5 ms·
> In fact, Godel's theorem ought to be used more, not less, in philosophy. Some, like me, believe it has profound implications to moral philosophy. See: https:/
by duckerude 8y ago
> In fact, Godel's theorem ought to be used more, not less, in philosophy. Some, like me, believe it has profound implications to moral philosophy. See: https://arxiv.org/abs/1805.08347 https://arxiv.org/abs/1805.08347
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.
- ngcc_hk 8y agoDoes these include any arithmetic statement? Any recursive self referral statement involved? If not, Godel theorem is irrelevant
- duckerude 8y agoIt does: > [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.
- deleted 8y ago[deleted]
- TuringTest 8y ago> [people] are not currently practically computable, but it seems physically possible to simulate them. 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.
- deleted 8y ago[deleted]
- jeromebaek 8y ago> people are not proper Turing machines. They have limited storage and limited running time. 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.
- duckerude 8y agoIf by regex machine you mean a deterministic finite state machine, then any particular DFSM has bounded memory use (based on the number of states) and bounded running time (based on the length of the input string). 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.
- jeromebaek 8y ago> any particular DFSM has bounded memory use (based on the number of states) and bounded running time (based on the length of the input string). This is wrong. This DFSM does not halt: node with arrow pointing back to the node on empty input.