Are free will and natural determinism in contradiction?
I'm not sure how relevant this is, but "natural determinism" is in contradiction with the central theory of nature within the physical sciences. The most accurate, successful, and vital theory of how things happen (more precisely, how they "move", but in the sense of mechanics and therefore causality, effects, interactions, results, etc., are all integral to this theory) is probabilistic, not deterministic. Determinism has been attacked/undermined mainly from two different areas of the sciences: quantum physics and complex systems. It is currently incompatible with modern physics and problematic for all sciences which seek to model natural phenomena.
But one might ask what is this "will" that is able to act of its own volition?
One might respond that "will" describes the ability of something else (e.g., a person) to act of that something else's volition. Humans (I'm leaving out other animals for simplicity) have a sense of self distinct from their physical existence even when they know that this "sense" is part of this existence. Unlike every other species on the planet, they also have language. The ability to speak in the first person and the ways in which different languages encode personhood (clitics, conjugation, pronouns, adfixation, etc.) are, despite their differences, universal in that there is no language in which a person is incapable of communicating a first-person perspective. Even more important, there is no languages which lacks the capacity to communicate the first-person perspective of epistemic states ("I think/believe/know/wonder", δήπου, εἰκότως, -
laam,
wellicht/allicht, etc.).
This reflects the impossibility of humans to conceptualize themselves apart from their sense of "self" ("I/me") such that they can e.g., reflect upon their current mental state and judge it to be faulty or flawed. This is perhaps somewhat notoriously stated by whom I forget with something like "no language has a present tense verb meaning "I think incorrectly". That is, while we may acknowledge we were (in the past) wrong, or doubt whether our current belief(s) are correct, we do not ever describe our current reasoning process as faulty because this would require us to reflect upon our current mental state. However, our current mental state encapsulates everything we could possibly reflect upon at any moment. If, for example, I were to react to some comment by some idiot on Fox News with the thought "what a moron" I can't simultaneously reflect upon the basis for that mental state which defined all that I have in mind (and in particular that the Fox News commentator is a moron) and have that mental state.
The point is that while it is perhaps impossible to define things like consciousness or the "mind" (as these involve defining that which defines), this doesn't mean we can't assert things about the reality an nature of such phenomena. Free will is the ability for whatever it is we conceptualize automatically as "I/me" (and are incapable of
not conceptualizing ourselves of or even being conscious of doing so, as this conceptualization is or is inseparable from consciousness) to "cause". Another way to phrase this is to refer to mental causation or the emergent property of "self" or "I"/me" from the brain to determine the brain's state (self-determination).
And how can that be tested?
One way would be to look at whether we live in a deterministic cosmos. It would appear we don't.
Even if I have 100% free will, I have some cause for my decisions, actions, or behavior, even if it's nothing more than I felt like it. Therefore free will is an oxymoron.
This is to argue that free will can't exist because we are capable of free will. In other words, free will involves (at the least) the ability to make decisions or perform actions such that we could have done otherwise. For any decision or action, the exercise of free will is to determine that, for whatever reasons, we should decide or act in a particular way. That there are reasons for our decisions/actions simply implies that, granted free will exists, we exercise it based upon a state of affairs in which we can exercise it. There is no free will without some capacity to weigh wants, desires, one's environment, etc., and "choose" some course of action or make some decision. You're conflating the context in which free will is exercised for its cause.