"

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:

- In algorithmics (halting problem)
- As demonstrated by Tarski's Truth Undefinabiliity Theorem

**Artificial
intelligence cannot pass the Turing test**

For more comments on the mathematical details of around this concept in terms of information entropy, please refer to my pdf presentation of the mind/mathematics duality.

More comments on the experimental testing of free will

"

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.

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 ;
- In conclusion, as the theory only postulates randomness with no explanation of its source, it is pointless to theoretically refer to the fact it gives a "probability law" as if such a law could really make rigorous sense ; 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).

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. More comments on this fact in the text on Bohmian mechanics.

Specifications for a Mind Makes Collapse interpretation of quantum physics

A mind/mathematics dualistic foundation of physical reality

Introduction to quantum physics (notions of states and measurements)

Main page of arguments on quantum physics interpretations

On materialism and its pathological pseudo-arguments far from science

my reply on quantum idealism and science