Yes they are, look at the derandomization program in computational complexity, or if you're slightly more forgiving with your definition of logic, then look at mixed strategies and Monte-Carlo algorithms.
Each series of words and arguments is equivalent because no understanding actually exists.
There is no mechanism behind picking one series of words over the other because a random number generator is behind anything.
You can’t trust such a system to produce any logical outcome, therefore free will (embodied understanding and decisions etc.) is required to conclude that free will doesn’t exist :)
That does not follow, a robot following the rules of correct reasoning can conclude (to a reasonable probability) that a statement is false. You may have very strong requirements in your definition of "understanding", but the robot can output a number between 0 and 1, and that's good enough for a conclusion by everyday language.
Saying an airplane concludes to tell the pilot to "pull up" is correct as far as I think most people see it.
Mathematicians have proven that there are true statements that can not be concluded to be true by following a set of rules or axioms.
Turing machine based robots will get stuck until the end of time stuck in infinite loops that humans are able to easily step out of. This is one of the requirements for understanding, so examples of robots aren’t very illuminating.
There are ways to detect that to an extent and abort in machine systems, and for humans you can see kind of analogous attacks against the immune system (it gets really, really crazy in there, real arms race stuff), but in general why do you expect humans to be specially invulnerable to Godel attacks? To the extent they're hard to attack, it's because they don't actually execute math.
Not true in practice, not enough energy on the universe to algorithmically derive everything. Also, someone with understanding and will would have to set up the program :)
Well then, how do you suppose the human brain does it ? Magic ? The answer of course is: it's heuristics all the way down.
But I don't think we can agree on anything here, I am a materialist and you seem to be a dualist. You may believe in some kind of god(s), (Otherwise how could will-ful humans emerge from will-less matter ?) and I don't intend to debate this here.
My worldview is that our brains exist in a material universe that is governed by physical rules, and until I see proof of the existence of some kind of soul that is somehow able to make decisions detached from our material condition (culture, health, environment, past history), I think my position is the most reasonable one.
