To be fair, it being physically possible to simulate people doesn't mean that human mind is computable/decidable.
Even if the "low-level" physical behavior of simulated neurons could be formalized, there's the possibility that the "high level" mind could belong to a different "emergent" layer that can't be represented by an axiomatic system.
In essence, you would have a computer program that represents a human mind, but the answers to problems asked to that mind would be evaluated as human replies, not formal expressions; and human replies are not axiomatic.
If not, Godel theorem is irrelevant
> [page 5] Just as humans can have free will because we can look at our own mental activities from a distance, so a program can be uncomputable because it can take as input its own self in data form.
But I don't think it holds up, because we don't have full access to our own mental activities, only to a grossly simplified model of our own mental activities.
In this sense, people aren't even proper regex machines. They have limited running time. But do you really believe the brain has less computational capacity than a regex machine?
> I think the conventional view is that free will is the requirement for both good and bad actions, not that free actions are by definition good.
What free will means is basically the core problem of moral philosophy, and different positions take different formulations of it. Consequentialists usually try to say that both bad and good actions are free (critics say consequentialists have absolutely zero freedom). Kantians say a free action following the categorical imperative is a good action. What I'm doing in this essay, though that's not the point of this particular essay, is showing a bijection between the categorical imperative and the halting problem.
If they're simple enough, they can be simulated by a brain, so a brain has more computational capacity. If you can make them as complex as you want, then they can match (and exceed) the computational capacity of the brain, just by incorporating all states a brain can have and pre-computing the transitions. For practical purposes it's almost always best to treat brains (and other computers, for that matter) as Turing-complete, but I think that strictly speaking they're closer to DFSMs.
But the point is that almost all predictions about people's decisions involve time bounds. When there's a time bound, those decisions become computable. "Will this program return 1" cannot be solved in general, but "Will this program return 1 within the next hour" can be.
This is wrong. This DFSM does not halt: node with arrow pointing back to the node on empty input.
I think you also need to have at least one transition for every symbol in the alphabet from every state for it to be a valid ε-NFA, and then it can be reduced to a DFSM, giving it a bounded running time.
DFAs can run in bounded time, because every symbol takes exactly one step to be processed, and there is only one way to process a string.
That also means NFAs can run in bounded time, by reducing them to DFAs first, but that's not a very satisfying explanation.
A NFA rejects a string if it can not end in an accepting state. It's not intuitively straightforward to see whether that's the case, but it can be done in bounded time by exhaustively checking possible paths (which is possible with a finite number of states and a finite input string).
You can't always perform that trick with Turing machines, because they can have infinitely many reachable states.
I've only skimmed it, and I'm not very familiar with moral philosophy, but this seems bizarre. If I understand it correctly, your claim is:
1. Free will is uncomputability (undecidability)
2. A good action is a free action (and therefore uncomputable)
3. A bad action is an action that pretends an uncomputable system is computable, thereby denying agency and humanity
I think 1. is suspect because people are not proper Turing machines. They have limited storage and limited running time. They are not currently practically computable, but it seems physically possible to simulate them. I don't think Gödel's theorem applies, although practical uncomputability might be a working substitute.
If you predict that some person will take some action, that's almost always a prediction that they will take that action within the next ten seconds/hours/decades. Actually simulating them is impossible for various reasons, but Gödel's theorem isn't one of them. You can't prove whether an arbitrary program will halt, but you can prove whether an arbitrary program will halt within the next hundred thousand execution steps.
2. seems like a really bizarre way to define goodness. I think morality is subjective enough that you could define it like that, but I don't know why you'd want to. I think the conventional view is that free will is the requirement for both good and bad actions, not that free actions are by definition good.
I think 3. might cover almost every thought we have about other people. Internal computable models of other people are how we operate, as far as I know. Again, you could define badness like that, but I don't see the point.
> [page 8] Now the question paraphrases to: does there exist an algorithm for me to love my child? Of course not. So the distinction between [shallow benefits] and [deep] benefits is that: there is an algorithm to bring about [shallow benefits], whereas there is no algorithm to bring about [deep] benefits.
Doesn't that conflict with the idea that we are Turing machines? If we are Turing machines, then everything we do is the output of some (possibly uncomputable) algorithm, including loving people.
I don't think this engages with Gödel's theorem in a useful way, or even depends on it.