In an article in The Stanford Encyclopaedia of Philosophy, Randolph Clarke discusses the evidence for an incompatibilist account of free will. (Incompatibilism is the view that free will isn’t compatible with determinism.)
“It is sometimes claimed […] that our experience when we make decisions and act constitutes evidence that there is indeterminism of the required sort in the required place. We can distinguish two parts of this claim: one, that in deciding and acting, things appear to us to be the way that one or another incompatibilist account says they are, and two, that this appearance is evidence that things are in fact that way. [… E]ven if this first part is correct, the second part seems dubious. If things are to be the way they are said to be by some incompatibilist account, then the laws of nature—laws of physics, chemistry, and biology—must be a certain way. […] And it is incredible that how things seem to us in making decisions and acting gives us insight into the laws of nature. Our evidence for the required indeterminism, then, will have to come from the study of nature, from natural science.”
I don’t understand the reason for the ‘incredible’ claim, and no reason is given for it in the article.
Yet, it seems that there is a pretty straightforward empirical argument that how things seem to us in various mental events or processes can in theory give us insight into the laws of nature. Basic idea: reflecting on what happens in one’s mind can give one (correct) predictions about what is happening in the brain (say), which in turn involves natural laws.
More detailed: The way things seem to us has already given us insight into cognitive or neurological events or processes. That is, we have an experience of something working in our mind, then we look for a correlate in brain processing, and in certain cases we have found correlates. (This is the basis of the belief that the mind is, in some important sense, the brain.) There must be natural laws which are compatible with these brain processes, if the brain is part of nature. Therefore, how things seem to be working in the mind can in theory give insight into natural laws.
The question is just how the sense of decision making maps onto nature. Are we really able to peer into the workings of nature (or something very closely related to it) on the inside, or is that not how the mind works? One view in the ‘hard problem’ of consciousness, for example, is similar to the former: through reflecting on consciousness, one can get a glimpse of the inner nature of physical reality.