This is scientific evidence, not mathematical proof.
One way to frame the concept of free will is that some subjective experiences cause rather than are caused by or are identical with, physical changes in the brain.
One way to test for causation is to see which one happens first. If free will (at least as defined above) is true, we expect that some subjective experiences should precede the corresponding physical change in the brain. If free will is false, then we should expect subjective experiences to be simultaneous with or come after the corresponding brain change.
Since the actual result of the experiment (brain change comes before subjective experience) is less likely under the "free will" hypothesis than it is under the alternative, by Bayes' rule, it should make you less confident of the existence of free will. If you believe that this result would be only slightly less likely even if free will were true (as you apparently do), then you should update your estimate only a little bit, but this is still the right kind of experiment to run if you want to test for free will.
One way to test for causation is to see which one happens first. If free will (at least as defined above) is true, we expect that some subjective experiences should precede the corresponding physical change in the brain. If free will is false, then we should expect subjective experiences to be simultaneous with or come after the corresponding brain change.
Only if you assume that "free will" implies only conscious decisions.
Your subconscious brain is part of the same self as "you". So whatever you think as your "free will" is also part of that, just that part of it plays as "voice inside your brain" (conscious thoughts) and some of it does not.
It's not like the subscoscious processing is done by some other entity and imposed upon you.
Comments
This is scientific evidence, not mathematical proof.
One way to frame the concept of free will is that some subjective experiences cause rather than are caused by or are identical with, physical changes in the brain.
One way to test for causation is to see which one happens first. If free will (at least as defined above) is true, we expect that some subjective experiences should precede the corresponding physical change in the brain. If free will is false, then we should expect subjective experiences to be simultaneous with or come after the corresponding brain change.
Since the actual result of the experiment (brain change comes before subjective experience) is less likely under the "free will" hypothesis than it is under the alternative, by Bayes' rule, it should make you less confident of the existence of free will. If you believe that this result would be only slightly less likely even if free will were true (as you apparently do), then you should update your estimate only a little bit, but this is still the right kind of experiment to run if you want to test for free will.
Only if you assume that "free will" implies only conscious decisions.
Your subconscious brain is part of the same self as "you". So whatever you think as your "free will" is also part of that, just that part of it plays as "voice inside your brain" (conscious thoughts) and some of it does not.
It's not like the subscoscious processing is done by some other entity and imposed upon you.