Just to sum up:
If our perception of the freedom to consciously choose and drive our own thought processes is a reality, then it is evidence of the supernatural, because there is no natural explanation for such freedom to exist.
So in order to support the denial of anything supernatural, you would have to deny the existence of human free will.
So does the truth lie in our perception of reality, or in the outcome of a human ability to think up ways to deny the supernatural. But where does this ability come from? What drives it?
We can easily deny both free will and the supernatural since 1) there is no evidence for either, and 2) both concepts are inherently irrational and as such are beyond empirical investigation.
Just suppose we park the irrational nature of the free will claim for a moment, and consider what science would have to do to come up with empirical evidence in favour of free will. The experiment might go something like this:
Sit a test subject down and ask him/her to choose a piece of fruit from the basket; maybe he goes for an apple, say.
Next, after ten seconds, put the arrow of time into reverse, wind the entire cosmos back 10 seconds and then let time run forward again.
If the test subject chooses a different fruit from the basket second time around, then you might argue you have discovered empirical evidence for free will.
Clearly we cannot do this, free will is bound to remain forever a speculation without any supporting evidence. And even if the subject did choose a pear the second time around, it would be argued that, there being no reason for the change of choice given all conditions are identical, the choice is random.
You cannot get away from the bare fact, that a choice requires a reason. For it not to be a random event, a choice must be a consequential outcome of the reason(s) that led to it.