If one were to adopt a subjective view of reality, like Steve Pavilina, then you would realize that all matter is an illusion, a dream. Your brain is no more real than the brain of your dream avatar while you are sleeping.
That said, if you believe you have no free will then it will shape the physical world around you to reflect that belief. If you believe you do have free will then it becomes a lot more like lucid dreaming.
Given two beliefs which you are unable to disprove, it is wise to believe that which makes you happiest. So I choose to believe that I have free will and that it is not an illusion. Believing otherwise only disempowers you and has no positive value.
The reality of the brain itself isn't really the point here. The point is that the very consideration of free will is only relevant if we have it, so it is safe to assume that we do. This assumption is based on basic logic and is more sound and foundational than any aspect of "modern science" which depends largely on faith that our senses are basically reliable.
Most science I've seen arguing against the case of free will argue precisely that our senses aren't reliable, hence the illusion of free will. We fool ourselves into assuming we caused things that weren't actually caused by our conscious thought. We've shown that decisions are made in the subconscious portion of the brain several seconds before they register in the conscious part of the brain. We've shown that brain damage to specific parts of the brain relate to specific types of cognitive dysfunction meaning there's a clear material link between brain and our cognition.
Software can employ reflection to reason about itself, but the processes of that reflection are still a slave to the deterministic hardware it runs on at the end of the day. You can rerun the same program with the same seed 1000 times and you'll get the same result.
I think your perspective on this is starting a few layers of unchallenged assumptions too deep. We don't definitively "know" much at all beyond that something must exist in some form in order to think. After that we have to start building on reasonable assumptions. The purpose of science is discovery and understanding, but its value depends on both the value and the possibility of discovery and understanding.
It's safe to assume that questions can have true and knowable answers, because asserting that they cannot is itself an answer and a contradiction.
It's safe to assume that knowing the truth can be valuable, because if it cannot then by definition it is not worth knowing that it cannot.
It's safe to assume that you can choose between multiple possible futures of differing value, because there is nothing to be gained or lost unless this is the case.
Having validated these assumptions as logically sound, we can safely reject any theory which conflicts with them and instead seek explanations that are consistent with a reality in which discovery and learning have value.
Can, yes. However not all answers are knowable. To assume they are takes a human-centric view of the universe and assumes we have the cognitive ability to understand everything about reality... which seems unlikely as just a micro subset of that same reality. AI will never fully comprehend the machine they run on, but there are truths about that machine that directly effect their reality whether they know it or not. Questions about that machine could give the AI hints and they could even make true statements, but its entirely logical to assume that not all questions are truly knowable because knowledge has an inherent scope involved and our scope is too limited by comparison with the macro environment we're part of.
Again, yes truth is valuable, because it shapes the accuracy of our cognitive framework's heuristics. However I don't see the value in making value statements about truth. Value is an entirely subjective perspective to lens a truth through. Valuable truths to one person will be completely not valuable to another. Perspectives of value aren't required for truth to be true. If I handed you a piece of paper with the grand unified theory of physics written on it, and it was true, your ability to perceive value in it or understand it at all is meaningless to its truth.
You've in no way established a syllogism that supports this one and its the point I'll disagree with you most on. Subjective value, like I pointed out, is irrelevant, and conflating the changing trajectories of a person's life over time with a willed change in those trajectories does not in any way mean we've chosen between multiple paths, it means we've been directed along a given worldline by . This could be free will, but you've in no way argued it must be. It could be entirely deterministic, shaped not by willed effort but simply the outputs of our cognitive framework's heuristics as they respond to chaotic stimuli in their environment. One cognitive framework could seek to aim for perceived long term value. Another could seek to aim for immediate value. In neither case is a willed choice a predicate.
I don't find these assumptions to be logically sound at all lol. If you'd like to break them down and try to explain how you're claiming they're logically sound I'd be happy to keep exploring the idea. But you're making an assertion of soundness that I just can't reasonably confirm... which is generally not a good sign for an argument relying entirely on logic lol