I believe in free will within a determinist physical structure, a belief I can demonstrate to be valid using the following argument.
Saying that effect B is the result of cause A is not the same as saying that cause A will always have the effect B. There is a level of likelihood in all occurrences but nothing is certain. The most likely probability we can imagine is that the sun will rise tomorrow, but even this is only a probability, even though the possibility of a meteor striking the earth or some other cosmic apocalypse occurring overnight is minuscule. Or consider the statement "if I drop a ball from the fifth floor it will fall to the ground." Most people would agree this is a fair example of determinism and, by deduction, predeterminism. But what if someone else catches the ball before it falls to the ground, or a white owl scoops it up in its beak? The more we remove ourselves from the realm of philosophy and into the real world, the more we see that the concept of determinism is a trick of the eye. If I board the bus for Stockport, does it become inevitable that I will arrive in Stockport? A pessimist could come up with a hundred possible obstacles that might prevent the desired effect occurring.
What if we dissect actions into their smallest possible denomination? If instead of the above statement I said, "If I let go of the ball, and it is unimpeded, it will fall," this statement may well be true, but it is not a statement of determinism only an example of a physical law in operation. The famous example of an arrow never reaching its target might be true in maths (because the distance between arrow and target is always halved but never completed) but clearly in the real world, observation, ie the arrow stopping with a th-dongg and the back quivering, tells us that the arrow has reached its target. Clearly there is a point when rational theorising fails us, and rational observation must take over. Perhaps at some sub-atomic level, the molecules of the arrow do not meet the molecules of the target, but that knowledge cannot then be used to make generalised statements about the destiny of man. Determinism, therefore, is not the strait jacket of free will that some people might think it is.
It is perfectly possible to live in a world where apples leaving branches inevitably obey gravity, and still to have free choice as human beings. Every morning we wake up we decide what to do with our day. Most of us will follow the same pre-set guidelines of having to go to work to earn money to pay the bills, but that is a social strait jacket and not a philosophical one. A radical government could change those guidelines in one sitting. If I decided one morning not to go to work and become a Tibetan monk instead, what has guided my decision? The answer is a combination of genetic and behavioural inputs that I was either born with or have acquired in the course of my life. The gene part I had not control over; if you believe in God you must blame Him, or if you prefer Darwinism, blame the random process of natural selection. The behavioural part, up to a point I had no control over, insofar as I have learnt that from parents and people who have been my mentors. But behaviour can be altered, and a strong will can overcome some pretty ingrained habits. In short what we do is up to us. The act of rebellion is a great expression of free will within society and has been proved to work time and time again throughout history. Was the French Revolution inevitable? With hindsight and a full understanding of all the variables involved we might answer yes. But without the supreme motivation and courage of a few inspired individuals at the time who dared to go against the grain, it may very well have passed us by, and with it all the benefits of social change that followed it.
Determinism within nature and the free will of individuals within society are both distinct from determinism established by God, as expressed by some theists. God may well know how things are going to turn out, but then so do the manufacturers of computer games, but this does not spoil the fun of getting there. A computer game may have a billion possible routes to the same outcome, the rescue of a princess, or the discovery of treasure, but to say that there is only one outcome is not the same as saying there is no free will for the player. The player must use his own skills, learning and initiative to overcome obstacles in his own way before arriving at the desired outcome. A skilled analyst, or perhaps the creator of the game, might be able to say in advance what sort of person will succeed best at his game, but that is not predeterminism, just good analysis.
Like the creator of computer games, God knows only how things begin and how things will end and though he knows all the possibilities that exist in between, he does not know how individuals will play the game. That's left up to us. We operate in a world of fixed physical laws, but have been given the expertise to defy them or use them to our advantage. Similarly, some people believe in a fixed morality, but to what extent we obey those moral laws is also up to us. We have free will to choose from within a structure of fixed determinants. This is a much healthier outlook than the strait jacket of the determinist who sees nothing in the future but a series of easily predictable and unavoidable outcomes.