Larry, you have not proven that 6 would be a prime number if PA proved 6 was a prime number, because PA does not prove that 6 is a prime number.
The theorem is only true for the phi that it’s true for.
The claim that phi must be true because if it’s true then it’s true, and if it’s false then “if PA |- phi then phi” has an officially true conclusion whenever PA does not imply phi, is bogus.
It’s simply and obviously bogus, and I don’t understand why there was any difficulty about seeing it.
Caledonian, it’s possible to care deeply about choices that were made in a seemingly-arbitrary way. For example, a college graduate who takes a job in one of eight cities where he got job offers, might within the year care deeply about that city’s baseball team. But if he had taken a different job it would be a completely different baseball team.
You might care about the result of arbitrary choices. I don’t say you necessarily will.
It sounds like you’re saying it’s wrong to care about morals unless they’re somehow provably correct? I’m not sure I get your objection. I want to point out that usually when we have a war, most of the people in each country choose sides based on which country they are in. Less than 50% of americans chose to oppose the current iraq fiasco before it happened. Imagine that russia had invaded iraq with the same pretexts we used, all of which would have worked as well for russia as well as they did for us. Russians had more reason than us to fear iraqi nukes, they didn’t want iraq supporting chechen terrorists, they thought Saddam was bad man, etc. imagine the hell we would have raised about it.… But I contend that well over a hundred million americans supported the war for no better reason that they were born in america and so they supported invasions by the US military.
Whether or not there’s some higher or plausible morality that says we should not choose our morals at random, still the fact is that most of us do choose our morals at random.
I haven’t read Roko’s blog, but from the reflection in Eliezer’s opposition I find I somewhat agree.
To the extent that morality is about what you do, the more you can do the higher the stakes.
If you can drive a car, your driving amplifies your ability to do good. And it amplifies your ability to do bad. If you have a morality that leaves you doing more good than bad, and driving increases the good and the bad you do proportionately, then your driving is a good thing.
True human beings have an insatiable curiousity, and they naturally want to find out about things, and one of the things they like is to find out how to do things. Driving a car is a value in itself until you’ve done it enough that it gets boring.
But if you have a sense of good and bad apart from curiousity, then it will probably seem like a good thing for good smart people to get the power to do lots of things, while stupid or evil people should get only powers that are reasonably safe for them to have.
“You should care about the moral code you have arbitrarily chosen.”
No, I shouldn’t. Which seems to be the focal point of this endless ‘debate’.
Well, you might choose to care about a moral code you have arbitrarily chosen. And it could be argued that if you don’t care about it then you haven’t “really” chosen it.
I agree with you that there needn’t be any platonic absolute morality that says you ought choose a moral code arbitrarily and care about it, or that if you do happen to choose a moral code arbitrarily that you should then care about it.
We are born with some theorems of right (in analogy to PA).
Kenny, I’d be fascinated to learn more about that. I didn’t notice it in my children, but then I wouldn’t necessarily notice.
When I was a small child people claimed that babies are born with only a fear of falling and a startle reflex for loud noises. I was pretty sure that was wrong, but it wasn’t clear to me what we’re born with. It takes time to learn to see. I remember when I invented the inverse square law for vision, and understood why things get smaller when they go farther away. It takes time to notice that parents have their own desires that need to be taken into account.
What is it that we’re born with? Do you have a quick link maybe?
Larry, one of them is counterfactual.
If you draw implications on a false asumption then the result is useful only to show that an assumption is false.
So if PA → 1=2 then PA → 1<>2. How is that useful?
If PA → 6 is prime then PA also → 6 is not prime.
Once you assume that PA implies something that PA actually implies is false, you get a logical contradiction. Either PA is inconsistent or PA does not imply the false thing.
How can it be useful to reason about what we could prove from false premises? What good is it to pretend that PA is inconsistent?
Honestly I do not understand how you can continue calling Eliezer a relativist when he has persistently claimed that what is right doesn’t depend on who’s asking and doesn’t depend on what anyone thinks is right.
Before I say anything else I want you to know that I am not a Communist.
Marx was right about everything he wrote about, but he didn’t know everything, I wouldn’t say that Marx had all the answers. When the time is ripe the proletariat will inevitably rise up and create a government that will organize the people, it will put everybody to work according to his abilities and give out the results according to the needs, and that will be the best thing that ever happened to anybody. But don’t call me a Communist, because I’m not one.
Oh well. Maybe Eliezer is saying something new and it’s hard to understand. So we keep mistaking what he’s saying for something old that we do understand.
To me he looks like a platonist. Our individual concepts of “right” are imperfect representations of the real true platonic “right” which exists independently of any or all of us.
I am more of a nominalist. I see our concepts as things that get continually re-created. We are born without any concept of “right” and we develop such concepts as we grow up, with the foundations in our families. The degree to which we develop similar concepts of “right” is a triumph for our societies. There’s nothing inevitable about it, but there’s a value to moral uniformity that goes beyond the particular beliefs.
So for example about “murder”. Americans mostly believe that killing is sometimes proper and necessary. Killing in self defense. Policemen must sometimes kill dangerous criminals. It’s vitally necessary to kill the enemy in wartime. Etc. We call it “murder” only when it is not justified, so of course we agree that murder is wrong.
We would be better off if we all agreed about when killing is “right”. Is it right to kill adulterous spouses? The people they have sex with? Is it right to kill IRS agents? Blasphemers? Four years ago a man I met in a public park threatened to kill me to keep me from voting for Kerry. Was he right? Whatever the rules are about killing, if we all agreed and we knew where we stood, we’d be better off than when we disagree and don’t know who to expect will try to kill us.
And that is why in the new society children will be taken from their parents and raised in common dormitories. Because individual families are too diverse, and they don’t all raise their children to understand that “from each according to his abilities, and to each according to his needs” is the most basic and important part of morality.
But don’t call me a Communist, I already explained that I wasn’t a Communist in my first sentence above.
But Larry, PA does not actually say that 6 is prime, and 6 is not prime.
You could say that if PA proved that every theorem is false then every theorem would be false.
Or what would it mean if PA proved that Lob’s theorem was false?
It’s customary to say that any conclusion from a false premise is true. If 6 is prime then God’s in his heaven, everything’s right with the world and we are all muppets. Also God’s in hell, everything’s wrong with the world, and we are all mutant ninja turtles. It doesn’t really matter what conclusions you draw from a false premise because the premnise is false.
Your argument about what conclusion we could draw if PA said that 6 is prime is entirely based on a false premise. PA does not say that 6 is prime.
Let me try to say that clearer.
Suppose that A is false.
How the hell are you going to show that if PA proves A true then A will be true, when A is actually false?
If you can’t prove what would happen if PA proved A true when A is actually false, then if you can prove that if PA proves A is true then A has to be true, it must be that A is true in the first place.
If this reasoning is correct then there isn’t much mystery involved here.
One more time. If PA proves you are a werewolf, then you’re really-and-truly a werewolf. PA never proves anything that isn’t actually true. OK, say you aren’t a werewolf. And I say I have a proof that if PA proves you’re a werewolf then you’re actually a werewolf. But in reality you aren’t a werewolf and PA does not prove you are. How do I prove that PA would do that, when PA does not do that?
Once more through the mill. If PA proves that 6 is a prime number, then 6 is really a prime number. Can you prove that if PA proved 6 was a prime number then 6 would be a prime number? How would you do it?
If you definitely can’t prove that, then what does it mean if I show you a proof that if PA proves 7 is a prime number then 7 must actually be prime? If you can’t make that proof unless 7 is prime, and you have the proof, then 7 is actually prime.
The problem is with trying to apply material implication when it does not work.
I went to the carnival and I met a fortune-teller. Everything she says comes true. Not only that, she told me that everything she says always comes true.
I said, “George Washington is my mother” and she said it wasn’t true.
I said, “Well, if George Washington was my mother would you tell me so?” and she refused to say she would. She said she won’t talk about what would be true if George Washingto was my mother, because George Washington is not my mother.
She says that everything she says comes true. She looked outside her little tent, and saw the sky was clear. She said, “If I tell you the sky is clear, then the sky is clear.”
“But what if it was raining right now? If you told me it was raining, would it be raining?”
“I won’t say what I’d tell you if it was raining right here right now, because it isn’t raining.”
“But if the sky is clear right now you’ll tell me the sky is clear.”
“Yes. Because it’s true.”
“So you’ll only tell me that (if you say the sky is clear then the sky really is clear), when the sky really is clear?”
“Yes. I only tell you about true things. I don’t tell you what I’d do if the world was some other way.”
“Oh.”
The same boy who rationalized a way into believing there was a chocolate cake in the asteroid belt, should know better than to rationalize himself into believing it is right to prefer joy over sorrow.
Obviously, he does know. So the next question is, why does he present material that he knows is wrong?
Professional mathematicians and scientists try not to do that because it makes them look bad. If you present a proof that’s wrong then other mathematicians might embarrass you at parties. But maybe Eliezer is immune to that kind of embarrassment. Socrates presented lots of obvious nonsense and people don’t think badly of him for it.
The usual reasons why not probably don’t apply to him. I don’t have any certainty why he does it, though.
When you try to predict what will happen it works pretty well to assume that it’s all deterministic and get what results you can. When you want to negotiate with somebody it works best to suppose they have free will and they might do whatever-the-hell they want.
When you can predict what inanimate objects will do with fair precision, that’s a sign they don’t have free will. And if you don’t know how to negotiate with them, you haven’t got a lot of incentive to assume they have free will. But particularly when they’re actually predictable.
The more predictable people get the less reason there is to suppose they have spirits etc motivating them. Unless it’s information about the spirits you manipulate to predict what they’ll do.
People keep using the term “moral relativism”. I did a Google search of the site and got a variety of topics with the term dating from 2007 and 2008. Here’s what it means to me.
Relative moral relativism means you affirm that to the best of your knowledge nobody has demonstrated any sort of absolute morality. That people differ in moralities, and if there’s anything objective to say one is right and another is wrong that you haven’t seen it. That very likely these different moralities are good for different purposes and different circumstances, and if a higher morality shows up it’s likely to affirm that the different moralities you’ve heard of tend to each have its place.
This is analogous to being an agnostic about gods. You haven’t seen evidence there’s any such thing as an objectively absolute morality, so you do not assert that there is such a thing.
Absolute moral relativism accepts all this and takes two steps further. First, the claim is that there is no objective way to judge one morality better than another. Second, the claim is that without any objective absolute morality you should not have any.
This is analogous to being an atheist. You assert that there is no such thing and that people who think there is suffer from fallacious superstitions.
I can be a relative moral relativist and stil say “This is my morality. I chose it and it’s mine. I don’t need it to be objectively true for me to choose it. You can choose something else and maybe it will turn out we can get along or maybe not. We’ll see.”
Why should you need an absolute morality that’s good all times and all places before you can practice any morality at all? Here I am, here’s how I live. It works for me. If you want to politely tell me I’m all wrong then I’ll listen politely as long as I feel like it.
We have quick muscles, so we do computation to decide how to organise those muscles.
Trees do not have quick muscles, so they don’t need that kind of computation.
Trees need to decide which directions to grow, and which directions to send their roots. Pee on the ground near a tree and it will grow rootlets in your direction, to collect the minerals you give it.
Trees need to decide which poisons to produce and where to pump them. When they get chewed on by bugs that tend to stay on the same leaf the trees tend to send their poisons to that leaf. When it’s bugs that tend to stay nearby the tree sends the poisons nearby. Trees can somewhat sense the chemicals that distressed trees near them make, and respond early to the particular sorts of threats those chemicals indicate.
Is all that built into the trees’ genes? Do they actually learn much? I dunno. I haven’t noticed anything like a brain in a tree. But I wouldn’t know what to look for. Our brains use a lot of energy, we have to eat a lot to maintain them. They work fast. Trees don’t need that speed.
I don’t know how smart trees are, or how fast they learn. The esperiments have not been done.
I don’t know how moral animals are that we share no common language with. Those experiments haven’t been done either. We can’t even design the experiments until we get an operational definition of morality.
What experiment would you perform to decide whether an animal was moral? What experiment would show whether an intelligent alien was moral? What experiment could show whether a human imprisoned for a vicious crime was moral?
If you can describe the experiment that shows the difference, then you have defined the term in a way that other people can reproduce.
If you’ve ever taken a mathematics course in school, you yourself may have been introduced to a situation where it was believed that there were right and wrong ways to factor a number into primes. Unless you were an exceptionally good student, you may have disagreed with your teacher over the details of which way was right, and been punished for doing it wrong.
My experience with math classes was much different from yours. When we had a disagreement, the teacher said, “How would we tell who’s right? Do you have a proof? Do you have a counter-example?”. And if somebody had a proof we’d listen to it. And if I jumped up and said “Wait, this proof is wrong!” then the teacher would say, “First you have to explain what he said up to the point you disagree, and see if he agrees that’s what he means. Then you can tell us why it’s wrong.”
I never got punished for being wrong. If I didn’t do homework correctly then I didn’t get credit for it, but there was no punishment involved.
But Eliezer described people who disagreed about how many stones to put in a pile and who had something that looked very much like wars about it. That isn’t like the math I experienced. But it’s very much like the morality I’ve experienced.
Nominull, don’t the primalists have a morality about heaps of stones?
They believe there are right ways and wrong ways to do it. They sometimes disagree about the details of which ways are right and they punish each other for doing it wrong.
How is that different from morality?
I think there is an important distinction between “kill or die” and “kill or be killed.” The wolf’s life may be at stake, but the rabbit clearly isn’t attacking the wolf. If I need a heart transplant, I would still not be justified in killing someone to obtain the organ.
Mario, you are making a subtler distinction than I was. There is no end to the number of subtle distinctions that can be made.
In warfare we can distinguish between infantrymen who are shooting directly at each other, versus infantry and artillery or airstrikes that dump explosives on them at little risk to themselves.
We can distinguish between soldiers who are fighting for their homes versus soldiers who are fighting beyond their own borders. Clearly it’s immoral to invade other countries, and not immoral to defend your own.
I’m sure we could come up with hundreds of ways to split up the situations that show they are not all the same. But how much difference do these differences really make? “Kill or die” is pretty basic. If somebody’s going to die anyway, and your actions can decide who it will be, do you have any right to choose?
This series of Potemkin essays makes me increasingly suspicious that someone’s trying to pull a fast one on the Empress.
Agreed. I’ve suspected for some time that—after laying out descriptions of how bias works—Eliezer is now presenting us with a series of arguments that are all bias, all the time, and noticing how we buy into it.
It’s not only the most charitable explanation, it’s also the most consistent explanation.
If you were to stipulate that the rabbit is the only source of nourishment available to the fox, this still in no way justifies murder. The fox would have a moral obligation to starve to death.
How different is it when soldiers are at war? They must kill or be killed. If the fact that enemy soldiers will kill them if they don’t kill the enemy first isn’t enough justification, what is?
Should the soldiers on each side sit down and argue out the moral justification for the war first, and the side that is unjustified should surrender?
But somehow it seems like they hardly ever do that....
I thought of a simpler way to say it.
If Hillary Clinton was a man, she wouldn’t be Bill Clinton’s wife. She’d be his husband.
Similarly, if PA proved that 6 was prime, it wouldn’t be PA. It would be Bill Clinton’s husband. And so ZF would not imply that 6 is actually prime.