@FBM,
Quote: It's said that the concept of free will has long been dead in the relevant sciences.
Many things have been said, true or not. I don't think there is any solid consensus on this issue yet, and even if there were, science is always provisional so no concept is ever completely dead.
Beside, I think a good argument can be made that the scientific method itself is predicated upon some degree of free (self-determined) thought, in the form of curiosity, intuition, creativity, observation and logic. Otherwise, if all mental processes are predetermined by a mix of biology and society, maybe scientists are just predetermined by society or biology to be wrong all the time.
Quote:Cows are routinely and necessarily rounded when studying complex phenomena.
Sure, but there is such a thing as over-simplification.
Quote:How can the mental act of deciding precede the relevant brain activity?
It doesn't need to precede it. All it takes to have some amount of freedom in mental processes is for such mental activity to be a necessary level of operation for the right result to be computed. IMO, we have thoughts for a reason. They play a role, they constitute a level or space where some causation occurs, one thought leading to another, e.g. in a mathematical proof.
Take a poem written on paper. What is the operative level, the right level at which the poem "works"? Not the ink dots. The ink and paper are only a physical support for a series of words and phrases. The same poem could be written on another sheet of paper with a different font and font color, or on stone, or on a computer RAM. The physical support would be entirely different, but it would still be still the same poem. Similarly, it is possible that the same thought be written in different ways in the brain, the mind allocating brain resources opportunistically to store the relevant information either here or there in the brain. In other words, mind over matter.