Correct me if I'm wrong as I've heard this is not possible to disprove the existence. I am though convinced this disproof is water tight.
Firstly, while it may be deemed difficult or impossible to disprove of free will, it is certainly impossible to prove there is free will. There is simply no experimental way for a person to follow a set of instructions and prove to themselves that there is a free will. Free will can only be "proved" to exist by unsubstantiated claims or references. It can be disproved though by simple reasoning.
Disproof of something that is in itself unprovable is not so much a necessity so this disproof is only to allow people who believe there is free will to systematically learn otherwise. - Feeling like you have free will is not proof!
Unless one can travel in time then one can not prove that they could perform any act in any other way than the way they did. One can not do an act and claim they could have done it otherwise. Please try if you will.
You may say "In 3 seconds time I will lift my tea cup or I wont."
1, 2, 3. Action.
Now prove that was free will. I don't believe you can unless you travel back in time to the exact situation and re-enact the opposite situation. You can not form an experiment by repeatedly counting to 3 and noting down whether you lift the cup or not. This experiment is not demonstrating free will it is only demonstrating the only possible way things could be.
There is no repeatable experiment to display free will. There is no one-off experiment to prove free will as a one-off experiment can not be proven without then being able to rewind time and demonstrate the opposite result.
The strongest case for free will in compatibility with determinism is the modern compatibilist approach of Dan Dennett and it is almost convincing. While I can never respond to a scholar such as him in the way he deserves I can state that the most valid claim made by him is in-fact unprovable. His case is so;
[paraphrased, I leave the research to you] "Evolution has favoured the ability to move out of the way of a moving car. So then evolution would favour the species which would plan to not be in the way of the car in the first place." [not his words, just a simple approximation of his point] The idea being that free will is a natural creation of evolution and due to its effectiveness in producing longer living beings it has been favoured by natural selection.
There is though no way to prove that this action is the entities free will or a determined response to a given situation. Evolution has certainly favoured reproduction and death avoidance but to say that we "therefore" have free will is no more valid a claim than the opposite claim that free will is an illusion. The latter claim though is further backed up by the very sticky and impossible to disprove point that you can not prove free will without also being able to travel in time. Also, if one could travel in time to prove free will, then there is no way in that experiment to prove that prior action has not influenced the repeated action.
Evolution is a genuine, amazing and proven fact and evolution could well have favoured, and it is very likely it would have, species with large brains which plan to avoid trouble. Great point and very likely true. There is though no proof, even given this, that the entity is exercising free will. It is far more likely that the action it makes are determined. Why should humans be exempt to the determinism on display in the universe? This claim of free will seems to me to be yet another false claim by humankind that it is special.
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