you indicated that you did not understand my critique of Randomness (as employed in Copenhagen interpretation). The critique is simple. It says that physical processes obey a probability distribution, say: the atom goes left 50% of time and right 50% of time. However, and here is the rub, on any given occasion, nothing - ABSOLUTELY NOTHING - determines which way the ball will go. That is, even if you knew all the facts in the universe the second before the ball moved, you could not predict which way it was going to go (with certainty) BECAUSE nothing IN the physical universe causes it to go in either direction. It just happens. Like magic.
You were wondering how it was possible for the actions of free will to be instantiated into the world. You suggest that, if free will actions are not determined or random, it is difficult to imagine how they could could connect to the physical world.
But that is exactly the point. The Copenhagen interpretation posits a force - ontological randomness - which, by definition, "causes" objects to go in one direction or another (i.e. they are "randomly" assigned) but nothing IN the physical world is responsible for the cause - if you search for it, you will never find it. Thus, randomness is itself "outside of the physical world" and you may ask your question: but how does it interact with the physical world? Well, says science, it just does.
My last point is that free will is a better explanation than Randomness. Both operate from outside of the physical world (in my view, free will originates from our non-physical spiritual selves as is the view of most free will proponents). But Free Will beats Randomness in that at least we say that there is a source X (= free will) that causes Y (=an action) through process Z (= act of choosing). Randomness makes less sense because there is no posited process (Z) by which the source (X) produces the action (Y). In Randomness, it just happens. Moreover, free will is intuitively far better, because we all experience that we have radical free will (to chose to lift our hand up or down - just try it!). Further, although this MAY be an illusion, that is a claim which requires argument and faces counter-arguments, and so it does not upset the fact that free will is intuitively a superior solution to Randomness. Furthermore, there is nothing in science that says free will CANNOT be correct as determinism can be overturned by using one or more of the plausible interpretations of QM (and replacing the world Random with Free Will).

A quote from Chalmers

In fact, one might argue that if one was to design elegant laws of physics that allow a role for the conscious mind, one could not do much better than the bipartite dynamics of standard quantum mechanics (...) There is some irony in the fact that philosophers reject interactionism on largely physical grounds (it is incompatible with physical theory), while physicists reject an interactionist interpretation of quantum mechanics on largely philosophical grounds (it is dualistic). Taken conjointly, these reasons carry little force, especially in light of the arguments against materialism elsewhere in this paper.

Is quantum randomness "at the right place" to be able to control behavior ?

This objection appears in diverse articles on the subject : "The kinds of indeterminacies discoverable at the quantum level may not correspond in any useful way to our ordinary idea of mental causes."
The answer is that quantum randomness is much more pervasive in reality than many people naively imagine when thinking that many phenomena, such as classical chaos and the randomness of statistical mechanics, can be understood without reference to quantum physics. I mean that while, admittedly, the place of not-yet-decohered forms of quantum superposition, that require the quantum mechanical concepts to be understood, seems limited to molecular scales irrelevant for consciousness, quantum randomness is anyway the real source of a large flow of effectively random data (classically probabilistic superpositions produced by decoherence), where free will has a wide margin for possible intervention. Namely at least, all the randomness that can be described as thermic actually has a quantum source, thus is an "absolute randomness" when analyzed in the framework of quantum physics, regardless the fact that, in the 19th century when quantum physics was not discovered yet, it was possible to describe this randomness as explainable in a deterministic framework. This explainability from pseudo-randomness is a pedagogical heritage of from the history of science, which many philosophers mistake as if it still kept nowadays the status of a scientific fact on the real source of this thermic randomness. It doesn't. More comments on this fact in the text on Bohmian mechanics.

See also

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